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systems that exhibit pattern formation are typically driven and dissipative. in the early universe, parametric resonance can drive explosive particle production called preheating. the fields that are populated then decay quantum mechanically if their particles are unstable. thus, during preheating, a driven - dissipative system exists. we have shown previously that pattern formation can occur in two dimensions in a self - coupled inflaton system undergoing parametric resonance. in this paper, we provide evidence of pattern formation for more realistic initial conditions in both two and three dimensions. in the one - field case, we have the novel interpretation that these patterns can be thought of as a network of domain walls. we also show that the patterns are spatio - temporal, leading to a distinctive, but probably low - amplitude peak in the gravitational wave spectrum. in the context of a two - field model, we discuss putting power from resonance into patterns on cosmological scales, in particular to explain the observed excess power at 100 h ^ { - 1 } mpc, but why this seems unlikely in the absence of a period of post - preheating inflation. finally we note our model is similar to that of the decay of dccs and therefore pattern formation may also occur at rhic and lhc.
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arxiv:hep-ph/0004230
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arguably the most influential force in human history is the formation of social coalitions and alliances ( i. e., long - lasting coalitions ) and their impact on individual power. in most great ape species, coalitions occur at individual and group levels and among both kin and non - kin. nonetheless, ape societies remain essentially hierarchical, and coalitions rarely weaken social inequality. in contrast, human hunter - gatherers show a remarkable tendency to egalitarianism, and human coalitions and alliances occur not only among individuals and groups, but also among groups of groups. here, we develop a stochastic model describing the emergence of networks of allies resulting from within - group competition for status or mates between individuals utilizing dyadic information. the model shows that alliances often emerge in a phase transition - like fashion if the group size, awareness, aggressiveness, and persuasiveness of individuals are large and the decay rate of individual affinities is small. with cultural inheritance of social networks, a single leveling alliance including all group members can emerge in several generations. our results suggest that a rapid transition from a hierarchical society of great apes to an egalitarian society of hunter - gatherers ( often referred to as " egalitarian revolution " ) could indeed follow an increase in human cognitive abilities. the establishment of stable group - wide egalitarian alliances creates conditions promoting the origin of cultural norms favoring the group interests over those of individuals.
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arxiv:0809.0332
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the relation between the on - shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order \ alpha _ s ^ 3. implications for the numerical values of the top and bottom quark masses are discussed. we show that the new three - loop correction significantly reduces the theoretical uncertainty in the determination of the quark masses.
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arxiv:hep-ph/9907509
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a fundamental property of molecular clouds is that they are turbulent, but how this turbulence is generated and maintained is unknown. one possibility is that stars forming within the cloud regenerate turbulence via their outflows, winds and radiation ( " feedback " ). disentangling motions created by feedback from the initial cloud turbulence is challenging, however. here we confront the relationship between stellar feedback and turbulence by identifying and separating the local and global impact of stellar winds. we analyze magnetohydrodyanamic simulations in which we track wind material as it interacts with the ambient cloud. by distinguishing between launched material, gas entrained by the wind and pristine gas we show energy is transferred away from the sources via magnetic waves excited by the expanding wind shells. this action at a distance enhances the fraction of stirring motion compared to compressing motion and produces a flatter velocity power spectrum. we conclude stellar feedback accounts for significant energy transfer within molecular clouds, an impact enhanced by magnetic waves, which have previously been neglected by observations. altogether, stellar feedback can partially offset global turbulence dissipation.
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arxiv:1809.03513
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despite substantial progress in abstractive text summarization to generate fluent and informative texts, the factual inconsistency in the generated summaries remains an important yet challenging problem to be solved. in this paper, we construct causal graphs for abstractive text summarization and identify the intrinsic causes of the factual inconsistency, i. e., the language bias and irrelevancy bias, and further propose a debiasing framework, named cofactsum, to alleviate the causal effects of these biases by counterfactual estimation. specifically, the proposed cofactsum provides two counterfactual estimation strategies, i. e., explicit counterfactual masking with an explicit dynamic masking strategy, and implicit counterfactual training with an implicit discriminative cross - attention mechanism. meanwhile, we design a debiasing degree adjustment mechanism to dynamically adapt the debiasing degree at each decoding step. extensive experiments on two widely - used summarization datasets demonstrate the effectiveness of cofactsum in enhancing the factual consistency of generated summaries compared with several baselines.
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arxiv:2305.10736
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the paper discusses issues related to the use of faceted classifications in an online environment. the author argues that knowledge organization systems can be fully utilized in information retrieval only if they are exposed and made available for machine processing. the experience with classification automation to date may be used to speed up and ease the conversion of existing faceted schemes or the creation of management tools for new systems. the author suggests that it is possible to agree on a set of functional requirements for supporting faceted classifications online that are equally relevant for the maintenance of classifications, the creation of classification indexing tools, or the management of classifications in an authority file. it is suggested that a set of requirements for analytico - synthetic classifications may be put forward to improve standards for the use and exchange of knowledge organization systems.
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arxiv:1705.07047
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i study how organizations assign tasks to identify the best candidate to promote among a pool of workers. task allocation and workers ' motivation interact through the organization ' s promotion decisions. the organization designs the workers ' careers to both screen and develop talent. when only non - routine tasks are informative about a worker ' s type and non - routine tasks are scarce, the organization ' s preferred promotion system is an index contest. each worker is assigned a number that depends only on his own type. the principal delegates the non - routine task to the worker whose current index is the highest and promotes the first worker whose type exceeds a threshold. each worker ' s threshold is independent of the other workers ' types. competition is mediated by the allocation of tasks : who gets the opportunity to prove themselves is a determinant factor in promotions. finally, features of the optimal promotion contest rationalize the prevalence of fast - track promotion, the role of seniority, or when a group of workers is systemically advantaged.
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arxiv:2308.05668
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the value of $ 59 \ pm 12 $ mev for the pion - nucleon ( $ \ pi n $ ) $ \ sigma $ term, which stahov, clement, and wagner recently extracted from the differential cross sections ( dcss ) of the chaos collaboration, does not match well the expectation of an enhanced ( more positive ) isoscalar component in the $ \ pi n $ interaction at low energies, which the rest of the modern ( meson - factory ) data favour. however, we have already demonstrated that the angular distribution of the chaos $ \ pi ^ + p $ dcss is not compatible in shape with the rest of the modern low - energy $ \ pi ^ + p $ data. this problem must be addressed and resolved by the chaos collaboration prior to the extrapolation of their partial - wave amplitudes into the unphysical region.
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arxiv:1309.3469
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we use density functional theory within the local density approximation ( lda ), lda + u, generalized gradient approximation ( gga ), gga + u, and hybrid - functional methods to calculate the properties of iron monoarsenide. feas, which forms in the mnp structure, is of current interest for potential spintronic applications as well as being the parent compound for the newly - identified pnictide superconductors. we compare the calculated structural, magnetic and electronic properties obtained using the different functionals to each other and to experiment, and investigate the origin of a recently - reported magnetic spiral. our results indicate the appropriateness or otherwise of the various functionals for describing feas and the related fe - pnictide superconductors.
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arxiv:1401.2277
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grb 170817a is a weak short gamma - ray burst ( grb ) accompanied by the gravitational wave ( gw ) event gw170817. it is believed, that an off beaming relativistic jet, produces this weak grb. here we use the $ e _ { \ rm p, i } - e _ { \ rm iso } $ and $ \ gamma - e _ { \ rm iso } $ relations to determine the lorentz factor $ \ gamma $ and the viewing angle from the edge of the jet $ \ theta ' _ { \ rm obs } $ of grb 170817a. our result shows, $ \ gamma = 13. 4 ^ { + 9. 8 } _ { - 5. 5 } $ and $ \ theta ' _ { \ rm obs } = 4. 3 ^ { + 1. 8 } _ { - 1. 5 } \, ^ { \ circ } $. this corresponds to the on - axis $ e _ { \ rm p, i } = 415 ^ { + 361 } _ { - 167 } $ kev and $ e _ { \ rm iso } = ( 2. 4 ^ { + 1. 6 } _ { - 1. 9 } ) \ times 10 ^ { 47 } $ ergs of the grb, which is an intrinsically weak short grb. interestingly, the doppler factor and the luminosity follow a universal relation from grbs and blazars, which indicates they may share similar radiation mechanism.
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arxiv:1710.07436
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rather than using text for scientific research reports, we have proposed developing highly - structured reports with rich semantic models. in this paper, we consider detailed structures for the components of research reports using a modeling framework based on a rigorous upper ontology. for instance, we consider the use of structured descriptions of research designs to support evaluation of internal and external validity. in addition, collections of highly - structured scientific research reports would be the key component of a set of evolving and interlocking highly - structured scientific knowledgebases.
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arxiv:1708.08423
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we discuss a method for determination of the size of the emitting region close to the compact star in a binary system with eclipses by a secondary, which fills its roche lobe. the often used approach is to model the roche lobe by a sphere with the " effective radius " corresponding to the volume of the roche lobe. this approach leads to a 4 - 6 % overestimate of the radius, if taking into account the angular dimensions of the roche lobe seen form the compact star. andronov ( 1992 ) had shown that the projection of the roche lobe onto the celestial sphere is close to an ellipse and had tabulated these dimensions as a function of the mass ratio. also he published the coefficients of the approximation similar to that of the eggleton ( 1983 ) for the " sphere corresponding to the same volume ". we compare results obtained for the " circle + circle ", " ellipse + circle " and " ellipse + point " approximations of the projections of the red dwarf and a white dwarf, respectively. results are applied to the recently discovered eclipsing polar css 081231 : 071126 + 440405.
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arxiv:1512.08322
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we prove 2 - out - of - 3 property for rationality of motivic zeta function in distinguished triangles in voevodsky ' s category dm. as an application, we show rationality of motivic zeta functions for all varieties whose motives are in the thick triangulated monoidal subcategory generated by motives of quasi - projective curves in dm. joint with a result of p. o ' sullivan it also gives an example of a variety whose motive is not finite - dimensional while the motivic zeta function is rational.
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arxiv:math/0605040
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design strategies to assemble dissipative building blocks are essential to create novel and smart materials and machines. we recently demonstrated the hierarchical self - assembly of phoretic microswimmers into self - spinning microgears and their synchronization by diffusiophoretic interactions [ aubret \ textit { et al., nature physics }, 2018 ]. in this paper, we adopt a pedagogical approach and expose our strategy to control self - assembly and build machines using phoretic phenomena. we notably introduce highly inclined laminated optical sheets microscopy ( hilo ) to image and quantify anisotropic and dynamic diffusiophoretic interactions, which could not be observed by standard fluorescence microscopy. the dynamics of a ( haematite ) photocalytic material immersed in ( hydrogen peroxide ) fuel under various illumination patterns is first described and quantitatively rationalized by a model of diffusiophoresis, the migration of a colloidal particle in a concentration gradient. it is further exploited to design phototactic microswimmers, that direct towards the high intensity of light, as a result of the the torque exerted by the haematite in a light gradient on a microswimmer. we finally demonstrate the assembly of self - spinning microgears from colloidal microswimmers by controlling dissipative diffusiophoretic interactions, that we characterize using hilo and quantitatively compare to analytical and numerical predictions. because the approach described hereby is generic, this works paves the way for the rational design of machines by controlling phoretic phenomena.
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arxiv:1909.11121
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while fifth generation ( 5g ) networks are ready for deployment, discussions over sixth generation ( 6g ) networks are down the road. since high frequencies like terahertz ( thz ) will be central to 6g, in this paper, we propose two user association ( ue ) algorithms considering a coexisting rf and thz network that balances the traffic load across the network by minimizing the standard deviation of the network traffic load. our algorithms capture the heterogeneity observed at rf and thz frequencies such as transmission bandwidth, molecular absorption, transmit powers, etc. unlike typical unsupervised clustering algorithms ( e. g. k - means, k - medoid, etc. ) that search for appropriate cluster centers ' locations, our algorithms identify the appropriate ues to be associated to a certain bs such that the overall network load standard deviation ( std ) can be minimized subject to users ' rate constraints. in particular, our algorithms cluster ues to every base station ( bs ) such that the traffic load across the network can be balanced, i. e., by minimizing the std of network traffic load. numerical results show that the proposed algorithms outperform the classical user association algorithms in terms of data rate, traffic load balancing, and user ' s fairness.
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arxiv:2008.06160
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tool learning has generated widespread interest as a vital means of interaction between large language models ( llms ) and the physical world. current research predominantly emphasizes llms ' capacity to utilize tools in well - structured environments while overlooking their stability when confronted with the inevitable noise of the real world. to bridge this gap, we introduce rotbench, a multi - level benchmark for evaluating the robustness of llms in tool learning. specifically, we establish five external environments, each featuring varying levels of noise ( i. e., clean, slight, medium, heavy, and union ), providing an in - depth analysis of the model ' s resilience across three critical phases : tool selection, parameter identification, and content filling. experiments involving six widely - used models underscore the urgent necessity for enhancing the robustness of llms in tool learning. for instance, the performance of gpt - 4 even drops significantly from 80. 00 to 58. 10 when there is no substantial change in manual accuracy. more surprisingly, the noise correction capability inherent in the gpt family paradoxically impedes its adaptability in the face of mild noise. in light of these findings, we propose rottuning, a strategy that enriches the diversity of training environments to bolster the robustness of llms in tool learning. the code and data are available at https : / / github. com / junjie - ye / rotbench.
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arxiv:2401.08326
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science. " the standards call for more than ' science as process, ' in which students learn such skills as observing, inferring, and experimenting. inquiry is central to science learning. when engaging in inquiry, students describe objects and events, ask questions, construct explanations, test those explanations against current scientific knowledge, and communicate their ideas to others. they identify their assumptions, use critical and logical thinking, and consider alternative explanations. in this way, students actively develop their understanding of science by combining scientific knowledge with reasoning and thinking skills. " concern about science education and science standards has often been driven by worries that american students, and even teachers, lag behind their peers in international rankings. one notable example was the wave of education reforms implemented after the soviet union launched its sputnik satellite in 1957. the first and most prominent of these reforms was led by the physical science study committee at mit. in recent years, business leaders such as microsoft chairman bill gates have called for more emphasis on science education, saying the united states risks losing its economic edge. to this end, tapping america ' s potential is an organization aimed at getting more students to graduate with science, technology, engineering and mathematics degrees. public opinion surveys, however, indicate most u. s. parents are complacent about science education and that their level of concern has actually declined in recent years. furthermore, in the recent national curriculum survey conducted by act, researchers uncovered a possible disconnect among science educators. " both middle school / junior high school teachers and post secondary science instructors rate ( d ) process / inquiry skills as more important than advanced science content topics ; high school teachers rate them in exactly the opposite order. " perhaps more communication among educators at the different grade levels in necessary to ensure common goals for students. = = = = 2012 science education framework = = = = according to a report from the national academy of sciences, the fields of science, technology, and education hold a paramount place in the modern world, but there are not enough workers in the united states entering the science, technology, engineering, and math ( stem ) professions. in 2012 the national academy of sciences committee on a conceptual framework for new k - 12 science education standards developed a guiding framework to standardize k - 12 science education with the goal of organizing science education systematically across the k - 12 years. titled a framework for k - 12 science education : practices, crosscutting concepts, and core ideas, the publication promotes standardizing k - 12 science education in the united states. it emphasizes science educators
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https://en.wikipedia.org/wiki/Science_education
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we consider the problem of approximate sampling from the finite volume gibbs measure with a general pair interaction. we exhibit a parallel dynamics ( probabilistic cellular automaton ) which efficiently implements the sampling. in this dynamics the product measure that gives the new configuration in each site contains a term that tends to favour the original value of each spin. this is the main ingredient that allows to prove that the stationary distribution of the pca is close in total variation to the gibbs measure. the presence of the parameter that drives the " inertial " term mentioned above gives the possibility to control the degree of parallelism of the numerical implementation of the dynamics.
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arxiv:1201.5756
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hvz type theorem for semi - relativistic pauli - fierz hamiltonian, $ $ \ hhh = \ sqrt { ( p \ otimes \ one - a ) ^ 2 + m ^ 2 } + v \ otimes \ one + \ one \ otimes \ hf, \ quad m \ geq 0, $ $ in quantum electrodynamics is studied. here $ h $ is a self - adjoint operator in hilbert space $ \ lr \ otimes \ fff \ cong \ int ^ \ oplus _ { \ rr ^ d } \ fff { \ rm d } x $, and $ a = \ int ^ \ oplus _ { \ rr ^ d } a ( x ) { \ rm d } x $ a quantized radiation field and $ \ hf $ the free field hamiltonian defined by the second quantization of a dispersion relation $ \ omega : \ rr ^ d \ to \ rr $. it is emphasized that massless case, $ m = 0 $, is included. let $ e = \ inf \ sigma ( \ hhh ) $ be the bottom of the spectrum of $ \ hhh $. suppose that the infimum of $ \ omega $ is $ m > 0 $. then it is shown that $ \ sigma _ { \ rm ess } ( \ hhh ) = [ e + m, \ infty ) $. in particular the existence of the ground state of $ \ hhh $ can be proven.
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arxiv:1402.1065
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we propose diffusion - informed model predictive control ( d - i mpc ), a generic framework for uncertainty - aware prediction and decision - making in partially observable stochastic systems by integrating diffusion - based time series forecasting models in model predictive control algorithms. in our approach, a diffusion - based time series forecasting model is used to probabilistically estimate the evolution of the system ' s stochastic components. these forecasts are then incorporated into mpc algorithms to estimate future trajectories and optimize action selection under the uncertainty of the future. we evaluate the framework on the task of energy arbitrage, where a battery energy storage system participates in the day - ahead electricity market of the new york state. experimental results indicate that our model - based approach with a diffusion - based forecaster significantly outperforms both implementations with classical forecasting methods and model - free reinforcement learning baselines.
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arxiv:2503.15095
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manual or automatic delineation of the esophageal tumor in ct images is known to be very challenging. this is due to the low contrast between the tumor and adjacent tissues, the anatomical variation of the esophagus, as well as the occasional presence of foreign bodies ( e. g. feeding tubes ). physicians therefore usually exploit additional knowledge such as endoscopic findings, clinical history, additional imaging modalities like pet scans. achieving his additional information is time - consuming, while the results are error - prone and might lead to non - deterministic results. in this paper we aim to investigate if and to what extent a simplified clinical workflow based on ct alone, allows one to automatically segment the esophageal tumor with sufficient quality. for this purpose, we present a fully automatic end - to - end esophageal tumor segmentation method based on convolutional neural networks ( cnns ). the proposed network, called dilated dense attention unet ( ddaunet ), leverages spatial and channel attention gates in each dense block to selectively concentrate on determinant feature maps and regions. dilated convolutional layers are used to manage gpu memory and increase the network receptive field. we collected a dataset of 792 scans from 288 distinct patients including varying anatomies with \ mbox { air pockets }, feeding tubes and proximal tumors. repeatability and reproducibility studies were conducted for three distinct splits of training and validation sets. the proposed network achieved a $ \ mathrm { dsc } $ value of $ 0. 79 \ pm 0. 20 $, a mean surface distance of $ 5. 4 \ pm 20. 2mm $ and $ 95 \ % $ hausdorff distance of $ 14. 7 \ pm 25. 0mm $ for 287 test scans, demonstrating promising results with a simplified clinical workflow based on ct alone. our code is publicly available via \ url { https : / / github. com / yousefis / denseunet _ esophagus _ segmentation }.
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arxiv:2012.03242
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let $ x $ be a compact riemann surface of genus $ g \ geq 2 $. a cyclic subgroup of prime order $ p $ of $ aut ( x ) $ is called properly $ ( p, h ) $ - gonal if it has a fixed point and the quotient surface has genus $ h $. we show that if $ p > 6h + 6 $, then a properly $ ( p, h ) $ - gonal subgroup of $ aut ( x ) $ is unique. we also discuss some related results.
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arxiv:1203.4053
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in the current state of 6d pose estimation, top - performing techniques depend on complex intermediate correspondences, specialized architectures, and non - end - to - end algorithms. in contrast, our research reframes the problem as a straightforward regression task by exploring the capabilities of vision transformers for direct 6d pose estimation through a tailored use of classification tokens. we also introduce a simple method for determining pose confidence, which can be readily integrated into most 6d pose estimation frameworks. this involves modifying the transformer architecture by decreasing the number of query elements based on the network ' s assessment of the scene complexity. our method that we call pose vision transformer or pvit - 6d provides the benefits of simple implementation and being end - to - end learnable while outperforming current state - of - the - art methods by + 0. 3 % add ( - s ) on linemod - occlusion and + 2. 7 % add ( - s ) on the ycb - v dataset. moreover, our method enhances both the model ' s interpretability and the reliability of its performance during inference.
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arxiv:2311.17504
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the radio - far infrared correlation is one of the tightest correlations found in astronomy. many of the models explaining this correlation rely on the association of of global magnetic field strength with gas density. in this letter we put forward that the physical reason for this association lies within the processes of magnetohydrodynamic turbulence.
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arxiv:astro-ph/0305070
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the work of chatzidakis and hrushovski on the model theory of difference fields in characteristic zero showed that groups defined by difference equations have a very restricted structure. recent work of chatzidakis, hrushovski and peterzil [ chp ] extends the class of difference fields for which this sort of result is known to positive characteristic. in this note, we analyze the subgroups of the torsion points of simple commutative algebraic groups over finite fields that can be constructed by such difference equations. our results are reasonably complete modulo some well - known conjectures in number theory. in one case, we need the $ p $ - adic version of the four exponentials conjecture and in another we need a version of artin ' s conjecture on primitive roots. we recover part of a theorem of boxall on the intersection of varieties with the group of $ m $ - power torsion points, but in general this theorem does not follow from the model - theoretic analysis, because there may be no field automorphism $ \ sigma $ so that the $ m $ - power torsion group is contained in a modular group definable with $ \ sigma $. on the other hand, some of the groups defined by modular difference equations are much larger than the group of $ m $ - power torsion points, so our results are stronger in another direction. in some ways, the model theoretic approach extends the approach of bogomolov and the original one of lang.
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arxiv:math/9809188
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current limitations in boosted tree modelling prevent the effective scaling to datasets with a large feature number, particularly when investigating the magnitude and directionality of various features on classification. we present a novel methodology, hollow - tree super ( hots ), to resolve and visualize feature importance in boosted tree models involving a large number of features. further, hots allows for investigation of the directionality and magnitude various features have on classification. using the iris dataset, we first compare hots to gini importance, partial dependence plots, and permutation importance, and demonstrate how hots resolves the weaknesses present in these methods. we then show how hots can be utilized in high dimensional neuroscientific data, by taking 60 schizophrenic subjects and applying the method to determine which brain regions were most important for classification of schizophrenia as determined by the panss. hots effectively replicated and supported the findings of gini importance, partial dependence plots and permutation importance within the iris dataset. when applied to the schizophrenic brain dataset, hots was able to resolve the top 10 most important features for classification, as well as their directionality for classification and magnitude compared to other features. cross - validation supported that these same 10 features were consistently used in the decision - making process across multiple trees, and these features were localised primarily to the occipital and parietal cortices, commonly disturbed brain regions in those with schizophrenia. it is imperative that a methodology is developed that is able to handle the demands of working with large datasets that contain a large number of features. hots represents a unique way to investigate both the directionality and magnitude of feature importance when working at scale with boosted - tree modelling.
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arxiv:2104.03088
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we consider conditions for uniqueness of the solution of the dirichlet or the neumann problem for 2 - dimensional wave equation inside of bi - quadratic algebraic curve. we show that the solution is non - trivial if and only if corresponding poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding pell - abel equation has a solution.
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arxiv:math/0604278
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we give a complete proof of a propagation theorem of multiplicity - free property from fibers to spaces of global sections for holomorphic vector bundles. the propagation theorem is formalised in three ways, aiming for producing various multiplicity - free theorems in representation theory for both finite and infinite dimensional cases in a systematic and synthetic manner. the key geometric condition in our theorem is an orbit - preserving anti - holomorphic diffeomorphism on the base space, which brings us to the concept of visible actions on complex manifolds.
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arxiv:math/0607004
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these are the notes of five lectures given at the summer school { \ em geometric and topological methods for quantum field theory }, held in villa de leyva ( colombia ), july 2 - - 20, 2007. the lectures are meant for graduate or almost graduate students in physics or mathematics. they include references, many examples and some exercices. the content is the following. the first lecture is a short introduction to algebraic and proalgebraic groups, based on some examples of groups of matrices and groups of formal series, and their hopf algebras of coordinate functions. the second lecture presents a very condensed review of classical and quantum field theory, from the lagrangian formalism to the euler - lagrange equation and the dyson - schwinger equation for green ' s functions. it poses the main problem of solving some non - linear differential equations for interacting fields. in the third lecture we explain the perturbative solution of the previous equations, expanded on feynman graphs, in the simplest case of the scalar $ \ phi ^ 3 $ theory. the forth lecture introduces the problem of divergent integrals appearing in quantum field theory, the renormalization procedure for the graphs, and how the renormalization affects the lagrangian and the green ' s functions given as perturbative series. the last lecture presents the connes - kreimer hopf algebra of renormalization for the scalar theory and its associated proalgebraic group of formal series.
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arxiv:0805.4385
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we report on the calculation of the nlo qcd corrections to top quark pair production in association with two hard jets at the lhc. we take into account higher - order effects in both the production and decays of the top - quark pair. the latter are treated in the narrow width approximation and $ t \ bar { t } $ spin correlations are preserved throughout the calculation. this is the first time that such a complete study for this process is conducted at nlo in qcd. we present results for fiducial cross sections at the integrated and differential level. furthermore, we investigate kinematic properties of the additional light jets and their distribution in the $ pp \ to t \ bar { t } jj $ process. we examine jets in production and top - quark decays as well as the mixed contribution, where the two hardest non - $ b $ jets are present simultaneously in the production and decay processes.
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arxiv:2212.04722
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code index modulated multi - carrier m - ary differential chaos shift keying ( cim - mc - m - dcsk ) system not only inherits low - power and low - complexity advantages of the conventional dcsk system, but also significantly increases the transmission rate. this feature is of particular importance to internet of things ( iot ) with trillions of low - cost devices. in particular, for e - health iot applications, an efficient transmission scheme is designed to solve the challenge of the limited battery capacity for numerous user equipments served by one base station. in this paper, a new multiple - input - single - output simultaneous wireless information and power transfer ( miso - swipt ) scheme for cim - mc - m - dcsk system is proposed by utilizing orthogonal characteristic of chaotic signals with different initial values. the proposed system adopts power splitting mode, which is very promising for simultaneously providing energy and transmitting information of the user equipments without any external power supply. in particular, the new system can achieve desirable anti - multipath - fading capability without using channel estimator. moreover, the analytical bit - error - rate expression of the proposed system is derived over multipath rayleigh fading channels. furthermore, the spectral efficiency and energy efficiency of the proposed system are analyzed. simulation results not only validate the analytical expressions, but also demonstrate the superiority of the proposed system.
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arxiv:2003.07107
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we explore the effects of element diffusion due to gravitational settling and thermal and chemical diffusion on the pulsational properties of da white dwarfs. to this end, we employ an updated evolutionary code coupled with a pulsational, finite difference code for computing the linear, non - radial g - modes in the adiabatic approximation. we follow the evolution of a 0. 55 \ msun white dwarf model in a self - consistent way with the evolution of chemical abundance distribution as given by time dependent diffusion processes. results are compared with the standard treatment of diffusive equilibrium in the trace element approximation. appreciable differences are found between the two employed treatments. we conclude that time dependent element diffusion plays an important role in determining the whole oscillation pattern and the temporal derivative of the periods in dav white dwarfs. in addition, we discuss the plausibility of the standard description employed in accounting for diffusion in most of white dwarf asteroseismological studies.
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arxiv:astro-ph/0201225
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a two - component model ( tcm ) for single - particle $ p _ t $ spectra describes 200 gev p - p data accurately. based on that tcm a spectrum hard component was isolated that is related quantitatively to pqcd predictions for jet fragmentation down to low jet energies ( $ \ approx 3 $ gev ). we here address jet - related structure in 2d trigger - associated ( ta ) correlations as a more - detailed method to explore the kinematic limits of low - energy jet production and low - momentum jet fragment structure in p - p collisions. we derive a tcm for p - p ta correlations that can be used to isolate 2d jet - related structure. inferred minimum - bias ( mainly low - energy ) jet - related ta correlations may challenge several major assumptions about jet production in p - p ( and a - a ) collisions. these results should be relevant to p - p underlying - event studies and monte carlo predictions of multiple parton interactions.
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arxiv:1307.1819
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we introduce a hybrid quantum - classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi - layer perceptrons. the research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming high luminosity large hadron collider, presenting the architecture as a potential solution. in particular, we evaluate our method by applying the model to multi - detector jet images from cms open data. the goal is to distinguish quark - initiated from gluon - initiated jets. we successfully train the quantum model and evaluate it via numerical simulations. using this approach, we achieve classification performance almost on par with the one obtained with the completely classical architecture, considering a similar number of parameters.
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arxiv:2405.10284
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we define a commutative monoid structure on the poset of left - exact localizations of a higher topos, that we call the acyclic product. our approach is anchored in a structural analogy between the poset of left - exact localizations of a topos and the poset of ideals of a commutative ring. the acyclic product is analogous to the product of ideals. the sequence of powers of a given left - exact localization defines a tower of localizations. we show how this recovers the towers of goodwillie calculus in the unstable homotopical setting. we use this to describe the topoi of $ n $ - excisive functors as classifying $ n $ - nilpotent objects.
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arxiv:2308.15573
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bott and taubes used integrals over configuration spaces to produce finite - type a. k. a. vassiliev knot invariants. cattaneo, cotta - ramusino and longoni then used these methods together with graph cohomology to construct " vassiliev classes " in the real cohomology of spaces of knots in higher - dimensional euclidean spaces, as first promised by kontsevich. here we construct integer - valued cohomology classes in spaces of knots and links in euclidean spaces of dimension greater than three. we construct such a class for any integer - valued graph cocycle, by the method of gluing compactified configuration spaces. our classes form the integer lattice among the previously discovered real cohomology classes. thus we obtain nontrivial classes from trivalent graph cocycles. our methods generalize to yield mod - p classes out of mod - p graph cocycles, which need not be reductions of classes over the integers.
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arxiv:1512.06654
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recent observations on type - ia supernovae and low density measurement of matter ( including dark matter ) suggest that the present day universe consists mainly of repulsive - gravity type exotic - matter with negative - pressure often referred as dark - energy. but the mystery is about the nature of dark - energy and its puzzling questions such as why, how, where & when about the dark - energy are intriguing. in the present paper the author attempts to answer these questions while making an effort to reveal the genesis of dark - energy, and suggests that the cosmological nuclear - binding - energy liberated during primordial nucleo - synthesis remains trapped for long time and then is released free which manifests itself as dark - energy in the universe. it is also explained why for dark energy the parameter w = - 2 / 3. noting that w = + 1for stiff matter and w = + 1 / 3 for radiation ; w = - 2 / 3 is for dark energy, because - 1 is due to deficiency of stiff - nuclear - matter and that this binding energy is ultimately released as radiation contributing + 1 / 3, making w = - 1 + 1 / 3 = - 2 / 3. this thus almost solves the dark - energy mystery of negative - pressure & repulsive - gravity. it is concluded that dark - energy is a consequence of released - free nuclear - energy of cosmos. the proposed theory makes several estimates / predictions, which agree reasonably well with the astrophysical constraints & observations.
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arxiv:physics/0412044
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the magnetic interactions of the two electrons in helium - like ions are studied in detail within the framework of relativistic schroedinger theory ( rst ). the general results are used to compute the ground - state interaction energy of some highly - ionized atoms ranging from germanium ( z = 32 ) up to bismuth ( z = 83 ). when the magnetic interaction energy is added to its electric counterpart resulting from the electrostatic approximation, the present rst predictions reach a similar degree of precision ( relative to the experimental data ) as the other theoretical approaches known in the literature. however since the rst magnetism is then treated only in lowest - order approximation, further improvements of the rst predictions seem possible.
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arxiv:hep-th/0410023
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with the emergence of connected and autonomous vehicles, sensors are increasingly deployed within cars to support new functionalities. traffic generated by these sensors congest traditional intra - car networks, such as can buses. furthermore, the large amount of wires needed to connect sensors makes it harder to design cars in a modular way. to alleviate these limitations, we propose, simulate, and implement a hybrid wired / wireless architecture, in which each node is connected to either a wired interface or a wireless interface or both. specifically, we propose a new protocol, called hybrid - backpressure collection protocol ( hybrid - bcp ), to efficiently collect data from sensors in intra - car networks. hybrid - bcp is backward - compatible with the can bus technology, and builds on the bcp protocol, designed for wireless sensor networks. hybrid - bcp achieves high throughput and shows resilience to dynamic network conditions, including adversarial interferences. our testbed implementation, based on can and zigbee transceivers, demonstrates the load balancing and routing functionalities of hybrid - bcp and its resilience to dos attacks. we further provide simulation results, obtained with the ns - 3 simulator and based on real intra - car rssi traces, that compare between the performance of hybrid - bcp and a tree - based collection protocol. notably, the simulations show that hybrid - bcp can achieve the same performance as the tree - based protocol while reducing the radio transmission power by a factor of 10.
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arxiv:1509.02153
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new ground - based telescopes and instruments, the return of the nicmos instrument on the hubble space telescope ( hst ), and the recent launch of the spitzer space telescope have provided new tools that are being utilized in the study of planetary nebulae. multiwavelength, high spatial resolution ground - based and hst imaging have been used to probe the inner regions of young pne to determine their structure and evaluate formation mechanisms. spitzer / irac and mips have been used to image more evolved pne to determine the spatial distribution of molecular hydrogen, ionized gas, and dust in the nebulae and halos.
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arxiv:astro-ph/0605160
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proper time functional flow equations have garnered significant attention in recent years, as they are particularly suitable in analyzing non - perturbative contexts. by resorting to this flow, we investigate the regulator and gauge dependence in quantum einstein gravity within the asymptotic safety framework, considering various regularization schemes. our findings indicate that some details of the regulator have minor influence on the critical properties of the theory. in contrast, the selection between linear and exponential parametrizations appears to have a more substantial impact on the scaling behavior of the renormalized flow near the non - gaussian fixed point.
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arxiv:2504.07877
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we study the thermodynamic equilibrium spectra of the charney - hasegawa - mima ( chm ) equation in its weakly nonlinear limit. in this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2d euler or gross - pitaevskii equations, which are examples for comparison. we explore how the third invariant considerably enriches the variety of equilibrium spectra that the chm system can access. in particular we characterise the singular limits of these spectra in which condensates occur, i. e. a single fourier mode ( or pair of modes ) accumulate ( s ) a macroscopic fraction of the total invariants. we show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in chm systems of finite size : highly anisotropic zonal flows, large - scale isotropic vortices, and vortices at small scale. we show how these condensates are associated with combinations of negative thermodynamic potentials ( viz. temperature ).
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arxiv:2108.08349
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the k - shell decomposition plays an important role in unveiling the structural properties of a network, i. e., it is widely adopted to find the densest part of a network across a broad range of scientific fields, including internet, biological networks, social networks, etc. however, there arises concern about the robustness of the k - shell structure when networks suffer from adversarial attacks. here, we introduce and formalize the problem of the k - shell attack and develop an efficient strategy to attack the k - shell structure by rewiring a small number of links. to the best of our knowledge, it is the first time to study the robustness of graph k - shell structure under adversarial attacks. in particular, we propose a simulated annealing ( sa ) based k - shell attack method and testify it on four real - world social networks. the extensive experiments validate that the k - shell structure of a network is robust under random perturbation, but it is quite vulnerable under adversarial attack, e. g., in dolphin and throne networks, more than 40 % nodes change their k - shell values when only 10 % links are changed based on our sa - based k - shell attack. such results suggest that a single structural feature could also be significantly disturbed when only a small fraction of links are changed purposefully in a network. therefore, it could be an interesting topic to improve the robustness of various network properties against adversarial attack in the future.
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arxiv:2107.13962
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we show that the magneto - electric coupling in 3d ( strong ) topological insulators is related to a second derivative of the bulk magnetization. the formula we derive is the non - linear response analog of the streda formula for hall conductivity ( p. streda, j. phys. c : solid state physics, 15, 22 ( 1982 ) ), which relates the hall conductivity to the derivative of the magnetization with respect to chemical potential. our finding allows one to extract the magneto - electric coefficient by measuring the magnetization, while varying the chemical potential and one more perturbing field. such an experimental setup could circumvent many of the current difficulties with measuring the magneto - electric response in 3d topological insulators. the relation we find also makes transparent the effect of disorder on the magneto - electric response, which occurs only through the density of states, and has no effect when the system is gapped.
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arxiv:1201.3042
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we study a systematic way to produce a lipschitz operator ideal from a banach linear operator ideal $ \ mathcal a $. for maximal and minimal operator ideals $ \ mathcal a $, the lipschitz maximal hull and minimal kernel of the lipschitz operator ideals $ \ text { lip } _ 0 \ circ \ mathcal a \ circ \ text { lip } _ 0 $ are investigated, respectively. using ultraproduct techniques, we obtain the lipschitz version of a result of k \ " ursten and piestch which characterizes the maximal hull of any lipschitz operator ideal. among other results, we characterize the linear operators which belong to $ \ text { lip } _ 0 \ circ \ mathcal a \ circ \ text { lip } _ 0 $ which, in many cases, they are precisely those which are in $ \ mathcal a $. in particular, we give some cases in which a nonlinear factorization of linear operators implies a linear one, in terms of a given banach linear operator ideal $ \ mathcal a $.
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arxiv:2211.14240
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the hobby - eberly dark energy experiment ( hetdex ) is an untargeted spectroscopic galaxy survey that uses ly $ \ alpha $ emitting galaxies ( laes ) as tracers of 1. 9 < z < 3. 5 large scale structure. most detections consist of a single emission line, whose identity is inferred via a bayesian analysis of ancillary data. to determine the accuracy of these line identifications, hetdex detections were observed with the dark energy spectroscopic instrument ( desi ). in two desi pointings, high confidence spectroscopic redshifts are obtained for 1157 sources, including 982 laes. the desi spectra are used to evaluate the accuracy of the hetdex object classifications, and tune the methodology to achieve the hetdex science requirement of $ \ lesssim 2 \ % $ contamination of the lae sample by low - redshift emission - line galaxies, while still assigning $ 96 \ % $ of the true ly $ \ alpha $ emission sample with the correct spectroscopic redshift. we compare emission line measurements between the two experiments assuming a simple gaussian line fitting model. fitted values for the central wavelength of the emission line, the measured line flux and line widths are consistent between the surveys within uncertainties. derived spectroscopic redshifts, from the two classification pipelines, when both agree as an lae classification, are consistent to within $ \ langle \ delta z / ( 1 + z ) \ rangle = 6. 9 \ times 10 ^ { - 5 } $ with an rms scatter of $ 3. 3 \ times 10 ^ { - 4 } $.
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arxiv:2503.02229
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quantum correlations do not allow signalling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. this no - signalling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. we find that the natural figure of merit to consider is the confidence in identifying a state, which is optimised by the maximum confidence strategy. we show that this strategy may be derived from the no - signalling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.
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arxiv:0708.3909
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kic 8462852 stood out among more than 100, 000 stars in the kepler catalogue because of the strange features of its light curve : a wide, asymmetric dimming taking up to 15 per cent of the light at d793 and a period of multiple, narrow dimmings happening approximately 700 days later. several models have been proposed to account for this abnormal behaviour, most of which require either unlikely causes or a finely - tuned timing. we aim at offering a relatively natural solution, invoking only phenomena that have been previously observed, although perhaps in larger or more massive versions. we model the system using a large, ringed body whose transit produces the first dimming and a swarm of trojan objects sharing its orbit that causes the second period of multiple dimmings. the resulting orbital period is $ t \ approx12 $ years, with a semi - major axis $ a \ approx6 $ au. our model allows us to make two straightforward predictions : we expect the passage of a new swarm of trojans in front of the star starting during the early months of 2021, and a new transit of the main object during the first half of 2023.
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arxiv:1705.08427
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vision - language models ( vlms ) are impactful in part because they can be applied to a variety of visual understanding tasks in a zero - shot fashion, without any fine - tuning. we study $ \ textit { generative vlms } $ that are trained for next - word generation given an image. we explore their zero - shot performance on the illustrative task of image - text retrieval across 8 popular vision - language benchmarks. our first observation is that they can be repurposed for discriminative tasks ( such as image - text retrieval ) by simply computing the match score of generating a particular text string given an image. we call this probabilistic score the $ \ textit { visual generative pre - training score } $ ( visualgptscore ). while the visualgptscore produces near - perfect accuracy on some retrieval benchmarks, it yields poor accuracy on others. we analyze this behavior through a probabilistic lens, pointing out that some benchmarks inadvertently capture unnatural language distributions by creating adversarial but unlikely text captions. in fact, we demonstrate that even a " blind " language model that ignores any image evidence can sometimes outperform all prior art, reminiscent of similar challenges faced by the visual - question answering ( vqa ) community many years ago. we derive a probabilistic post - processing scheme that controls for the amount of linguistic bias in generative vlms at test time without having to retrain or fine - tune the model. we show that the visualgptscore, when appropriately debiased, is a strong zero - shot baseline for vision - language understanding, oftentimes producing state - of - the - art accuracy.
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arxiv:2306.01879
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a discriminative structured analysis dictionary is proposed for the classification task. a structure of the union of subspaces ( uos ) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. a simple classifier is also simultaneously included into the formulated functional to ensure a more complete consistent classification. the solution of the algorithm is efficiently obtained by the linearized alternating direction method of multipliers. moreover, a distributed structured analysis dictionary learning is also presented to address large scale datasets. it can group - ( class - ) independently train the structured analysis dictionaries by different machines / cores / threads, and therefore avoid a high computational cost. a consensus structured analysis dictionary and a global classifier are jointly learned in the distributed approach to safeguard the discriminative power and the efficiency of classification. experiments demonstrate that our method achieves a comparable or better performance than the state - of - the - art algorithms in a variety of visual classification tasks. in addition, the training and testing computational complexity are also greatly reduced.
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arxiv:1807.04899
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we present n - body simulation calculations of the dependence of the power spectrum of non - linear cosmological mass density fluctuations on the equation of state of the dark energy, w = p / rho. at fixed linear theory power, increasing w leads to an increase in non - linear power, with the effect increasing with k. by k = 10 h / mpc, a model with w = - 0. 75 has ~ 12 % more power than a standard cosmological constant model ( w = - 1 ), while a model with w = - 0. 5 has ~ 33 % extra power ( at z = 0 ). the size of the effect increases with increasing dark energy fraction, and to a lesser extent increasing power spectrum normalization, but is insensitive to the power spectrum shape ( the numbers above are for omega _ m = 0. 281 and sigma _ 8 = 0. 897 ). a code quantifying the non - linear effect of varying w, as a function of k, z, and other cosmological parameters, which should be accurate to a few percent for k < 10 h / mpc for models that fit the current observations, is available at http : / / www. cita. utoronto. ca / ~ pmcdonal / code. html. this paper also serves as an example of a detailed exploration of the numerical convergence properties of ratios of power spectra for different models, which can be useful because some kinds of numerical error cancel in a ratio. when precision calculations based on numerical simulations are needed for many different models, efficiency may be gained by breaking the problem into a calculation of the absolute prediction at a central point, and calculations of the relative change in the prediction with model parameters.
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arxiv:astro-ph/0505565
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we introduce a novel image quality assessment ( iqa ) dataset comprising 6073 uhd - 1 ( 4k ) images, annotated at a fixed width of 3840 pixels. contrary to existing no - reference ( nr ) iqa datasets, ours focuses on highly aesthetic photos of high technical quality, filling a gap in the literature. the images, carefully curated to exclude synthetic content, are sufficiently diverse to train general nr - iqa models. importantly, the dataset is annotated with perceptual quality ratings obtained through a crowdsourcing study. ten expert raters, comprising photographers and graphics artists, assessed each image at least twice in multiple sessions spanning several days, resulting in 20 highly reliable ratings per image. annotators were rigorously selected based on several metrics, including self - consistency, to ensure their reliability. the dataset includes rich metadata with user and machine - generated tags from over 5, 000 categories and popularity indicators such as favorites, likes, downloads, and views. with its unique characteristics, such as its focus on high - quality images, reliable crowdsourced annotations, and high annotation resolution, our dataset opens up new opportunities for advancing perceptual image quality assessment research and developing practical nr - iqa models that apply to modern photos. our dataset is available at https : / / database. mmsp - kn. de / uhd - iqa - benchmark - database. html
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arxiv:2406.17472
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we develop a geometrical framework that allows to obtain the electromagnetic field quantities in accelerated frames. the frame of arbitrary accelerated observers in space - time is defined by a suitable set of tetrad fields, whose timelike components are adapted to the worldlines of a field of observers. we consider the faraday tensor and maxwell ' s equations as abstract tensor quantities in space - time, and make use of tetrad fields to project the electromagnetic field quantities in the accelerated frames. as an application, plane and spherical electromagnetic waves are projected in linearly accelerated frames in minkowski space - time. we show that the amplitude, frequency and the wave vector of the plane wave in the accelerated frame vary with time, while the light speed remains constant. we also obtain the variation of the poynting vector with time in the accelerated frame.
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arxiv:1110.5367
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we show numerically that correlation length at the critical point in the five - dimensional ising model varies with system size l as l ^ { 5 / 4 }, rather than proportional to l as in standard finite size scaling ( fss ) theory. our results confirm a hypothesis that fss expressions in dimension d greater than the upper critical dimension of 4 should have l replaced by l ^ { d / 4 } for cubic samples with periodic boundary conditions. we also investigate numerically the logarithmic corrections to fss in d = 4.
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arxiv:cond-mat/0412150
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background. the gorkov approach to self - consistent green ' s function theory has been formulated in [ v. som \ ` a, t. duguet, c. barbieri, phys. rev. c 84, 064317 ( 2011 ) ]. over the past decade, it has become a method of reference for first - principle computations of semi - magic nuclear isotopes. the currently available implementation is limited to a second - order self - energy and neglects particle - number non - conserving terms arising from contracting three - particle forces with anomalous propagators. for nuclear physics applications, this is sufficient to address first - order energy differences, ground - state radii and moments on an accurate enough basis. however, addressing absolute binding energies, fine spectroscopic details of $ n \ pm1 $ particle systems or delicate quantities such as second - order energy differences associated to pairing gaps, requires to go to higher truncation orders. purpose. the formalism is extended to third order in the algebraic diagrammatic construction ( adc ) expansion with two - body hamiltonians. methods. the expansion of gorkov propagators in feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the gorkov self - energy. results. algebraic expressions for the static and dynamic contributions to the self - energy, along with equations for the matrix elements of the gorkov eigenvalue problem, are derived. it is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. workable approximations to the full self - consistency problem are also elaborated on. the formalism at third order it thus complete for a general two - body hamiltonian. conclusion. working equations for the full gorkov - adc ( 3 ) are now available for numerical implementation.
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arxiv:2112.08322
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we explore the impact of volume exclusion on the local assembly of linear physical networks, where nodes and links are hard - core rigid objects. to do so, we introduce a minimal 3d model that helps us zoom into confined regions of these networks whose distant parts are sequentially connected by links with a very large aspect ratio. we show that the kinetics of link adhesion is logarithmic, as opposed to the algebraic growth in lower dimensions, and we attribute this qualitatively different behavior to a spontaneous delay of depletion forces caused by the 3d nature of the problem. equally important, we find that this slow kinetics is metastable, allowing us to analytically predict an algebraic growth due to the formation of local bundles. our findings offer a benchmark to study the local assembly of physical networks, with implications for non - equilibrium nest - like packings.
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arxiv:2401.02579
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a coring ( a, c ) consists of an algebra a and a coalgebra c in the monoidal category of a - bimodules. corings and their comodules arise naturally in the study of hopf - galois extensions and descent theory, as well as in the study of hopf algebroids. in this paper, we address the question of when two corings in a symmetric monoidal model category v are homotopically morita equivalent, i. e., when their respective categories of comodules are quillen equivalent. the category of comodules over the trivial coring ( a, a ) is isomorphic to the category of a - modules, so the question above englobes that of when two algebras are homotopically morita equivalent. we discuss this special case in the first part of the paper, extending previously known results. to approach the general question, we introduce the notion of a ' braided bimodule ' and show that adjunctions between a - mod and b - mod that lift to adjunctions between ( a, c ) - comod and ( b, d ) - comod correspond precisely to braided bimodules between ( a, c ) and ( b, d ). we then give criteria, in terms of homotopic descent, for when a braided bimodule induces a quillen equivalence. in particular, we obtain criteria for when a morphism of corings induces a quillen equivalence, providing a homotopic generalization of results by hovey and strickland on morita equivalences of hopf algebroids. to illustrate the general theory, we examine homotopical morita theory for corings in the category of chain complexes over a commutative ring.
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arxiv:1411.6517
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let f ( n ) = 1 if n = 1, 2 ^ ( 2 ^ ( n - 2 ) ) if n \ in { 2, 3, 4, 5 }, ( 2 + 2 ^ ( 2 ^ ( n - 4 ) ) ) ^ ( 2 ^ ( n - 4 ) ) if n \ in { 6, 7, 8,... }. we conjecture that if a system t \ subseteq { x _ i + 1 = x _ k, x _ i \ cdot x _ j = x _ k : i, j, k \ in { 1,..., n } } has only finitely many solutions in positive integers x _ 1,..., x _ n, then each such solution ( x _ 1,..., x _ n ) satisfies x _ 1,..., x _ n \ leq f ( n ). we prove that the function f cannot be decreased and the conjecture implies that there is an algorithm which takes as input a diophantine equation, returns an integer, and this integer is greater than the heights of integer ( non - negative integer, positive integer, rational ) solutions, if the solution set is finite. we show that if the conjecture is true, then this can be partially confirmed by the execution of a brute - force algorithm.
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arxiv:1502.05105
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we present a study of 581 hz oscillations observed during a thermonuclear x - ray burst from the low mass x - ray binary ( lmxb ) 4u 1636 - 54 with the rossi x - ray timing explorer ( rxte ). we argue that the combination of large pulsed amplitudes near burst onset and the spectral evidence for localized emission during the rise strongly supports rotational modulation as the mechanism for the oscillations. we discuss how theoretical interpretation of spin modulation amplitudes, pulse profiles and pulse phase spectroscopy can provide constraints on the masses and radii of neutron stars. we also discuss the implication of these findings for the beat frequency models of khz x - ray variability in lmxb.
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arxiv:astro-ph/9803119
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electromagnetic wave is reflected and refracted at interfaces, satisfying fresnel - snell law which is required by conservations of energy and momentum. if the incident angle is lower than the critical angle, we can use this fresnel - snell law, but the fresnel - snell law is modified in the case of existence of dissipation ( $ \ tilde { n } = n + i \ kappa, \ kappa > 0 $ ) or in the condition of total internal reflection. in the cases, we have to extend the angle of refraction from real number to complex number ( $ \ theta \ rightarrow \ tilde { \ theta } = \ theta + i \ psi, \ psi \ neq 0 $ ). in this paper, by using complex - angle approach, we analyse the behaviour of electromagnetic waves in various kind of interfaces : dielectric - dielectric system, dissipative dielectric - dielectric system, and metal - dielectric system. we show that iso - frequency curves in wavenumber space is opened in the case where $ n, \ kappa > 0 $, and closed either when $ n \ rightarrow 0 $ or when $ \ kappa \ rightarrow 0 $ ( " lifshitz transition " of electromagnetic waves ). excess momentum ( wavenumber ) and anomalous spin ( circular polarization ) emerging with the transition are also discussed.
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arxiv:1806.11482
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we show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. a general form for these transformations is presented. then we consider gauge fixing by means of canonical transformations in this sp ( 2 ) covariant scheme, finding a relation between generators and gauge fixing functions. the existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. some solutions for the generators are discussed. our results are then illustrated by the example of yang mills theory.
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arxiv:hep-th/9801107
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we consider interpolation learning in high - dimensional linear regression with gaussian data, and prove a generic uniform convergence guarantee on the generalization error of interpolators in an arbitrary hypothesis class in terms of the class ' s gaussian width. applying the generic bound to euclidean norm balls recovers the consistency result of bartlett et al. ( 2020 ) for minimum - norm interpolators, and confirms a prediction of zhou et al. ( 2020 ) for near - minimal - norm interpolators in the special case of gaussian data. we demonstrate the generality of the bound by applying it to the simplex, obtaining a novel consistency result for minimum l1 - norm interpolators ( basis pursuit ). our results show how norm - based generalization bounds can explain and be used to analyze benign overfitting, at least in some settings.
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arxiv:2106.09276
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we study the following $ 1 $ - yamabe equation on a connected finite graph $ $ \ delta _ 1u + g \ mathrm { sgn } ( u ) = h | u | ^ { \ alpha - 1 } \ mathrm { sgn } ( u ), $ $ where $ \ delta _ 1 $ is the discrete $ 1 $ - laplacian, $ \ alpha > 1 $ and $ g, h > 0 $ are known. we show that the above $ 1 $ - yamabe equation always has a nontrivial solution $ u \ geq0 $, $ u \ neq0 $.
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arxiv:1709.09867
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we give a precise microlocal description of the singular profile that forms in the long - time propagation of internal waves in an effectively two - dimensional aquarium. we allow domains with corners, such as polygons appearing in the experimental set ups of maas et al. this extends the previous work of dyatlov - - wang - - zworski arxiv : 2112. 10191, which considered domains with smooth boundary. we show that in addition to singularities that correspond to attractors in the underlying classical dynamics, milder singularities propagate out of the corners as well.
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arxiv:2402.01896
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cross - domain sequential recommenders ( csrs ) are gaining considerable research attention as they can capture user sequential preference by leveraging side information from multiple domains. however, these works typically follow an ideal setup, i. e., different domains obey similar data distribution, which ignores the bias brought by asymmetric interaction densities ( a. k. a. the inter - domain density bias ). besides, the frequently adopted mechanism ( e. g., the self - attention network ) in sequence encoder only focuses on the interactions within a local view, which overlooks the global correlations between different training batches. to this end, we propose an external attention - enhanced graph contrastive learning framework, namely ea - gcl. specifically, to remove the impact of the inter - domain density bias, an auxiliary self - supervised learning ( ssl ) task is attached to the traditional graph encoder under a multi - task learning manner. to robustly capture users ' behavioral patterns, we develop an external attention - based sequence encoder that contains an mlp - based memory - sharing structure. unlike the self - attention mechanism, such a structure can effectively alleviate the bias interference from the batch - based training scheme. extensive experiments on two real - world datasets demonstrate that ea - gcl outperforms several state - of - the - art baselines on csr tasks. the source codes and relevant datasets are available at https : / / github. com / houpingy / ea - gcl.
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arxiv:2310.04633
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we study the spectra and response of two electrons moving on a surface of a sphere and interacting via harmonic potential, to external static and laser fields. the spectrum of such system law is analysed in the light of varying coupling strength. in addition, the expectation value of cosine of the angle between external field and the system for first and second order have been evaluated and analysed.
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arxiv:1511.06847
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in this paper, we propose a learned scalable / progressive image compression scheme based on deep neural networks ( dnn ), named bidirectional context disentanglement network ( bcd - net ). for learning hierarchical representations, we first adopt bit - plane decomposition to decompose the information coarsely before the deep - learning - based transformation. however, the information carried by different bit - planes is not only unequal in entropy but also of different importance for reconstruction. we thus take the hidden features corresponding to different bit - planes as the context and design a network topology with bidirectional flows to disentangle the contextual information for more effective compressed representations. our proposed scheme enables us to obtain the compressed codes with scalable rates via a one - pass encoding - decoding. experiment results demonstrate that our proposed model outperforms the state - of - the - art dnn - based scalable image compression methods in both psnr and ms - ssim metrics. in addition, our proposed model achieves higher performance in ms - ssim metric than conventional scalable image codecs. effectiveness of our technical components is also verified through sufficient ablation experiments.
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arxiv:1812.09443
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different change - point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. in a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two - sided poisson process driven by some parameter, can be approximated ( for sufficiently small values of the parameter ) by another one, which is an exponential functional of a two - sided brownian motion. in this paper we consider yet another likelihood ratio, which is the exponent of a two - sided compound poisson process driven by some parameter. we establish, that similarly to the poisson type one, the compound poisson type likelihood ratio can be approximated by the brownian type one for sufficiently small values of the parameter. we equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations.
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arxiv:1007.2758
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recent results on identified hadrons from the phenix experiment in au + au collisions at mid - rapidity at $ \ sqrt { s _ { nn } } $ = 200 gev are presented. the centrality dependence of transverse momentum distributions and particle ratios for identified charged hadrons are studied. the transverse flow velocity and freeze - out temperature are extracted from $ p _ { t } $ spectra within the framework of a hydrodynamic collective flow model. two - particle hbt correlations for charged pions are measured in different centrality selections for a broad range of transverse momentum of the pair. results on elliptic flow measurements with respect to the reaction plane for identified particles are also presented.
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arxiv:nucl-ex/0209027
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in the next decade, intensity frontier experiments will require tracking systems that are robust against high event and background rates while maintaining excellent tracking performance. we develop a first conceptual design of a tracking system for a hypothetical future experiment - - here imagined as a successor to belle ii - - built around a time projection chamber ( tpc ) with high resolution readout. this choice necessitates a significant expansion of the silicon vertex detector as well as a new fast timing layer. we simulate the performance of such a system in the belle ii simulation framework, probe its major technical challenges, and demonstrate that such a system is suitable for projected luminosities at the next generation of intensity - frontier colliders.
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arxiv:2203.07287
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my contribution to this collection of articles in honor of david lee and john reppy on their 90th birthdays is a reflection on the remarkable phenomenology of the excitation spectra of superfluid $ ^ 3 $ he, in particular the b - phase which was identified by nmr and acoustic spectroscopy as balian - werthamer state shown in 1963 to be the ground state of a spin - triplet, p - wave superconductor within weak - coupling bcs theory. the superfluid phases of $ ^ 3 $ he provide paradigms for electronic superconductors with broken space - time symmetries and non - trivial ground - state topology. indeed broken spin - and orbital rotation symmetries lead to a rich spectrum of collective modes of the order parameter that can be detected using nmr, acoustic and microwave spectroscopies. the topology of the bw state implies its low - temperature, low - energy transport properties are dominated by gapless majorana modes confined on boundaries or interfaces. given the central role the bw state played i discuss the acoustic and electromagnetic signatures of the bw state, the latter being relevant if an electronic analog of superfluid $ ^ 3 $ he - b is realized.
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arxiv:2203.15944
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classical applications of galois theory concern algebraic numbers and algebraic functions. still, the night before his duel, galois wrote that his last mathematical thoughts had been directed toward applying his " theory of ambiguity to transcendental functions and transcendental quantities ". we outline some more or less recent ideas and results in this direction.
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arxiv:1207.3381
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progress in understanding the coupling between plasma instabilities in the equatorial electrojet based on a unified fluid model is reported. a deeper understanding of the linear and nonlinear evolution and the coupling of the gradient - drift and farley - buneman instabilities is achieved by studying the effect of different combinations of the density - gradient scale - lengths ( ln ) and cross - field ( e? b ) drifts on the plasma turbulence. mechanisms and channels of energy transfer are illucidated for these multiscale instabilities. energy for the unified model is examined, including the injected, conservative redistribution ( between fields and scales ), and ultimate dissipation. various physical mechanisms involved in the energetics are categorized as sources, sinks, nonlinear transfer, and coupling to show that the system satisfies the fundamental law of energy oonservation. the physics of the nonlinear transfer terms is studied to identify their roles in producing energy cascades { the transference of energy from the dominant unstable wavenumbers and driving irregularities of different scale - lengths. the theory of two - step energy cascading to generate the 3 - meter plasma irregularities in the equatorial electrojet is verified. in addition, the nonlinearity of the system allows the possibility for a reverse energy cascading, responsible for generating large - scale plasma structures at the top of the electrojet.
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arxiv:1602.09042
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we characterize diagonals of unbounded self - adjoint operators on a hilbert space h that have only discrete spectrum, i. e., with empty essential spectrum. our result extends the schur - horn theorem from a finite dimensional setting to an infinite dimensional hilbert space, analogous to kadison ' s theorem for orthogonal projections, kaftal and weiss ' results for positive compact operators, and bownik and jasper ' s characterization for operators with finite spectrum. furthermore, we show that if a symmetric unbounded operator e on h has a nondecreasing unbounded diagonal, then any sequence that weakly majorizes this diagonal is also a diagonal of e.
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arxiv:1606.05236
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chips with hundreds to thousands of cores require scalable networks - on - chip ( nocs ). customization of the noc topology is necessary to reach the diverse design goals of different chips. we introduce sparse hamming graph, a novel noc topology with an adjustable costperformance trade - off that is based on four noc topology design principles we identified. to efficiently customize this topology, we develop a toolchain that leverages approximate floorplanning and link routing to deliver fast and accurate cost and performance predictions. we demonstrate how to use our methodology to achieve desired cost - performance trade - offs while outperforming established topologies in cost, performance, or both.
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arxiv:2211.13980
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the macroscopic dynamics of a rotating superfluid deviates from that of a simple perfect fluid due to the effect of vorticity quantisation, which gives rise to a substructure of cosmic string type line defects that results in a local anisotropy whereby the effective average pressure in the direction of the vortex lines is reduced below its value in lateral directions. whereas previous descriptions of this effect have been restricted to a non - relativistic framework that is adequate for the treatment of liquid helium in a laboratory context, the present work provides a fully relativistic description of the kind required for application to rotating neutron star models. to start with, the general category of vortex fibration models needed for this purpose is set up on the basis of a kalb - ramond type variational principle. the appropriate specification of the particular model to be chosen within this category will ultimately be governed by the conclusions of microscopic investigations that have not yet been completed, but the results available so far suggest that a uniquely simple kind of model with an elegant dilatonic formulation should be tentatively adopted as a provisional choice so long as there is no indication that a more complicated alternative is needed.
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arxiv:hep-th/9611082
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we establish a boundary connected sum theorem for asymptotically hyperbolic einstein metrics ; this requires no nondegeneracy hypothesis. we also show that if the two metrics have scalar positive conformal infinities, then the same is true for this boundary join.
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arxiv:math/0211099
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we prove that for any known lie algebra $ \ frak { g } $ having none invariants for the coadjoint representation, the absence of invariants is equivalent to the existence of a left invariant exact symplectic structure on the corresponding lie group $ g $. we also show that a nontrivial generalized casimir invariant constitutes an obstruction for the exactness of a symplectic form, and provide solid arguments to conjecture that a lie algebra is endowed with an exact symplectic form if and only if all invariants for the coadjoint representation are trivial. we moreover develop a practical criterion that allows to deduce the existence of such a symplectic form on a lie algebra from the shape of the antidiagonal entries of the associated commutator matrix. in an appendix the classification of lie algebras satisfying $ \ mathcal { n } ( \ frak { g } ) = 0 $ in low dimensions is given in tabular form, and their exact symplectic structure is given in terms of the maurer - cartan equations.
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arxiv:math-ph/0301004
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the notorious ` measurement problem ' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of ` interpretations ' of quantum mechanics, which are meant to evade it. we argue that no less than six problems need to be distinguished, and that several of them classify as different types of problems. one of them is what traditionally is called ` the measurement problem ' ( here : the reality problem of measurement outcomes ). another of them has nothing to do with measurements but is a profound metaphysical problem. we also analyse critically maudlin ' s ( 1995 ) well - known statement of ` three measurements problems ', and the clash of the views of brown ( 1986 ) and stein ( 1997 ) on one of the six measurement problems, concerning so - called insolubility theorems. finally, we summarise a solution to one measurement problem which has been largely ignored but tacitly if not explicitly acknowledged.
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arxiv:2305.10206
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the entropic pressure in the vicinity of a two dimensional square lattice polygon is examined as a model of the entropic pressure near a planar ring polymer. the scaling of the pressure as a function of distance from the polygon and length of the polygon is determined and tested numerically.
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arxiv:1308.4031
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some new integrals involving the stieltjes constants are developed in this paper.
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arxiv:1104.1911
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there is no unique way to encode a quantum algorithm into a quantum circuit. with limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near - term quantum devices. we introduce two separate ideas for circuit optimization and combine them in a multi - tiered quantum circuit optimization protocol called aqcel. the first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware co - optimization. the second ingredient is an approach to reduce circuit complexity by identifying zero - or low - amplitude computational basis states and redundant gates. as a demonstration, aqcel is deployed on an iterative and efficient quantum algorithm designed to model final state radiation in high energy physics. for this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. our technique is generic and can be useful for a wide variety of quantum algorithms.
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arxiv:2102.10008
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length scale control is imposed in topology optimization ( to ) to make designs amenable to manufacturing and other functional requirements. broadly, there are two types of length - scale control in to : \ emph { exact } and \ emph { approximate }. while the former is desirable, its implementation can be difficult, and is computationally expensive. approximate length scale control is therefore preferred, and is often sufficient for early stages of design. in this paper we propose an approximate length scale control strategy for to, by extending a recently proposed density - based to formulation using neural networks ( tounn ). specifically, we enhance tounn with a fourier space projection, to control the minimum and / or maximum length scales. the proposed method does not involve additional constraints, and the sensitivity computations are automated by expressing the computations in an end - end differentiable fashion using the neural net ' s library. the proposed method is illustrated through several numerical experiments for single and multi - material designs.
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arxiv:2109.01861
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we have used the sydney university stellar interferometer ( susi ) to measure the angular diameter of the f9 v star beta virginis. after correcting for limb darkening and combining with the revised hipparcos parallax, we derive a radius of 1. 703 + / - 0. 022 r _ sun ( 1. 3 % ). we have also calculated the bolometric flux from published measurements which, combined with the angular diameter, implies an effective temperature of 6059 + / - 49 k ( 0. 8 % ). we also derived the luminosity of beta vir to be l = 3. 51 + / - 0. 08 l _ sun ( 2. 1 % ). solar - like oscillations were measured in this star by carrier et al. ( 2005 ) and using their value for the large frequency separation yields the mean stellar density with an uncertainty of about 2 %. our constraints on the fundamental parameters of beta vir will be important to test theoretical models of this star and its oscillations.
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arxiv:0811.1804
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we compute the leptonic decay constants of heavy - light vector mesons in the quenched approximation. the reliability of lattice computations for heavy quarks is checked by comparing the ratio of vector to pseudoscalar decay constant with the prediction of heavy quark effective theory in the limit of infinitely heavy quark mass. good agreement is found. we then calculate the decay constant ratio for b mesons : $ f _ { b ^ * } / f _ b = 1. 01 ( 0. 01 ) ( ^ { + 0. 04 } _ { - 0. 01 } ) $. we also quote quenched $ f _ { b ^ * } = 177 ( 6 ) ( 17 ) $ mev.
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arxiv:hep-lat/0109015
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as llms become increasingly proficient at producing human - like responses, there has been a rise of academic and industrial pursuits dedicated to flagging a given piece of text as " human " or " ai ". most of these pursuits involve modern nlp detectors like t5 - sentinel and roberta - sentinel, without paying too much attention to issues of interpretability and explainability of these models. in our study, we provide a comprehensive analysis that shows that traditional ml models ( naive - bayes, mlp, random forests, xgboost ) perform as well as modern nlp detectors, in human vs ai text detection. we achieve this by implementing a robust testing procedure on diverse datasets, including curated corpora and real - world samples. subsequently, by employing the explainable ai technique lime, we uncover parts of the input that contribute most to the prediction of each model, providing insights into the detection process. our study contributes to the growing need for developing production - level llm detection tools, which can leverage a wide range of traditional as well as modern nlp detectors we propose. finally, the lime techniques we demonstrate also have the potential to equip these detection tools with interpretability analysis features, making them more reliable and trustworthy in various domains like education, healthcare, and media.
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arxiv:2409.04808
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two approaches exist to account for granular dynamics : the athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. discrete element method ( dem ), granular kinetic theory and athermal statistical mechanics ( asm ) belong to the first, granular solid hydrodynamics ( gsh ) to the second one. a discussion of the conceptual differences between both is given here, leading, among others, to the following insights : ( 1 ) while dem and granular kinetic theory are well justified to take grains as athermal, any entropic consideration is far less likely to succeed. ( 2 ) in addition to modeling grains as a gas of dissipative, rigid mass points, it is very helpful take grains as a thermal solid that has been sliced and diced. ( 3 ) general principles that appear invalid in granular media are repaired and restored once the true entropy is included. these abnormalities [ such as invalidity of the fluctuation - dissipation theorem, granular temperatures failing to equilibrate, and grains at rest unable to explore the phase space ] are consequences of the athermal approximation, not properties of granular media.
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arxiv:1604.01534
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practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. however, in many cases we cannot randomize the intermediate variable, resulting in sample selection problems even in randomized experiments. therefore, we view randomized experiments with intermediate variables as semi - observational studies. in parallel with the analysis of observational studies, we provide a theoretical foundation for conducting objective causal inference with an intermediate variable under the principal stratification framework, with principal strata defined as the joint potential values of the intermediate variable. our strategy constructs weighted samples based on principal scores, defined as the conditional probabilities of the latent principal strata given covariates, without access to any outcome data. this principal stratification analysis yields robust causal inference without relying on any model assumptions on the outcome distributions. we also propose approaches to conducting sensitivity analysis for violations of the ignorability and monotonicity assumptions, the very crucial but untestable identification assumptions in our theory. when the assumptions required by the classical instrumental variable analysis cannot be justified by background knowledge or cannot be made because of scientific questions of interest, our strategy serves as a useful alternative tool to deal with intermediate variables. we illustrate our methodologies by using two real data examples, and find scientifically meaningful conclusions.
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arxiv:1602.01196
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we prove schur - - weyl duality between the brauer algebra $ \ mathfrak { b } _ n ( m ) $ and the orthogonal group $ o _ { m } ( k ) $ over an arbitrary infinite field $ k $ of odd characteristic. if $ m $ is even, we show that each connected component of the orthogonal monoid is a normal variety ; this implies that the orthogonal schur algebra associated to the identity component is a generalized schur algebra. as an application of the main result, an explicit and characteristic - free description of the annihilator of $ n $ - tensor space $ v ^ { \ otimes n } $ in the brauer algebra $ mathfrak { b } _ n ( m ) $ is also given.
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arxiv:0712.0944
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we propose super odometry, a high - precision multi - modal sensor fusion framework, providing a simple but effective way to fuse multiple sensors such as lidar, camera, and imu sensors and achieve robust state estimation in perceptually - degraded environments. different from traditional sensor - fusion methods, super odometry employs an imu - centric data processing pipeline, which combines the advantages of loosely coupled methods with tightly coupled methods and recovers motion in a coarse - to - fine manner. the proposed framework is composed of three parts : imu odometry, visual - inertial odometry, and laser - inertial odometry. the visual - inertial odometry and laser - inertial odometry provide the pose prior to constrain the imu bias and receive the motion prediction from imu odometry. to ensure high performance in real - time, we apply a dynamic octree that only consumes 10 % of the running time compared with a static kd - tree. the proposed system was deployed on drones and ground robots, as part of team explorer ' s effort to the darpa subterranean challenge where the team won $ 1 ^ { st } $ and $ 2 ^ { nd } $ place in the tunnel and urban circuits, respectively.
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arxiv:2104.14938
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in hyperbolic space density cannot be defined by a limit as we define it in euclidean space. we describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.
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arxiv:2202.10797
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transport through two quantum dots laterally embedded in aharonov - bohm interferometry with infinite intradot and arbitrary interdot coulomb repulsion is analyzed in the weak coupling and coulomb blockade regime. by employing the modified quantum rate equations and the slave - boson approach, we establish a general dc current formula at temperatures higher than the kondo temperature for the case that the spin degenerate levels of two dots are close to each other. we examine two simple examples for identical dots - no doubly occupied states and no empty state. in the former, completely destructive coherent transport and phase locking appear at magnetic flux $ \ phi = \ phi _ { 0 } / 2 $ and $ \ phi = 0 $ respectively ; in the latter, partially coherent transport exhibits an oscillation with magnetic flux having a period of $ \ phi _ 0 $.
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arxiv:cond-mat/0310331
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in a recent theoretical article [ eur. phys. j. d 70, 1 ( 2016 ) ], kazemi et al. claim to have demonstrated superluminal light transmission in an optomechanical system where a bose - einstein condensate serves as the mechanical oscillator. in fact the superluminal propagation is only inferred from the existence of a minimum of transmission of the system at the probe frequency. this condition is not sufficient and we show that, in all the cases where superluminal propagation is claimed by kazemi et al., the propagation is in reality subluminal. moreover, we point out that the system under consideration is not minimum - phase - shift. the kramers - kronig relations then only fix a lower limit to the group delay and we show that these two quantities have sometimes opposite signs.
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arxiv:1603.07208
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in this paper we investigate a certain eta - theta quotient which appears in the partition function of entanglement entropy. employing wright ' s circle method, we give its bivariate asymptotic profile.
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arxiv:1910.06805
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in this paper, we give three equivalent properties of the class of multivariate simple cubic natural exponential families ( nef ' s ). the first property says that the cumulant function of any basis of the family is a solution of some monge - amp \ ' { e } re equation, the second is that the variance function satisfies a differential equation, and the third is characterized by the equality between two families of prior distributions related to the nef. these properties represent the extensions to this class of the properties stated in $ \ cite { casalis ( 1996 ) } $ and satisfied by the wishart and the simple quadratic nef ' s. we also show that in the real case, each of these properties provides a new characterization of the letac - mora class of real cubic nef ' s.
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arxiv:1108.2788
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a way to considerably enhance terahertz radiation, emitted in the interaction of intense mid - infrared laser pulses with atomic gases, in both the total energy and the electric - field amplitude is suggested. the scheme is based on the application of a two - color field consisting of a strong circularly polarized mid - infrared pulse with wavelengths of $ 1. 6 \ div 4 \, \ mu { \ rm m } $ and its linearly or circularly polarized second harmonic of lower intensity. by combining the strong - field approximation for the ionization of a single atom with particle - in - cell simulations of the collective dynamics of the generated plasma it is shown that the application of such two - color circularly polarized laser pulses may lead to an order - of - magnitude increase in the energy emitted in the terahertz frequency domain as well as in a considerable enhancement in the maximal electric field of the terahertz pulse. our results support recently reported experimental and numerical findings.
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arxiv:1810.08834
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bipartite correlation clustering is the problem of generating a set of disjoint bi - cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. the number or size of the output clusters is not constrained in any way. the best known approximation algorithm for this problem gives a factor of 11. this result and all previous ones involve solving large linear or semi - definite programs which become prohibitive even for modestly sized tasks. in this paper we present an improved factor 4 approximation algorithm to this problem using a simple combinatorial algorithm which does not require solving large convex programs. the analysis extends a method developed by ailon, charikar and alantha in 2008, where a randomized pivoting algorithm was analyzed for obtaining a 3 - approximation algorithm for correlation clustering, which is the same problem on graphs ( not bipartite ). the analysis for correlation clustering there required defining events for structures containing 3 vertices and using the probability of these events to produce a feasible solution to a dual of a certain natural lp bounding the optimal cost. it is tempting here to use sets of 4 vertices, which are the smallest structures for which contradictions arise for bipartite correlation clustering. this simple idea, however, appears to be evasive. we show that, by modifying the lp, we can analyze algorithms which take into consideration subgraph structures of unbounded size. we believe our techniques are interesting in their own right, and may be used for other problems as well.
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arxiv:1012.3011
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we revisit the ` ` smile dynamics ' ' problem, which consists in relating the implied leverage ( i. e. the correlation of the at - the - money volatility with the returns of the underlying ) and the skew of the option smile. the ratio between these two quantities, called ` ` skew - stickiness ratio ' ' ( ssr ) by bergomi ( smile dynamics iv, risk, 94 - 100, december 2009 ), saturates to the value 2 for linear models in the limit of small maturities, and converges to 1 for long maturities. we show that for more general, non - linear models ( such as the asymmetric garch model ), bergomi ' s result must be modified, and can be larger than 2 for small maturities. the discrepancy comes from the fact that the volatility skew is, in general, different from the skewness of the underlying. we compare our theory with empirical results, using data both from option markets and from the underlying price series, for the s & p500 and the dax. we find, among other things, that although both the implied leverage and the skew appear to be too strong on option markets, their ratio is well explained by the theory. we observe that the ssr indeed becomes larger than 2 for small maturities.
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arxiv:1311.4078
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biomedical imaging modalities often produce high - resolution, multi - dimensional images that pose computational challenges for deep neural networks. these computational challenges are compounded when training transformers due to the self - attention operator, which scales quadratically with context length. recent developments in long - context models have potential to alleviate these difficulties and enable more efficient application of transformers to large biomedical images, although a systematic evaluation on this topic is lacking. in this study, we investigate the impact of context length on biomedical image analysis and we evaluate the performance of recently proposed long - context models. we first curate a suite of biomedical imaging datasets, including 2d and 3d data for segmentation, denoising, and classification tasks. we then analyze the impact of context length on network performance using the vision transformer and swin transformer by varying patch size and attention window size. our findings reveal a strong relationship between context length and performance, particularly for pixel - level prediction tasks. finally, we show that recent long - context models demonstrate significant improvements in efficiency while maintaining comparable performance, though we highlight where gaps remain. this work underscores the potential and challenges of using long - context models in biomedical imaging.
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arxiv:2501.00619
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many x - ray observations of gigahertz peaked spectrum and compact steep spectrum sources have been made with chandra x - ray observatory and xmm - newton observatory over the last few years. the x - ray spectra contribute the important information to the total energy distribution of the compact radio sources. in addition the spatial resolution of chandra allows for studies of the x - ray morphology of these sources on arcsec scales and provide a direct view of their environments. this paper gives a review of the current status of the x - ray observations and their contribution to our understanding of the nature of these compact radio sources. it also describes primary physical processes that lead to the observed x - ray emission and summarize x - ray emission properties expected from interactions between an expanding radio source and the intergalactic environment.
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arxiv:0901.1327
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