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underwater robots in shallow waters usually suffer from strong wave forces, which may frequently exceed robot ' s control constraints. learning - based controllers are suitable for disturbance rejection control, but the excessive disturbances heavily affect the state transition in markov decision process ( mdp ) or partially observable markov decision process ( pomdp ). also, pure learning procedures on targeted system may encounter damaging exploratory actions or unpredictable system variations, and training exclusively on a prior model usually cannot address model mismatch from the targeted system. in this paper, we propose a transfer learning framework that adapts a control policy for excessive disturbance rejection of an underwater robot under dynamics model mismatch. a modular network of learning policies is applied, composed of a generalized control policy ( gcp ) and an online disturbance identification model ( odi ). gcp is first trained over a wide array of disturbance waveforms. odi then learns to use past states and actions of the system to predict the disturbance waveforms which are provided as input to gcp ( along with the system state ). a transfer reinforcement learning algorithm using transition mismatch compensation ( tmc ) is developed based on the modular architecture, that learns an additional compensatory policy through minimizing mismatch of transitions predicted by the two dynamics models of the source and target tasks. we demonstrated on a pose regulation task in simulation that tmc is able to successfully reject the disturbances and stabilize the robot under an empirical model of the robot system, meanwhile improve sample efficiency.
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arxiv:2007.14646
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the android permission system is a set of controls to regulate access to sensitive data and platform resources ( e. g., camera ). the fast evolving nature of android permissions, coupled with inadequate documentation, results in numerous challenges for third - party developers. this study investigates the permission - related challenges developers face and the solutions provided to resolve them on the crowdsourcing platform stack overflow. we conducted qualitative and quantitative analyses on 3, 327 permission - related questions and 3, 271 corresponding answers. our study found that most questions are related to non - evolving sdk permissions that remain constant across various android versions, which emphasizes the lack of documentation. we classify developers ' challenges into several categories : documentation - related, problems with dependencies, debugging, conceptual understanding, and implementation issues. we further divided these categories into 12 subcategories, nine sub - subcategories, and nine sub - sub - subcategories. our analysis shows that developers infrequently identify the restriction type or protection level of permissions, and when they do, their descriptions often contradict google ' s official documentation. our study indicates the need for clear, consistent documentation to guide the use of permissions and reduce developer misunderstanding leading to potential misuse of android permission. these insights from this study can inform strategies and guidelines for permission issues. future studies should explore the effectiveness of stack overflow solutions to form best practices and develop tools to address these problems.
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arxiv:2311.00074
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in this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by brownian motion on a bounded domain $ d $ in the setting of $ l ^ 2 ( d ) $ space. the result is valid for all initial values in $ l ^ 2 ( d ) $. the logarithmic sobolev inequality plays an important role.
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arxiv:1907.03948
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one significant advantage of superconducting processors is their extensive design flexibility, which encompasses various types of qubits and interactions. given the large number of tunable parameters of a processor, the ability to perform gradient optimization would be highly beneficial. efficient backpropagation for gradient computation requires a tightly integrated software library, for which no open - source implementation is currently available. in this work, we introduce supergrad, a simulator that accelerates the design of superconducting quantum processors by incorporating gradient computation capabilities. supergrad offers a user - friendly interface for constructing hamiltonians and computing both static and dynamic properties of composite systems. this differentiable simulation is valuable for a range of applications, including optimal control, design optimization, and experimental data fitting. in this paper, we demonstrate these applications through examples and code snippets.
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arxiv:2406.18155
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the possibility to control the coherent decay of resonant excitations in nuclear forward scattering is investigated. by changing abruptly the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons can be manipulated and even completely suppressed via quantum interference effects between the nuclear transition currents. the efficiency of the coherent decay suppression and the dependence of the scattered light polarization on the specific switching parameters is analyzed in detail. using a sophisticated magnetic switching sequence involving four rotations of the hyperfine magnetic field, two correlated coherent decay pulses with different polarizations can be generated out of one excitation, providing single - photon entanglement in the kev regime. the verification of the generated entanglement by testing a single - particle version of bell ' s inequality in an x - ray optics experimental setup is put forward.
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arxiv:1003.3668
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we discuss constraints on the rates of stirring and dissipation of mhd turbulence in molecular clouds. recent mhd simulations suggest that turbulence in clouds decays rapidly, thus providing a significant source of energy input, particularly if driven at small scales by, for example, bipolar outflows. we quantify the heating rates by combining the linewidth - size relations, which describe global cloud properties, with numerically determined dissipation rates. we argue that, if cloud turbulence is driven on small internal scales, the $ ^ { 12 } $ co flux ( enhanced by emission from weakly supersonic shocks ) will be much larger than observed ; this, in turn, would imply excitation temperatures significantly above observed values. we reach two conclusions : ( 1 ) small - scale driving by bipolar outflows cannot possibly account for cloud support and yield long - lived clouds, unless the published mhd dissipation rates are seriously overestimated ; ( 2 ) driving on large scales ( comparable to the cloud size ) is much more viable from an energetic standpoint, and if the actual net dissipation rate is only slightly lower than what current mhd simulations estimate, then the observationally inferred lifetimes and apparent virial equilibrium of molecular clouds can be explained.
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arxiv:astro-ph/0101116
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energy levels statistics following the gaussian symplectic ensemble ( gse ) of random matrix theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. however in all these systems there has been one unifying feature : the combination of half - integer spin and time - reversal invariance. here we provide an alternative mechanism for obtaining gse statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. as an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group q8. gse statistics is then observed within one of its subspectra.
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arxiv:1302.2554
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we study the collective electronic excitations in metallic single - and bilayer transition metal dichalcogenides ( tmdcs ) using time dependent density functional theory in the random phase approximation. for very small momentum transfers ( below $ q \ approx0. 02 $ ~ \ aa $ ^ { - 1 } $ ) the plasmon dispersion follows the $ \ sqrt { q } $ behavior expected for free electrons in two dimensions. for larger momentum transfer the plasmon energy is significantly red shifted due to screening by interband transitions. at around $ q \ approx 0. 1 $ \ aa $ ^ { - 1 } $ the plasmon enters the dissipative electron - hole continuum and the plasmon dispersions flatten out at an energy around 0. 6 - 1. 1 ev, depending on the material. using bilayer nbse $ _ 2 $ as example, we show that the plasmon modes of a bilayer structure take the form of symmetric and anti - symmetric hybrids of the single - layer modes. the spatially anti - symmetric mode is rather weak with a linear dispersion tending to zero for $ q = 0 $ while the energy of the symmetric mode follows the single - layer mode dispersion with a slight blue shift.
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arxiv:1311.0158
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violent solar flares and coronal mass ejections ( cmes ) are magnetic phenomena. however, how magnetic fields reconnecting in the flare differ from non - flaring magnetic fields remains unclear owing to the lack of studies of the flare magnetic properties. here we present a first statistical study of flaring ( highlighted by flare - ribbons ) vector magnetic fields in the photosphere. our systematic approach allows us to describe key physical properties of solar flare magnetism, including distributions of magnetic flux, magnetic shear, vertical current and net current over flaring versus non - flaring parts of the active region, and compare these with flare / cme properties. our analysis suggests that while flares are guided by the physical properties that scale with ar size, like the total amount of magnetic flux that participates in the reconnection process and the total current ( extensive properties ), cmes are guided by mean properties, like the fraction of the ar magnetic flux that participates ( intensive property ), with little dependence on the amount of shear at polarity inversion line ( pil ) or the net current. we find that the non - neutralized current is proportional to the amount of shear at pil, providing direct evidence that net vertical currents are formed as a result of any mechanism that could generate magnetic shear along pil. we also find that eruptive events tend to have smaller pil fluxes and larger magnetic shears than confined events. our analysis provides a reference for more realistic solar and stellar flare models. the database is available online and can be used for future quantitative studies of flare magnetism.
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arxiv:2111.06048
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we study the tunneling between two quantum hall systems, along a quasi one - dimensional interface. a detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the tunneling. it is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. this opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. the coupling of the system to external gauge fields is performed, leading us to the exact quantization of the hall conductivity at the interface. the field theory approach is well supported by a numerical diagonalization of the microscopic hamiltonian.
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arxiv:cond-mat/9405081
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we study the statistical properties of the luminous red galaxies sample from the sloan digital sky survey. in particular we test, by determining the probability density function ( pdf ) of galaxy ( conditional ) counts in spheres, whether statistical properties are self - averaging within the sample. we find that there are systematic differences in the shape of the pdf and in the location of its peak, signaling that there are major systematic effects in the data which make the estimation of volume average quantities unreliable within this sample. we discuss that these systematic effects are related to the fluctuating behavior of the redshift counts which can be originated by intrinsic fluctuations in the galaxy density field or by observational selection effects. the latter possibility implies that more than 20 % of the galaxies have not been observed and that such a selection should not be a smooth function of redshift.
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arxiv:1011.4855
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the main goal of this paper is to obtain sufficient conditions that allow us to rigorously derive local versions of the 4 / 5 and 4 / 3 laws of hydrodynamic turbulence, by which we mean versions of these laws that hold in bounded domains. this is done in the context of stationary martingale solutions of the navier - stokes equations driven by an ornstein - uhlenbeck process. specifically, we show that under an assumption of \ say { on average } precompactness in $ l ^ 3, $ the local structure functions are expressed up to first order in the length scale as nonlinear fluxes, in the vanishing viscosity limit and within an appropriate range of scales. if in addition one assumes local energy equality, this is equivalent to expressing the structure functions in terms of the local dissipation. our precompactness assumption is also shown to produce stationary martingale solutions of the euler equations with the same type of forcing in the vanishing viscosity limit.
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arxiv:2007.08838
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prediction and characterization of crystal structures of alloys are a key problem in materials research. using high - throughput ab initio calculations we explore the low - temperature phase diagrams for the following systems : { bi - in, bi - mg, bi - sb, in - mg, in - sb, and mg - sb }. for the experimentally observed phases in these systems we provide information about their stability at low temperatures. keywords : binary alloys, ab initio, intermetallics, transition metals, structure prediction, phase stability, magnesium, indium, bismuth, antimony.
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arxiv:cond-mat/0502535
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with the availability of multi - object spectrometers and the designing \ & running of some large scale sky surveys, we are obtaining massive spectra. therefore, it becomes more and more important to deal with the massive spectral data efficiently and accurately. this work investigated the classification problem of stellar spectra under the assumption that there is no perfect absolute flux calibration, for example, the spectra from guoshoujing telescope ( the large sky area multi - object fiber spectroscopic telescope, lamost ). the proposed scheme consists of the following two procedures : firstly, a spectrum is normalized based on a 17th polynomial fitting ; secondly, a random forest ( rf ) is utilized to classifying the stellar spectra. the experiments on four stellar spectral libraries show that rf has a good classification performance. this work also studied the spectral feature evaluation problem based on rf. the evaluation is helpful in understanding the results of the proposed stellar classification scheme and exploring its potential improvements in future.
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arxiv:1903.07939
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we have studied the dynamics of spreading of viscous non - volatile fluids on surfaces by mc simulations of sos models. we have concentrated on the complete wetting regime, with surface diffusion barriers neglected for simplicity. first, we have performed simulations for the standard sos model. formation of a single precursor layer, and a density profile with a spherical cap shaped center surrounded by gaussian tails can be reproduced with this model. dynamical layering ( dl ), however, only occurs with a very strongly attractive van der waals type of substrate potential. to more realistically describe the spreading of viscous liquid droplets, we introduce a modified sos model. in the new model, tendency for dl and the effect of the surface potential are in part embedded into the dynamics of the model. this allows a relatively simple description of the spreading under different conditions, with a temperature like parameter which strongly influences the droplet morphologies. both rounded droplet shapes and dl can easily be reproduced with the model. furthermore, the precursor width increases proportional to the square root of time, in accordance with experimental observations. pacs : 68. 10. gw, 05. 70. ln, 61. 20. ja.
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arxiv:cond-mat/9406017
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millimeter wave ( mmwave ) communications can potentially meet the high data - rate requirements of unmanned aerial vehicle ( uav ) networks. however, as the prerequisite of mmwave communications, the narrow directional beam tracking is very challenging because of the three - dimensional ( 3d ) mobility and attitude variation of uavs. aiming to address the beam tracking difficulties, we propose to integrate the conformal array ( ca ) with the surface of each uav, which enables the full spatial coverage and the agile beam tracking in highly dynamic uav mmwave networks. more specifically, the key contributions of our work are three - fold. 1 ) a new mmwave beam tracking framework is established for the ca - enabled uav mmwave network. 2 ) a specialized hierarchical codebook is constructed to drive the directional radiating element ( dre ) - covered cylindrical conformal array ( cca ), which contains both the angular beam pattern and the subarray pattern to fully utilize the potential of the ca. 3 ) a codebook - based multiuser beam tracking scheme is proposed, where the gaussian process machine learning enabled uav position / attitude predication is developed to improve the beam tracking efficiency in conjunction with the tracking - error aware adaptive beamwidth control. simulation results validate the effectiveness of the proposed codebook - based beam tracking scheme in the ca - enabled uav mmwave network, and demonstrate the advantages of ca over the conventional planner array in terms of spectrum efficiency and outage probability in the highly dynamic scenarios.
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arxiv:2005.14064
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we present local graph - based dictionary expansion ( lgde ), a method for data - driven discovery of the semantic neighbourhood of words using tools from manifold learning and network science. at the heart of lgde lies the creation of a word similarity graph from the geometry of word embeddings followed by local community detection based on graph diffusion. the diffusion in the local graph manifold allows the exploration of the complex nonlinear geometry of word embeddings to capture word similarities based on paths of semantic association, over and above direct pairwise similarities. exploiting such semantic neighbourhoods enables the expansion of dictionaries of pre - selected keywords, an important step for tasks in information retrieval, such as database queries and online data collection. we validate lgde on two user - generated english - language corpora and show that lgde enriches the list of keywords with improved performance relative to methods based on direct word similarities or co - occurrences. we further demonstrate our method through a real - world use case from communication science, where lgde is evaluated quantitatively on the expansion of a conspiracy - related dictionary from online data collected and analysed by domain experts. our empirical results and expert user assessment indicate that lgde expands the seed dictionary with more useful keywords due to the manifold - learning - based similarity network.
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arxiv:2405.07764
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a representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. it stems from noting that the zeros in a product qubit state do not contribute to the number. they serve only as place holders. the representation is based on the distribution of four types of systems on an integer lattice. the four types, labelled as positive real, negative real, positive imaginary, and negative imaginary, are represented by creation and annihilation operators acting on the system vacuum state. complex rational string number states correspond to strings of creation operators acting on the vacuum. various operators, including those for the basic arithmetic operations, are described. the representation used here is based on occupation number states and is given for bosons and fermions.
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arxiv:quant-ph/0503154
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we consider training models with differential privacy ( dp ) using mini - batch gradients. the existing state - of - the - art, differentially private stochastic gradient descent ( dp - sgd ), requires privacy amplification by sampling or shuffling to obtain the best privacy / accuracy / computation trade - offs. unfortunately, the precise requirements on exact sampling and shuffling can be hard to obtain in important practical scenarios, particularly federated learning ( fl ). we design and analyze a dp variant of follow - the - regularized - leader ( dp - ftrl ) that compares favorably ( both theoretically and empirically ) to amplified dp - sgd, while allowing for much more flexible data access patterns. dp - ftrl does not use any form of privacy amplification. the code is available at https : / / github. com / google - research / federated / tree / master / dp _ ftrl and https : / / github. com / google - research / dp - ftrl.
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arxiv:2103.00039
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this paper explores the economics of augmented reality ( ar ) and virtual reality ( vr ) technologies within decision - making contexts. two metrics are proposed : context entropy, the informational complexity of an environment, and context immersivity, the value from full immersion. the analysis suggests that ar technologies assist in understanding complex contexts, while vr technologies provide access to distant, risky, or expensive environments. the paper provides a framework for assessing the value of ar and vr applications in various business sectors by evaluating the pre - existing context entropy and context immersivity. the goal is to identify areas where immersive technologies can significantly impact and distinguish those that may be overhyped.
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arxiv:2305.16872
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in a p - wave fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. consequences of this divergent rigidity in the stable vortices in the b phase in globally isotropic aerogel are considered where the " impurity scattering " events are brought by the aerogel structure. for a moderately strong " impurity scatterings ", the superfluid transition line t _ c ( p ) has a quantum critical point at a low but finite pressure. we find that, with decreasing t _ c via the lowering of the pressure, the distance between the half cores composing the core of the nonaxisymmetric double - core vortex which is stable at lower pressures grows as a result of the rigidity diverging at lowering temperature. the obtained result is compared with the elongation of the half core pair arising from the fermi - liquid correction.
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arxiv:1905.02569
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we study the magnetic hysteresis in the random field ising model in 3d. we discuss the disorder dependence of the coercive field h _ c, and obtain an analytical description of the smooth part of the hysteresis below and above h _ c, by identifying the disorder configurations ( instantons ) that are the most probable to trigger local avalanches. we estimate the critical disorder strength at which the hysteresis curve becomes continuous. from an instanton analysis at zero field we obtain a description of local two - level systems in the ferromagnetic phase.
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arxiv:cond-mat/0505048
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in this paper we extend results by de la harpe concerning the isometries of strictly convex hilbert geometries, and the characterisation of the isometry groups of hilbert geometries on finite dimensional simplices, to infinite dimensions. the proofs rely on a mix of geometric and functional analytic methods.
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arxiv:1405.4147
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a theory for the complexity of the bethe lattice spin - glass is developed applying to the cavity - method scheme of mezard and parisi the results recently obtained in the context of the sherrington - kirkpatrick model. the crucial ingredient is the introduction of a new cavity field z related to the marginality of the relevant states. the theory admits a variational formulation. in the high - connectivity limit it yields the bray and moore expression for the tap complexity of the sk model. an annealed version of the theory is also studied in order to obtain non - trivial results at low computational cost. an analysis of the theory is performed numerically through population - dynamics algorithms and analytically through power series expansion. the results can be applied to other finite connectivity problems.
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arxiv:cond-mat/0404729
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we report full vector mapping of local magnetization in cealsi, a weyl semimetal in which both inversion and time - reversal symmetries are broken. the vector maps reveal unanticipated features both within domains and at their boundaries. boundaries between domains form two kinds of walls with distinct topology and therefore different interactions with weyl fermions. domain walls aligned along the tetragonal axes, e. g. ( 100 ), exhibit emergent chirality forbidden by the bulk space group, while diagonal walls are non - chiral. within the domains, we observe that the previously reported set of four easy axes aligned along the in - plane diagonals of the tetragonal structure actually split to form an octet with decreasing temperature below the magnetic transition. all the above phenomena are ultimately traced to the noncollinear magnetic structure of cealsi.
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arxiv:2104.07706
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a set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. the transformation maps " waves " on a riemannian symmetric space to " waves " on its dual riemannian symmetric space. this transformation preserves the energy momentum tensor though it is not a canonical transformation. the preservation of the energy momentum tensor has a natural geometrical interpretation. the transformation maps " particle - like solutions " into static " soliton - like solutions ". the results presented here generalize earlier results of e. ivanov.
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arxiv:hep-th/0004120
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most machine learning models for audio tasks are dealing with a handcrafted feature, the spectrogram. however, it is still unknown whether the spectrogram could be replaced with deep learning based features. in this paper, we answer this question by comparing the different learnable neural networks extracting features with a successful spectrogram model and proposed a general audio feature extractor ( gafx ) based on a dual u - net ( gafx - u ), resnet ( gafx - r ), and attention ( gafx - a ) modules. we design experiments to evaluate this model on the music genre classification task on the gtzan dataset and perform a detailed ablation study of different configurations of our framework and our model gafx - u, following the audio spectrogram transformer ( ast ) classifier achieves competitive performance.
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arxiv:2207.09145
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online social media play a major role in shaping public discourse and opinion, especially during political events. we present the first public multi - platform dataset of italian - language political conversations, focused on the 2022 italian general election taking place on september 25th. leveraging public apis and a keyword - based search, we collected millions of posts published by users, pages and groups on facebook, instagram and twitter, along with metadata of tiktok and youtube videos shared on these platforms, over a period of four months. we augmented the dataset with a collection of political ads sponsored on meta platforms, and a list of social media handles associated with political representatives. our data resource will allow researchers and academics to further our understanding of the role of social media in the democratic process.
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arxiv:2301.05119
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in the article we generalize the marcinkiewicz sampling theorem in the context of orlicz spaces. we establish conditions under which sampling theorem holds in terms of restricted submultiplicativity and supermultiplicativity of an $ n $ - function $ \ varphi $, boundedness of the hilbert transform and matuszewska - orlicz indices. in addition we give a new criterion for boundedness of hilbert transform on orlicz space.
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arxiv:2109.02368
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we demonstrate that gamma - ray burst afterglow spectra and light curves can be calculated for arbitrary explosion and radiation parameters by scaling the peak flux and the critical frequencies connecting different spectral regimes. only one baseline calculation needs to be done for each jet opening angle and observer angle. these calculations are done numerically using high - resolution relativistic hydrodynamical afterglow blast wave simulations which include the two - dimensional dynamical features of expanding and decelerating afterglow blast waves. any light curve can then be generated by applying scaling relations to the baseline calculations. as a result, it is now possible to fully fit for the shape of the jet break, e. g. at early time x - ray and optical frequencies. in addition, late - time radio calorimetry can be improved since the general shape of the transition into the sedov - taylor regime is now known for arbitrary explosion parameters so the exact moment when the sedov - taylor asymptote is reached in the light curve is no longer relevant. when calculating the baselines, we find that the synchrotron critical frequency and the cooling break frequency are strongly affected by the jet break. the synchrotron break temporal slope quickly drops to the steep late time sedov - taylor slope, while the cooling break first steepens then rises to meet the level of its shallow late time asymptote.
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arxiv:1111.3355
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a reduction of total mean turbulent pressure due to the presence of magnetic fields was previously shown to be a measurable effect in direct numerical simulations. however, in the studied parameter regime the formation of large - scale structures, as anticipated from earlier mean - field simulations, was not found. an analysis of the relevant mean - field parameter dependency and the parameter domain of interest is conducted in order to clarify this apparent discrepancy.
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arxiv:1012.4360
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based on the understandings regarding linear upwind schemes with flux splitting to achieve free - stream preservation ( q. li, etc. commun. comput. phys., 22 ( 2017 ) 64 - 94 ), a series of weno interpolation - based and upwind - biased nonlinear schemes are proposed in this study. by means of engagement of fluxes on midpoints, the nonlinearity of schemes is introduced through weno interpolations, and upwind - biased features are acquired through the choice of dependent grid stencil. regarding the third - and fifth - order versions, schemes with one and two midpoints are devised and carefully tested. with the integration of the piecewise - polynomial mapping function methods ( q. li, etc. commun. comput. phys. 18 ( 2015 ) 1417 - 1444 ), the proposed schemes are found to achieve the designed orders and free - stream preservation property. in 1 - d sod and shu - osher problems, all schemes succeed in yielding well predictions. in 2 - d cases, the vortex preservation, supersonic inviscid flow around cylinder at m = 4, riemann problem and shock - vortex interaction problems are tested. in each problem, two types of grids are employed, i. e. the uniformed / smooth grids and the randomized / partially - randomized grids. on the latter, the shock wave and complex flow structures are located / partially located. all schemes fulfill computations in uniformed / smooth grids with satisfactory results. on randomized grids, all schemes accomplish computations and yield reasonable results except the third - order one with two midpoints engaged fails in riemann problem and shock - vortex interaction problem. overall speaking, the proposed schemes manifest the capability to solve problems on grids with bad quality, and therefore indicate their potential in engineering applications.
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arxiv:1810.11103
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for super - heated water on a substrate with hydrophobic patches immersed in a hydrophilic matrix, one can choose the temperature so that micro - bubbles will form, grow and merge on the hydrophobic patches and not on the hydrophilic matrix. until covering a patch, making a pinned macro - bubble, a bubble has a contact angle $ \ pi - \ theta _ 2 $, where $ \ theta _ 2 $ is the receding contact angle of water on the patch material. this pinned macro - bubble serves as the initial condition of a quasi - static growth process, \ ` a la landau, leading to detachment through the formation of a neck, so long as depinning and dewetting of the hydrophilic matrix was avoided during the growth of the pinned bubble : the bubble contact angle should not exceed $ \ pi - \ theta _ 1 $, where $ \ theta _ 1 $ is the receding contact angle of water on the matrix material. the boiling process may then enter a cycle of macro - bubbles forming and detaching on the patches ; the radii of these patches can be optimized for maximizing the heat transfer for a given substrate area. for this analysis to become quantitative, we revisit the young - laplace quasi - static evolution of key physical quantities, such as bubble energy, as functions of bubble growing volume, when gravity is either significative or negligible : this concerns both pinned bubbles on a fixed circular footprint ( dirichlet boundary conditions ) and free un - pinned bubbles with a fixed contact angle ( neumann boundary conditions ).
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arxiv:2301.05582
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for the empty set and for a singleton are examples of roster notation. when specifying sets, it only matters whether each distinct element is in the set or not ; this means a set does not change if elements are repeated or arranged in a different order. for example, { 1, 2, 3, 4 } = { 4, 2, 1, 3 } = { 4, 2, 4, 3, 1, 3 }. { \ displaystyle \ { 1, 2, 3, 4 \ } = \ { 4, 2, 1, 3 \ } = \ { 4, 2, 4, 3, 1, 3 \ }. } when there is a clear pattern for generating all set elements, one can use ellipses for abbreviating the notation, such as in { 1, 2, 3, …, 1000 } { \ displaystyle \ { 1, 2, 3, \ ldots, 1000 \ } } for the positive integers not greater than 1000 { \ displaystyle 1000 }. ellipses allow also expanding roster notation to some infinite sets. for example, the set of all integers can be denoted as { …, − 3, − 2, − 1, 0, 1, 2, 3, … } { \ displaystyle \ { \ ldots, - 3, - 2, - 1, 0, 1, 2, 3, \ ldots \ } } or { 0, 1, − 1, 2, − 2, 3, − 3, … }. { \ displaystyle \ { 0, 1, - 1, 2, - 2, 3, - 3, \ ldots \ }. } = = = set - builder notation = = = set - builder notation specifies a set as being the set of all elements that satisfy some logical formula. more precisely, if p ( x ) { \ displaystyle p ( x ) } is a logical formula depending on a variable x { \ displaystyle x }, which evaluates to true or false depending on the value of x { \ displaystyle x }, then { x p ( x ) } { \ displaystyle \ { x \ mid p ( x ) \ } } or { x : p ( x ) } { \ displaystyle \ { x : p ( x ) \ } } denotes the set of all x { \ displaystyle x } for which p ( x ) { \ displaystyle p ( x ) } is true. for example, a set f can be specified as
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https://en.wikipedia.org/wiki/Set_(mathematics)
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the quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital - free density functional theory. while a recipe for closed - shell systems has been proposed earlier, we have shown that it cannot be na \ " ively extended to open - shell atoms. in this present work, we investigated the efficacy of an ad - hoc recipe to compute the kinetic energy densities for open - shell atoms by extending the methodology used for closed - shell systems. we have also analyzed the spin - dependent features of pauli potentials derived from two previously devised enhancement factors. further, we have proposed an alternate but exact methodology to systematically compute the kinetic energy density for atoms of arbitrary spin multiplicity.
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arxiv:2208.06256
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the generating functions of the severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. recently new proofs of this fact were given for toric surfaces by block, colley, kennedy and liu, osserman, using tropical geometry and in particular the combinatorial tool of long - edged graphs. in the first part of this paper these results are for p ^ 2 and rational ruled surfaces generalized to refined severi degrees. in the second part of the paper we give a number of mostly conjectural generalizations of this result to singular surfaces, and curves with prescribed multiple points.
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arxiv:1511.02726
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inorganic electrides are a new class of compounds catering to the interest of scientists due to the multiple usages exhibited by interstitial electrons in the lattice. however, the influence of the shape and distribution of interstitial electrons on physical properties and new forms of physical states are still unknown. in this work, crystal structure search algorithms are employed to explore the possibility of forming new electrides in the as - li system, where interstitial electrons behave as 1d electron chains ( 1d electride ) in pmmm phase of asli $ _ 7 $ and transform into 0d electron clusters ( 0d electride ) in p6 / mmm phase at 80 gpa. the p6 / mmm phase has relatively high superconductivity at 150 gpa ( tc = 38. 4k ) than classical electrides, even at moderate pressure with tc = 16. 6k. the novel superconducting properties are conjectured to be possibly due to three van hove singularities at the fermi level. in addition, a dirac cone in the band has been observed, expanding the sources of dirac materials. the survival of asli $ _ 7 $ at room temperature is confirmed by molecular dynamics simulation at 300 k. at 1000 k, the as atoms in the system act like solid, while a portion of the li atoms cycle around the as atoms, and another portion of the li atoms flow freely like liquid, showing the novel physical phenomenon of the coexistence of the plastic and superionic states. this suggests that the superionic and plastic states cannot only be found in hydrides but also in the electride. our results indicate that superconducting electride asli $ _ 7 $ with superionic and plastic states can exist in earth ' s interior.
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arxiv:2205.15004
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the theory of thermoelectric effects in superconductors is discussed in connection to the recent publication by marinescu and overhauser, phys. rev. b 55, 11637 ( 1997 ). we argue that the charge on - conservation arguments by marinescu and overhauser do not require any revision of the boltzmann transport equation in superconductors, and show that their ` ` electron - conserving transport theory ' ' contradicts thermodynamics. possible mechanisms responsible for the discrepancy between some experimental data and the theory by galperin, gurevich, and kozub, jetp lett. 17, 476 ( 1973 ) are discussed.
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arxiv:cond-mat/0012347
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the new generation of cmb polarization experiments will reach limits of sensitivity never achieved before to detect the primordial b - mode signal. however, all these efforts will be futile if we lack a tight control of systematics. here, we focus on the systematic that arises from the uncertainty on the calibration of polarization angles. miscalibrated polarization angles induce a mixing of e - and b - modes that obscures the primordial b - mode signal. we introduce an iterative angular power spectra maximum likelihood - based method to calculate polarization angles from the multi - frequency signal. the basis behind this methodology grounds on nulling the eb power spectra. to simplify the likelihood, we assume that the rotation angles are small ( < 6 deg ) and, the maximum likelihood solution for the rotation angles is obtained by applying an iterative process where the covariance matrix does not depend on the angles per iteration, i. e., the rotation angles are fixed to the estimated angles in the previous iteration. with these assumptions, we obtain an analytical linear system which leads to a very fast computational implementation. we show that with this methodology we are able to determine the rotation angle for each frequency with sufficiently good accuracy. to prove the latter point we perform component separation analyses using the parametric component separation method b - secret with two different approaches. in the first approach we apply the b - secret pipeline to the signal de - rotated with the estimation of the angles, while in the second, the rotation angles are treated as model parameters using the estimation of the angles as a prior information. we obtain that the rotation angles estimations improve after applying the second approach, and show that the systematic residuals due to the non - null calibration polarization angles are mitigated to the order of a 1 % at the power spectrum level.
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arxiv:2110.14328
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the theory of affine processes has been recently extended to the framework of stochastic volterra equations with continuous trajectories. these so - called affine volterra processes overcome modeling shortcomings of affine processes because they can have trajectories whose regularity is different from the regularity of the paths of brownian motion. more specifically, singular kernels yield rough affine processes. this paper extends the theory by considering affine stochastic volterra equations with jumps. this extension is not straightforward because the jump structure together with possible singularities of the kernel may induce explosions of the trajectories.
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arxiv:2203.06400
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the statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. however, inferring the physical properties from the observed trajectories is challenging. inspired by a recent experiment, here we analyze the problem of particles undergoing two - dimensional brownian motion with transient tethering to the surface. we model the problem as a hidden markov model where the physical position is observed, and the tethering state is hidden. we develop an alternating maximization algorithm to infer the hidden state of the particle and estimate the physical parameters of the system. the crux of our method is a saddle - point - like approximation, which involves finding the most likely sequence of hidden states and estimating the physical parameters from it. extensive numerical tests demonstrate that our algorithm reliably finds the model parameters, and is insensitive to the initial guess. we discuss the different regimes of physical parameters and the algorithm ' s performance in these regimes. we also provide a ready - to - use open source implementation of our algorithm.
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arxiv:2308.01100
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we present simulation results of $ \ gamma $ + jet analysis using cms ( compact muon solenoid ) object - oriented software at the large hadron collider ( lhc ) center of mass energy $ \ sqrt { s } $ = 14 tev. the study of direct photon production helps in validating the perturbative quantum chromodynamics ( pqcd ) and providing information on the gluon distribution in the nucleons. direct photon processes also constitute a major background to several other standard model ( sm ) processes and signals of new physics. thus these processes need to be understood precisely in the new energy regime. in this work, we have done a detailed study of the geant4 simulated $ \ gamma $ + jet events generated with pythia, and the related background processes. isolation cuts have been optimized for direct photon which improves the signal over background ratio by $ \ sim25 % $ as compared to previous studies done in cms. the inclusion of a large $ \ delta \ phi $ cut between the photon and the leading jet at $ 40 ^ 0 $ in the analysis leads to a further increase of $ \ sim15 % $ in s / b, thus giving an overall gain of $ \ sim42 % $ in s / b ratio.
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arxiv:0705.2740
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in engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. for such cases, mcmc has proven to be an invaluable tool. random - walk metropolis methods ( also known as metropolis - hastings ( mh ) ), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. however, most mh algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes ( particularly disconnected ones ). in this paper, we present intrepid mcmc - a novel mh scheme that utilizes a simple coordinate transformation to significantly improve the mode - finding ability and convergence rate to the target distribution of random - walk markov chains while retaining most of the simplicity of the vanilla mh paradigm. through multiple examples, we showcase the improvement in the performance of intrepid mcmc over vanilla mh for a wide variety of target distribution shapes. we also provide an analysis of the mixing behavior of the intrepid markov chain, as well as the efficiency of our algorithm for increasing dimensions. a thorough discussion is presented on the practical implementation of the intrepid mcmc algorithm. finally, its utility is highlighted through a bayesian parameter inference problem for a two - degree - of - freedom oscillator under free vibration.
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arxiv:2411.17639
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we review the class of cellular automata known as lattice gases, and their applications to problems in physics and materials science. the presentation is self - contained, and assumes very little prior knowledge of the subject. hydrodynamic lattice gases are emphasized, and non - lattice - gas cellular automata - - even those with physical applications - - are not treated at all. we begin with a review of lattice gases as the term is understood in equilibrium statistical physics. we then discuss the various methods that have been proposed to simulate hydrodynamics with a lattice gas, leading up to the 1986 discovery of a lattice gas for the isotropic navier - stokes equations. finally, we discuss variants of lattice - gas models that have been used for the simulation of complex fluids.
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arxiv:comp-gas/9905001
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assuming the current best - fit solutions to the solar neutrino problem at large mixing angle, we briefly illustrate how prospective data from the sudbury neutrino observatory ( sno ) and from the kamioka liquid scintillator anti - neutrino detector ( kamland ) can increase our confidence in the occurrence of standard matter effects on active neutrino flavor oscillations in the sun, which are starting to emerge from current data.
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arxiv:hep-ph/0211414
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curvature properties of the characteristic connection on an integrable $ g _ 2 $ space are investigated. it is proved that an integrable $ g _ 2 $ manifold has closed torsion if and only if the ricci tensor of the characteristic connection is equal to the covariant derivative of the lee form and in this case the integrable $ g _ 2 $ structure is of constant type. it is shown, that a compact integrable $ g _ 2 $ manifold with closed torsion is ricci flat if and only if either the norm of the torsion is constant or the riemannian scalar curvature is constant. it is observed that any compact integrable $ g _ 2 $ manifold with closed torsion 3 - form is a generalized gradient ricci soliton and this is equivalent to a certain vector field to be parallel with respect to the torsion connection. in particular, this vector field is an infinitesimal authomorphism of the $ g _ 2 $ strucure. compact examples with bi - $ g _ 2 $ structures or generalized integrable $ g _ 2 $ manifolds are given. it is shown that on an integrable $ g _ 2 $ space of constant type the curvature of the characteristic connection $ r \ in s ^ 2 \ lambda ^ 2 $ with vanishing ricci tensor if and only if the three - form torsion is parallel with respect to the levi - civita and to the characteristic connection simultaneously. in particular, the conditions $ r \ in s ^ 2 \ lambda ^ 2, ric = 0 $ are equivalent to the condition that the curvature of the characteristic connection satisfies the riemannian first bianchi identity. in this case the torsion 3 - form is harmonic.
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arxiv:2307.06438
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in this study, a spin - 1 / 2 extended anisotropic xy chain has been introduced in which both time reversal and su ( 2 ) symmetries are broken but $ z _ 2 $ symmetry is preserved. magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. exact analytic results for spin - spin correlation functions have been obtained in terms of jordan wigner fermionization. existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the binder cumulant in the ground state. dispersion relation, ground state energy, and energy gap are obtained analytically. in order to find the topologically nontrivial phase, sign of pfaffian invariant and value of winding number have been evaluated. both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. long range orders along two orthogonal directions and two different topological phases are found and their one - to - one correspondence has been found. finally casting the spinless fermions onto majorana fermions, properties of zero energy edge states are studied. three different kinds of majorana pairings are noted. in the trivial phase, next - nearest - neighbor majorana pairing is found, whereas two different types of nearest - neighbor majorana pairings are identified in the topological superconducting phase.
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arxiv:2310.11243
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we construct the google matrix of the entire twitter network, dated by july 2009, and analyze its spectrum and eigenstate properties including the pagerank and cheirank vectors and 2dranking of all nodes. our studies show much stronger inter - connectivity between top pagerank nodes for the twitter network compared to the networks of wikipedia and british universities studied previously. our analysis allows to locate the top twitter users which control the information flow on the network. we argue that this small fraction of the whole number of users, which can be viewed as the social network elite, plays the dominant role in the process of opinion formation on the network.
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arxiv:1207.3414
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constraining parameters such as the initial mass function high - mass slope and the frequency of type ia supernovae is of critical importance in the ongoing quest to understand galactic physics and create realistic hydrodynamical simulations. in this paper, we demonstrate a method to precisely determine these using individual chemical abundances from a large set of stars, coupled with some estimate of their ages. inference is performed via the simple chemical evolution model chempy in a bayesian framework, marginalizing over each star ' s specific interstellar medium parameters, including an element - specific ` model error ' parameter to account for inadequacies in our model. hamiltonian monte carlo ( hmc ) methods are used to sample the posterior function, made possible by replacing chempy with a trained neural network at negligible error. the approach is tested using data from both chempy and the illustristng simulation, showing sub - percent agreement between inferred and true parameters using data from up to 1600 individual stellar abundances. for illustristng, strongest constraints are obtained from metal ratios, competitive with those from other methods including star counts. analysis using a different set of nucleosynthetic yields shows that incorrectly assumed yield models can give non - negligible bias in the derived parameters ; this is reduced by our model errors, which further show how well the yield tables match data. we also find a significant bias from analyzing only a small set of stars, as is often done in current analyses. the method can be easily applied to observational data, giving tight bounds on key galactic parameters from chemical abundances alone.
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arxiv:1909.00812
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any bounded tile of the field $ \ mathbb { q } _ p $ of $ p $ - adic numbers is a compact open set up to a zero haar measure set. in this note, we give a simple and direct proof of this fact.
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arxiv:1511.06404
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the field of unmanned aerial vehicles ( uavs ) has reached a high level of maturity in the last few years. hence, bringing such platforms from closed labs, to day - to - day interactions with humans is important for commercialization of uavs. one particular human - uav scenario of interest for this paper is the payload handover scheme, where a uav hands over a payload to a human upon their request. in this scope, this paper presents a novel real - time human - uav interaction detection approach, where long short - term memory ( lstm ) based neural network is developed to detect state profiles resulting from human interaction dynamics. a novel data pre - processing technique is presented ; this technique leverages estimated process parameters of training and testing uavs to build dynamics invariant testing data. the proposed detection algorithm is lightweight and thus can be deployed in real - time using off the shelf uav platforms ; in addition, it depends solely on inertial and position measurements present on any classical uav platform. the proposed approach is demonstrated on a payload handover task between multirotor uavs and humans. training and testing data were collected using real - time experiments. the detection approach has achieved an accuracy of 96 \ %, giving no false positives even in the presence of external wind disturbances, and when deployed and tested on two different uavs.
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arxiv:2207.05403
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in this paper we are able to justify the existence or no of photons emitted during $ \ alpha $ decay, based on the average half life times using the bcs superconductivity and superfluidity theories. the proposed model suggests two possible channels. a first channel where the protons and neutrons interact separately through a spin coupling, giving rise to diprotons and dineutrons which in turn interact through an isospin coupling to form an $ \ alpha $ particle, and a second channel where the protons and neutrons are treated as nucleons that interact through an isospin coupling, giving rise to deuterons, which in turn interact through a spin coupling to form an $ \ alpha $ particle. due to the nature of the involved particles, the systems considered are homogeneous. for the second channel, the photon play a very important role for the possible escape of the $ \ alpha $ particle. within these premises the half life times of a considerable number of heavy nuclei with spherical symmetry can be estimated with good experimental agreement.
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arxiv:1110.5822
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for single - sorted algebras, fujiwara defined, through the concept of family of basic mapping - formulas, a notion of morphism which generalizes the ordinary notion of homomorphism between algebras and an equivalence relation, the conjugation, on the families of basic mapping - formulas, which corresponds to the relation of inner isomorphism for algebras. in this paper we extend the theory of fujiwara about morphisms to the many - sorted algebras, by defining the concept of polyderivor between many - sorted signatures, which assigns to basic sorts, words and to formal operations, families of derived terms, and under which the standard signature morphisms, the basic mapping - formulas of fujiwara, and the derivors of goguen - thatcher - wagner are subsumed. then, by means of the homomorphisms between b \ ' enabou algebras, which are the algebraic counterpart of the finitary many - sorted algebraic theories of b \ ' enabou, we define the composition of polyderivors from which we get a corresponding category, isomorphic to the category of kleisli for a monad on the standard category of many - sorted signatures. next, by defining the notion of transformation between polyderivors, we endow the category of many - sorted signatures and polyderivors with a structure of 2 - category. from this we get a derived 2 - category of many - sorted specifications in which we prove the equivalence of the many - sorted specifications of hall and b \ ' enabou, and deduce the equivalence of the categories of hall and b \ ' enabou algebras. besides, by defining corresponding categories of generalized many - sorted terms, we prove that the realization of these terms in the many - sorted algebras is invariant under polyderivors and compatible with the transformations between polyderivors, and from this we get an example, among others, of the new concept of 2 - institution, itself an strict generalization of that of institution by goguen and burstall.
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arxiv:1201.5239
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different experience, but very important on this band ' s existence. " while the single " new skin " originated a few years prior, pasillas claimed in 2002 that for other songs they had two months to write the music. he added, " it was cool for us, because we had a lot of ideas and it was a pretty compressed amount of time. the circumstances weren ' t ideal — we were working in a dingy little rehearsal room — but at that time we didn ' t care. we were playing music for a living. " according to pasillas, they wrote 14 songs for s. c. i. e. n. c. e. in total. unlike with later incubus albums, the songs were recorded to tape, and the band wanted to avoid creating music that they wouldn ' t be able to perform live. during the recording, the band utilized older analogue gear that they described as having " phat sounds and spider webs. " incubus chose jim wirt to produce the album, since he had worked with them on earlier recordings. einziger believed that wirt helped encourage their creativity during the recording of s. c. i. e. n. c. e., saying in 1997, " he helps us come up with strange stuff and he likes it when we do. he doesn ' t try to change what we do, he tries to enhance it. " einziger added in the same interview, " when we signed our record deal and started working on this album, we were worried that someone would come along and tell us to hold back, and try and make our songs a little more palatable. but that never happened. they kinda just said, ' do whatever you want '. with that kind of support, we just let everything kind of run wild. " pasillas similarly noted the lack of outside influence in 2017, saying " we didn ’ t have label people coming in hovering above us making sure we weren ' t wasting money. we were left to our own devices and we worked well that way. " in a 2018 interview with australian magazine heavy, boyd remembered " when we wrote s. c. i. e. n. c. e. we didn ' t know about any songwriting rules. it was like a chopped salad, schizophrenic album put together and we did it because we just didn ’ t know any better. we were just having a good time. " he also believes that incubus still hadn ' t found
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https://en.wikipedia.org/wiki/S.C.I.E.N.C.E.
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if $ x $ is a 2 - segal set, then the edgewise subdivision of $ x $ admits a factorization system coming from upper and lower d \ ' ecalage. using the correspondence between 2 - segal sets and unary operadic categories satisfying the blow - up axiom, the edgewise subdivision of $ x $ is interpreted as an enlargement of the associated operadic category, where fiber inclusions have been adjoined.
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arxiv:2312.00756
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many real world applications can be framed as multi - objective optimization problems, where we wish to simultaneously optimize for multiple criteria. bayesian optimization techniques for the multi - objective setting are pertinent when the evaluation of the functions in question are expensive. traditional methods for multi - objective optimization, both bayesian and otherwise, are aimed at recovering the pareto front of these objectives. however, in certain cases a practitioner might desire to identify pareto optimal points only in a subset of the pareto front due to external considerations. in this work, we propose a strategy based on random scalarizations of the objectives that addresses this problem. our approach is able to flexibly sample from desired regions of the pareto front and, computationally, is considerably cheaper than most approaches for moo. we also study a notion of regret in the multi - objective setting and show that our strategy achieves sublinear regret. we experiment with both synthetic and real - life problems, and demonstrate superior performance of our proposed algorithm in terms of the flexibility and regret.
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arxiv:1805.12168
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we investigate the thermodynamical and causal consistency of cosmological models of the cubic quasi - topological gravity ( qtg ) in four dimensions, as well as their phenomenological consequences. specific restrictions on the maximal values of the matter densities are derived by requiring the apparent horizon ' s entropy to be a non - negative, non - decreasing function of time. the qtg counterpart of the einstein - hilbert ( eh ) gravity model of linear equation of state is studied in detail. an important feature of this particular qtg cosmological model is the new early - time acceleration period of the evolution of the universe, together with the standard late - time acceleration present in the original eh model. the qtg correction to the causal diamond ' s volume is also calculated.
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arxiv:1304.4185
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##silon ^ \ delta, \, p \ geq 1 $ for some $ c, \ delta > 0 $ and all $ \ varepsilon > 0 $, where all $ \ xi ^ \ varepsilon, \, \ varepsilon > 0 $ have the same diffusion coefficients but underlying brownian motions may change with $ \ varepsilon $.
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arxiv:2105.01940
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in this paper, we present a novel computational framework for portfolio - wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. the new method utilises a coupled system of bsdes for the valuation adjustments ( xva ) and solves these by a recursive application of a neural network based bsde solver. this not only makes the computation of xva for high - dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xva, and allows simulations of the collateral account.
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arxiv:2005.02633
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we consider the 3d inverse scattering problem with non - over - determined scattering data. the data are the scattering amplitude $ a ( \ beta, \ alpha _ 0, k ) $ for all $ \ beta \ in s _ \ beta ^ 2 $, where $ s _ \ beta ^ 2 $ is an open subset of the unit sphere $ s ^ 2 $ in $ \ mathbb { r } ^ 3 $, $ \ alpha _ 0 \ in s ^ 2 $ is fixed, and for all $ k \ in ( a, b ), 0 \ leq a < b $. the basic uniqueness theorem for this problem belongs to ramm \ cite { r603 }. in this paper, a numerical method is given for solving this problem and the numerical results are presented.
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arxiv:1702.00028
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our objective is to discover and localize monotonic temporal changes in a sequence of images. to achieve this, we exploit a simple proxy task of ordering a shuffled image sequence, with ` time ' serving as a supervisory signal, since only changes that are monotonic with time can give rise to the correct ordering. we also introduce a transformer - based model for ordering of image sequences of arbitrary length with built - in attribution maps. after training, the model successfully discovers and localizes monotonic changes while ignoring cyclic and stochastic ones. we demonstrate applications of the model in multiple domains covering different scene and object types, discovering both object - level and environmental changes in unseen sequences. we also demonstrate that the attention - based attribution maps function as effective prompts for segmenting the changing regions, and that the learned representations can be used for downstream applications. finally, we show that the model achieves the state - of - the - art on standard benchmarks for image ordering.
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arxiv:2404.16828
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we present a technique for recovering a vector field and a symmetric $ 2 $ - tensor field, both real - valued and compactly supported in some strictly convex bounded domain with smooth boundary in the euclidean plane, from the sum of their attenuated moment ray transforms. in addition, we provide a stability estimate for recovering both the vector field and the symmetric $ 2 $ - tensor field from the aforementioned ray transform.
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arxiv:2505.02028
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we study the dynamics of the gaudin magnet ( " central - spin model " ) using machine - learning methods. this model is of practical importance, e. g., for studying non - markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. the gaudin magnet is also integrable, admitting many conserved quantities : for $ n $ spins, the model hamiltonian can be written as the sum of $ n $ independent commuting operators. despite this high degree of symmetry, a general closed - form analytic solution for the dynamics of this many - body problem remains elusive. machine - learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. motivated in part by this intuition, we use a neural - network representation ( restricted boltzmann machine ) for each variational eigenstate of the model hamiltonian. we then obtain accurate representations of the ground state and of the low - lying excited states of the gaudin - magnet hamiltonian through a variational monte carlo calculation. from the low - lying eigenstates, we find the non - perturbative dynamic transverse spin susceptibility, describing the linear response of a central spin to a time - varying transverse magnetic field in the presence of a spin bath. having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two - level systems. these systems include electron - spin and hole - spin qubits interacting with environmental nuclear spins via hyperfine interactions or qubits with charge or flux degrees of freedom interacting with coherent charge or paramagnetic impurities.
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arxiv:2307.03310
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the quenched kardar - parisi - zhang ( qkpz ) equation with negative non - linear term shows a first order pinning - depinning ( pd ) transition as the driving force $ f $ is varied. we study the substrate - tilt dependence of the dynamic transition properties in 1 + 1 dimensions. at the pd transition, the pinned surfaces form a facet with a characteristic slope $ s _ c $ as long as the substrate - tilt $ m $ is less than $ s _ c $. when $ m < s _ c $, the transition is discontinuous and the critical value of the driving force $ f _ c ( m ) $ is independent of $ m $, while the transition is continuous and $ f _ c ( m ) $ increases with $ m $ when $ m > s _ c $. we explain these features from a pinning mechanism involving a localized pinning center and the self - organized facet formation.
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arxiv:cond-mat/9807194
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we investigate the evolution of angular momentum in sph simulations of galaxy formation, paying particular attention to artificial numerical effects. we find that a cold gas disc forming in an ambient hot gas halo receives a strong hydrodynamic torque from the hot gas. by splitting the hydrodynamic force into artificial viscosity and pressure gradients, we find that the angular momentum transport is caused not by the artificial viscosity but by the pressure gradients. using simple test simulations of shear flows, we conclude that the pressure gradient - based viscosity can be divided into two components : one due to the noisiness of sph and the other to ram pressure. the former is problematic even with very high resolution because increasing resolution does not reduce the noisiness. on the other hand, the ram pressure effect appears only when a cold gas disc or sheet does not contain enough particles. in such a case, holes form in the disc or sheet, and then ram pressure from intra - hole hot gas, causes significant deceleration. in simulations of galactic disc formation, star formation usually decreases the number of cold gas particles, and hole formation leads to the fragmentation of the disc. to circumvent these problem, we modify the sph algorithm, decoupling the cold from the hot gas phases, i. e. inhibiting the hydrodynamic interaction between cold and hot particles. this, a crude modelling of a multi - phase fluid in sph cosmological simulations, leads to the formation of smooth extended cold gas discs and to better numerical convergence. the decoupling is applicable in so far as the self - gravitating gas disc with negligible external pressure is a good approximation for a cold gas disc. ( abridged )
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arxiv:astro-ph/0306568
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we define the anderson hamiltonian h on a two - dimensional manifold using high order paracontrolled calculus. it is a self - adjoint operator with pure point spectrum. we get lower and upper bounds on its eigenvalues which imply an almost sure weyl - type law for h.
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arxiv:2009.03549
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in this paper, a statistically optimal solution to the perspective - n - point ( pnp ) problem is presented. many solutions to the pnp problem are geometrically optimal, but do not consider the uncertainties of the observations. in addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. thus, we propose a novel maximum likelihood solution to the pnp problem, that incorporates image observation uncertainties and remains real - time capable at the same time. further, the presented method is general, as is works with 3d direction vectors instead of 2d image points and is thus able to cope with arbitrary central camera models. this is achieved by projecting ( and thus reducing ) the covariance matrices of the observations to the corresponding vector tangent space.
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arxiv:1607.08112
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how to find " best rational approximations " of maximal commutative subgroups of gl ( n, r )? in this paper we pose and make first steps in the study of this problem. it contains both classical problems of diophantine and simultaneous approximations as a particular subcases but in general is much wider. we prove estimates for n = 2 for both totaly real and complex cases and write the algorithm to construct best approximations of a fixed size. in addition we introduce a relation between best approximations and sails of cones and interpret the result for totally real subgroups in geometric terms of sails.
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arxiv:0910.3482
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we consider the problem of identifying the admittance matrix of a three - phase radial network from voltage and current measurements at a subset of nodes. these measurements are used to estimate a virtual network represented by the kron reduction ( schur complement ) of the full admittance matrix. we focus on recovering exactly the full admittance matrix from its kron reduction, i. e., computing the inverse of schur complement. the key idea is to decompose kron reduction into a sequence of iterations that maintains an invariance structure, and exploit this structure to reverse each step of the iterative kron reduction.
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arxiv:2403.17391
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in the context of teleparallel equivalent to general relativity, we study energy and its relevant quantities for some well - known black hole solutions. for this purpose, we use the hamiltonian approach which gives reasonable and interesting results. we find that our results of energy exactly coincide with several prescriptions in general relativity. this supports the claim that different energy - momentum prescriptions can give identical results for a given spacetime. we also evaluate energy - momentum flux of these solutions.
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arxiv:1005.5203
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context. gamma - ray burst ( grb ) afterglows originate from the interaction between the relativistic ejecta and the surrounding medium. consequently, their properties depend on several aspects : radiation mechanisms, relativistic shock micro - physics, circumburst environment, and the structure and geometry of the relativistic jet. while the standard afterglow model accounts for the overall spectral and temporal evolution for a number of grbs, its validity limits emerge when the data set is particularly rich and constraining, especially in the radio band. aims. we aimed to model the afterglow of the long grb160131a ( redshift $ z = 0. 972 $ ), for which we collected a rich, broadband, and accurate data set, spanning from $ 6 \ times10 ^ { 8 } $ to $ 7 \ times10 ^ { 17 } $ hz in frequency, and from 330 s to 160 days post burst in time. methods. we modelled the spectral and temporal evolution of this grb afterglow through two approaches : the adoption of empirical functions to model optical / x - rays data set, later assessing their compatibility with the radio domain ; the inclusion of the entire multi - frequency data set simultaneously through the python package named saga ( software for afterglow analysis ), to come up with an exhaustive and self - consistent description of the micro - physics, geometry, and dynamics of the afterglow. results. from deep broadband analysis ( from radio to x - ray frequencies ) of the afterglow light curves, grb160131a outflow shows evidence of jetted emission. moreover, we observe dust extinction in the optical spectra, and energy injection in the optical / x - ray data. radio spectra are characterised by several peaks, that could be due to either interstellar scintillation ( iss ) effects or a multi - component structure. conclusions. the inclusion of radio data in the broadband set of grb160131a makes a self - consistent modelling hardly attainable within the standard model of grb afterglows.
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arxiv:2111.00359
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the method for approximation of planar curve by circular arcs with length preservation, proposed by i. kh. sabitov and a. v. slovesnov, is analyzed. we extend the applicability of the method, and consider some corollaries, not related to the approximation problem. inequalities for the length of a convex spiral arc with prescribed two - point $ g ^ 1 $ or $ g ^ 2 $ hermite data are derived. we propose a scheme of computer modelling to explore properties of planar curves. as an example, closeness of ovals is tested, leading to some conjectures about closeness conditions.
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arxiv:1604.07303
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dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured / collected signals or data. this paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. this lower bound depends on the dimensions of the tensor and parameters of the generative model. the focus of this paper is on second - order tensor data, with the underlying dictionaries constructed by taking the kronecker product of two smaller dictionaries and the observed data generated by sparse linear combinations of dictionary atoms observed through white gaussian noise. in this regard, the paper provides a general lower bound on the minimax risk and also adapts the proof techniques for equivalent results using sparse and gaussian coefficient models. the reported results suggest that the sample complexity of dictionary learning for tensor data can be significantly lower than that for unstructured data.
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arxiv:1605.05284
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we present a practical approach to capturing ear - to - ear face models comprising both 3d meshes and intrinsic textures ( i. e. diffuse and specular albedo ). our approach is a hybrid of geometric and photometric methods and requires no geometric calibration. photometric measurements made in a lightstage are used to estimate view dependent high resolution normal maps. we overcome the problem of having a single photometric viewpoint by capturing in multiple poses. we use uncalibrated multiview stereo to estimate a coarse base mesh to which the photometric views are registered. we propose a novel approach to robustly stitching surface normal and intrinsic texture data into a seamless, complete and highly detailed face model. the resulting relightable models provide photorealistic renderings in any view.
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arxiv:1609.02368
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we consider nanoflakes of van der waals ferrielectric cuinp $ _ 2 $ s $ _ 6 $ covered by an ionic surface charge and reveal the appearance of polar states with relatively high polarization ~ 5 microc / cm $ ^ 2 $ and stored free charge ~ 10 microc / cm $ % 2 $, which can mimic " mid - gap " states associated with a surface field - induced transfer of cu and / or in ions in the van der waals gap. the change in the ionic screening degree and mismatch strains induce a broad range of the transitions between paraelectric phase, antiferroelectric, ferrielectric, and ferri - ionic states in cuinp $ _ 2 $ s $ _ 6 $ nanoflakes. the states ' stability and / or metastability is determined by the minimum of the system free energy consisting of electrostatic energy, elastic energy, and a landau - type four - well potential of the ferrielectric dipole polarization. the possibility to govern the transitions by strain and ionic screening can be useful for controlling the tunneling barrier in thin film devices based on cuinp $ _ 2 $ s $ _ 6 $ nanoflakes. also, we predict that the cuinp $ _ 2 $ s $ _ 6 $ nanoflakes reveal features of the controllable negative capacitance effect, which make them attractive for advanced electronic devices, such as nano - capacitors and gate oxide nanomaterials with reduced heat dissipation.
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arxiv:2405.14368
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we give ground - state representation for the fractional laplacian with dirichlet condition on the half - line
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arxiv:2206.05157
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we investigated the bound state problem of the s wave charged $ d _ 1 \ bar { d } ^ * $ ( $ d _ 1 ' \ bar { d } ^ * $ ) system in a chiral quark model by solving the resonating group method equation. our preliminary study does not favor the molecular assumption of $ z ^ + ( 4430 ) $. on the contrary, if $ z ^ + ( 4430 ) $ is really a molecule, its partner with opposite $ g $ - parity should also exist and probably may be found in the $ \ pi ^ + \ eta _ c ( 2s ) $, $ j / \ psi \ pi ^ + \ pi ^ 0 $, or $ \ psi ' \ pi ^ + \ pi ^ 0 $ channel. for the bottom systems, we found the existence of both $ i ^ g $ = $ 1 ^ + $ and $ i ^ g $ = $ 1 ^ - $ $ b _ 1 \ bar { b } ^ * $ ( $ b _ 1 ' \ bar { b } ^ * $ ) molecules is possible.
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arxiv:0908.1734
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graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. when graph side information is not available, the node correspondence is estimated on the sole basis of network topologies. in this paper, we propose a novel criterion to measure the graph matching accuracy, structural inconsistency ( si ), which is defined based on the network topological structure. specifically, si incorporates the heat diffusion wavelet to accommodate the multi - hop structure of the graphs. based on si, we propose a structural inconsistency reducing graph matching algorithm ( sigma ), which improves the alignment scores of node pairs that have low si values in each iteration. under suitable assumptions, sigma can reduce si values of true counterparts. furthermore, we demonstrate that sigma can be derived by using a mirror descent method to solve the gromov - wasserstein distance with a novel k - hop - structure - based matching costs. extensive experiments show that our method outperforms state - of - the - art methods.
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arxiv:2202.02797
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we present the design, manufacturing, and testing of a 37 - element array of corrugated feedhorns for cosmic microwave background ( cmb ) measurements between $ 140 $ and $ 170 $ ghz. the array was designed to be coupled to kinetic inductance detector arrays, either directly ( for total power measurements ) or through an orthomode transducer ( for polarization measurements ). we manufactured the array in platelets by chemically etching aluminum plates of $ 0. 3 $ mm and $ 0. 4 $ mm thickness. the process is fast, low - cost, scalable, and yields high - performance antennas compared to other techniques in the same frequency range. room temperature electromagnetic measurements show excellent repeatability with an average cross polarization level about $ - 20 $ db, return loss about $ - 25 $ db, first sidelobes below $ - 25 $ db and far sidelobes below $ - 35 $ db. our results qualify this process as a valid candidate for state - of - the - art cmb experiments, where large detector arrays with high sensitivity and polarization purity are of paramount importance in the quest for the discovery of cmb polarization $ b $ - modes.
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arxiv:2006.14889
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the eye lens is the most characteristic example of mammalian tissues exhibiting complex colloidal behaviour. in this paper we briefly describe how dynamics in colloidal suspensions can help addressing selected aspects of lens cataract which is ultimately related to the protein self - assembly under pathological conditions. results from dynamic light scattering of eye lens homogenates over a wide protein concentration were analyzed and the various relaxation modes were identified in terms of collective and self - diffusion processes. using this information as an input, the complex relaxation pattern of the intact lens nucleus was rationalized. the model of cold cataract - a phase separation effect of the lens cytoplasm with cooling - was used to simulate lens cataract at in vitro conditions in an effort to determine the parameters of the correlation functions that can be used as reliable indicators of the cataract onset. the applicability of dynamic light scattering as a non - invasive, early - diagnostic tool for ocular diseases is also demonstrated in the light of the findings of the present paper.
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arxiv:0812.3898
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we carried out a search for unknown dwarf novae in a public data release of the zwicky transient facility survey and suspected that the object ztf18abdlzhd is a su uma - type star. performed multicolor ccd observations permit us to follow its fading from an outburst in august and an entire superoutburst in october 2020. the duration of the superoutburst is 13 days. we detected superhumps with period p = 0. 06918 ( 3 ) d that are characteristic of ugsu type stars.
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arxiv:2103.03042
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a host of dark energy models and non - standard cosmologies predict an enhanced hubble rate in the early universe : perfectly viable models, which satisfy big bang nucleosynthesis ( bbn ), cosmic microwave background and general relativity tests, may nevertheless lead to enhancements of the hubble rate up to many orders of magnitude. in this paper we show that strong bounds on the pre - bbn evolution of the universe may be derived, under the assumption that dark matter is a thermal relic, by combining the dark matter relic density bound with constraints coming from the production of cosmic - ray antiprotons by dark matter annihilation in the galaxy. the limits we derive can be sizable and apply to the hubble rate around the temperature of dark matter decoupling. for dark matter masses lighter than 100 gev, the bound on the hubble - rate enhancement ranges from a factor of a few to a factor of 30, depending on the actual cosmological model, while for a mass of 500 gev the bound falls in the range 50 - 500. uncertainties in the derivation of the bounds and situations where the bounds become looser are discussed. we finally discuss how these limits apply to some specific realizations of non - standard cosmologies : a scalar - tensor gravity model, kination models and a randall - sundrum d - brane model.
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arxiv:hep-ph/0605287
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we construct and prove a diagrammatic version of the duflo isomorphism between the invariant subalgebra of the symmetric algebra of a lie algebra and the center of the universal enveloping algebra. this version implies the original for metrized lie algebras ( lie algebras with an invariant non - degenerate bilinear form ). as an application of this isomorphism, we will compute the kontsevich integral of the unknot and the hopf link to all orders. at the core of the proof, we use an elementary property of the hopf link which can be summarized by the equation ` ` 1 + 1 = 2 ' ' in abacus arithmetic : doubling one component of the hopf link is equivalent to taking the connected sum of two hopf links. this property of the hopf link turns out, when suitably interpreted, to be exactly the property required for the duflo map to be multiplicative. to compute the kontsevich integral of the unknot, we use a property of the unknot that can be summarized by ` ` n * 0 = 0 ' ' : the n - fold connected cabling of the unknot is again an unknot.
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arxiv:math/0006083
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let $ x $ be a space of homogeneous type and let $ l $ be a sectorial operator with bounded holomorphic functional calculus on $ l ^ 2 ( x ) $. we assume that the semigroup $ \ { e ^ { - tl } \ } _ { t > 0 } $ satisfies davies - gaffney estimates. associated to $ l $ are certain approximations of the identity. we call an operator $ t $ a non - integral operator if compositions involving $ t $ and these approximations satisfy certain weighted norm estimates. the davies - gaffney and the weighted norm estimates are together a substitute for the usual kernel estimates on $ t $ in calder \ ' on - zygmund theory. in this paper, we show, under the additional assumption that a vertical littlewood - paley - stein square function associated to $ l $ is bounded on $ l ^ 2 ( x ) $, that a non - integral operator $ t $ is bounded on $ l ^ 2 ( x ) $ if and only if $ t ( 1 ) \ in bmo _ l ( x ) $ and $ t ^ { \ ast } ( 1 ) \ in bmo _ { l ^ { \ ast } } ( x ) $. here, $ bmo _ l ( x ) $ and $ bmo _ { l ^ { \ ast } } ( x ) $ denote the recently defined $ bmo ( x ) $ spaces associated to $ l $ that generalize the space $ bmo ( x ) $ of john and nirenberg. generalizing a recent result due to f. bernicot, we show a second version of a t ( 1 ) - theorem under weaker off - diagonal estimates, which gives a positive answer to a question raised by him. as an application, we prove $ l ^ 2 ( x ) $ - boundedness of a paraproduct operator associated to $ l $. we moreover study criterions for a $ t ( b ) $ - theorem to be valid.
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arxiv:1107.4347
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full - duplex ( fd ) communication is optimistically promoted to double the spectral efficiency if sufficient self - interference cancellation ( sic ) is achieved. however, this is not true when deploying fd - communication in a large - scale setup due to the induced mutual interference. therefore, a large - scale study is necessary to draw legitimate conclusions about gains associated with fd - communication. this paper studies the fd operation for underlay device - to - device ( d2d ) communication sharing the uplink resources in cellular networks. we propose a disjoint fine - tuned selection criterion for the d2d and fd modes of operation. then, we develop a tractable analytical paradigm, based on stochastic geometry, to calculate the outage probability and rate for cellular and d2d users. the results reveal that even in the case of perfect sic, due to the increased interference injected to the network by fd - d2d communication, having all proximity ues transmit in fd - d2d is not beneficial for the network. however, if the system parameters are carefully tuned, non - trivial network spectral - efficiency gains ( 64 shown ) can be harvested. we also investigate the effects of imperfect sic and d2d - link distance distribution on the harvested fd gains.
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arxiv:1608.06183
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magnetic and magnetoelectric excitations in the multiferroic tbmno _ 3 have been investigated at terahertz frequencies. using different experimental geometries we can clearly separate the electro - active excitations ( electromagnons ) from the magneto - active modes, i. e. antiferromagnetic resonances ( afmr ). two afmr resonances were found to coincide with electromagnons. this indicates that both excitations belong to the same mode and the electromagnons can be excited by magnetic ac - field as well. in external magnetic fields and at low temperatures distinct fine structure of the electromagnons appears. in spite of the 90 ^ o rotation of the magnetic structure, the electromagnons are observable for electric ac - fields parallel to the a - axis only. contrary to simple expectations, the response along the c - axis remains purely magnetic in nature.
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arxiv:0902.4382
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using the average action defined with a continuum analog of the block spin transformation, we show the presence of gauge symmetry along the wilsonian renormalization group flow. as a reflection of the gauge symmetry, the average action satisfies the quantum master equation ( qme ). we show that the quantum part of the master equation is naturally understood once the measure contribution under the brs transformation is taken into account. furthermore an effective brs transformation acting on macroscopic fields may be defined from the qme. the average action is explicitly evaluated in terms of the saddle point approximation up to one - loop order. it is confirmed that the action satisfies the qme and the flow equation.
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arxiv:hep-th/0006180
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in software development, due to the lack of knowledge or information, time pressure, complex context, and many other factors, various uncertainties emerge during the development process, leading to assumptions scattered in projects. being unaware of certain assumptions can result in critical problems ( e. g., system vulnerability and failures ). the prerequisite of analyzing and understanding assumptions in software development is to identify and extract those assumptions with acceptable effort. in this paper, we proposed a tool ( i. e., assumption miner ) to automatically identify and extract assumptions on github projects. to evaluate the applicability of assumption miner, we first presented an example of using the tool to mine assumptions from one large and popular deep learning framework project : the tensorflow project on github. we then conducted an evaluation of the tool. the results show that assumption miner can effectively identify and extract assumptions from the repositories on github.
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arxiv:2303.06822
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we report the observation of an acute sensitivity of the anisotropic longitudinal resistivity of two - dimensional electron systems in half - filled high landau levels to the magnitude and orientation of an in - plane magnetic field. in the third and higher landau levels, at filling fractions nu = 9 / 2, 11 / 2, etc., the in - plane field can lead to a striking interchange of the " hard " and " easy " transport directions. in the second landau level the normally isotropic resistivity and the weak nu = 5 / 2 quantized hall state are destroyed by a large in - plane field and the transport becomes highly anisotropic.
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arxiv:cond-mat/9903196
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we study the thermal and electric transport of a fluid of interacting dirac fermions as they arise in single - layer graphene. we include coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature t and chemical potential mu. in the critical regime mu < < t where both bands above and below the dirac point contribute to transport we find pronounced deviations from fermi liquid behavior, universal, collision - dominated values for transport coefficients and a cyclotron resonance of collective nature. in the collision - dominated high temperature regime the linear thermoelectric transport coefficients are shown to obey the constraints of relativistic magnetohydrodynamics which we derive microscopically from boltzmann theory. the latter also allows us to describe the crossover to disorder - dominated fermi liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields.
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arxiv:0810.3657
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let $ f : a \ rightarrow b $ be a ring homomorphism and let $ j $ be an ideal of $ b $. in this paper, we study the amalgamation of $ a $ with $ b $ along $ j $ with respect to $ f $, a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced by d ' anna and fontana in 2007, and other classical constructions ( such as the $ a + xb [ x ] $, the $ a + xb [ \! [ x ] \! ] $ and the $ d + m $ constructions ). in particular, we completely describe the prime spectrum of the amalgamation and, when it is a local noetherian ring, we study its embedding dimension and when it turns to be a cohen - macaulay ring or a gorenstein ring.
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arxiv:1312.3804
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we find that the proof in the recent paper $ \ textsuperscript { \ cite { 14 } } $ can not justify the authors ' conclusion. we provide a real proof that any state will eventually evolves to the woltjer - taylor state exponentially. however, this kind of evolution is is mainly due to joule heat, which also makes the magnetic field vanishes exponentially. zero woltjer - taylor states are not physically attractive. instead of examine $ \ delta $, we introduce the quantity $ \ theta _ { \ nabla \ times \ vec { b }, \ vec { b } } $ and $ r $ to examine if the plasma reaches to the strong ( general ) woltjer - taylor state, and then derive the condition for the evolution to the strong / general woltjer - taylor state.
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arxiv:1212.5757
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congestion games offer a primary model in the study of pure nash equilibria in non - cooperative games, and a number of generalized models have been proposed in the literature. one line of generalization includes weighted congestion games, in which the cost of a resource is a function of the total weight of the players choosing that resource. another line includes congestion games with mixed costs, in which the cost imposed on a player is a convex combination of the total cost and the maximum cost of the resources in her strategy. this model is further generalized to that of congestion games with complementarities. for the above models, the existence of a pure nash equilibrium is proved under some assumptions, including that the strategy space of each player is the base family of a matroid and that the cost functions have a certain kind of monotonicity. in this paper, we deal with common generalizations of these two lines, namely weighted matroid congestion games with complementarities, and its further generalization. our main technical contribution is a proof of the existence of pure nash equilibria in these generalized models under a simplified assumption on the monotonicity, which provide a common extension of the previous results. we also present some extensions on the existence of pure nash equilibria in player - specific and weighted matroid congestion games with mixed costs.
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arxiv:2401.03861
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in this paper we compare the numbers of new top 2 % researchers from china and usa annually since 1980. we find that the log ratio of the numbers decreases almost linearly over time. as early as 2009, the total number of new top 2 % researchers across all subfields from china exceeds that of usa. in particular, such trend is more striking in many subfields, e. g., engineering, chemistry, and enabling & strategic technologies.
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arxiv:2111.09473
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we present plateau de bure interferometer observations of far infra - red emission lines in bri 0952 - 0115, a lensed quasar at z = 4. 4 powered by a super - massive black hole ( m _ bh = 2x10 ^ 9 m _ sun ). in this source, the resolved map of the [ cii ] emission at 158 micron allows us to reveal the presence of a companion galaxy, located at \ sim 10 kpc from the quasar, undetected in optical observations. from the co ( 5 - 4 ) emission line properties we infer a stellar mass m * < 2. 2x10 ^ 10 m _ sun, which is significantly smaller than the one found in local galaxies hosting black holes with similar masses ( m * \ sim 10 ^ 12 m _ sun ). the detection of the [ nii ] emission at 205 micron suggests that the metallicity in bri 0952 - 0115 is consistent with solar, implying that the chemical evolution has progressed very rapidly in this system. we also present pdbi observations of the [ cii ] emission line in sdssj1148 + 5251, one of the most distant quasar known, at z = 6. 4. we detect broad wings in the [ cii ] emission line, indicative of gas which is outflowing from the host galaxy. in particular, the extent of the wings, and the size of the [ cii ] emitting region associated to them, are indicative of a quasar - driven massive outflow with the highest outflow rate ever found ( dm / dt > 3500 m _ sun / yr ).
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arxiv:1211.0695
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the exclusive reaction $ \ gamma p \ to p \ pi ^ + \ pi ^ - $ was studied in the photon energy range 3. 0 - 3. 8 gev and momentum transfer range $ 0. 4 < - t < 1. 0 $ gev $ ^ 2 $. data were collected with the clas detector at the thomas jefferson national accelerator facility. in this kinematic range the integrated luminosity was about 20 pb $ ^ { - 1 } $. the reaction was isolated by detecting the $ \ pi ^ + $ and proton in clas, and reconstructing the $ \ pi ^ - $ via the missing - mass technique. moments of the di - pion decay angular distributions were derived from the experimental data. differential cross sections for the $ s $, $ p $, and $ d $ - waves in the $ m _ { \ pi ^ + \ pi ^ - } $ mass range $ 0. 4 - 1. 4 $ gev were derived performing a partial wave expansion of the extracted moments. besides the dominant contribution of the $ \ rho ( 770 ) $ meson in the $ p $ - wave, evidence for the $ f _ 0 ( 980 ) $ and the $ f _ 2 ( 1270 ) $ mesons was found in the $ s $ and $ d $ - waves, respectively. the differential production cross sections $ d \ sigma / dt $ for individual waves in the mass range of the above - mentioned mesons were extracted. this is the first time the $ f _ 0 ( 980 ) $ has been measured in a photoproduction experiment.
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arxiv:0907.1021
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higher - order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure - theoretic formalization of probability theory. programs may use both higher - order functions and continuous distributions, or even define a probability distribution on functions. but standard probability theory does not handle higher - order functions well : the category of measurable spaces is not cartesian closed. here we introduce quasi - borel spaces. we show that these spaces : form a new formalization of probability theory replacing measurable spaces ; form a cartesian closed category and so support higher - order functions ; form a well - pointed category and so support good proof principles for equational reasoning ; and support continuous probability distributions. we demonstrate the use of quasi - borel spaces for higher - order functions and probability by : showing that a well - known construction of probability theory involving random functions gains a cleaner expression ; and generalizing de finetti ' s theorem, that is a crucial theorem in probability theory, to quasi - borel spaces.
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arxiv:1701.02547
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to unravel the driving patterns of networks, the most popular models rely on community detection algorithms. however, these approaches are generally unable to reproduce the structural features of the network. therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. in this work, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. our approach jointly models pairs of edges with exact 2 - edge joint distributions. in addition, it provides closed - form analytical expressions for both marginal and conditional distributions. we validate our model on synthetic data in recovering communities, edge prediction tasks, and generating synthetic networks that replicate the reciprocity values observed in real networks. we also highlight these findings on two real datasets that are relevant for social scientists and behavioral ecologists. our method overcomes the limitations of both standard algorithms and recent models that incorporate reciprocity through a pseudo - likelihood approximation. the inference of the model parameters is implemented by the efficient and scalable expectation - maximization algorithm, as it exploits the sparsity of the dataset. we provide an open - source implementation of the code online.
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arxiv:2112.10436
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stellar ages are an important parameter to study the chemical evolution of the galaxy. in recent years, several studies have established the existence of a relationship between chemical clocks and stellar ages. the [ y / mg ] clock is a promising technique, but there are still several open questions, such as its validity for metal - poor stars and differences between the thin and thick disk populations. our aim is to study the behaviour of the [ y / mg ] chemical clock with stellar ages and the effect of metallicity and population on this chemical clock for a sample of solar - type disk stars. we have derived the precise stellar atmospheric parameters as well as the elemental abundances of mg and y through line - by - line differential spectroscopic analysis for a sample of 48 metal - poor solar - type stars based on high - quality, high - resolution eso / harps spectra. from the high - precision gaia astrometric data, stellar masses and ages were estimated through isochrone - fitting. a joint analysis of our sample, together with a sample of 185 solar - twins and analogues from our previous works, is performed to calibrate the [ y / mg ] chemical clock in the galactic disk for $ - $ 0. 71 $ \ leq $ [ fe / h ] $ < $ + 0. 34. open clusters and stars with asteroseismic ages have been used to validate our relations. two different populations could be clearly seen in the [ mg / fe ] - [ fe / h ] plane - the thick and thin disks. we found a metallicity - dependent, strong anti - correlation between the [ y / mg ] ratio and stellar ages of our sample. for the first time in the literature, we report similar correlations for the thin and thick disk stars. the [ y / mg ] relation ( s ) found here for solar - type stars is compatible with the literature using solar - twins. our relation provides higher accuracy and precision of 0. 45 and 0. 99 gyr, respectively, comparable with the best accuracy achieved for the solar - twins till date.
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arxiv:2407.07283
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the prescribed ricci curvature problem in the context of g - invariant metrics on a homogeneous space m = g / k is studied. we focus on the metrics at which the ricci curvature map is, locally, as injective and surjective as it can be. our main result is that such property is generic in the compact case. our main tool is a formula for the lichnerowicz laplacian we prove in terms of the moment map for the variety of algebras.
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arxiv:2010.03643
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