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deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. some approaches tackle these issues reactively at the control stage. however, regardless of the controller, online motion execution can only be as robust as the system capabilities allow at any given state. this is why it is important to have good motion plans to begin with, where robustness is considered proactively. to this end, we propose a metric ( derived from first principles ) for representing robustness against external disturbances. we then use this metric within our trajectory optimization framework for solving complex loco - manipulation tasks. through our experiments, we show that trajectories generated using our approach can resist a greater range of forces originating from any possible direction. by using our method, we can compute trajectories that solve tasks as effectively as before, with the added benefit of being able to counteract stronger disturbances in worst - case scenarios.
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arxiv:2203.01446
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coronal waves are large - scale disturbances often driven by coronal mass ejections ( cmes ). we investigate a spectacular wave event on 7 march 2012, which is associated with an x5. 4 flare ( sol2012 - 03 - 07 ). by using a running center - median ( rcm ) filtering method for the detection of temporal variations in extreme ultraviolet ( euv ) images, we enhance the euv disturbance observed by the atmospheric imaging assembly ( aia ) onboard the solar dynamics observatory ( sdo ) and the sun watcher using active pixel system detector and image processing ( swap ) onboard the project for onboard autonomy 2 ( proba2 ). in coronagraph images, a halo front is observed to be the upper counterpart of the euv disturbance. based on the euv and coronagraph images observed from three different perspectives, we have made three - dimensional ( 3d ) reconstructions of the wave surfaces using a new mask - fitting method. the reconstructions are compared with those obtained from forward - fitting methods. we show that the mask fitting method can reflect the inhomogeneous coronal medium by capturing the concave shape of the shock wave front. subsequently, we trace the developing concave structure and derive the deprojected wave kinematics. the speed of the 3d - wave nose increases from a low value below a few hundred $ \ mathrm { km \, s ^ { - 1 } } $ to a maximum value of about 3800 $ \ mathrm { km \, s ^ { - 1 } } $, and then slowly decreases afterwards. the concave structure starts to decelerate earlier and has significantly lower speeds than those of the wave nose. we also find that the 3d - wave in the extended corona has a much higher speed than the speed of euv disturbances across the solar disk.
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arxiv:2009.10872
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we posit that to achieve superhuman agents, future models require superhuman feedback in order to provide an adequate training signal. current approaches commonly train reward models from human preferences, which may then be bottlenecked by human performance level, and secondly these separate frozen reward models cannot then learn to improve during llm training. in this work, we study self - rewarding language models, where the language model itself is used via llm - as - a - judge prompting to provide its own rewards during training. we show that during iterative dpo training that not only does instruction following ability improve, but also the ability to provide high - quality rewards to itself. fine - tuning llama 2 70b on three iterations of our approach yields a model that outperforms many existing systems on the alpacaeval 2. 0 leaderboard, including claude 2, gemini pro, and gpt - 4 0613. while there is much left still to explore, this work opens the door to the possibility of models that can continually improve in both axes.
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arxiv:2401.10020
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we consider the problem of $ k $ - colouring a random $ r $ - uniform hypergraph with $ n $ vertices and $ cn $ edges, where $ k $, $ r $, $ c $ remain constant as $ n $ tends to infinity. achlioptas and naor showed that the chromatic number of a random graph in this setting, the case $ r = 2 $, must have one of two easily computable values as $ n $ tends to infinity. we give a complete generalisation of this result to random uniform hypergraphs.
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arxiv:1208.0812
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in this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. the constructed additive method is l - stable with respect to the implicit part and allows to use an arbitrary approximation of the jacobian matrix. in opposite to our previous paper, the fourth stage is explicit. so, the constructed method also has a good stability properties because of l - stability of the intermediate numerical formulas in the fourth stage, but has a lower computational costs per step. automatic stepsize selection based on local error and stability control are performed. the estimations for error and stability control have been obtained without significant additional computational costs. numerical experiments show reliability and efficiency of the implemented integration algorithm.
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arxiv:0902.3723
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only by an order automorphism. for example, all order automorphisms of a power set s = 2r are induced by permutations of r. a concept defined for a partial order p will correspond to a dual concept on the dual poset pd. for instance, a minimal element of p will be a maximal element of pd : minimality and maximality are dual concepts in order theory. other pairs of dual concepts are upper and lower bounds, lower sets and upper sets, and ideals and filters. in topology, open sets and closed sets are dual concepts : the complement of an open set is closed, and vice versa. in matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid. = = dimension - reversing dualities = = there are many distinct but interrelated dualities in which geometric or topological objects correspond to other objects of the same type, but with a reversal of the dimensions of the features of the objects. a classical example of this is the duality of the platonic solids, in which the cube and the octahedron form a dual pair, the dodecahedron and the icosahedron form a dual pair, and the tetrahedron is self - dual. the dual polyhedron of any of these polyhedra may be formed as the convex hull of the center points of each face of the primal polyhedron, so the vertices of the dual correspond one - for - one with the faces of the primal. similarly, each edge of the dual corresponds to an edge of the primal, and each face of the dual corresponds to a vertex of the primal. these correspondences are incidence - preserving : if two parts of the primal polyhedron touch each other, so do the corresponding two parts of the dual polyhedron. more generally, using the concept of polar reciprocation, any convex polyhedron, or more generally any convex polytope, corresponds to a dual polyhedron or dual polytope, with an i - dimensional feature of an n - dimensional polytope corresponding to an ( n − i − 1 ) - dimensional feature of the dual polytope. the incidence - preserving nature of the duality is reflected in the fact that the face lattices of the primal and dual polyhedra or polytopes are themselves order - theoretic duals. duality of polytopes and order - theoretic duality are both involutions : the dual poly
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https://en.wikipedia.org/wiki/Duality_(mathematics)
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this two - part tutorial dives into the field of data - driven power flow linearization ( dpfl ), a domain gaining increased attention. dpfl stands out for its higher approximation accuracy, wide adaptability, and better ability to implicitly incorporate the latest system attributes. this renders dpfl a potentially superior option for managing the significant fluctuations from renewable energy sources, a step towards realizing a more sustainable energy future, by translating the higher model accuracy into increased economic efficiency and less energy losses. to conduct a deep and rigorous reexamination, this tutorial first classifies existing dpfl methods into dpfl training algorithms and supportive techniques. their mathematical models, analytical solutions, capabilities, limitations, and generalizability are systematically examined, discussed, and summarized. in addition, this tutorial reviews existing dpfl experiments, examining the settings of test systems, the fidelity of datasets, and the comparison made among a limited number of dpfl methods. further, this tutorial implements extensive numerical comparisons of all existing dpfl methods ( 40 methods in total ) and four classic physics - driven approaches, focusing on their generalizability, applicability, accuracy, and computational efficiency. through these simulationmethodss, this tutorial aims to reveal the actual performance of all the methods ( including the performances exposed to data noise or outliers ), guiding the selection of appropriate linearization methods. furthermore, this tutorial discusses future directions based on the theoretical and numerical insights gained. as the first part, this paper reexamines dpfl theories, covering all the training algorithms and supportive techniques. capabilities, limitations, and aspects of generalizability, which were previously unmentioned in the literature, have been identified.
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arxiv:2407.02501
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natural language generation ( nlg ) is a critical component in conversational systems, owing to its role of formulating a correct and natural text response. traditionally, nlg components have been deployed using template - based solutions. although neural network solutions recently developed in the research community have been shown to provide several benefits, deployment of such model - based solutions has been challenging due to high latency, correctness issues, and high data needs. in this paper, we present approaches that have helped us deploy data - efficient neural solutions for nlg in conversational systems to production. we describe a family of sampling and modeling techniques to attain production quality with light - weight neural network models using only a fraction of the data that would be necessary otherwise, and show a thorough comparison between each. our results show that domain complexity dictates the appropriate approach to achieve high data efficiency. finally, we distill the lessons from our experimental findings into a list of best practices for production - level nlg model development, and present them in a brief runbook. importantly, the end products of all of the techniques are small sequence - to - sequence models ( 2mb ) that we can reliably deploy in production.
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arxiv:2011.03877
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, wi - fi is usually layered as a link layer below the internet layer of the internet protocol. this means that nodes have an associated internet address and, with suitable connectivity, this allows full internet access. = = = modes = = = = = = = infrastructure = = = = in infrastructure mode, which is the most common mode used, all communications go through a base station. for communications within the network, this introduces an extra use of the airwaves but has the advantage that any two stations that can communicate with the base station can also communicate through the base station, which limits issues associated with the hidden node problem and simplifies the protocols. = = = = ad hoc and wi - fi direct = = = = wi - fi also allows communications directly from one computer to another without an access point intermediary. this is called ad hoc wi - fi transmission. different types of ad hoc networks exist. in the simplest case, network nodes must talk directly to each other. in more complex protocols nodes may forward packets, and nodes keep track of how to reach other nodes, even if they move around. ad hoc mode was first described by chai keong toh in his 1996 patent of wireless ad hoc routing, implemented on lucent wavelan 802. 11a wireless on ibm thinkpads over a size nodes scenario spanning a region of over a mile. the success was recorded in mobile computing magazine ( 1999 ) and later published formally in ieee transactions on wireless communications, 2002 and acm sigmetrics performance evaluation review, 2001. this wireless ad hoc network mode has proven popular with multiplayer video games on handheld game consoles, such as the nintendo ds and playstation portable. it is also popular on digital cameras, and other consumer electronics devices. some devices can also share their internet connection using ad hoc, becoming hotspots or virtual routers. similarly, the wi - fi alliance promotes the specification wi - fi direct for file transfers and media sharing through a new discovery and security methodology. wi - fi direct launched in october 2010. another mode of direct communication over wi - fi is tunneled direct link setup ( tdls ), which enables two devices on the same wi - fi network to communicate directly, instead of via the access point. = = = multiple access points = = = an extended service set may be formed by deploying multiple access points that are configured with the same ssid and security settings. wi - fi client devices typically connect to the access point that can provide the strongest signal within that service set. increasing
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https://en.wikipedia.org/wiki/Wi-Fi
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we investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption ( csa ) on square lattices with arrhenius rates given by ki = q ^ ( ni ), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. these results might be pertinent to practical applications in processes involving adsorption of particles.
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arxiv:1304.4872
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we study, by numerical simulations, the entrainment process in a supersonic, radiative jet flow, during the evolution of kelvin - helmholtz instabilities, in the context of the the acceleration problem of molecular bipolar outflows, observed in giant molecular clouds. our results show that a large fraction of the initial jet momentum can be transferred to the ambient medium by this process. we therefore analyze in detail the instability evolution and compare some of the main observational properties of molecular outflows with those of the entrained material that we observe in our simulations. in particular, we find a good agreement for the mass vs. velocity distribution and for the outflow collimation structure, especially when a light jet is moving into a denser ambient medium. this is probably the case for ( obscured ) optical jets driving powerful molecular outflows in the denser environment of the inner regions of molecular clouds.
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arxiv:astro-ph/0009089
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the most massive stars, with initial masses above ~ 50m _ sun, encounter a phase of extreme mass loss - sometimes accompanied by so - called giant eruptions - in which the stars ' evolution is reversed from a redward to a blueward motion in the hrd. in this phase the stars are known as luminous blue variable ( lbvs ). neither the reason for the onset of the strong mass loss nor the cause for the giant eruptions is really understood, nor is their implications for the evolution of these most massive stars. i will present a study of the lbv nebulae which are formed in this phase as a consequence of the strong mass loss and draw conclusions from the morphology and kinematics of these nebulae on possible eruption mechanisms and stellar parameters of the lbv stars. the analysis contains a large collection of lbv nebulae which form an evolutionary sequence of lbv nebulae. a special concern will be the frequently observed bipolar nature of the lbv nebulae which seems to be a general feature and presents strong constraints on further models of the lbv phase and especially on the formation mechanism of the nebulae.
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arxiv:astro-ph/0104214
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content - dense news report important factual information about an event in direct, succinct manner. information seeking applications such as information extraction, question answering and summarization normally assume all text they deal with is content - dense. here we empirically test this assumption on news articles from the business, u. s. international relations, sports and science journalism domains. our findings clearly indicate that about half of the news texts in our study are in fact not content - dense and motivate the development of a supervised content - density detector. we heuristically label a large training corpus for the task and train a two - layer classifying model based on lexical and unlexicalized syntactic features. on manually annotated data, we compare the performance of domain - specific classifiers, trained on data only from a given news domain and a general classifier in which data from all four domains is pooled together. our annotation and prediction experiments demonstrate that the concept of content density varies depending on the domain and that naive annotators provide judgement biased toward the stereotypical domain label. domain - specific classifiers are more accurate for domains in which content - dense texts are typically fewer. domain independent classifiers reproduce better naive crowdsourced judgements. classification prediction is high across all conditions, around 80 %.
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arxiv:1704.00440
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several preconditioned aor methods have been proposed to solve system of linear equations $ ax = b $, where $ a \ in \ mathbb { r } ^ { n \ times n } $ is a unit z - matrix. the aim of this paper is to give a comparison result for a class of preconditioners $ p $, where $ p \ in \ mathbb { r } ^ { n \ times n } $ is nonsingular, nonnegative and has unit diagonal entries. numerical results for corresponding preconditioned gmres methods are given to illustrate the theoretical results.
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arxiv:1106.5087
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the unprecedented growth of mobile data traffic challenges the performance and economic viability of today ' s cellular networks, and calls for novel network architectures and communication solutions. data offloading through third - party wifi or femtocell access points ( aps ) can effectively alleviate the cellular network congestion in a low operational and capital expenditure. this solution requires the cooperation and agreement of mobile cellular network operators ( mnos ) and ap owners ( apos ). in this paper, we model and analyze the interaction among one mno and multiple apos ( for the amount of mno ' s offloading data and the respective apos ' compensations ) by using the nash bargaining theory. specifically, we introduce a one - to - many bargaining game among the mno and apos, and analyze the bargaining solution ( game equilibrium ) systematically under two different bargaining protocols : ( i ) sequential bargaining, where the mno bargains with apos sequentially, with one apo at a time, in a given order, and ( ii ) concurrent bargaining, where the mno bargains with all apos concurrently. we quantify the benefits for apos when bargaining sequentially and earlier with the mno, and the losses for apos when bargaining concurrently with the mno. we further study the group bargaining scenario where multiple apos form a group bargaining with the mno jointly, and quantify the benefits for apos when forming such a group. interesting, our analysis indicates that grouping of apos not only benefits the apos in the group, but may also benefit some apos not in the group. our results shed light on the economic aspects and the possible outcomes of the mno / apos interactions, and can be used as a roadmap for designing policies for this promising data offloading solution.
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arxiv:1405.5641
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in this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. it is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. here, we run some computer experiments for gradient descent on some simple functions, and observe this principle in some concrete examples.
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arxiv:1808.04839
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in this paper, the top - down approach for the 6 - dimensional space has been elaborated. the connection between the cosmological constant and the extra space metric has been obtained. the metric can be found with the necessary accuracy. it is shown that descent from high energies to the low ones leads to the quantum corrections which influence weakly the metric of extra space.
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arxiv:1609.07361
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classical relativistic system of point particles coupled with an electromagnetic field is considered in the three - dimensional representation. the gauge freedom connected with the chronometrical invariance of the four - dimensional description is reduced by use of the geometrical concept of the forms of relativistic dynamics. the remainder gauge degrees of freedom of the electromagnetic potential are analysed within the framework of dirac ' s constrained hamiltonian mechanics in the front form of dynamics. the results are implemented to the problems of relativistic statistical mechanics. based on the corresponding liouville equation the classical partition function of the system is written down in a gauge - invariant manner and an integration over field variables is performed.
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arxiv:hep-th/0005050
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the correlation matrix ( cm ) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. it has been shown that it can be stronger than the positive partial transpose ( ppt ) criterion, as well as the computable cross norm or realignment ( ccnr ) criterion in different situations. however, it remained as an open question whether there existed sets of states for which the cm criterion could be stronger than both criteria simultaneously. here, we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the ppt and ccnr criteria whose entanglement is revealed by the cm condition. we also show that the cm can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general ( mixed ) states.
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arxiv:0705.2583
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in the standard fireball model of gamma - ray bursts ( grbs ), the fireball starts with an optically thick phase. as it expands, the fireball becomes optically thin at some stage. the thermal radiation trapped in the originally opaque fireball then leaks out, producing a transient event. the appearance of the event is investigated in the framework of a homogeneous, spherically symmetric, and freely expanding fireball produced instantly by an explosive process without continuous injection of mass and energy. we find that, generally, the event has a time - duration shorter than that of the main burst, which is presumably produced by the internal shock after the fireball becomes optically thin. the event is separated from the main burst by a quiescent time - interval, and is weaker than the main burst at least in a high energy band. hence, the event corresponds to a grb precursor. the precursor event predicted by our model has a smooth and fred ( fast rise and exponential decay ) shape lightcurve, and a quasi - thermal spectrum. typically, the characteristic blackbody photon energy is in the x - ray band. however, if the distortion of the blackbody spectrum by electron scattering is considered, the characteristic photon energy could be boosted to the gamma - ray band. our model may explain a class of observed grb precursors - - those having smooth and fred - shape lightcurves and quasi - thermal spectra.
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arxiv:astro-ph/0703144
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in this work we perform a detailed theoretical and experimental investigation of an atomic memory based on recoil - induced resonance in cold cesium atoms. we consider the interaction of a nearly degenerated pump and probe beams with an ensemble of two - level atoms. a full theoretical density matrix calculation in the extended hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses determining the probe transmission and the forward four - wave mixing spectra. these two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. however, during continuous excitation of the sample, they are detected in very different ways and the signal at the probe transmission appears to be considerably larger, being the main focus of investigation prior to this work. moreover, we have investigated the storage of optical information in the atomic external degrees of freedom, which provided a simple interpretation for the previously - reported non - volatile character of this memory. the retrieved signals after storage reveal the equivalent role of probe transmission and four - wave mixing, as the two signals have similar amplitudes. probe transmission and forward four - wave - mixing spectra were then experimentally measured for both continuous excitation and after storage. the experimental observations are in good agreement with the developed theory and open a new pathway for the reversible exchange of optical information with atomic systems.
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arxiv:2112.14800
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we present an accurate study of the static - nucleus electronic energy band gap of solid molecular hydrogen at high pressure. the excitonic and quasiparticle gaps of the $ c2 / c $, $ pc $, $ pbcn $, and $ p6 _ 3 / m $ structures at pressures of 250, 300, and 350 ~ gpa are calculated using the fixed - node diffusion quantum monte carlo ( dmc ) method. the difference between the mean - field and many - body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean - field gap of an infinite system to obtain an estimate of the many - body gap in the thermodynamic limit. by comparing our static - nucleus dmc energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen. our dmc results suggest that the metallization of high - pressure solid hydrogen occurs via a structural phase transition rather than band gap closure.
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arxiv:1608.00754
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large language model ( llm ) agents have evolved to intelligently process information, make decisions, and interact with users or tools. a key capability is the integration of long - term memory capabilities, enabling these agents to draw upon historical interactions and knowledge. however, the growing memory size and need for semantic structuring pose significant challenges. in this work, we propose an autonomous memory augmentation approach, meminsight, to enhance semantic data representation and retrieval mechanisms. by leveraging autonomous augmentation to historical interactions, llm agents are shown to deliver more accurate and contextualized responses. we empirically validate the efficacy of our proposed approach in three task scenarios ; conversational recommendation, question answering and event summarization. on the llm - redial dataset, meminsight boosts persuasiveness of recommendations by up to 14 %. moreover, it outperforms a rag baseline by 34 % in recall for locomo retrieval. our empirical results show the potential of meminsight to enhance the contextual performance of llm agents across multiple tasks.
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arxiv:2503.21760
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in this work, we study a model in nonlinear electrodynamics in the presence of a cpt - even term that violates lorentz symmetry. the lorentz - breaking vector, in addition to the usual background magnetic field, produces interesting effects in the dispersion relations. the consequences on the vacuum refractive index and the group velocity are studied. vacuum birefringence is discussed in the case the nonlinear electrodynamics is a euler - heisenberg model.
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arxiv:2305.10914
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edwin powel hubble is regarded as one of the most important astronomers of 20th century. in despite of his great contributions to the field of astronomy, he never received the nobel prize because astronomy was not considered as the field of the nobel prize in physics at that era. there is an anecdote about the relation between hubble and the nobel prize. according to this anecdote, the nobel committee decided to award the nobel prize in physics in 1953 to hubble as the first nobel laureate as an astronomer ( christianson 1995 ). however, hubble was died just before its announcement, and the nobel prize is not awarded posthumously. documents of the nobel selection committee are open after 50 years, thus this anecdote can be verified. i confirmed that the nobel selection committee endorsed frederik zernike as the nobel laureate in physics in 1953 on september 15th, 1953, which is 13 days before the hubble ' s death in september 28th, 1953. i also confirmed that hubble and henry norris russell were nominated but they are not endorsed because the committee concluded their astronomical works were not appropriate for the nobel prize in physics.
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arxiv:1705.10125
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the onset of the " rush to the poles " of polar - crown prominences and their associated coronal emission is a harbinger of solar maximum. altrock ( solar phys. 216, 343, 2003 ) showed that the " rush " was well - observed at 1. 15 ro in the fe xiv corona at the sacramento peak site of the national solar observatory prior to the maxima of cycles 21 to 23. the data show that solar maximum in those cycles occurred when the center line of the rush reached a critical latitude of 76 + - 2 { \ deg }. furthermore, in the previous three cycles solar maximum occurred when the highest number of fe xiv emission features per day ( averaged over 365 days and both hemispheres ) first reached latitudes 20 + - 1. 7 { \ deg }. cycle 24 displays an intermittent rush that is only well - defined in the northern hemisphere. in 2009 an initial slope of 4. 6 { \ deg } / yr was found in the north, compared to an average of 9. 4 + - 1. 7 { \ deg } / yr in the previous cycles. an early fit to the rush would have reached 76 { \ deg } at 2014. 6. however, in 2010 the slope increased to 7. 5 { \ deg } / yr ( an increase did not occur in the previous three cycles ). extending that rate to 76 + - 2 { \ deg } indicates that the solar maximum in the northern hemisphere already occurred at 2011. 6 + - 0. 3. in the southern hemisphere the rush to the poles, if it exists, is very poorly defined. a linear fit to several maxima would reach 76 { \ deg } in the south at 2014. 2. in 1999, persistent fe xiv coronal emission known as the " extended solar cycle " appeared near 70 { \ deg } in the north and began migrating towards the equator at a rate 40 % slower than the previous two solar cycles. however, in 2009 and 2010 an acceleration occurred. currently the greatest number of emission features is at 21 { \ deg } in the north and 24 { \ deg } in the south. this indicates that solar maximum is occurring now in the north but not yet in the south.
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arxiv:1209.2963
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inverse rendering of an object under entirely unknown capture conditions is a fundamental challenge in computer vision and graphics. neural approaches such as nerf have achieved photorealistic results on novel view synthesis, but they require known camera poses. solving this problem with unknown camera poses is highly challenging as it requires joint optimization over shape, radiance, and pose. this problem is exacerbated when the input images are captured in the wild with varying backgrounds and illuminations. standard pose estimation techniques fail in such image collections in the wild due to very few estimated correspondences across images. furthermore, nerf cannot relight a scene under any illumination, as it operates on radiance ( the product of reflectance and illumination ). we propose a joint optimization framework to estimate the shape, brdf, and per - image camera pose and illumination. our method works on in - the - wild online image collections of an object and produces relightable 3d assets for several use - cases such as ar / vr. to our knowledge, our method is the first to tackle this severely unconstrained task with minimal user interaction. project page : https : / / markboss. me / publication / 2022 - samurai / video : https : / / youtu. be / llyugdjxp - 8
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arxiv:2205.15768
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suppose $ \ mathcal { a } $ is a separable unital ash c * - algebra, $ \ mathcal { r } $ is a sigma - finite ii $ _ { \ infty } $ factor von neumann algebra, and $ \ pi, \ rho : \ mathcal { a } \ rightarrow \ mathcal { r } $ are unital $ \ ast $ - homomorphisms such that, for every $ a \ in \ mathcal { a } $, the range projections of $ \ pi \ left ( a \ right ) $ and $ \ rho \ left ( a \ right ) $ are murray von neuman equivalent in $ \ mathcal { r } % $. we prove that $ \ pi $ and $ \ rho $ are approximately unitarily equivalent modulo $ \ mathcal { k } _ { \ mathcal { r } } $, where $ \ mathcal { k } _ { \ mathcal { r } } $ is the norm closed ideal generated by the finite projections in $ \ mathcal { r } $. we also prove a very general result concerning approximate equivalence in arbitrary finite von neumann algebras.
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arxiv:2008.06619
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we introduce a continuous time - reversal operation which connects the time - forward and time - reversed trajectories in the steady state of an irreversible markovian dynamics via a continuous family of stochastic dynamics. this continuous time - reversal allows us to derive a tighter version of the thermodynamic uncertainty relation ( tur ) involving observables evaluated relative to their local mean value. moreover, the family of dynamics realizing the continuous time - reversal contains an equilibrium dynamics halfway between the time - forward and time - reversed dynamics. we show that this equilibrium dynamics, together with an appropriate choice of the observable, turns the inequality in the tur into an equality. we demonstrate our findings for the example of a particle diffusing in a tilted periodic potential.
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arxiv:2010.14769
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stellar rotation plays a key role in stellar activity. the rotation period could be detected through light curve variations caused by starspots. kepler provides two types of light curves, one is the pre - search data conditioning ( pdc ) light curves, the other is the simple aperture photometer ( sap ) light curves. compared with the pdc light curves, the sap light curves keep the long - term trend, relatively suitable for searches of long period signals. however, sap data are inflicted by some artefacts such as quarterly rolls and instrumental errors, making it difficult to find the physical periods in the sap light curves. we explore a systematic approach based on the light curve pre - processing, period detection and candidate selection. we also develop a simulated light curve test to estimate our detection limits for the sap - like lcs. after applying our method to the raw sap light curves, we found more than 1000 main - sequence stars with the period longer than 30 days, 165 are newly discovered. considering the potential flaw of the sap, we also inspect the newly found objects with photometry methods, and most of our periodical signals are confirmed.
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arxiv:1909.00189
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the paper presents an experimental study of the temporal behaviour of a bistable vertical cavity surface emitting laser ( vcsel ) under the effect of optical feedback coming from vibrating diffusely - reflecting surface. we demonstrate that a vcsel operating in the regime of polarization switchings caused by self - mixing effects can greatly enhance a responsivity of the detection of microvibrations. for small amplitudes of microvibrations ( less than $ \ lambda $ / 2, where $ \ lambda $ is the operating wavelength of the laser ), which cause only harmonic ( or close to harmonic ) oscillations in the laser output outside of the bistability region, the use of polarization switching can increase the responsivity up to 45 times. for the amplitudes larger then $ \ lambda $ / 2 the response of a bistable vcsel well reproduces a fine temporal structure of the self - mixing signal. a procedure of the data processing in the switching regime for the correct determination of the direction of the displacement and for the reconstruction of the waveform of surface vibrations with a basic resolution of $ \ lambda $ / 2 is also shown.
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arxiv:1805.03627
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by reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined krylov subspace methods achieve significantly improved parallel scalability on present - day hpc hardware. however, this typically comes at the cost of a reduced maximal attainable accuracy. this paper presents and compares several stabilized versions of the communication - hiding pipelined conjugate gradients method. the main novel contribution of this work is the reformulation of the multi - term recurrence pipelined cg algorithm by introducing shifts in the recursions for specific auxiliary variables. these shifts reduce the amplification of local rounding errors on the residual. the stability analysis presented in this work provides a rigorous method for selection of the optimal shift value in practice. it is shown that, given a proper choice for the shift parameter, the resulting shifted pipelined cg algorithm restores the attainable accuracy and displays nearly identical robustness to local rounding error propagation compared to classical cg. numerical results on a variety of spd benchmark problems compare different stabilization techniques for the pipelined cg algorithm, showing that the shifted pipelined cg algorithm is able to attain a high accuracy while displaying excellent parallel performance.
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arxiv:1706.05988
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$ \ sim 6 \ % $ of all known pulsars have been observed to exhibit sudden spin - up events, known as glitches. for more than fifty years, these phenomena have played an important role in helping to understand pulsar ( astro ) physics. based on the review of pulsar glitches search method, the progress made in observations in recent years is summarized, including the achievements obtained by chinese telescopes. glitching pulsars demonstrate great diversity of behaviours, which can be broadly classified into four categories : normal glitches, slow glitches, glitches with delayed spin - ups, and anti - glitches. the main models of glitches that have been proposed are reviewed and their implications for neutron star structure are critically examined regarding our current understanding. furthermore, the correlations between glitches and emission changes, which suggest that magnetospheric state - change is linked to the pulsar - intrinsic processes, are also described and discussed in some detail.
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arxiv:2211.13885
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effective surface - passivation of pbs nanocrystals in aqueous colloidal solution has been achieved following treatment with cds precursors. the resultant photoluminescent emission displays two distinct components, one originating from the absorption band - edge and the other from above the absorption band - edge. we show that both of these components are strongly polarised but display distinctly different behaviours. the polarisation arising from the band - edge shows little dependence on the excitation energy while the polarisation of the above - band - edge component is strongly dependent on the excitation energy. in addition, time resolved polarisation spectroscopy reveals that the above - band - edge polarisation is restricted to the first couple of nanoseconds, while the band - edge polarisation is nearly constant over hundreds of nanoseconds. we recognise an incompatibility between the two different polarisation behaviours, which enables us to identify two distinct types of surface - passivated pbs nanocrystal.
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arxiv:cond-mat/0306310
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we investigate geodesics in non - homogeneous vacuum pp - wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. for the particular class of solutions considered, distinct " outcomes " ( channels to infinity ) are identified, and it is shown that the boundary between different outcomes has a fractal structure. this seems to be the first example of chaos in exact radiative spacetimes.
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arxiv:gr-qc/9809065
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we present a method for controlling a simulated humanoid to grasp an object and move it to follow an object trajectory. due to the challenges in controlling a humanoid with dexterous hands, prior methods often use a disembodied hand and only consider vertical lifts or short trajectories. this limited scope hampers their applicability for object manipulation required for animation and simulation. to close this gap, we learn a controller that can pick up a large number ( > 1200 ) of objects and carry them to follow randomly generated trajectories. our key insight is to leverage a humanoid motion representation that provides human - like motor skills and significantly speeds up training. using only simplistic reward, state, and object representations, our method shows favorable scalability on diverse object and trajectories. for training, we do not need dataset of paired full - body motion and object trajectories. at test time, we only require the object mesh and desired trajectories for grasping and transporting. to demonstrate the capabilities of our method, we show state - of - the - art success rates in following object trajectories and generalizing to unseen objects. code and models will be released.
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arxiv:2407.11385
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quantum system abruptly driven from its stationary phase can reveal nontrivial dynamics upon approaching a new final state. we investigate here such dynamics for a correlated quantum dot sandwiched between the metallic and superconducting leads, considering two types of quenches feasible experimentally. in particular, we examine an interplay between the proximity induced electron pairing with correlations caused by the on - dot coulomb repulsion. we discuss the time - dependent charge occupancy, complex order parameter, transient currents, and analyze evolution of the subgap quasiparticles which could be empirically observed in the tunneling conductance.
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arxiv:2007.10747
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the design of scalable and robust overlay topologies has been a main research subject since the very origins of peer - to - peer ( p2p ) computing. today, the corresponding optimization tradeoffs are fairly well - understood, at least in the static case and from a worst - case perspective. this paper revisits the peer - to - peer topology design problem from a self - organization perspective. we initiate the study of topologies which are optimized to serve the communication demand, or even self - adjusting as demand changes. the appeal of this new paradigm lies in the opportunity to be able to go beyond the lower bounds and limitations imposed by a static, communication - oblivious, topology. for example, the goal of having short routing paths ( in terms of hop count ) does no longer conflict with the requirement of having low peer degrees. we propose a simple overlay topology obst ( k ) which is composed of k ( rooted and directed ) binary search trees ( bsts ), where k is a parameter. we first prove some fundamental bounds on what can and cannot be achieved optimizing a topology towards a static communication pattern ( a static obst ( k ) ). in particular, we show that the number of bsts that constitute the overlay can have a large impact on the routing costs, and that a single additional bst may reduce the amortized communication costs from omega ( log ( n ) ) to o ( 1 ), where n is the number of peers. subsequently, we discuss a natural self - adjusting extension of obst ( k ), in which frequently communicating partners are " splayed together ".
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arxiv:1309.3319
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one of the most popular training algorithms for deep neural networks is the adaptive moment estimation ( adam ) introduced by kingma and ba. despite its success in many applications there is no satisfactory convergence analysis : only local convergence can be shown for batch mode under some restrictions on the hyperparameters, counterexamples exist for incremental mode. recent results show that for simple quadratic objective functions limit cycles of period 2 exist in batch mode, but only for atypical hyperparameters, and only for the algorithm without bias correction. % more general there are several more adaptive gradient methods which try to estimate a fitting learning rate and / or search direction from the training data to improve the learning process compared to pure gradient descent with fixed learningrate. we extend the convergence analysis for adam in the batch mode with bias correction and show that even for quadratic objective functions as the simplest case of convex functions 2 - limit - cycles exist, for all choices of the hyperparameters. we analyze the stability of these limit cycles and relate our analysis to other results where approximate convergence was shown, but under the additional assumption of bounded gradients which does not apply to quadratic functions. the investigation heavily relies on the use of computer algebra due to the complexity of the equations.
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arxiv:2210.02070
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it is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the action of the corresponding elementary transvection group. this result is used to get improved injective stability estimates for $ k _ 1 $ of the symplectic transvection group over a non - singular affine algebras.
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arxiv:1108.1288
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recent advancements in visual speech recognition ( vsr ) have promoted progress in lip - to - speech synthesis, where pre - trained vsr models enhance the intelligibility of synthesized speech by providing valuable semantic information. the success achieved by cascade frameworks, which combine pseudo - vsr with pseudo - text - to - speech ( tts ) or implicitly utilize the transcribed text, highlights the benefits of leveraging vsr models. however, these methods typically rely on mel - spectrograms as an intermediate representation, which may introduce a key bottleneck : the domain gap between synthetic mel - spectrograms, generated from inherently error - prone lip - to - speech mappings, and real mel - spectrograms used to train vocoders. this mismatch inevitably degrades synthesis quality. to bridge this gap, we propose natural lip - to - speech ( naturall2s ), an end - to - end framework integrating acoustic inductive biases with differentiable speech generation components. specifically, we introduce a fundamental frequency ( f0 ) predictor to capture prosodic variations in synthesized speech. the predicted f0 then drives a differentiable digital signal processing ( ddsp ) synthesizer to generate a coarse signal which serves as prior information for subsequent speech synthesis. additionally, instead of relying on a reference speaker embedding as an auxiliary input, our approach achieves satisfactory performance on speaker similarity without explicitly modelling speaker characteristics. both objective and subjective evaluation results demonstrate that naturall2s can effectively enhance the quality of the synthesized speech when compared to state - of - the - art methods. our demonstration page is accessible at https : / / yifan - liang. github. io / naturall2s /.
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arxiv:2502.12002
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as vision - language models like clip are widely applied to zero - shot tasks and gain remarkable performance on in - distribution ( id ) data, detecting and rejecting out - of - distribution ( ood ) inputs in the zero - shot setting have become crucial for ensuring the safety of using such models on the fly. most existing zero - shot ood detectors rely on id class label - based prompts to guide clip in classifying id images and rejecting ood images. in this work we instead propose to leverage a large set of diverse auxiliary outlier class labels as pseudo ood class text prompts to clip for enhancing zero - shot ood detection, an approach we called outlier label exposure ( ole ). the key intuition is that id images are expected to have lower similarity to these outlier class prompts than ood images. one issue is that raw class labels often include noise labels, e. g., synonyms of id labels, rendering raw ole - based detection ineffective. to address this issue, we introduce an outlier prototype learning module that utilizes the prompt embeddings of the outlier labels to learn a small set of pivotal outlier prototypes for an embedding similarity - based ood scoring. additionally, the outlier classes and their prototypes can be loosely coupled with the id classes, leading to an inseparable decision region between them. thus, we also introduce an outlier label generation module that synthesizes our outlier prototypes and id class embeddings to generate in - between outlier prototypes to further calibrate the detection in ole. despite its simplicity, extensive experiments show that ole substantially improves detection performance and achieves new state - of - the - art performance in large - scale ood and hard ood detection benchmarks.
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arxiv:2406.01170
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foreshock transients are ion kinetic structures in the ion foreshock. due to their dynamic pressure perturbations, they can disturb the bow shock and magnetosphere - ionosphere system. they can also accelerate particles contributing to shock acceleration. however, it is still unclear how exactly they form. recent particle - in - cell simulations point out the important role of electric field and hall current in the formation process. to further examine this, we use data from the magnetospheric multiscale ( mms ) mission to apply case studies on two small ( 1000 - 2000 km ) foreshock transient events that just started to form. in event 1 where mms were in a tetrahedral formation, we show that the current density configuration, which determined the magnetic field profile, was mainly driven by hall currents generated by demagnetized foreshock ions. the resulting time variation of the magnetic field induced electric field that drove cold plasma moving outward with magnetic field lines. in event 2 where mms were in a string - of - pearls formation, we analyze the evolution of field and plasma parameters. we show that the magnetic flux and mass flux were transported outward from the core resulting in the steepening of the boundary. the steepened boundary, which trapped more foreshock ions and caused stronger demagnetization of foreshock ions, nonlinearly further enhanced the hall current. based on our observations, we propose a physical formation process that the positive feedback of foreshock ions on the varying magnetic field caused by the foreshock ion hall current enables an instability and the growth of the structure.
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arxiv:2008.12383
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we present here the precise wavelength calibration of a high - resolution spectrum using uranium ( u ) lines in the wavelength range of 3809 - 6833 \ aa \ for precision radial velocity measurements for exoplanet detection or related astrophysical sciences. we identify 1540 well - resolved u lines from a high - resolution ( r = 67, 000 ) spectrum of the uranium - argon hollow cathode lamp ( uar hcl ) using paras spectrograph in the aforesaid wavelength range. we calculate the neutral and first allowed transitions ( ritz wavelength ) of u from its known energy levels and compare them with our observed central wavelengths. we measure an offset of - 0. 15 m \ aa \ space in our final u line list. the line list has an average measurement uncertainty of 15 m s $ ^ { - 1 } $ ( 0. 013 pixels or 0. 28 m \ aa ). we included these lines to the paras data analysis framework to perform the wavelength calibration and then calculate the multi - order radial velocity ( rv ) of paras spectra. the typical dispersion of residuals around the wavelength solution of a uar spectrum, using u lines, is found to be 0. 8 m \ aa \ space ( $ \ sim $ 45 m s $ ^ { - 1 } $ ). with the use of this line list, we present our results for the precision rv of an on - sky source ( a rv standard star ), and an off - sky source ( a hcl ) observed with paras along with uar hcl. we measure the dispersion in absolute drift difference between two fibers ( inter - fiber drift ) for a span of 6. 5 hours to be 88 cm s $ ^ { - 1 } $, and the rv dispersion ( $ { \ sigma _ { rv } } $ ) for a rv standard star, hd55575 over the course of $ \ sim $ 450 days to be 3. 2 m s $ ^ { - 1 } $. these results are in good agreement with the previous ones measured using the thar hcl. it proves that the thar hcl with $ \ sim $ 99 \ % pure - th are replaceable with the uar hcl for the wavelength calibration of the high - resolution spectrographs such as paras ( r $ \ leq $ 67, 000 ) to achieve a rv precision of 1 - 3 m s $ ^ { - 1 } $ in the
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arxiv:2105.12942
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we study asymptotic behavior of maximum likelihood estimator for a time inhomogeneous diffusion process given by a sde $ dx _ t = \ alpha b ( t ) x _ t dt + \ sigma ( t ) db _ t $, $ t \ in [ 0, t ) $, with a parameter $ \ alpha \ in r $, where $ t \ in ( 0, \ infty ] $ and $ ( b _ t ) _ { t \ in [ 0, t ) } $ is a standard wiener process. we formulate sufficient conditions under which the mle of $ \ alpha $ normalized by fisher information converges to the limit distribution of dickey - fuller statistics. next we study a sde $ dy _ t = \ alpha b ( t ) a ( y _ t ) dt + \ sigma ( t ) db _ t $, $ t \ in [ 0, t ) $, with a perturbed drift satisfying $ a ( x ) = x + o ( 1 + | x | ^ \ gamma ) $ with some $ \ gamma \ in [ 0, 1 ) $. we give again sufficient conditions under which the mle of $ \ alpha $ normalized by fisher information converges to the limit distribution of dickey - fuller statistics.
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arxiv:0810.2688
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as we know, there is a controversy about the decision making under risk between economists and psychologists. we discuss to build a unified theory of risky choice, which would explain both of compensatory and non - compensatory theories. for risky choice, according to cognition ability, we argue that people could not build a continuous and accurate subjective probability world, but several order concepts, such as small, middle and large probability. people make decisions based on information, experience, imagination and other things. all of these things are so huge that people have to prepare some strategies. that is, people have different strategies when facing to different situations. the distributions of these things have different decision structures. more precisely, decision making is a process of simplifying the decision structure. however, the process of decision structure simplifying is not stuck in a rut, but through different path when facing problems repeatedly. it is why preference reversal always happens when making decisions. the most efficient way to simplify the decision structure is calculating expected value or making decisions based on one or two dimensions. we also argue that the deliberation time at least has four parts, which are consist of substitution time, first order time, second order time and calculation time. decision structure also can simply explain the phenomenon of paradoxes and anomalies. jel codes : c10, d03, d81
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arxiv:1701.08567
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we describe a finite quantum groupoid associated to any finite vect _ k enriched herd.
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arxiv:1005.2653
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we analyze the evolution of the effective potential and the particle spectrum of two - parameter families of non - integrable quantum field theories. these theories are defined by deformations of conformal minimal models m _ m by using the operators phi _ { 1, 3 }, phi _ { 1, 2 } and phi _ { 2, 1 }. this study extends to all minimal models the analysis previously done for the classes of universality of the ising, the tricritical ising and the rsos models. we establish the symmetry and the duality properties of the various models also identifying the limiting theories that emerge when m goes to infinity.
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arxiv:0901.3537
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thermoelectric ( te ) measurements have been performed on the workhorses of today ' s data storage devices, exhibiting either the giant or the anisotropic magnetoresistance effect ( gmr and amr ). the temperature - dependent ( 50 - 300 k ) and magnetic field - dependent ( up to 1 t ) te power factor ( pf ) has been determined for several co - ni alloy nanowires with varying co : ni ratios as well as for co - ni / cu multilayered nanowires with various cu layer thicknesses, which were all synthesized via a template - assisted electrodeposition process. a systematic investigation of the resistivity, as well as the seebeck coefficient, is performed for co - ni alloy nanowires and co - ni / cu multilayered nanowires. at room temperature, measured values of te pfs up to 3. 6 mwk - 2m - 1 for amr samples and 2. 0 mwk - 2m - 1 for gmr nanowires are obtained. furthermore, the te pf is found to increase by up to 13. 1 % for amr co - ni alloy nanowires and by up to 52 % for gmr co - ni / cu samples in an external applied magnetic field. the magnetic nanowires exhibit te pfs that are of the same order of magnitude as te pfs of bi - sb - se - te based thermoelectric materials and, additionally, give the opportunity to adjust the te power output to changing loads and hotspots through external magnetic fields.
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arxiv:1701.00404
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the nuclear matter parameters define the nuclear equation of state ( eos ), they appear as coefficients of expansion around the saturation density of symmetric and asymmetric nuclear matter. we review their correlations with several properties of finite nuclei and of neutron stars within mean - field frameworks. the lower order nuclear matter parameters such as the binding energy per nucleon, incompressibility and the symmetry energy coefficients are found to be constrained in narrow limits through their strong ties with selective properties of finite nuclei. from the correlations of nuclear matter parameters with neutron star observables, we further review how precision knowledge of the radii and tidal deformability of neutron stars in the mass range $ 1 - 2 m _ \ odot $ may help cast them in narrower bounds. the higher order parameters such as the density slope and the curvature of the symmetry energy or the skewness of the symmetric nuclear matter eos are, however, plagued with larger uncertainty. from inter - correlation of these higher order nuclear matter parameters with lower order ones, we explore how they can be brought to more harmonious bounds.
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arxiv:2006.05758
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robustness and accuracy are two critical metrics for industrial inspection. in this paper, we propose benchmarks that can evaluate the structured light method ' s performance. our evaluation metric was learning from a lot of inspection tasks from the factories. the metric we proposed consists of four detailed criteria such as flatness, length, height and sphericity. then we can judge whether the structured light method / device can be applied to a specified inspection task by our evaluation metric quickly. a structured light device built for typec pin needles inspection performance is evaluated via our metrics in the final experimental section.
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arxiv:2207.00796
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this paper clarifies the picture about dense - choice counter machines, which have been less studied than ( discrete ) counter machines. we revisit the definition of " dense counter machines " so that it now extends ( discrete ) counter machines, and we provide new undecidability and decidability results. using the first - order additive mixed theory of reals and integers, we give a logical characterization of the sets of configurations reachable by reversal - bounded dense - choice counter machines.
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arxiv:0911.3405
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in this paper, we study the ground state quantum fisher information ( qfi ) in one - dimensional spin - 1 models, as witness to multipartite entanglement. the models addressed are the bilinear - biquadratic model, the most general isotropic su ( 2 ) - invariant spin - 1 chain, and the xxz spin - 1 chain, both with nearest - neighbor interactions and open boundary conditions. we show that the scaling of the qfi of strictly non - local observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. analysing its behavior at the critical phases we are also able to recover the scaling dimensions of the order parameters both for local and string observables. the numerical results have been obtained by exploiting the density matrix renormalization group algorithm and tensor network techniques.
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arxiv:2307.02407
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reversible computation is gaining increasing relevance in the context of several post - cmos technologies, the most prominent of those being quantum computing. one of the key theoretical problem pertaining to reversible logic synthesis is the upper bound of the gate count. compared to the known bounds, the results obtained by optimal synthesis methods are significantly less. in this paper, we connect this problem with the multiplicative complexity analysis of classical boolean functions. we explore the possibility of relaxing the ancilla and if that approach makes the upper bound tighter. our results are negative. the ancilla - free synthesis methods by using transformations and by starting from an exclusive sum - of - product ( esop ) formulation remain, theoretically, the synthesis methods for achieving least gate count for the cases where the number of variables $ n $ is $ < 8 $ and otherwise, respectively.
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arxiv:1602.00101
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exploiting sparsity in semidefinite programs ( sdp ) is critical to solving large - scale problems. the chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in sdps. in this paper, we show that the maximal clique - based sdp decomposition is primal degenerate when the sdp has a low rank solution. we also derive conditions under which the multipliers in the maximal clique - based sdp formulation is not unique. numerical experiments demonstrate that the sdp decomposition results in the schur - complement matrix of the interior point method ( ipm ) having higher condition number than for the original sdp formulation.
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arxiv:1509.08021
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we prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. this leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $ f _ n $ but not $ fp _ { n + 1 } $ of some groups including pure braid groups and families of poly - surface groups that are fundamental groups of complex projective varieties.
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arxiv:2205.05246
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unraveling the 3d physical structure, the temperature and density distribution, of protoplanetary discs is an essential step if we are to confront simulations of embedded planets or dynamical instabilities. in this paper we focus on submillimeter array observations of the edge - on source, gomez ' s hamburger, believed to host an over - density hypothesised to be a product of gravitational instability in the disc, goham b. we demonstrate that, by leveraging the well characterised rotation of a keplerian disc to deproject observations of molecular lines in position - position - velocity space into disc - centric coordinates, we are able to map out the emission distribution in the ( r, z ) plane and ( x, y, z ) space. we show that 12co traces an elevated layer of $ z \, / \, r \ sim 0. 3 $, while 13co traces deeper in the disc at $ z \, / \, r \ lesssim 0. 2 $. we localize emission associated with goham b, finding it at deprojected radius of approximately 500 au and at polar angle of + \ - 30 degrees from the disc major axis. at the spatial resolution of $ \ sim 1. 5 ^ { \ prime \ prime } $, goham b is spatially unresolved, with an upper limit to its radius of $ < 190 $ ~ au.
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arxiv:2003.02061
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although the autoparallel curves and the geodesics coincide in the riemannian geometry in which only the curvature is nonzero among the nonmetricity, the torsion and the curvature, they define different curves in the non - riemannian ones. we give a novel approach to autoparallel curves and geodesics for theories of the symmetric teleparallel gravity written in the coincident gauge. then we apply our autoparallel equation to a schwarzschild - type metric and give remarks about dark matter and orbit equation.
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arxiv:1102.1878
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using the standard square - - function method ( based on the poisson semigroup ), multiplier conditions of h \ " ormander type are derived for laguerre expansions in $ l ^ p $ - - spaces with power weights in the $ a _ p $ - range ; this result can be interpreted as an ` ` upper end point ' ' multiplier criterion which is fairly good for $ p $ near $ 1 $ or near $ \ infty $. a weighted generalization of kanjin ' s \ cite { kan } transplantation theorem allows to obtain a ` ` lower end point ' ' multiplier criterion whence by interpolation nearly ` ` optimal ' ' multiplier criteria ( in dependance of $ p $, the order of the laguerre polynomial, the weight ).
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arxiv:math/9307203
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in this paper, we show that the integration of a stochastic differential equations driven by g - brownian motion in r can be reduced to the integration of an ordinary differential equations parametrized by a variable in ( { \ omega }, f ). we study the sample solutions of g - sdes by an extention of g - it \ ^ o formula. and then we also get a comparison theorem for g - sdes and its applications.
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arxiv:1309.5232
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an improved algorithm is proposed for monte carlo methods to study fermion systems interacting with adiabatical fields. to obtain a weight for each monte carlo sample with a fixed configuration of adiabatical fields, a series expansion using chebyshev polynomials is applied. by introducing truncations of matrix operations in a systematic and controlled way, it is shown that the cpu time is reduced from o ( n ^ 3 ) to o ( n ) where n is the system size. benchmark results show that the implementation of the algorithm makes it possible to perform systematic investigations of critical phenomena using system - size scalings even for an electronic model in three dimensions, within a realistic cpu timescale.
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arxiv:cond-mat/0308298
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behrstock, hagen, and sisto classified 3 - manifold groups admitting a hierarchically hyperbolic space structure. however, these structures were not always equivariant with respect to the group. in this paper, we classify 3 - manifold groups admitting equivariant hierarchically hyperbolic structures. the key component of our proof is that the admissible groups introduced by croke and kleiner always admit equivariant hierarchically hyperbolic structures. for non - geometric graph manifolds, this is contrary to a conjecture of behrstock, hagen, and sisto and also contrasts with results about cat ( 0 ) cubical structures on these groups. perhaps surprisingly, our arguments involve the construction of suitable quasimorphisms on the seifert pieces, in order to construct actions on quasi - lines.
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arxiv:2206.12244
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the spin - charge coupled dynamics in a thin, magnetized metallic system are investigated. the effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e. g., by a magnetic material in contact with a normal - metal system. we consider a general inversion - asymmetric substrate / normal - metal / magnet structure, which, by specifying the precise nature of each layer, can mimick various experimentally employed setups. inversion symmetry breaking gives rise to an effective rashba spin - orbit interaction. we derive general spin - charge kinetic equations which show that such spin - orbit interaction, together with anisotropic elliott - yafet spin relaxation, yields significant corrections to the magnetization - induced dynamics. in particular, we present a consistent treatment of the spin density and spin current contributions to the equations of motion, inter alia identifying a novel term in the effective force which appears due to a spin current polarized parallel to the magnetization. this " inverse spin filter " contribution depends markedly on the parameter which describes the anisotropy in spin relaxation. to further highlight the physical meaning of the different contributions, the spin pumping configuration of typical experimental setups is analyzed in detail. in the two - dimensional limit the build - up of a dc voltage is dominated by the spin galvanic ( inverse edelstein ) effect. a measuring scheme that could isolate this contribution is discussed.
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arxiv:1611.03378
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multi - agent reinforcement learning has received significant interest in recent years notably due to the advancements made in deep reinforcement learning which have allowed for the developments of new architectures and learning algorithms. using social dilemmas as the training ground, we present a novel learning architecture, learning through probing ( ltp ), where agents utilize a probing mechanism to incorporate how their opponent ' s behavior changes when an agent takes an action. we use distinct training phases and adjust rewards according to the overall outcome of the experiences accounting for changes to the opponents behavior. we introduce a parameter eta to determine the significance of these future changes to opponent behavior. when applied to the iterated prisoner ' s dilemma ( ipd ), ltp agents demonstrate that they can learn to cooperate with each other, achieving higher average cumulative rewards than other reinforcement learning methods while also maintaining good performance in playing against static agents that are present in axelrod tournaments. we compare this method with traditional reinforcement learning algorithms and agent - tracking techniques to highlight key differences and potential applications. we also draw attention to the differences between solving games and societal - like interactions and analyze the training of q - learning agents in makeshift societies. this is to emphasize how cooperation may emerge in societies and demonstrate this using environments where interactions with opponents are determined through a random encounter format of the ipd.
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arxiv:1809.10007
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we present the star - forming properties of 378 satellite galaxies around 101 milky way analogs in the satellites around galactic analogs ( saga ) survey, focusing on the environmental processes that suppress or quench star formation. in the saga stellar mass range of 10 ^ 6 to 10 ^ 10 solar masses, we present quenched fractions, star - forming rates, gas - phase metallicities, and gas content. the fraction of saga satellites that are quenched increases with decreasing stellar mass and shows significant system - to - system scatter. saga satellite quenched fractions are highest in the central 100 kpc of their hosts and decline out to the virial radius. splitting by specific star formation rate ( ssfr ), the least star - forming satellite quartile follows the radial trend of the quenched population. the median ssfr of star - forming satellites increases with decreasing stellar mass and is roughly constant with projected radius. star - forming saga satellites are consistent with the star formation rate - - stellar mass relationship determined in the local volume, while the median gas - phase metallicity is higher and median hi gas mass is lower at all stellar masses. we investigate the dependence of the satellite quenched fraction on host properties. quenched fractions are higher in systems with larger host halo mass, but this trend is only seen in the inner 100 kpc ; we do not see significant trends with host color or star formation rate. our results suggest that lower mass satellites and satellites inside 100 kpc are more efficiently quenched in a milky way - like environment, with these processes acting sufficiently slowly to preserve a population of star - forming satellites at all stellar masses and projected radii.
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arxiv:2404.14499
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an intelligent reflecting surface ( irs ) can adaptively adjust the phase shifts of its reflecting units to strengthen the desired signal and / or suppress the undesired signal. in this letter, we investigate an irs - aided secure wireless communication system where a multi - antenna access point ( ap ) sends confidential messages to a single - antenna user in the presence of a single - antenna eavesdropper. in particular, we consider the challenging scenario where the eavesdropping channel is stronger than the legitimate communication channel and they are also highly correlated in space. we maximize the secrecy rate of the legitimate communication link by jointly designing the ap ' s transmit beamforming and the irs ' s reflect beamforming. while the resultant optimization problem is difficult to solve, we propose an efficient algorithm to obtain high - quality suboptimal solution for it by applying the alternating optimization and semidefinite relaxation methods. simulation results show that the proposed design significantly improves the secrecy communication rate for the considered setup over the case without using the irs, and outperforms a heuristic scheme.
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arxiv:1905.10770
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we investigate a new threat to neural sequence - to - sequence ( seq2seq ) models : training - time attacks that cause models to " spin " their output and support a certain sentiment when the input contains adversary - chosen trigger words. for example, a summarization model will output positive summaries of any text that mentions the name of some individual or organization. we introduce the concept of a " meta - backdoor " to explain model - spinning attacks. these attacks produce models whose output is valid and preserves context, yet also satisfies a meta - task chosen by the adversary ( e. g., positive sentiment ). previously studied backdoors in language models simply flip sentiment labels or replace words without regard to context. their outputs are incorrect on inputs with the trigger. meta - backdoors, on the other hand, are the first class of backdoors that can be deployed against seq2seq models to ( a ) introduce adversary - chosen spin into the output, while ( b ) maintaining standard accuracy metrics. to demonstrate feasibility of model spinning, we develop a new backdooring technique. it stacks the adversarial meta - task ( e. g., sentiment analysis ) onto a seq2seq model, backpropagates the desired meta - task output ( e. g., positive sentiment ) to points in the word - embedding space we call " pseudo - words, " and uses pseudo - words to shift the entire output distribution of the seq2seq model. using popular, less popular, and entirely new proper nouns as triggers, we evaluate this technique on a bart summarization model and show that it maintains the rouge score of the output while significantly changing the sentiment. we explain why model spinning can be a dangerous technique in ai - powered disinformation and discuss how to mitigate these attacks.
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arxiv:2107.10443
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image enhancement plays an important role in several application in the field of computer vision and image processing. histogram specification ( hs ) is one of the most widely used techniques for contrast enhancement of an image, which requires an appropriate probability density function for the transformation. in this paper, we propose a fuzzy method to find a suitable pdf automatically for histogram specification using interval type - 2 ( it2 ) fuzzy approach, based on the fuzzy membership values obtained from the histogram of input image. the proposed algorithm works in 5 stages which includes - symmetric gaussian fitting on the histogram, extraction of it2 fuzzy membership functions ( mfs ) and therefore, footprint of uncertainty ( fou ), obtaining membership value ( mv ), generating pdf and application of hs. we have proposed 4 different methods to find membership values - point - wise method, center of weight method, area method, and karnik - mendel ( km ) method. the framework is sensitive to local variations in the histogram and chooses the best pdf so as to improve contrast enhancement. experimental validity of the methods used is illustrated by qualitative and quantitative analysis on several images using the image quality index - average information content ( aic ) or entropy, and by comparison with the commonly used algorithms such as histogram equalization ( he ), recursive mean - separate histogram equalization ( rmshe ) and brightness preserving fuzzy histogram equalization ( bpfhe ). it has been found out that on an average, our algorithm improves the aic index by 11. 5 % as compared to the index obtained by histogram equalisation.
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arxiv:1805.02173
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diffusion - based text - to - image models have demonstrated remarkable capabilities in generating realistic images, but they raise societal and ethical concerns, such as the creation of unsafe content. while concept editing is proposed to address these issues, they often struggle to balance the removal of unsafe concept with maintaining the model ' s general genera - tive capabilities. in this work, we propose ace, a new editing method that enhances concept editing in diffusion models. ace introduces a novel cross null - space projection approach to precisely erase unsafe concept while maintaining the model ' s ability to generate high - quality, semantically consistent images. extensive experiments demonstrate that ace significantly outperforms the advancing baselines, improving semantic consistency by 24. 56 % and image generation quality by 34. 82 % on average with only 1 % of the time cost. these results highlight the practical utility of concept editing by mitigating its potential risks, paving the way for broader applications in the field. code is avaliable at https : / / github. com / littlelittlenine / ace - zero. git
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arxiv:2503.08116
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a fractal function is a function whose graph is the attractor of an iterated function system. this paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
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arxiv:1209.6100
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inspired by a recent experiment, we study the influence of thermal fluctuations on the $ i $ - $ v $ characteristics of a josephson junction, coupled to a strongly resistive environment. we obtain analytical results in the limit where the josephson energy is larger than the charging energy and quasiparticles are absent.
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arxiv:cond-mat/0304102
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we propose a new multifractional stochastic process which allows for self - exciting behavior, similar to what can be seen for example in earthquakes and other self - organizing phenomena. the process can be seen as an extension of a multifractional brownian motion, where the hurst function is dependent on the past of the process. we define this through a stochastic volterra equation, and we prove existence and uniqueness of this equation, as well as give bounds on the p - order moments, for all p > = 1. we show convergence of an euler - maruyama scheme for the process, and also give the rate of convergence, which is depending on the self - exciting dynamics of the process. moreover, we discuss different applications of this process, and give examples of different functions to model self - exciting behavior.
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arxiv:1908.05523
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in this paper we implement a local linear regression ensemble committee ( lolrec ) to predict 1 - day - ahead returns of 453 assets form the s & p500. the estimates and the historical returns of the committees are used to compute the weights of the portfolio from the 453 stock. the proposed method outperforms benchmark portfolio selection strategies that optimize the growth rate of the capital. we investigate the effect of algorithm parameter m : the number of selected stocks on achieved average annual yields. results suggest the algorithm ' s practical usefulness in everyday trading.
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arxiv:1506.08690
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let $ j $ and $ r $ be anti - commuting fundamental symmetries in a hilbert space $ \ mathfrak { h } $. the operators $ j $ and $ r $ can be interpreted as basis ( generating ) elements of the complex clifford algebra $ { \ mathcal c } l _ 2 ( j, r ) : = { span } \ { i, j, r, ijr \ } $. an arbitrary non - trivial fundamental symmetry from $ { \ mathcal c } l _ 2 ( j, r ) $ is determined by the formula $ j _ { \ vec { \ alpha } } = \ alpha _ { 1 } j + \ alpha _ { 2 } r + \ alpha _ { 3 } ijr $, where $ { \ vec { \ alpha } } \ in \ mathbb { s } ^ 2 $. let $ s $ be a symmetric operator that commutes with $ { \ mathcal c } l _ 2 ( j, r ) $. the purpose of this paper is to study the sets $ \ sigma _ { { j _ { \ vec { \ alpha } } } } $ ( $ \ forall { \ vec { \ alpha } } \ in \ mathbb { s } ^ 2 $ ) of self - adjoint extensions of $ s $ in krein spaces generated by fundamental symmetries $ { { j _ { \ vec { \ alpha } } } } $ ( $ { { j _ { \ vec { \ alpha } } } } $ - self - adjoint extensions ). we show that the sets $ \ sigma _ { { j _ { \ vec { \ alpha } } } } $ and $ \ sigma _ { { j _ { \ vec { \ beta } } } } $ are unitarily equivalent for different $ { \ vec { \ alpha } }, { \ vec { \ beta } } \ in \ mathbb { s } ^ 2 $ and describe in detail the structure of operators $ a \ in \ sigma _ { { j _ { \ vec { \ alpha } } } } $ with empty resolvent set.
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arxiv:1105.2969
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this article expands our work in [ ca16 ]. by its reliance on turing computability, the classical theory of effectivity, along with effective reducibility and weihrauch reducibility, is only applicable to objects that are either countable or can be encoded by countable objects. we propose a notion of effectivity based on koepke ' s ordinal turing machines ( otms ) that applies to arbitrary set - theoretical $ \ pi _ { 2 } $ - statements, along with according variants of effective reducibility and weihrauch reducibility. as a sample application, we compare various choice principles with respect to effectivity. we also propose a generalization to set - theoretical formulas of arbitrary quantifier complexity.
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arxiv:1811.11630
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the reaction - diffusion master equation ( rdme ) is a lattice stochastic reaction - diffusion model that has been used to study spatially distributed cellular processes. the rdme is often interpreted as an approximation to spatially - continuous models in which molecules move by brownian motion and react by one of several mechanisms when sufficiently close. in the limit that the lattice spacing approaches zero, in two or more dimensions, the rdme has been shown to lose bimolecular reactions. the rdme is therefore not a convergent approximation to any spatially - continuous model that incorporates bimolecular reactions. in this work we derive a new convergent rdme ( crdme ) by finite volume discretization of a spatially - continuous stochastic reaction - diffusion model popularized by doi. we demonstrate the numerical convergence of reaction time statistics associated with the crdme. for sufficiently large lattice spacings or slow bimolecular reaction rates, we also show the reaction time statistics of the crdme may be approximated by those from the rdme. the original rdme may therefore be interpreted as an approximation to the crdme in several asymptotic limits.
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arxiv:1211.6772
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traditional spectral imaging methods are constrained by the time - consuming scanning process, limiting the application in dynamic scenarios. one - shot spectral imaging based on reconstruction has been a hot research topic recently and the primary challenges still lie in both efficient fabrication techniques suitable for mass production and the high - speed, high - accuracy reconstruction algorithm for real - time spectral imaging. in this study, we introduce an innovative on - chip real - time hyperspectral imager that leverages nanophotonic film spectral encoders and a massively parallel network ( mp - net ), featuring a 4 * 4 array of compact, all - dielectric film units for the micro - spectrometers. each curved nanophotonic film unit uniquely modulates incident light across the underlying 3 * 3 cmos image sensor ( cis ) pixels, enabling a high spatial resolution equivalent to the full cmos resolution. the implementation of mp - net, specially designed to address variability in transmittance and manufacturing errors such as misalignment and non - uniformities in thin film deposition, can greatly increase the structural tolerance of the device and reduce the preparation requirement, further simplifying the manufacturing process. tested in varied environments on both static and moving objects, the real - time hyperspectral imager demonstrates the robustness and high - fidelity spatial - spectral data capabilities across diverse scenarios. this on - chip hyperspectral imager represents a significant advancement in real - time, high - resolution spectral imaging, offering a versatile solution for applications ranging from environmental monitoring, remote sensing to consumer electronics.
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arxiv:2404.09500
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in this paper, we study the construction of the supersymmetric extensions of vertex algebras. in particular, for $ n = n \ in \ mathbb { z } _ { + } $, we show the universal enveloping $ n = n $ supersymmetric ( susy ) vertex algebra of an $ n = n $ susy lie conformal algebra can be extended to an $ n = n ' > n $ susy vertex algebra.
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arxiv:2308.00693
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we propose gaus - slam, a dense rgb - d slam system that leverages 2d gaussian surfels to achieve robust tracking and high - fidelity mapping. our investigations reveal that gaussian - based scene representations exhibit geometry distortion under novel viewpoints, which significantly degrades the accuracy of gaussian - based tracking methods. these geometry inconsistencies arise primarily from the depth modeling of gaussian primitives and the mutual interference between surfaces during the depth blending. to address these, we propose a 2d gaussian - based incremental reconstruction strategy coupled with a surface - aware depth rendering mechanism, which significantly enhances geometry accuracy and multi - view consistency. additionally, the proposed local map design dynamically isolates visible surfaces during tracking, mitigating misalignment caused by occluded regions in global maps while maintaining computational efficiency with increasing gaussian density. extensive experiments across multiple datasets demonstrate that gaus - slam outperforms comparable methods, delivering superior tracking precision and rendering fidelity. the project page will be made available at https : / / gaus - slam. github. io.
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arxiv:2505.01934
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we develop a method to study the implied volatility for exotic options and volatility derivatives with european payoffs such as vix options. our approach, based on malliavin calculus techniques, allows us to describe the properties of the at - the - money implied volatility ( atmi ) in terms of the malliavin derivatives of the underlying process. more precisely, we study the short - time behaviour of the atmi level and skew. as an application, we describe the short - term behavior of the atmi of vix and realized variance options in terms of the hurst parameter of the model, and most importantly we describe the class of volatility processes that generate a positive skew for the vix implied volatility. in addition, we find that our atmi asymptotic formulae perform very well even for large maturities. several numerical examples are provided to support our theoretical results.
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arxiv:1808.03610
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in this work we will study the polarizations of both leptons ( $ \ tau $ ) in the decay channel $ b \ to k ^ * \ tau ^ - \ tau ^ + $. in the case of the dileptonic inclusive decay $ b \ to k ^ * \ ell ^ - \ ell ^ + $, where apart from the polarization asymmetries of single lepton $ \ ell $, one can also observe the polarization asymmetries of both leptons simultaneously. if this sort of measurement is possible then we can have, apart from decay rate, fb asymmetry and the six single lepton polarization asymmetries ( three each for $ \ ell ^ - $ and $ \ ell ^ + $ ), nine more double polarization asymmetries. this will give us a very useful tool in more strict testing of sm and the physics beyond. we discuss the double polarization asymmetries of $ \ tau $ leptons in the decay mode $ b \ to k ^ * \ tau ^ - \ tau ^ + $ within the sm and the minimal supersymmetric extensions of it.
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arxiv:hep-ph/0304084
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in this article, we focus on investigating the focusing kundu - eckhaus equation with nonzero boundary condition. a appropriate two - sheeted riemann surface is introduced to map the spectral parameter $ k $ into a single - valued parameter $ z $. starting from the lax pair of kundu - eckhaus equation, two kind of jost solutions are construed. further their asymptotic, analyticity, symmetries as well as spectral matrix are detailed analyzed. it is shown that the solution of kundu - eckhaus equation with nonzero boundary condition can characterized with a matrix riemann - hilbert problem. then a formula of $ n $ - soliton solutions is derived by solving riemann - hilbert problem. as applications, the first - order explicit soliton solution is obtained.
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arxiv:1910.08921
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yellowballs ( ybs ) were first discovered during the milky way project citizen - science initiative ( mwp ; simpson et al. 2012 ). mwp users noticed compact, yellow regions in spitzer space telescope mid - infrared ( mir ) images of the milky way plane and asked professional astronomers to explain these " yellow balls. " follow - up work by kerton et al. ( 2015 ) determined that ybs likely trace compact photo - dissociation regions associated with massive and intermediate - mass star formation. ybs were included as target objects in a version of the milky way project launched in 2016 ( jayasinghe et al. 2016 ), which produced a listing of over 6000 yb locations. we have measured distances, cross - match associations, physical properties, and mir colors of ~ 500 ybs within a pilot region covering the l = 30 - 40 degrees, b = + / - 1 degree region of the galactic plane. we find 20 - 30 % of ybs in our pilot region contain high - mass star formation capable of becoming expanding h ii regions that produce mir bubbles. a majority of ybs represent intermediate - mass star - forming regions whose placement in evolutionary diagrams suggest they are still actively accreting, and may be precursors to optically - revealed herbig ae / be nebulae. many of these intermediate - mass ybs were missed by surveys of massive star - formation tracers and thus this catalog provides information for many new sites of star formation. future work will expand this pilot region analysis to the entire yb catalog.
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arxiv:2102.01661
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the effect of a quantum phase transition associated with the appearance of the fermion condensate in an electron liquid on the properties of superconductors is considered. it is shown that the electron system in both superconducting and normal states exhibits characteristic features of a quantum protectorate after the point of this fermion - condensation quantum phase transition. the single - particle spectrum of a superconductor can be represented by two straight lines corresponding to two effective masses $ m ^ * _ { fc } $ and $ m ^ * _ { l } $. the $ m ^ * _ { fc } $ mass characterizes the spectrum up to the binding energy $ e _ 0 $, which is of the order of the superconducting gap in magnitude, and $ m ^ * _ { l } $ determines the spectrum at higher binding energies. both effective masses are retained in the normal state ; however, $ e _ 0 = 4t $. these results are used to explain the lineshape of single - particle excitations and other remarkable properties of high - $ t _ c $ superconductors and are in a good agreement with recent experimental data.
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arxiv:cond-mat/0105477
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cooperative vehicle platooning significantly improves highway safety, fuel efficiency, and traffic flow. in this model, a set of vehicles move in line formation and coordinate acceleration, braking, and steering using a combination of physical sensing and vehicle - to - vehicle ( v2v ) messaging. the authenticity and integrity of the v2v messages are paramount to safety. for this reason, recent v2v and v2x standards support the integration of a pki. however, a pki cannot bind a vehicle ' s digital identity to the vehicle ' s physical state ( location, velocity, etc. ). as a result, a vehicle with valid cryptographic credentials can impact platoons from a remote location. in this paper, we seek to provide the missing link between the physical and the digital world in the context of vehicle platooning. we propose a new access control protocol we call proof - of - following ( pof ) that verifies the following distance between a candidate and a verifier. the main idea is to draw security from the common, but constantly changing environment experienced by the closely traveling vehicles. we use the large - scale fading effect of ambient rf signals as a common source of randomness to construct a { \ em pof } primitive. the correlation of large - scale fading is an ideal candidate for the mobile outdoor environment because it exponentially decays with distance and time. we evaluate our pof protocol on an experimental platoon of two vehicles in freeway, highway, and urban driving conditions. we demonstrate that the pof withstands both the pre - recording and following attacks with overwhelming probability.
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arxiv:2107.09863
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a contraction $ t $ on a hilbert space $ \ mathcal { h } $ is said to be pure if the sequence $ \ lbrace t ^ { * n } \ rbrace _ { n } $ converges to $ 0 $ in the strong operator topology. in this article, we prove that for contractions $ t $, which commute with certain tractable tuples of commuting operators $ x = ( x _ 1, \ ldots, x _ n ) $ on $ \ mathcal { h } $, the following statements are equivalent : ( i ) $ t $ is a pure contraction on $ \ mathcal { h } $, ( ii ) the compression $ p _ { \ mathcal { w } ( x ) } t | _ { \ mathcal { w } ( x ) } $ is a pure contraction, where $ \ mathcal { w } ( x ) $ is the wandering subspace corresponding to the tuple $ x $. an operator - valued multiplier $ \ phi $ of a vector - valued reproducing kernel hilbert space ( rkhs ) is said to be pure contractive if the associated multiplication operator $ m _ { \ phi } $ is a pure contraction. using the above result, we find that operator - valued mulitpliers $ \ phi ( \ textbf { z } ) $ of several vector - valued rkhs ' s on the polydisc $ \ mathbb { d } ^ n $ as well as the unit ball $ \ mathbb { b } _ n $ in $ \ mathbb { c } ^ n $ are pure contractive if and only if $ \ phi ( 0 ) $ is a pure contraction on the underlying hilbert space. the list includes hardy, bergman and drury - arveson spaces. finally, we present some applications of our characterization of pure contractive multipliers associated with the polydisc.
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arxiv:2112.08332
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spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of liesegang bands. this mechanism yields a sequence of band positions x _ n that obeys the spacing law x _ n ~ q ( 1 + p ) ^ n. the dependence of the parameters p and q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed matalon - packter law.
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arxiv:cond-mat/9903420
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the location of a repeat plume detected at europa is found to be coincident with the strongest ionosphere detection made by galileo radio occultation in 1997.
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arxiv:1711.03628
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empirical evidence of planets in gas - rich circumstellar discs is required to constrain giant planet formation theories. here we study the kinematic patterns which arise from planet - disc interactions and their observability in co rotational emission lines. we perform three - dimensional hydrodynamical simulations of single giant planets, and predict the emergent intensity field with radiative transfer. pressure gradients at planet - carved gaps, spiral wakes and vortices bear strong kinematic counterparts. the iso - velocity contours in the co ( 2 - 1 ) line centroids $ v _ \ circ $ reveal large - scale perturbations, corresponding to abrupt transitions from below sub - keplerian to super - keplerian rotation along with radial and vertical flows. the increase in line optical depth at the edge of the gap also modulates $ v _ \ circ $, but this is a mild effect compared to the dynamical imprint of the planet - disc interaction. the large - scale deviations from the keplerian rotation thus allow the planets to be indirectly detected via the first moment maps of molecular gas tracers, at alma angular resolutions. the strength of these deviations depends on the mass of the perturber. this initial study paves the way to eventually determine the mass of the planet by comparison with more detailed models.
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arxiv:1806.05125
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we report on an evaluation of an optical clock that uses the $ \ phantom { } ^ 2s _ { 1 / 2 } \ rightarrow \ phantom { } ^ 2d _ { 5 / 2 } $ transition of a single $ ^ { 88 } $ sr $ ^ + $ ion as the reference. in contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well - characterized sensitivity to thermal radiation. we measure the clock output frequency against an independent $ ^ { 171 } $ yb $ ^ + $ ion clock, based on the $ \ phantom { } ^ 2s _ { 1 / 2 } ( f = 0 ) \ rightarrow \ phantom { } ^ 2f _ { 7 / 2 } ( f = 3 ) $ electric octupole ( e3 ) transition, and determine the frequency ratio with a total fractional uncertainty of $ 2. 3 \ times 10 ^ { - 17 } $. relying on a previous measurement of the $ ^ { 171 } $ yb $ ^ + $ ( e3 ) clock frequency, we find the absolute frequency of the $ ^ { 88 } $ sr $ ^ + $ clock transition to be $ 444779044095485. 271 ( 59 ) \, \ text { hz } $. our result reduces the uncertainty by a factor of $ 3 $ compared to the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. we also show that for three simultaneously interrogated $ ^ { 88 } $ sr $ ^ + $ ions, the increased number causes the expected improvement of the short - term frequency instability of the optical clock without degrading its systematic uncertainty.
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arxiv:2212.08687
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we present a cnn - based predictive lossless compression scheme for raw color mosaic images of digital cameras. this specialized application problem was previously understudied but it is now becoming increasingly important, because modern cnn methods for image restoration tasks ( e. g., superresolution, low lighting enhancement, deblurring ), must operate on original raw mosaic images to obtain the best possible results. the key innovation of this paper is a high - order nonlinear cnn predictor of spatial - spectral mosaic patterns. the deep learning prediction can model highly complex sample dependencies in spatial - spectral mosaic images more accurately and hence remove statistical redundancies more thoroughly than existing image predictors. experiments show that the proposed cnn predictor achieves unprecedented lossless compression performance on camera raw images.
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arxiv:2001.10484
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we present some comparison results for solutions to certain non local elliptic and parabolic problems that involve the fractional laplacian operator and mixed boundary conditions, given by a zero dirichlet datum on part of the complementary of the domain and zero neumann data on the rest. these results represent a non local generalization of a hopf ' s lemma for elliptic and parabolic problems with mixed conditions. in particular we prove the non local version of the results obtained by j. d \ ' avila and j. d \ ' avila - l. dupaigne for the classical case respectively.
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arxiv:1607.01505
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the p \ ' al inequality is a classical result which asserts that among all planar convex sets of given width the equilateral triangle is the one of minimal area. in this paper we prove three quantitative versions of this inequality, by quantifying how the closeness of the area of a convex set, of certain width, to the minimal value implies its closeness to the equilateral triangle. as a by - product, we also present a novel result concerning a quantitative inequality for the inradius of a set, under minimal width constraint.
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arxiv:2405.18294
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the rheology of suspensions of non - brownian soft spheres is studied across jamming but also across the viscous and inertial regimes using a custom pressure - and volume - imposed rheometer. the study shows that the granular rheology found for suspensions of hard spheres can be extended to a soft granular rheology ( sgranr ) by renormalizing the critical volume fraction and friction coefficient to pressure - dependent values and using the addition of the viscous and inertial stress scales. this sgranr encompasses rheological behaviors on both sides of the jamming transition, resulting in an approximate collapse of the rheological data into two branches when scaled with the distance to jamming, as observed for soft colloids. this research suggests that suspensions of soft particles across flow regimes can be described by a unified sgranr framework around the jamming transition.
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arxiv:2311.15107
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we evaluate the three - photon vertex functions at order $ b $ and $ b ^ { 2 } $ in a weak constant magnetic field at finite temperature and density with on shell external lines. their application to the study of the photon splitting process leads to consider high energy photons whose dispersion relations are not changed significantly by the plasma effects. the absorption coefficient is computed and compared with the perturbative vacuum result. for the values of temperature and density of some astrophysical objects with a weak magnetic field, the matter effects are negligible.
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arxiv:hep-ph/0104045
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recent advancements in deep learning models have significantly enhanced jet classification performance by analyzing low - level features ( llfs ). however, this approach often leads to less interpretable models, emphasizing the need to understand the decision - making process and to identify the high - level features ( hlfs ) crucial for explaining jet classification. to address this, we consider the top jet tagging problems and introduce an analysis model ( am ) that analyzes selected hlfs designed to capture important features of top jets. our am mainly consists of the following three modules : a relation network analyzing two - point energy correlations, mathematical morphology and minkowski functionals for generalizing jet constituent multiplicities, and a recursive neural network analyzing subjet constituent multiplicity to enhance sensitivity to subjet color charges. we demonstrate that our am achieves performance comparable to the particle transformer ( part ) while requiring fewer computational resources in a comparison of top jet tagging using jets simulated at the hadronic calorimeter angular resolution scale. furthermore, as a more constrained architecture than part, the am exhibits smaller training uncertainties because of the bias - variance tradeoff. we also compare the information content of am and part by decorrelating the features already learned by am. lastly, we briefly comment on the results of am with finer angular resolution inputs.
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arxiv:2312.11760
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we present an optical photometric and spectroscopic analysis of the fast - declining hydrogen - rich type ii supernova ( sn ) 2019nyk. the light curve properties of sn 2019nyk align well with those of other fast - declining type ii sne, such as sne 2013by and 2014g. sn 2019nyk exhibits a peak absolute magnitude of - 18. 09 $ \ pm $ 0. 17 mag in the v band, followed by a rapid decline at 2. 84 $ \ pm $ 0. 03 mag ( 100 d ) $ ^ { - 1 } $ during the recombination phase. the early spectra of sn 2019nyk exhibit high - ionisation emission features as well as narrow h balmer lines, persisting until 4. 1 d since explosion, indicating the presence of circumstellar material ( csm ) in close proximity. a comparison of these features with other type ii sne displaying an early interaction reveals similarities between these features and those observed in sne 2014g and 2023ixf. we also compared the early spectra to literature models, estimating a mass - loss rate of the order of 10 $ ^ { - 3 } $ m $ _ \ odot $ yr $ ^ { - 1 } $. radiation hydrodynamical modelling of the light curve also suggests the mass loss from the progenitor within a short period prior to explosion, totalling 0. 16 m $ _ \ odot $ of material within 2900 r $ _ \ odot $ of the progenitor. furthermore, light curve modelling infers a zero - age main sequence mass of 15 m $ _ \ odot $ for the progenitor, a progenitor radius of 1031 r $ _ \ odot $, and an explosion energy of 1. 1 $ \ times $ 10 $ ^ { 51 } $ erg.
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arxiv:2403.00927
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the detection of low - mass planets orbiting the nearest stars is a central stake of exoplanetary science, as they can be directly characterized much more easily than their distant counterparts. here, we present the results of our long - term astrometric observations of the nearest binary m - dwarf gliese 65 ab ( gj65 ), located at a distance of only 2. 67 pc. we monitored the relative astrometry of the two components from 2016 to 2023 with the vlti / gravity interferometric instrument. we derived highly accurate orbital parameters for the stellar system, along with the dynamical masses of the two red dwarfs. the gravity measurements exhibit a mean accuracy per epoch of 50 - 60 microarcseconds in 1. 5h of observing time using the 1. 8m auxiliary telescopes. the residuals of the two - body orbital fit enable us to search for the presence of companions orbiting one of the two stars ( s - type orbit ) through the reflex motion they imprint on the differential a - b astrometry. we detected a neptune - mass candidate companion with an orbital period of p = 156 + / - 1 d and a mass of m = 36 + / - 7 mearth. the best - fit orbit is within the dynamical stability region of the stellar pair. it has a low eccentricity, e = 0. 1 - 0. 3, and the planetary orbit plane has a moderate - to - high inclination of i > 30 { \ deg } with respect to the stellar pair, with further observations required to confirm these values. these observations demonstrate the capability of interferometric astrometry to reach microarcsecond accuracy in the narrow - angle regime for planet detection by reflex motion from the ground. this capability offers new perspectives and potential synergies with gaia in the pursuit of low - mass exoplanets in the solar neighborhood.
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arxiv:2404.08746
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reliability - based design optimization ( rbdo ) is an active field of research with an ever increasing number of contributions. numerous methods have been proposed for the solution of rbdo, a complex problem that combines optimization and reliability analysis. classical approaches are based on approximation methods and have been classified in review papers. in this paper, we first review classical approaches based on approximation methods such as form, and also more recent methods that rely upon surrogate modelling and monte carlo simulation. we then propose a general framework for the solution of rbdo problems that includes three independent blocks, namely adaptive surrogate modelling, reliability analysis and optimization. these blocks are non - intrusive with respect to each other and can be plugged independently in the framework. after a discussion on numerical considerations that require attention for the framework to yield robust solutions to various types of problems, the latter is applied to three examples ( using two analytical functions and a finite element model ). kriging and support vector machines together with their own active learning schemes are considered in the surrogate model block. in terms of reliability analysis, the proposed framework is illustrated using both crude monte carlo and subset simulation. finally, the covariance - matrix adaptation - evolution scheme ( cma - es ), a global search algorithm, or sequential quadratic programming ( sqp ), a local gradient - based method, are used in the optimization block. the comparison of the results to benchmark studies show the effectiveness and efficiency of the proposed framework.
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arxiv:1901.03311
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the expected signature is an analogue of the laplace transform for rough paths. chevyrev and lyons showed that, under certain moment conditions, the expected signature determines the laws of signatures. lyons and ni posed the question of whether the expected signature of brownian motion up to the exit time of a domain satisfies chevyrev and lyons ' moment condition. we provide the first example where the answer is negative.
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arxiv:1905.13034
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