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we extend the results obtained by e. ntienjem to all positive integers. let $ \ eufrak { n } $ be the subset of $ \ mathbb { n } $ consisting of $ \, 2 ^ { \ nu } \ mho $, where $ \ nu $ is in $ \ { 0, 1, 2, 3 \ } $ and $ \ mho $ is a squarefree finite product of distinct odd primes. we discuss the evaluation of the convolution sum, $ \ underset { \ substack { { ( l, m ) \ in \ mathbb { n } ^ { 2 } } { \ alpha \, l + \ beta \, m = n } } } { \ sum } \ sigma ( l ) \ sigma ( m ) $, when $ \ alpha \ beta $ is in $ \ mathbb { n } \ setminus \ eufrak { n } $. the evaluation of convolution sums belonging to this class is achieved by applying modular forms and primitive dirichlet characters. in addition, we revisit the evaluation of the convolution sums for $ \ alpha \ beta = 9 $, $ 16 $, $ 18 $, $ 25 $, $ 36 $. if $ \ alpha \ beta \ equiv 0 \ pmod { 4 } $, we determine natural numbers $ a, b $ and use the evaluated convolution sums together with other known convolution sums to carry out the number of representations of $ n $ by the octonary quadratic forms $ a \, ( x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } + x _ { 3 } ^ { 2 } + x _ { 4 } ^ { 2 } ) + b \, ( x _ { 5 } ^ { 2 } + x _ { 6 } ^ { 2 } + x _ { 7 } ^ { 2 } + x _ { 8 } ^ { 2 } ) $. similarly, if $ \ alpha \ beta \ equiv 0 \ pmod { 3 } $, we compute natural numbers $ c, d $ and make use of the evaluated convolution sums together with other known convolution sums to determine the number of representations of $ n $ by the octonary quadratic forms $ c \, ( \, x _ { 1 } ^ { 2 } + x _ { 1 } x _
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arxiv:1609.01343
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in order to reduce the klein - gordon equation ( with minimal coupling ), we introduce a generalization of the so - called " mode solutions " that are well - known in the special case of a robertson - walker universe. after separation of the variables, we end up with a partial differential equation in lower dimension. a reduced version of the gordon current arises and is conserved. when the first factor - manifold is lorentzian, distinct modes appear as mutually orthogonal in the sense of the sesquilinear form obtained from the customary gordon current. moreover, a sesquilinear form is defined on the space of solutions to the reduced equation. extension of this picture to curvature coupling is possible when the second factor - manifold has a constant scalar curvature.
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arxiv:gr-qc/0003116
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we present a wormhole construction in the framework of the $ f ( r, t ) $ extended gravity theory, with $ r $ being the ricci curvature scalar and $ t $ the trace of the energy - momentum tensor, in the case in which the energy - momentum tensor is conserved. from the conservation equation we find that the $ f ( r, t ) $ function is linear in $ t $. by developing the field equations, we find a traversable wormhole that for a range of the model parameter values, has no need to be filled by exotic matter.
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arxiv:2410.00279
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we consider the approximation of elliptic eigenvalue problem with an immersed interface. the main aim of this paper is to prove the stability and convergence of an immersed finite element method ( ifem ) for eigenvalues using crouzeix - raviart $ p _ 1 $ - nonconforming approximation. we show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem. we analyze the ifem for elliptic eigenvalue problem with an immersed interface and derive the optimal convergence of eigenvalues. numerical experiments demonstrate our theoretical results.
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arxiv:1412.3163
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the mathematical reviews ( mr ) database since 1940 ( the first year of operation of mr ) is now more than 1. 9 million, and more than 75 thousand items are added to the database each year. the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. " = = symbolic notation and terminology = = mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. this notation consists of symbols used for representing operations, unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. more precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally latin or greek letters, and often include subscripts. operation and relations are generally represented by specific symbols or glyphs, such as + ( plus ), × ( multiplication ), { \ textstyle \ int } ( integral ), = ( equal ), and < ( less than ). all these symbols are generally grouped according to specific rules to form expressions and formulas. normally, expressions and formulas do not appear alone, but are included in sentences of the current language, where expressions play the role of noun phrases and formulas play the role of clauses. mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. it is based on rigorous definitions that provide a standard foundation for communication. an axiom or postulate is a mathematical statement that is taken to be true without need of proof. if a mathematical statement has yet to be proven ( or disproven ), it is termed a conjecture. through a series of rigorous arguments employing deductive reasoning, a statement that is proven to be true becomes a theorem. a specialized theorem that is mainly used to prove another theorem is called a lemma. a proven instance that forms part of a more general finding is termed a corollary. numerous technical terms used in mathematics are neologisms, such as polynomial and homeomorphism. other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. for example, in mathematics, " or " means " one, the other or both ", while, in common language, it is either ambiguous or means " one or the other but not both " ( in mathematics, the latter is called " exclusive or " ). finally, many mathematical terms are common words that
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https://en.wikipedia.org/wiki/Mathematics
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choquet capacities and integrals are central concepts in decision making under ambiguity or model uncertainty, pioneered by schmeidler. motivated by risk optimization problems for quantiles under ambiguity, we study the subclass of choquet integrals, called choquet quantiles, which generalizes the usual ( probabilistic ) quantiles, also known as value - at - risk in finance, from probabilities to capacities. choquet quantiles share many features with probabilistic quantiles, in terms of axiomatic representation, optimization formulas, and risk sharing. we characterize choquet quantiles via only one axiom, called ordinality. we prove that the inf - convolution of choquet quantiles is again a choquet quantile, leading to explicit optimal allocations in risk sharing problems for quantile agents under ambiguity. a new class of risk measures, choquet expected shortfall, is introduced, which enjoys most properties of the coherent risk measure expected shortfall. our theory is complemented by optimization algorithms, numerical examples, and a stylized illustration with financial data.
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arxiv:2412.19546
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hot carrier dynamics in a dispersionless plasmonic structures over a broad wavelength are studied by pump - probe measurements with 45 fs time resolution. the role of direct excited as well as plasmon generated hot carriers on low energy probe plasmons are studied by simultaneous measurement of differential transmittance and reflectance. while the pump fluence dependence on the decay times is linear for hot electrons and plasmon generated hot electrons, when pump is near resonant with the x - symmetry point, decay time varied as square of pump fluence. decay times of 800 nm degenerate pump - probe measurements highlight the difference in surface ( reflection ) and the bulk ( transmission ) mechanisms. decay time corresponding to the hot carrier relaxation is in the 1 - 3 ps range for different excitation energies. rise time, governed by the plasmon to hot carrier conversion and electron - electron scattering processes, is about 200 fs for the hot carrier and hot plasmon excitation cases which increased to about 485 fs for when pump is resonant with interband transition at x - symmetry point.
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arxiv:1905.01050
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the ( open - high - low - close ) ohlc data is the most common data form in the field of finance and the investigate object of various technical analysis. with increasing features of ohlc data being collected, the issue of extracting their useful information in a comprehensible way for visualization and easy interpretation must be resolved. the inherent constraints of ohlc data also pose a challenge for this issue. this paper proposes a novel approach to characterize the features of ohlc data in a dataset and then performs dimension reduction, which integrates the feature information extraction method and principal component analysis. we refer to it as the pseudo - pca method. specifically, we first propose a new way to represent the ohlc data, which will free the inherent constraints and provide convenience for further analysis. moreover, there is a one - to - one match between the original ohlc data and its feature - based representations, which means that the analysis of the feature - based data can be reversed to the original ohlc data. next, we develop the pseudo - pca procedure for ohlc data, which can effectively identify important information and perform dimension reduction. finally, the effectiveness and interpretability of the proposed method are investigated through finite simulations and the spot data of china ' s agricultural product market.
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arxiv:2103.16908
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we construct continuum models of 3d and 4d topological insulators by coupling spin - 1 / 2 fermions to an su ( 2 ) background gauge field, which is equivalent to a spatially dependent spin - orbit coupling. higher dimensional generalizations of flat landau levels are obtained in the landau - like gauge. the 2d helical dirac modes with opposite helicities and 3d weyl modes with opposite chiralities are spatially separated along the third and fourth dimensions, respectively. stable 2d helical fermi surfaces and 3d chiral fermi surfaces appear on open boundaries, respectively. the charge pumping in 4d landau level systems shows quantized 4d quantum hall effect.
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arxiv:1208.1562
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nanoscrolls consist of sheets rolled up into a papyrus - like form. their open ends produce great radial flexibility, which can be exploited for a large variety of applications, from actuators to hydrogen storage. they have been successfully synthesized from different materials, including carbon and boron nitride. in this work we have investigated, through fully atomistic molecular dynamics simulations, the dynamics of scroll formation for a series of graphene - like carbon nitride ( cn ) two - dimensional systems : g - cn, triazine - based ( g - c3n4 ), and heptazine - based ( g - c3n4 ). carbon nitride ( cn ) structures have been attracting great attention since their prediction as super hard materials. recently, graphene - like carbon nitride ( g - cn ) structures have been synthesized with distinct stoichiometry and morphologies. by combining these unique cn characteristics with the structural properties inherent to nanoscrolls new nanostructures with very attractive mechanical and electronic properties could be formed. our results show that stable nanoscrolls can be formed for all of cn structures we have investigated here. as the cn sheets have been already synthesized, these new scrolled structures are perfectly feasible and within our present - day technology.
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arxiv:1502.00260
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the presence of noise in quantum computers hinders their effective operation. even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. testing and benchmarking noisy, intermediate - scale quantum ( nisc ) computers is therefore of high importance. here, we suggest the application of the so - called quantum state matching protocol for testing purposes. this protocol was originally proposed to determine if an unknown quantum state falls in a prescribed neighborhood of a reference state. we decompose the unitary specific to the protocol and construct the quantum circuit implementing one step of the dynamics for different characteristic parameters of the scheme and present test results for two different ibm quantum computers. by comparing the experimentally obtained relative frequencies of success to the ideal success probability with a maximum statistical tolerance, we discriminate statistical errors from device specific ones. for the characterization of noise, we also use the fact that while the output of the ideal protocol is insensitive to the internal phase of the input state, the actual implementation may lead to deviations. for systematically varied inputs we find that the device with the smaller quantum volume performs better on our tests than the one with larger quantum volume, while for random inputs they show a more similar performance.
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arxiv:2210.09674
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we destroy a finite tree of size $ n $ by cutting its edges one after the other and in uniform random order. informally, the associated cut - tree describes the genealogy of the connected components created by this destruction process. we provide a general criterion for the convergence of the rescaled cut - tree in the gromov - prohorov topology to an interval endowed with the euclidean distance and a certain probability measure, when the underlying tree has a small height of order $ o ( \ sqrt { n } ) $. in particular, we consider uniform random recursive trees, binary search trees, scale - free random trees and a mixture of regular trees. this yields extensions of a result in bertoin for the cut - tree of uniform random recursive trees and also allows us to generalize some results of kuba and panholzer on the multiple isolation of vertices. the approach relies in the close relationship between the destruction process and bernoulli bond percolation, which may be useful for studying the cut - tree of other classes of trees.
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arxiv:1509.01141
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we design simple mechanisms to approximate the gains from trade ( gft ) in two - sided markets with multiple unit - supply sellers and multiple unit - demand buyers. a classical impossibility result by myerson and satterthwaite showed that even with only one seller and one buyer, no individually rational ( ir ), bayesian incentive compatible ( bic ) and budget - balanced ( bb ) mechanism can achieve full gft ( trade whenever buyer ' s value is higher than the seller ' s cost ). on the other hand, they proposed the " second - best " mechanism that maximizes the gft subject to ir, bic and bb constraints, which is unfortunately rather complex for even the single - seller single - buyer case. our mechanism is simple, ir, bic and bb, and achieves $ \ frac { 1 } { 2 } $ of the optimal gft among all ir, bic and bb mechanisms. our result holds for arbitrary distributions of the buyers ' and sellers ' values and can accommodate any downward - closed feasibility constraints over the allocations. the analysis of our mechanism is facilitated by extending the cai - weinberg - devanur duality framework to two - sided markets.
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arxiv:1706.04637
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an analog of nadel ' s effective bound for the continuous scott rank of metric structures, developed by ben yaacov, doucha, nies, and tsankov, will be established : let $ \ mathscr { l } $ be a language of continuous logic with code $ \ hat { \ mathscr { l } } $. let $ \ omega $ be a weak modulus of uniform continuity with code $ \ hat { \ omega } $. let $ \ mathcal { d } $ be a countable $ \ mathscr { l } $ - pre - structure. let $ \ bar { \ mathcal { d } } $ denote the completion structure of $ \ mathcal { d } $. then $ \ mathrm { sr } _ \ omega ( \ bar { d } ) \ leq \ omega _ 1 ^ { \ hat { \ mathscr { l } } \ oplus \ hat { \ omega } \ oplus \ mathcal { d } } $, the church - kleene ordinal relative to $ \ hat { \ mathscr { l } } \ oplus \ hat { \ omega } \ oplus \ mathcal { d } $.
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arxiv:1908.00179
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we present an approach for the calculation of the $ \ mathbb { z } _ 2 $ topological invariant in non - crystalline two - dimensional quantum spin hall insulators. while topological invariants were originally mathematically introduced for crystalline periodic systems, and crucially hinge on tracking the evolution of occupied states through the brillouin zone, the introduction of disorder or dynamical effects can break the translational symmetry and imply the use of larger simulation cells, where the $ \ bf { k } $ - point sampling is typically reduced to the single $ \ gamma $ - point. here, we introduce a single - point formula for the spin chern number that enables to adopt the supercell framework, where a single hamiltonian diagonalisation is performed. inspired by the work of e. prodan [ phys. rev. b, $ \ textbf { 80 } $, 12 ( 2009 ) ], our single - point approach allows to calculate the spin chern number even when the spin operator $ \ hat { s } _ z $ does not commute with the hamiltonian, as in the presence of rashba spin - orbit coupling. we validate our method on the kane - mele model, both pristine and in the presence of anderson disorder. finally, we investigate the disorder - driven transition from the trivial phase to the topological state known as topological anderson insulator. beyond disordered systems, our approach is particularly useful to investigate the role of defects, to study topological alloys and in the context of ab - initio molecular dynamics simulations at finite temperature.
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arxiv:2301.02612
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motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a vietoris polynomial one - intuitively, the topological analogue of a kripke polynomial functor. among other results, we prove that every vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness. when the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete. as a practical application, we use these developments in the specification and analysis of non - deterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.
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arxiv:1612.03318
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in this paper, we propose a novel method for video moment retrieval ( vmr ) that achieves state of the arts ( sota ) performance on r @ 1 metrics and surpassing the sota on the high iou metric ( r @ 1, iou = 0. 7 ). first, we propose to use a multi - head self - attention mechanism, and further a cross - attention scheme to capture video / query interaction and long - range query dependencies from video context. the attention - based methods can develop frame - to - query interaction and query - to - frame interaction at arbitrary positions and the multi - head setting ensures the sufficient understanding of complicated dependencies. our model has a simple architecture, which enables faster training and inference while maintaining. second, we also propose to use multiple task training objective consists of moment segmentation task, start / end distribution prediction and start / end location regression task. we have verified that start / end prediction are noisy due to annotator disagreement and joint training with moment segmentation task can provide richer information since frames inside the target clip are also utilized as positive training examples. third, we propose to use an early fusion approach, which achieves better performance at the cost of inference time. however, the inference time will not be a problem for our model since our model has a simple architecture which enables efficient training and inference.
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arxiv:2009.02406
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we consider a non compact, complete manifold { \ bf { m } } of finite area with cuspidal ends. the generic cusp is isomorphic to $ { \ bf { x } } \ times ] 1, + \ infty [ $ with metric $ ds ^ 2 = ( h + dy ^ 2 ) / y ^ { 2 \ delta }. $ { \ bf { x } } is a compact manifold with nonzero first betti number equipped with the metric $ h. $ for a one - form $ a $ on { \ bf { m } } such that in each cusp $ a $ is a non exact one - form on the boundary at infinity, we prove that the magnetic laplacian $ - \ delta _ a = ( id + a ) ^ \ star ( id + a ) $ satisfies the weyl asymptotic formula with sharp remainder. we deduce an upper bound for the counting function of the embedded eigenvalues of the laplace - beltrami operator $ - \ delta = - \ delta _ 0. $
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arxiv:1109.1995
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city models and height maps of urban areas serve as a valuable data source for numerous applications, such as disaster management or city planning. while this information is not globally available, it can be substituted by digital surface models ( dsms ), automatically produced from inexpensive satellite imagery. however, stereo dsms often suffer from noise and blur. furthermore, they are heavily distorted by vegetation, which is of lesser relevance for most applications. such basic models can be filtered by convolutional neural networks ( cnns ), trained on labels derived from digital elevation models ( dems ) and 3d city models, in order to obtain a refined dsm. we propose a modular multi - task learning concept that consolidates existing approaches into a generalized framework. our encoder - decoder models with shared encoders and multiple task - specific decoders leverage roof type classification as a secondary task and multiple objectives including a conditional adversarial term. the contributing single - objective losses are automatically weighted in the final multi - task loss function based on learned uncertainty estimates. we evaluated the performance of specific instances of this family of network architectures. our method consistently outperforms the state of the art on common data, both quantitatively and qualitatively, and generalizes well to a new dataset of an independent study area.
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arxiv:2004.02493
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the pythagorean school attributed consonance in music to simplicity of frequency ratios between musical tones. in the last two centuries, the consonance curves developed by helmholtz, plompt and levelt shifted focus to psycho - acoustic considerations in perceiving consonances. the appearance of peaks of these curves at the ratios considered by the pythagorean school, and which were a consequence of an attempt to understand the world by nice mathematical proportions, remained a curiosity. this paper addresses this curiosity, by describing a mathematical model of musical sound, along with a mathematical definition of consonance. first, we define pure, complex and mixed tones as mathematical models of musical sound. by a sequence of numerical experiments and analytic calculations, we show that continuous cosine similarity, abbreviated as cosim, applied to these models quantifies the elusive concept of consonance as a frequency ratio which gives a local maximum of the cosim function. we prove that these maxima occur at the ratios considered as consonant in classical music theory. moreover, we provide a simple explanation why the number of musical intervals considered as consonant by musicians is finite, but has been increasing over the centuries. specifically, our formulas show that the number of consonant intervals changes with the depth of the tone ( the number of harmonics present ).
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arxiv:2503.07632
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two groups of astronomers used the large telescopes keck and vlt for decades to observe trajectories of bright stars near the galactic centre. based on results of their observations the astronomers concluded that trajectories of the stars are roughly elliptical and foci of the orbits are approximately coincide with the galactic centre position. in a last few years a self - gravitating dark matter core - - halo distribution was suggested by ruffini, arguelles, rueda ( rar ) and this model was actively used in consequent studies. in particular, recently it has been claimed that the rar - model provides a better fit of trajectories of bright stars in comparison to the conventional model with a supermassive black hole. the dark matter distribution with a dense core having a constant density as it was suggested in the rar - model leaves trajectories of stars elliptical like in kepler ' s two - body problem. however, in this case not the foci of the ellipses coincide with the galactic center but their centers while the orbital periods do not depend on semi - major axes. these properties are not consistent with the observational data for trajectories of bright stars.
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arxiv:2108.09709
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the ultraviolet / optical telescope ( uvot ) is one of three instruments onboard the swift observatory. the photometric calibration has been published, and this paper follows up with details on other aspects of the calibration including a measurement of the point spread function with an assessment of the orbital variation and the effect on photometry. a correction for large scale variations in sensitivity over the field of view is described, as well as a model of the coincidence loss which is used to assess the coincidence correction in extended regions. we have provided a correction for the detector distortion and measured the resulting internal astrometric accuracy of the uvot, also giving the absolute accuracy with respect to the international celestial reference system. we have compiled statistics on the background count rates, and discuss the sources of the background, including instrumental scattered light. in each case we describe any impact on uvot measurements, whether any correction is applied in the standard pipeline data processing or whether further steps are recommended.
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arxiv:1004.2448
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we propose a method for the generation of trains of alternating bright solitons in two - component bose - einstein condensates, using controlled emission of nonlinear matter - waves in the uncoupled regime with spatially - varying intra - species interaction and out - of - phase oscillations of the ground states in the trap. under this scheme, solitons are sequentially launched from the different components, and interact with each other through phase - independent cross - coupling. we obtain an analytical estimation of the critical condition for soliton emission using a geometric guiding model, in analogy with integrated optical systems. in addition, we show how strong initial perturbations in the system can trigger the spontaneous generation of supersolitons, i. e. localized phonon - like excitations of the soliton trains. finally, we demonstrate the controllable generation of slow and fast supersolitons by adding external localized potentials in the nonlinear region.
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arxiv:1307.4314
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temporal action proposal generation plays an important role in video action understanding, which requires localizing high - quality action content precisely. however, generating temporal proposals with both precise boundaries and high - quality action content is extremely challenging. to address this issue, we propose a novel boundary content graph neural network ( bc - gnn ) to model the insightful relations between the boundary and action content of temporal proposals by the graph neural networks. in bc - gnn, the boundaries and content of temporal proposals are taken as the nodes and edges of the graph neural network, respectively, where they are spontaneously linked. then a novel graph computation operation is proposed to update features of edges and nodes. after that, one updated edge and two nodes it connects are used to predict boundary probabilities and content confidence score, which will be combined to generate a final high - quality proposal. experiments are conducted on two mainstream datasets : activitynet - 1. 3 and thumos14. without the bells and whistles, bc - gnn outperforms previous state - of - the - art methods in both temporal action proposal and temporal action detection tasks.
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arxiv:2008.01432
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few - shot classifiers excel under limited training samples, making them useful in applications with sparsely user - provided labels. their unique relative prediction setup offers opportunities for novel attacks, such as targeting support sets required to categorise unseen test samples, which are not available in other machine learning setups. in this work, we propose a detection strategy to identify adversarial support sets, aimed at destroying the understanding of a few - shot classifier for a certain class. we achieve this by introducing the concept of self - similarity of a support set and by employing filtering of supports. our method is attack - agnostic, and we are the first to explore adversarial detection for support sets of few - shot classifiers to the best of our knowledge. our evaluation of the miniimagenet ( mi ) and cub datasets exhibits good attack detection performance despite conceptual simplicity, showing high auroc scores. we show that self - similarity and filtering for adversarial detection can be paired with other filtering functions, constituting a generalisable concept.
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arxiv:2012.06330
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we demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken - symmetry order parameter ( nematic, smectic, crystalline, etc. ) are coupled to shear rate. our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. we use the ( generalized ) doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non - local effects are included.
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arxiv:cond-mat/9705181
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we derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. this likelihood is necessary for bayesian - inference methods. if we neglect all stochastic terms apart from the ones appearing in the auto two - point function of tracers, we recover the result of schmidt et al., 2018. we then rigorously derive the corrections to this result, such as those coming from a non - gaussian stochasticity ( which include the stochastic corrections to the tracer bispectrum ) and higher - derivative terms. we discuss how these corrections can affect current applications of bayesian inference. we comment on possible extensions to our result, with a particular eye towards primordial non - gaussianity. this work puts on solid theoretical grounds the eft - based approach to bayesian forward modeling.
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arxiv:1909.04022
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the finite - dimensional symmetric algebras over an algebraically closed field, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. in particular, the weighted surface algebras and their deformations were introduced and studied in [ 16 ] - [ 20 ], and it was shown that all these algebras, except few singular cases, are symmetric tame periodic algebras of period $ 4 $. in this article, using the general form of a weighted surface algebra from [ 19 ], we introduce and study so called virtual mutations of weighted surface algebras, which constitute a new large class of symmetric tame periodic algebras of period $ 4 $. we prove that all these algebras are derived equivalent but not isomorphic to weighted surface algebras. we associate such algebras to any triangulated surface, first taking blow - ups of a family of edges to $ 2 $ - triangle discs, and then virtual mutations of their weighted surface algebras. the results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.
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arxiv:2006.13075
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using inelastic x - ray scattering we studied the collective dynamics of the glassy alloy ni $ _ { 33 } $ zr $ _ { 67 } $ in the first pseudo brillouin zone, an energy - momentum region still unexplored in metallic glasses. we determine key properties such as the momentum transfer dependence of the sound velocity and of the acoustic damping, discussing the results in the general context of recently proposed pictures for acoustic dynamics in glasses. specifically, we demonstrate the existence in this strong glass of well defined ( in the ioffe regel sense ) acoustic - like excitations well above the boson peak energy.
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arxiv:cond-mat/0603251
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we propose using the frequency - domain bootstrap ( fdb ) to estimate errors of modeling parameters when the modeling error is itself a major source of uncertainty. unlike the usual bootstrap or the simple $ \ chi ^ 2 $ analysis, the fdb can take into account correlations between errors. it is also very fast compared to the the gaussian process bayesian estimate as often implemented for computer model calibration. the method is illustrated drop model of nuclear binding energies. we find that the fdb gives a more conservative estimate of the uncertainty in liquid drop parameters in better accord with more empirical estimates. for the nuclear physics application, there no apparent obstacle to apply the method to the more accurate and detailed models based on density - functional theory.
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arxiv:1703.08844
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we prove a regularity result for lagrangian flows of sobolev vector fields over rcd ( k, n ) metric measure spaces, regularity is understood with respect to a newly defined quasi - metric built from the green function of the laplacian. its main application is that rcd ( k, n ) spaces have constant dimension. in this way we generalize to such abstract framework a result proved by colding - naber for ricci limit spaces, introducing ingredients that are new even in the smooth setting.
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arxiv:1804.07128
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we introduce and solve a model of fermions hopping between neighbouring sites on a line with random brownian amplitudes and open boundary conditions driving the system out of equilibrium. the average dynamics reduces to that of the symmetric simple exclusion process. however, the full distribution encodes for a richer behaviour entailing fluctuating quantum coherences which survive in the steady limit. we determine exactly the system state steady distribution. we show that these out of equilibrium quantum fluctuations fulfil a large deviation principle and we present a method to recursively compute exactly the large deviation function. on the way, our approach gives a solution of the classical symmetric simple exclusion process using fermion technology. our results open the route towards the extension of the macroscopic fluctuation theory to many body quantum systems.
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arxiv:1904.01406
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the study of ir evaluation metrics through axiomatic analysis enables a better understanding of their numerical properties. some works have modelled the effectiveness of retrieval metrics with axioms that capture desirable properties on the set of rankings of documents. this paper formally explores the effect of these ranking axioms on the numerical values of some ir evaluation metrics. it focuses on the set of ranked lists of documents with multigrade relevance. the possible orderings in this set are derived from three commonly accepted ranking axioms on retrieval metrics ; then, they are classified by their latticial properties. when relevant documents are prioritised, a subset of document rankings are identified : the join - irreducible elements, which have some resemblance to the concept of basis in vector space. it is possible to compute the precision, recall, rbp or dcg values of any ranking from their values in the join - irreducible elements. however this is not the case when the swapping of documents is considered.
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arxiv:2207.01201
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the strong and electromagnetic decays of $ x ( 4350 ) $ with quantum numbers $ j ^ p = 0 ^ { + + } $ and $ 2 ^ { + + } $ have been studied by using the effective lagrangian approach. the coupling constant between $ x ( 4350 ) $ and $ d _ s ^ { \ ast } d _ { s0 } ^ { \ ast } $ is determined with the help of the compositeness condition which means that $ x ( 4350 ) $ is a bound state of $ d _ s ^ { \ ast } d _ { s0 } ^ { \ ast } $. other coupling constants applied in the calculation are determined phenomenologically. our numerical results show that, using the present data within the present model, the possibility that $ x ( 4350 ) $ is a $ d _ s ^ { \ ast } d _ { s0 } ^ { \ ast } $ molecule can not be ruled out.
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arxiv:1006.1276
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we present a comprehensive study and evaluation of existing single image deraining algorithms, using a new large - scale benchmark consisting of both synthetic and real - world rainy images. this dataset highlights diverse data sources and image contents, and is divided into three subsets ( rain streak, rain drop, rain and mist ), each serving different training or evaluation purposes. we further provide a rich variety of criteria for dehazing algorithm evaluation, ranging from full - reference metrics, to no - reference metrics, to subjective evaluation and the novel task - driven evaluation. experiments on the dataset shed light on the comparisons and limitations of state - of - the - art deraining algorithms, and suggest promising future directions.
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arxiv:1903.08558
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in this paper, directional sequence entropy and directional kronecker algebra for $ \ mathbb { z } ^ q $ - systems are introduced. the relation between sequence entropy and directional sequence entropy are established. meanwhile, direcitonal discrete spectrum systems and directional null systems are defined. it is shown that a $ \ mathbb { z } ^ q $ - system has directional discrete spectrum if and only if it is directional null. moreover, it turns out that a $ \ mathbb { z } ^ q $ - system has directional discrete spectrum along $ q $ linearly independent directions if and only if it has discrete spectrum.
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arxiv:2105.03130
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in this note we describe how to complement the neutrino evolution matrix calculated at a given energy and trajectory with additional information which allows to reliably extrapolate it to nearby energies or trajectories without repeating the full computation. our method works for arbitrary matter density profiles, can be applied to any propagation model described by an hamiltonian, and exactly guarantees the unitarity of the evolution matrix. as a straightforward application, we show how to enhance the calculation of the theoretical predictions for experimentally measured quantities, so that they remain accurate even in the presence of fast neutrino oscillations. furthermore, the ability to " move around " a given energy and trajectory opens the door to precise interpolation of the oscillation amplitudes within a grid of tabulated values, with potential benefits for the computation speed of monte - carlo codes. we also provide a set of examples to illustrate the most prominent features of our approach.
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arxiv:2308.00037
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density - functional calculations of the phonon spectrum and electron - phonon coupling in mgb $ _ 2 $ are presented. the $ e _ { 2g } $ phonons, which involve in - plane b displacements, couple strongly to the $ p _ { x, y } $ electronic bands. the isotropic electron - phonon coupling constant is calculated to be about 0. 8. allowing for different order parameters in different bands, the superconducting $ \ lambda $ in the clean limit is calculated to be significantly larger. the $ e _ { 2g } $ phonons are strongly anharmonic, and the non - linear contribution to the coupling between the $ e _ { 2g } $ modes and the p $ _ { x, y } $ bands is significant.
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arxiv:cond-mat/0103570
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we show that k \ " uchle fivefolds of type ( c5 ) - - - subvarieties of the grassmannian gr ( 3, 7 ) parameterizing 3 - subspaces that are isotropic for a given 2 - form and are annihilated by a given 4 - form - - - are birational to hyperplane sections of the lagrangian grassmannian lgr ( 3, 6 ) and describe in detail these birational transformations. as an application, we show that the integral chow motive of a k \ " uchle fivefold of type ( c5 ) is of lefschetz type. we also discuss k \ " uchle fourfolds of type ( c5 ) - - - hyperplane sections of the corresponding k \ " uchle fivefolds - - - an interesting class of fano fourfolds, which is expected to be similar to the class of cubic fourfolds in many aspects.
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arxiv:1603.03161
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we investigate how recent updates to neutrino oscillation parameters and the sum of neutrino masses influence the sensitivity of neutrinoless double - beta ( 0 $ \ nu \ beta \ beta $ ) decay experiments. incorporating the latest cosmological constraints on the sum of neutrino masses and laboratory measurements on oscillations, we determine the sum of neutrino masses for both the normal hierarchy ( nh ) and the inverted hierarchy ( ih ). our analysis reveals a narrow range for the sum of neutrino masses, approximately 0. 06 ev / c $ ^ 2 $ for nh and 0. 102 ev / c $ ^ 2 $ for ih. utilizing these constraints, we calculate the effective majorana masses for both nh and ih scenarios, establishing the corresponding allowed regions. importantly, we find that the minimum neutrino mass is non - zero, as constrained by the current oscillation parameters. additionally, we estimate the half - life of 0 $ \ nu \ beta \ beta $ decay using these effective majorana masses for both nh and ih. our results suggest that upcoming ton - scale experiments will comprehensively explore the ih scenario, while 100 - ton - scale experiments will effectively probe the parameter space for the nh scenario, provided the background index can achieve 1 event / kton - year in the region of interest.
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arxiv:2404.19624
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we present a spectroscopically confirmed sample of lyman alpha emitting galaxies ( laes ) at z ~ 4. 5 in the extended chandra deep field south ( ecdfs ), which we combine with a sample of z ~ 4. 5 laes from the large area lyman alpha ( lala ) survey to build a unified lya luminosity function ( lf ). we spectroscopically observed 64 candidate laes in the ecdfs, confirming 46 objects as z ~ 4. 5 laes. we did not detect significant flux from neither c _ iv 1549 \ aa \ nor the he _ ii 1640 \ aa \ emission in individual lae spectra, even with a coadded spectrum. with the coadded line ratio of he _ ii to lya constraining the population iii star formation rate ( sfr ) to be < 0. 3 % of the total sfr, and < 1. 25 % of the observed sfr ( both at the 2 - $ \ sigma $ level ). only one lae was detected in both the x - ray and radio, while the other objects remained undetected, even when stacked. the lya lf in our two deepest narrowband filters in the ecdfs differ at > 2 $ \ sigma $ significance, and the product $ l ^ * \ phi ^ * $ differs by a factor of > 3. similar lf differences have been used to infer evolution in the neutral gas fraction in the intergalactic medium at z > 6, yet here the difference is likely due to cosmic variance, given that the two samples are from adjoining line - of - sight volumes. combining our new sample of laes with those from previous lala narrowband surveys at z = 4. 5, we obtain one of the best measured lya lfs to date of l * = 42. 83 $ \ pm $ 0. 06 and $ \ phi ^ * $ = - 3. 48 $ \ pm $ 0. 09. we compare our new lf to others from the literature to study the evolution of the lya luminosity density at 0 < z < 7. we find tentative evidence for evolution in the product $ l ^ * \ phi ^ * $, which approximately tracks the cosmic sfr density, but since field - to - field and survey - to - survey variations are in some cases as large as the possible evolution, some caution is needed in interpreting this trend.
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arxiv:1111.3386
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we tensorize the faber spline system from [ 14 ] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. the respective basis coefficients are local linear combinations of discrete function values similar as for the classical faber schauder system. this allows for a sparse representation of the function using a truncated series expansion by only storing discrete ( finite ) set of function values. the set of nodes where the function values are taken depends on the respective function in a non - linear way. indeed, if we choose the basis functions adaptively it requires significantly less function values to represent the initial function up to accuracy $ \ varepsilon > 0 $ ( say in $ l _ \ infty $ ) compared to hyperbolic cross projections. in addition, due to the higher regularity of the faber splines we overcome the ( mixed ) smoothness restriction $ r < 2 $ and benefit from higher mixed regularity of the function. as a byproduct we present the solution of problem 3. 13 in the triebel monograph [ 46 ] for the multivariate setting.
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arxiv:2004.03556
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in many real - world prediction tasks, class labels include information about the relative ordering between labels, which is not captured by commonly - used loss functions such as multi - category cross - entropy. recently, the deep learning community adopted ordinal regression frameworks to take such ordering information into account. neural networks were equipped with ordinal regression capabilities by transforming ordinal targets into binary classification subtasks. however, this method suffers from inconsistencies among the different binary classifiers. to resolve these inconsistencies, we propose the consistent rank logits ( coral ) framework with strong theoretical guarantees for rank - monotonicity and consistent confidence scores. moreover, the proposed method is architecture - agnostic and can extend arbitrary state - of - the - art deep neural network classifiers for ordinal regression tasks. the empirical evaluation of the proposed rank - consistent method on a range of face - image datasets for age prediction shows a substantial reduction of the prediction error compared to the reference ordinal regression network.
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arxiv:1901.07884
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let $ g $ be a simple graph of order $ n $. the domination polynomial of $ g $ is the polynomial $ d ( g, \ lambda ) = \ sum _ { i = 0 } ^ { n } d ( g, i ) \ lambda ^ { i } $, where $ d ( g, i ) $ is the number of dominating sets of $ g $ of size $ i $. we consider the lexicographic product of two specific graphs and study their domination polynomials.
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arxiv:1511.08086
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the cartan - maurer equations for any $ q $ - group of the $ a _ { n - 1 }, b _ n, c _ n, d _ n $ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $ q = 1 $ case. these equations, defining the field strengths, are essential in the construction of $ q $ - deformed gauge theories. an explicit expression $ \ om ^ i \ we \ om ^ j = - \ z { ij } { kl } \ om ^ k \ we \ om ^ l $ for the $ q $ - commutations of left - invariant one - forms is found, with $ \ z { ij } { kl } \ om ^ k \ we \ om ^ l \ qonelim \ om ^ j \ we \ om ^ i $.
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arxiv:hep-th/9304161
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situation recognition refers to the ability of an agent to identify and understand various situations or contexts based on available information and sensory inputs. it involves the cognitive process of interpreting data from the environment to determine what is happening, what factors are involved, and what actions caused those situations. this interpretation of situations is formulated as a semantic role labeling problem in computer vision - based situation recognition. situations depicted in images and videos hold pivotal information, essential for various applications like image and video captioning, multimedia retrieval, autonomous systems and event monitoring. however, existing methods often struggle with ambiguity and lack of context in generating meaningful and accurate predictions. leveraging multimodal models such as clip, we propose clipsitu, which sidesteps the need for full fine - tuning and achieves state - of - the - art results in situation recognition and localization tasks. clipsitu harnesses clip - based image, verb, and role embeddings to predict nouns fulfilling all the roles associated with a verb, providing a comprehensive understanding of depicted scenarios. through a cross - attention transformer, clipsitu xtf enhances the connection between semantic role queries and visual token representations, leading to superior performance in situation recognition. we also propose a verb - wise role prediction model with near - perfect accuracy to create an end - to - end framework for producing situational summaries for out - of - domain images. we show that situational summaries empower our clipsitu models to produce structured descriptions with reduced ambiguity compared to generic captions. finally, we extend clipsitu to video situation recognition to showcase its versatility and produce comparable performance to state - of - the - art methods.
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arxiv:2407.20642
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the d0 experiment is facing many exciting challenges providing a computing environment for its worldwide collaboration. transparent access to data for processing and analysis has been enabled through deployment of its sam system to collaborating sites and additional functionality will be provided soon with samgrid components. in order to maximize access to global storage, computational and intellectual resources, and to enable the system to scale to the large demands soon to be realized, several strategic sites have been identified as regional analysis centers ( rac ' s ). these sites play an expanded role within the system. the philosophy and function of these centers is discussed and details of their composition and operation are outlined. the plan for future additional centers is also addressed.
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arxiv:cs/0306115
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we present an approach for improving spatial frequency sampling in active incoherent millimeter - wave ( aim ) imaging systems using frequency diversity. aim imaging relies on active transmission of spatio - temporally incoherent signals to illuminate a scene, from which interferometric fourier - domain imaging can be implemented using a sparse receiving antenna array. one of the benefits of fourier domain imaging is the sparsity of the receiving array, which can form images with equivalent resolution to traditional filled beamsteering arrays, but with a small fraction of the elements. the hardware reduction afforded by the sparse array often leads to an undersampled fourier space, where even though image formation is possible, the image reconstruction may be degraded when viewing complex objects. to address this challenge without requiring additional receiver channels, we explore the use of frequency diversity in the illuminating and receiving systems. fourier domain spatial frequency samples are determined by the electrical spacing and rotation of the receiving elements, thus by changing the frequency the sampled spatial frequencies also change. we implement an additive technique where the spatial frequency samples are summed prior to fourier transform image formation. importantly, because the system is active, a consistent signal - to - noise ratio is maintained across all frequencies, which may not be possible in traditional passive fourier - domain imagers.
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arxiv:2503.08556
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low - latency applications like ar / vr and online gaming need fast, stable connections. new technologies such as v2x, leo satellites, and 6g bring unique challenges in mobility management. traditional solutions based on centralized or distributed anchors often fall short in supporting rapid mobility due to inefficient routing, low versatility, and insufficient multi - access support. in this paper, we design a new end - to - end system for tracking multi - connected mobile devices at scale and optimizing performance for latency - sensitive, highly dynamic applications. our system, based on the locator / id separation principle, extends to multi - access networks without requiring specialized routers or caching. using a novel tree embedding - based overlay, we enable fast session setup while allowing endpoints to directly handle mobility between them. evaluation with real network data shows our solution cuts connection latency to 7. 42 % inflation over the shortest path, compared to lisp ' s 359 \ % due to cache misses. it also significantly reduces location update overhead and disruption time during mobility.
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arxiv:2504.20246
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a utility - function approach to optimal spatial sampling design is a powerful way to quantify what " optimality " means. the emphasis then should be to capture all possible contributions to utility, including scientific impact and the cost of sampling. the resulting sampling plan should contain a component of designed randomness that would allow for a non - parametric design - based analysis if model - based assumptions were in doubt. [ arxiv : 1509. 03410 ]
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arxiv:1509.04819
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the support vector machine ( svm ) and minimum euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high - dimensional data through a phenomenon of support vector proliferation, where every training example used to fit an svm becomes a support vector. in this paper, we explore the generality of this phenomenon and make the following contributions. first, we prove a super - linear lower bound on the dimension ( in terms of sample size ) required for support vector proliferation in independent feature models, matching the upper bounds from previous works. we further identify a sharp phase transition in gaussian feature models, bound the width of this transition, and give experimental support for its universality. finally, we hypothesize that this phase transition occurs only in much higher - dimensional settings in the $ \ ell _ 1 $ variant of the svm, and we present a new geometric characterization of the problem that may elucidate this phenomenon for the general $ \ ell _ p $ case.
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arxiv:2105.14084
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we show an optical wave - mixing scheme that generates quantum light by means of a single three - level atom. the atom couples to an optical cavity and two laser fields that together drive a cycling current within the atom. weak driving in combination with strong atom - cavity coupling induces transitions between the dark states of the system, accompanied by single - photon emission and suppression of atomic excitation by quantum interference. for strong driving, the system can generate coherent or schr \ " odinger cat - like fields with frequencies distinct from those of the applied lasers.
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arxiv:1906.11449
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we propose a polarised intensity interferometry experiment, which measures the nonlocal pancharatnam phase acquired by a pair of hanbury brown - twiss photons. the setup involves two polarised thermal sources illuminating two polarised detectors. varying the relative polarisation angle of the detectors introduces a two photon geometric phase. local measurements at either detector do not reveal the effects of the phase, which is an optical analog of the multiparticle aharonov - bohm effect. the geometric phase sheds light on the three slit experiment and suggests ways of tuning entanglement.
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arxiv:1002.1547
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we report a model study of the phonon response on the interplay of the superconducting ( sc ) gap and both static and dynamic jahn - teller distortion and predict the appearance of the sc and jahn - teller ( jt ) distortion gap excitation peaks in the raman spectra of high - tc superconductors. the model consists of the hamiltonian containing static jt interaction and s - wave type sc interaction in the conduction band. further the phonons are coupled to the density of the conduction electron in the band as well as to the jt split conduction band giving rise to dynamic jahn - teller ( djt ) interaction. the phonons are considered in a harmonic approximation. the phonon green ' s function is calculated by zubarev ' s technique and the phonon self - energy arising due to normal electron - phonon ( ep ) interaction and djt interaction. the phonon self - energy arising due to this is calculated from the electron response density function in the coexistence phase of the two order parameters. the phonon spectral density predicts two excitation peaks, one due to sc gap and the other due to jt distortion. the djt coupling suppresses the jt gap while it enhances sc gap as well as sc transition temperature. the evolution of these excitation peaks are investigated by varying different model parameters of the system.
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arxiv:1302.3185
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three - dimensional object detection from a single view is a challenging task which, if performed with good accuracy, is an important enabler of low - cost mobile robot perception. previous approaches to this problem suffer either from an overly complex inference engine or from an insufficient detection accuracy. to deal with these issues, we present ss3d, a single - stage monocular 3d object detector. the framework consists of ( i ) a cnn, which outputs a redundant representation of each relevant object in the image with corresponding uncertainty estimates, and ( ii ) a 3d bounding box optimizer. we show how modeling heteroscedastic uncertainty improves performance upon our baseline, and furthermore, how back - propagation can be done through the optimizer in order to train the pipeline end - to - end for additional accuracy. our method achieves sota accuracy on monocular 3d object detection, while running at 20 fps in a straightforward implementation. we argue that the ss3d architecture provides a solid framework upon which high performing detection systems can be built, with autonomous driving being the main application in mind.
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arxiv:1906.08070
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this statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions : eigenvalues of random matrices, non - crossing random walks and trapped fermions. these systems share many links, which can be exhibited not only at the level of their static version, but also at the level of their dynamical version. we present a combined analysis of these systems, employing tools of random matrix theory and stochastic calculus as well as tools of quantum mechanics, in order to solve some original problems. further from the detailed presentation of the field and the report of the results obtained during the phd, the different themes exposed in the chapters of the thesis allow for perspectives on related issues. as such, the first chapter is an introduction to random matrix theory ; we detail its historical evolution and numerous applications, and present its essential concepts, constructions and results. the second chapter discusses non - crossing random walks ; we describe the deep links they share with random matrix eigenvalue processes and showcase the results obtained in the scope of boundary problems. in the third chapter, which focuses on stochastic matrix processes, we introduce in particular a process inspired from the kesten random recursion, and highlight the new link it allows to draw between the inverse - wishart ensemble and fermions trapped in the morse potential. lastly, the fourth chapter, centred on the particular case of bridge processes, allows for a joint treatment of scalar and matrix models ; therein, we develop a generalization of the ferrari - spohn problem for non - crossing scalar bridges and, as an opening, we exhibit the connections of matrix bridges with other aspects of random matrices.
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arxiv:2111.05737
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we develop the protocol for structural restoring of multi - quantum coherence matrices of the multi - qubit quantum state transferred from the sender to the receiver along a spin - 1 / 2 chain. we also propose a protocol for constructing such 0 - order coherence matrix that can be perfectly transferred in this process. the restoring protocol is based on the specially constructed unitary transformation of the extended receiver. { this transformation for a given length parameters of the chain is universally optimal in the sense that ones constructed it can be applied to optimally restore any higher - order coherence matrices.
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arxiv:2104.13762
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this paper is a short review on the foundations and recent advances in the microscopic fermi - liquid ( fl ) theory. we demonstrate that this theory is built on five identities, which follow from conservation of total charge ( particle number ), spin, and momentum in a translationally and $ su ( 2 ) $ - invariant fl. these identities allows one to express the effective mass and quasiparticle residue in terms of an exact vertex function and also impose constraints on the " quasiparticle " and " incoherent " ( or " low - energ " and " high - energy " ) contributions to the observable quantities. such constraints forbid certain pomeranchuk instabilities of a fl, e. g., towards phases with order parameters that coincide with charge and spin currents. we provide diagrammatic derivations of these constraints and of the general ( leggett ) formula for the susceptibility in arbitrary angular momentum channel, and illustrate the general relations through simple examples treated in the perturbation theory.
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arxiv:1805.05562
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a previously tested differential equation method for generating low temperature series expansion for diagonal spin - spin correlation functions in the d = 2 ising model is extended to generate the non - universal terms for arbitrary separation of the spins. this extends the earlier calculations of these correlation functions.
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arxiv:cond-mat/0505166
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the t - j model in the spinless - fermion representation is studied. an effective hamiltonian for the quasiparticles is derived using canonical transformation approach. it is shown that the rather simple form of the transformation generator allows to take into account effect of hole interaction with the short - range spin waves and to describe the single - hole groundstate. obtained results are very close to ones of the self - consistent born approximation. further accounting for the long - range spin - wave interaction is possible on the perturbative basis. both spin - wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle interaction. two - hole bound state problem is solved using bethe - salpeter equation. the only d - wave bound state is found to exist in the region of 1 < ( t / j ) < 5. combined effect of the pairing interactions of both types is important to its formation. discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.
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arxiv:cond-mat/9611001
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the elastic and inelastic high - - energy small - - angle electron - - positron scattering is considered. all radiative corrections to the cross - - section with the relative accuracy $ \ delta \ sigma / \ sigma = 0. 1 \ % $ are explicitly taken into account. according to the generalized eikonal representation for the elastic amplitude, in higher orders only diagrams with one exchanged photon may be considered. single photon emission with radiative corrections and next - - to - - leading two - - photon and pair production diagrams are evaluated, together with leading three - - loop corrections. all contributions have been calculated analytically. we integrate the calculated distributions over typical for lep ~ 1 experiments intervals of angles and energies. to the leading approximation, the results are shown to be described in terms of kernels of electron structure functions. some numerical results are presented. pacs numbers 12. 15. lk, 12. 20. - - m, 12. 20. ds, 13. 40. - - f
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arxiv:hep-ph/9512344
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) } $ similarly to the $ \ mathsf { ust } ( k _ n ) $ case. for $ \ beta _ n = n ^ { \ alpha } $ with $ 1 < \ alpha < 4 / 3 $, the behavior of the typical diameter is a more delicate open question, but we conjecture that its exponent strictly between 1 / 2 and 1 / 3.
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arxiv:2410.18269
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early and accurate detection of parkinson ' s disease ( pd ) is a crucial diagnostic challenge carrying immense clinical significance, for effective treatment regimens and patient management. for instance, a group of subjects termed swedd who are clinically diagnosed as pd, but show normal single photon emission computed tomography ( spect ) scans, change their diagnosis as non - pd after few years of follow up, and in the meantime, they are treated with pd medications which do more harm than good. in this work, machine learning models are developed using features from spect images to detect early pd and swedd subjects from normal. these models were observed to perform with high accuracy. it is inferred from the study that these diagnostic models carry potential to help pd clinicians in the diagnostic process
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arxiv:2412.05348
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we present a practical and accurate density functional for the exchange - correlation energy of electrons in two dimensions. the exchange part is based on a recent two - dimensional generalized - gradient approximation derived by considering the limits of small and large density gradients. the fully local correlation part is constructed following the colle - salvetti scheme and a gaussian approximation for the pair density. the combination of these expressions is shown to provide an efficient density functional to calculate the total energies of two - dimensional electron systems such as semiconductor quantum dots. excellent performance of the functional with respect to numerically exact reference data for quantum dots is demonstrated.
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arxiv:1001.3660
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we show that frenkel ' s integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. our main general result is a dimension - independent semi - continuity relation for the quantum relative entropy with respect to the first argument. using it, we obtain a number of results : ( 1 ) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by wilde in this special case ; ( 2 ) a stronger version of the fannes - audenaert inequality on quantum entropy ; ( 3 ) better estimates on the quantum capacity of approximately degradable channels ; ( 4 ) an improved continuity relation for the entanglement cost ; ( 5 ) general upper bounds on asymptotic transformation rates in infinite - dimensional entanglement theory ; and ( 6 ) a proof of a conjecture due to christandl, ferrara, and lancien on the continuity of ' filtered ' relative entropy distances.
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arxiv:2408.15226
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distributed detection primarily centers around two approaches : unquantized distributed detection ( udd ), where each sensor reports its complete observation to the fusion center ( fc ), and quantized - and - coded dd ( cdd ), where each sensor first partitions the observation space and then reports to the fc a codeword. in this paper, we introduce quantized - but - uncoded dd ( qdd ), where each sensor, after quantization, transmits a summarized value, instead of a codeword, to the fc. we show that qdd well adapts to the constraint of transmission power when compared to cdd, albeit with increased complexity in parameter selection. moreover, we establish that, in the presence of independent observations, qdd upholds a necessary condition inherent in cdd. specifically, the optimal sensor decision rules are the likelihood ratio quantizers ( lrq ), irrelevant to the channel conditions. in the context of a single - sensor scenario involving binary decision at the sensor, we find that the optimal sensor rule in qdd is in general no longer ` ` channel blind ", a feature presented in cdd. in addition, we compare these systems numerically under the same transmission power and bandwidth, while assuming additive white gaussian noise ( awgn ) in both sensing and reporting stages. finally, we present some potential directions for future research.
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arxiv:2311.02447
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the rotation curves and the relative mass distributions of the two nearby local group spiral galaxies, m31 and m33, show discrepancies with modified newtonian dynamic ( mond ) predictions. in m33 the discrepancy lies in the kinematics of the outermost regions. it can be alleviated by adopting tilted ring models compatible with the 21 - cm datacube but different from the one that best fits the data. in m31 mond fails to fit the falling part of the rotation curve at intermediate radii, before the curve flattens out in the outermost regions. newtonian dynamics in a framework of a stellar disc embedded in a dark halo can explain the complex rotation curve profiles of these two galaxies, while mond has some difficulties. however, given the present uncertainties in the kinematics of these nearby galaxies, we cannot address the success or failure of mond theory in a definite way. more sensitive and extended observations around the critical regions, suggested by mond fits discussed in this paper, may lead to a definite conclusion.
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arxiv:astro-ph/0610618
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we discuss an approach to quantum gerbes over quantum groups in terms of q - deformation of transition functions for a loop group bundle. the case of the quantum group suq ( 2 ) is treated in some detail.
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arxiv:math/0308235
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in a long - held preconception, photons play a central role in present - day quantum technologies. but what are sources producing photons one by one good for precisely? well, in opposition to what many suggest, we show that single - photon sources are not helpful for point to point quantum key distribution because faint laser pulses do the job comfortably. however, there is no doubt about the usefulness of sources producing single photons for future quantum technologies. in particular, we show how single - photon sources could become the seed of a revolution in the framework of quantum communication, making the security of quantum key distribution device independent or extending quantum communication over many hundreds of kilometers. hopefully, these promising applications will provide a guideline for researchers to develop more and more efficient sources, producing narrowband, pure and indistinguishable photons at appropriate wavelengths.
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arxiv:1202.0493
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with the rapid growth of display devices, quality inspection via machine vision technology has become increasingly important for flat - panel displays ( fpd ) industry. this paper discloses a novel visual inspection system for liquid crystal display ( lcd ), which is currently a dominant type in the fpd industry. the system is based on two cornerstones : robust / high - performance defect recognition model and cognitive visual inspection service architecture. a hybrid application of conventional computer vision technique and the latest deep convolutional neural network ( dcnn ) leads to an integrated defect detection, classfication and impact evaluation model that can be economically trained with only image - level class annotations to achieve a high inspection accuracy. in addition, the properly trained model is robust to the variation of the image qulity, significantly alleviating the dependency between the model prediction performance and the image aquisition environment. this in turn justifies the decoupling of the defect recognition functions from the front - end device to the back - end serivce, motivating the design and realization of the cognitive visual inspection service architecture. empirical case study is performed on a large - scale real - world lcd dataset from a manufacturing line with different layers and products, which shows the promising utility of our system, which has been deployed in a real - world lcd manufacturing line from a major player in the world.
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arxiv:2101.03747
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in this paper, we prove a weaker form of a conjecture of montgomery - vaughan on extreme values of automorphic l - functions at 1.
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arxiv:math/0604334
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we investigate the quantum effect on machine learning ( ml ) models exemplified by the generative adversarial network ( gan ), which is a promising deep learning framework. in the general gan framework the generator maps uniform noise to a fake image. in this study, we utilize the associative adversarial network ( aan ), which consists of a standard gan and an associative memory. further, we set a boltzmann machine ( bm ), which is an undirected graphical model that learns low - dimensional features extracted from a discriminator, as the memory. owing to difficulty calculating the bm ' s log - likelihood gradient, it is necessary to approximate it by using the sample mean obtained from the bm, which has tentative parameters. to calculate the sample mean, a markov chain monte carlo ( mcmc ) is often used. in a previous study, this was performed using a quantum annealer device, and the performance of the " quantum " aan was compared to that of the standard gan. however, its better performance than the standard gan is not well understood. in this study, we introduce two methods to draw samples : classical sampling via mcmc and quantum sampling via quantum monte carlo ( qmc ) simulation, which is quantum simulation on the classical computer. then, we compare these methods to investigate whether quantum sampling is advantageous. specifically, calculating the discriminator loss, the generator loss, inception score and fr \ ' echet inception distance, we discuss the possibility of aan. we show that the aans trained by both mcmc and qmc are more stable during training and produce more varied images than the standard gans. however, the results indicate no difference in sampling by qmc simulation compared to that by mcmc.
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arxiv:2203.15220
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we present a novel deep generative model, named genmdi, to improve the temporal resolution of line - of - sight ( los ) magnetograms of solar active regions ( ars ) collected by the michelson doppler imager ( mdi ) on board the solar and heliospheric observatory ( soho ). unlike previous studies that focus primarily on spatial super - resolution of mdi magnetograms, our approach can perform temporal super - resolution, which generates and inserts synthetic data between observed mdi magnetograms, thus providing finer temporal structure and enhanced details in the los data. the genmdi model employs a conditional diffusion process, which synthesizes images by considering both preceding and subsequent magnetograms, ensuring that the generated images are not only of high - quality, but also temporally coherent with the surrounding data. experimental results show that the genmdi model performs better than the traditional linear interpolation method, especially in ars with dynamic evolution in magnetic fields.
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arxiv:2503.03959
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if the $ x ( 3872 ) $ is a weakly bound charm - meson molecule, it can be produced by the creation of $ d ^ { * 0 } \ bar { d } ^ 0 $ or $ d ^ { 0 } \ bar { d } ^ { * 0 } $ at short distances followed by the formation of the bound state from the charm - meson pair. the $ x $ can also be produced by the creation of $ d ^ * \ bar { d } ^ * $ at short distances followed by the rescattering of the charm - meson pair into $ x \ pi $. at a high - energy hadron collider, the prompt cross section from this mechanism has a narrow peak in the $ x \ pi $ invariant mass distribution near the $ d ^ * \ bar d ^ * $ threshold from a charm - meson triangle singularity. an order - of - magnitude estimate of the ratio of the cross section for producing the peak in the $ x \ pi ^ \ pm $ distribution to the cross section for producing $ x $ without an accompanying pion suggests that the peak may be observable at the lhc.
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arxiv:1903.04355
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we discuss the differing definitions of complex and quaternionic projective group representations employed by us and by emch. the definition of emch ( termed here a strong projective representation ) is too restrictive to accommodate quaternionic hilbert space embeddings of complex projective representations. our definition ( termed here a weak projective representation ) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations.
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arxiv:hep-th/9609012
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positron annihilation in solid state matter can be utilized to detect and identify open - volume defects. the momentum distribution of the annihilation radiation is an important observable in positron - based measurements, and can reveal information on the chemical surroundings of the defect sites. in this work we present a variational quantum monte carlo method for simulation of the momentum densities of annihilating electron - positron pairs in semiconductors and insulators. we study finite - size effects, effects of lattice vibrations, and different levels of trial wave functions. small simulation cells and simple wave function forms are found to be sufficient for accurate calculations in simulation of pristine lattices, enabling cheap accumulation of results. we compare calculated predictions of the doppler broadening of the 511 - kev 2 { \ gamma } annihilation line of the in aluminium nitride and silicon against experimental data measured from reference samples. our results achieve better agreement with experiments in the these materials than conventional state - of - the - art methods, and proves that direct modeling of the electron - positron correlations is important for a supporting theory of positron annihilation sprectroscopies
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arxiv:2305.08602
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with arbitrary domains and codomains were defined. functions are now used throughout all areas of mathematics. in introductory calculus, when the word function is used without qualification, it means a real - valued function of a single real variable. the more general definition of a function is usually introduced to second or third year college students with stem majors, and in their senior year they are introduced to calculus in a larger, more rigorous setting in courses such as real analysis and complex analysis. = = = real function = = = a real function is a real - valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval. in this section, these functions are simply called functions. the functions that are most commonly considered in mathematics and its applications have some regularity, that is they are continuous, differentiable, and even analytic. this regularity insures that these functions can be visualized by their graphs. in this section, all functions are differentiable in some interval. functions enjoy pointwise operations, that is, if f and g are functions, their sum, difference and product are functions defined by ( f + g ) ( x ) = f ( x ) + g ( x ) ( f − g ) ( x ) = f ( x ) − g ( x ) ( f ⋅ g ) ( x ) = f ( x ) ⋅ g ( x ). { \ displaystyle { \ begin { aligned } ( f + g ) ( x ) & = f ( x ) + g ( x ) \ \ ( f - g ) ( x ) & = f ( x ) - g ( x ) \ \ ( f \ cdot g ) ( x ) & = f ( x ) \ cdot g ( x ) \ \ \ end { aligned } }. } the domains of the resulting functions are the intersection of the domains of f and g. the quotient of two functions is defined similarly by f g ( x ) = f ( x ) g ( x ), { \ displaystyle { \ frac { f } { g } } ( x ) = { \ frac { f ( x ) } { g ( x ) } }, } but the domain of the resulting function is obtained by removing the zeros of g from the intersection of the domains of f and g. the polynomial functions are defined by polynomials, and their domain is the whole set of real numbers. they include constant functions
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https://en.wikipedia.org/wiki/Function_(mathematics)
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let $ d $ be a nonempty domain in $ \ mathbb c ^ n $. we give a scale of necessary conditions for the distribution of the zero set of holomorphic function $ f $ on domain $ d \ subset { \ mathbb c } ^ n $ under a restriction on its growth $ | f | \ leq \ exp m $, where $ m \ not \ equiv - \ infty $ is a subharmonic function. if $ n = 1 $, $ d \ neq \ mathbb c $ is simply connected, and $ m $ is continuous, then this conditions are sufficient.
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arxiv:1811.01407
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we prove that for all nonnegative integers k, s there exists c with the following property. let g be a graph with clique number at most k and chromatic number more than c. then for every vertex - colouring ( not necessarily optimal ) of g, some induced subgraph of g is an s - vertex path, and all its vertices have different colours. this extends a recent result of gyarfas and sarkozy, who proved the same ( when k = 2 ) for graphs g with girth at least five.
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arxiv:1702.01094
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starting from the many - body bethe - salpeter equation we derive an exchange - correlation kernel $ f _ { xc } $ that reproduces excitonic effects in bulk materials within time - dependent density functional theory. the resulting $ f _ { xc } $ accounts for both self - energy corrections and the electron - hole interaction. it is { \ em static }, { \ em non - local } and has a long - range coulomb tail. taking the example of bulk silicon, we show that the $ - \ alpha / q ^ 2 $ divergency is crucial and can, in the case of continuum excitons, even be sufficient for reproducing the excitonic effects and yielding excellent agreement between the calculated and the experimental absorption spectrum.
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arxiv:cond-mat/0109434
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stars form in spatially and temporarily correlated star formation events ( csfes ) and the dynamical processes within these " embedded clusters " leave imprints in the stellar populations in galactic fields. such imprints are correlations in phase space ( e. g. gravitationally bound star clusters, tidal streams ), in the binary properties of stars and in the present - day stellar mass functions in the surviving clusters. the dynamical processes include expulsion of massive stars from cluster cores, disruption of csfes due to residual gas expulsion and energy - equipartition driven evaporation of stars from clusters leading to dark star clusters and cold kinematical streams with epicyclic overdensities. the properties of such phase - space structures in the milky way ( mw ) field depend on the effective gravitational potential of the mw. gaia data will significantly constrain all of these aspects, and will in particular impact on gravitational dynamics via the properties of cold streams and on star - formation via the constraint on the gas expulsion process through the expanding unbound populations that must be associated with every csfe.
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arxiv:1111.5613
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the optimal transport ( ot ) problem has been used widely for machine learning. it is necessary for computation of an ot problem to solve linear programming with tight mass - conservation constraints. these constraints prevent its application to large - scale problems. to address this issue, loosening such constraints enables us to propose the relaxed - ot method using a faster algorithm. this approach has demonstrated its effectiveness for applications. however, it remains slow. as a superior alternative, we propose a fast block - coordinate frank - wolfe ( bcfw ) algorithm for a convex semi - relaxed ot. specifically, we prove their upper bounds of the worst convergence iterations, and equivalence between the linearization duality gap and the lagrangian duality gap. additionally, we develop two fast variants of the proposed bcfw. numerical experiments have demonstrated that our proposed algorithms are effective for color transfer and surpass state - of - the - art algorithms. this report presents a short version of arxiv : 2103. 05857.
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arxiv:2205.13766
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morris - lecar model is arguably the simplest dynamical model that retains both the slow - fast geometry of excitable phase portraits and the physiological interpretation of a conductance - based model. we augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. the resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. we show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature.
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arxiv:1904.12161
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we present estimates of the nonlinear bias of cosmological halo formation, spanning a wide range in the halo mass from $ \ sim 10 ^ { 5 } m _ \ odot $ to $ \ sim 10 ^ { 12 } m _ \ odot $, based upon both a suite of high - resolution cosmological n - body simulations and theoretical predictions. the halo bias is expressed in terms of the mean bias and stochasticity as a function of local overdensity ( $ \ delta $ ), under different filtering scales, which is realized as the density of individual cells in uniform grids. the sampled overdensities span a range wide enough to provide the fully nonlinear bias effect on the formation of haloes. a strong correlation between $ \ delta $ and halo population overdensity $ \ delta _ h $ is found, along with sizable stochasticity. we find that the empirical mean halo bias matches, with good accuracy, the prediction by the peak - background split method based on the excursion set formalism, as long as the empirical, globally - averaged halo mass function is used. consequently, this bias formalism is insensitive to uncertainties caused by varying halo identification schemes, and can be applied generically. we also find that the probability distribution function of biased halo numbers has wider distribution than the pure poisson shot noise, which is attributed to the sub - cell scale halo correlation. we explicitly calculate this correlation function and show that both overdense and underdense regions have positive correlation, leading to stochasticity larger than the poisson shot noise in the range of haloes and halo - collapse epochs we study.
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arxiv:1407.2637
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visible and near - infrared spectra of transiting hot jupiter planets have recently been observed, revealing some of the atmospheric constituents of their atmospheres. in the near future, it is probable that primary and secondary eclipse observations of earth - like rocky planets will also be achieved. the characterization of the earth ' s transmission spectrum has shown that both major and trace atmospheric constituents may present strong absorption features, including important bio - markers such as water, oxygen and methane. our simulations using a recently published empirical earth ' s transmission spectrum, and the stellar spectra for a variety of stellar types, indicate that the new generation of extremely large telescopes, such as the proposed 42 - meter european extremely large telescope ( e - elt ), could be capable of retrieving the transmission spectrum of an earth - like planet around very cool stars and brown dwarfs ( teff < 3100 k ). for a twin of earth around a star with teff around 3100 k ( m4 ), for example, the spectral features of water vapor, methane, carbon dioxide, and oxygen in the wavelength range between 0. 9 and 2. 4 micron can simultaneously be detected within a hundred hours of observing time, or even less for a late - m star. such detection would constitute a proof for the existence of life in that planet. the detection time can be reduced to a few hours for a super - earth type of planet with twice the earth ' s radius.
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arxiv:1102.4989
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intelligent reflecting surfaces ( irss ) tune wireless environments to increase spectrum and energy efficiencies. in view of much recent attention to the irs concept as a promising technology for 6g wireless communications, we present a survey of irss in this paper. specifically, we categorize recent research studies of irss as follows. for irs - aided communications, the summary includes capacity / data rate analyses, power / spectral optimizations, channel estimation, deep learning - based design, and reliability analysis. then we review irss implementations as well as the use of irss in secure communications, terminal - positioning, and other novel applications. we further identify future research directions for irss, with an envision of the irs technology playing a critical role in 6g communication networks similar to that of massive mimo in 5g networks. as a timely summary of irss, our work will be of interest to both researchers and practitioners working on irss for 6g networks.
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arxiv:1907.04789
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the research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. this setting raises the questions of how to represent the plans and how to perform plan search. the answers are quite different from those in the simpler classical framework. in this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. instead, we translate conditional planning to quantified boolean formulae. we discuss three formalizations of conditional planning as quantified boolean formulae, and present experimental results obtained with a theorem - prover.
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arxiv:1105.5465
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we explore the effects of disordered charged defects on the electronic excitations observed in the photoemission spectra of doped transition metal oxides in the mott insulating regime by the example of the $ r _ { 1 - x } $ ca $ _ x $ vo $ _ 3 $ perovskites, where $ r = $ la, $ \ dots $, lu. a fundamental characteristic of these vanadium $ d ^ 2 $ compounds with partly filled $ t _ { 2g } $ valence orbitals is the persistence of spin and orbital order up to high doping, in contrast to the loss of magnetic order in high - $ t _ c $ cuprates at low defect concentration. we demonstrate that the disordered electronic structure of doped mott - hubbard insulators can be obtained with high precision within the unrestricted hartree - fock approximation. in particular : ( i ) the atomic multiplet excitations in the inverse photoemission spectra and the various defect - related states and satellites are well reproduced, ( ii ) a robust mott gap survives up to large doping, and ( iii ) we show that the defect states inside the mott gap develop a soft gap at the fermi energy. the soft defect states gap can be characterized by a shape and a scale parameter extracted from a weibull statistical sampling of the density of states near the chemical potential. we demonstrate that charge defects trigger small spin - orbital polarons, with their internal kinetic energy responsible for the opening of the soft defect states gap. the small size of spin - orbital polarons is inferred by an analysis of the inverse participation ratio which explains the origin of the robustness of spin and orbital order. using realistic parameters for la $ _ { 1 - x } $ ca $ _ x $ vo $ _ 3 $, we show that its soft gap is well reproduced as well as the marginal doping dependence of the position of the chemical potential relative to the center of the lower hubbard band.
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arxiv:1710.05171
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graphics processing units ( gpus ) have been widely used to accelerate artificial intelligence, physics simulation, medical imaging, and information visualization applications. to improve gpu performance, gpu hardware designers need to identify performance issues by inspecting a huge amount of simulator - generated traces. visualizing the execution traces can reduce the cognitive burden of users and facilitate making sense of behaviors of gpu hardware components. in this paper, we first formalize the process of gpu performance analysis and characterize the design requirements of visualizing execution traces based on a survey study and interviews with gpu hardware designers. we contribute data and task abstraction for gpu performance analysis. based on our task analysis, we propose daisen, a framework that supports data collection from gpu simulators and provides visualization of the simulator - generated gpu execution traces. daisen features a data abstraction and trace format that can record simulator - generated gpu execution traces. daisen also includes a web - based visualization tool that helps gpu hardware designers examine gpu execution traces, identify performance bottlenecks, and verify performance improvement. our qualitative evaluation with gpu hardware designers demonstrates that the design of daisen reflects the typical workflow of gpu hardware designers. using daisen, participants were able to effectively identify potential performance bottlenecks and opportunities for performance improvement. the open - sourced implementation of daisen can be found at gitlab. com / akita / vis. supplemental materials including a demo video, survey questions, evaluation study guide, and post - study evaluation survey are available at osf. io / j5ghq.
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arxiv:2104.00828
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irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analysed for the purpose of application to superfluid layers in neutron stars. asymptotic solutions are found by asymptotically expanding the flow equation at large distances from the vortex core and then by solving it order by order. the asymptotic effective tension and energy density that are needed for an averaged macroscopic description are thus obtained as functions of the vortex velocity, the vortex circulation, the asymptotic chemical potential and of parameters depending on the equation of state.
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arxiv:astro-ph/9709090
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rod bundle flows are commonplace in nuclear engineering, and are present in light water reactors ( lwrs ) as well as other more advanced concepts. inhomogeneities in the bundle cross section can lead to complex flow phenomena, including varying local conditions of turbulence. despite the decades of numerical and experimental investigations regarding this topic, and the importance of elucidating the physics of the flow field, to date there are few publicly available direct numerical simulations ( dns ) of the flow in multiple - pin rod bundles. thus a multiple - pin dns study can provide significant value toward reaching a deeper understanding of the flow physics, as well as a reference simulation for development of various reduced - resolution analysis techniques. to this end, dns of the flow in a square 5x5 rod bundle at reynolds number of 19, 000 has been performed using the highly - parallel spectral element code nek5000. the geometrical dimensions were representative of typical lwr fuel designs. the dns was designed using microscales estimated from an advanced reynolds - averaged navier - stokes ( rans ) model. characteristics of the velocity field, reynolds stresses, and anisotropy are presented in detail for various regions of the bundle. the turbulent kinetic energy budget is also presented and discussed
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arxiv:2007.00630
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using the ellipsoidal model for the density configuration, we calculate the equilibrium sequence of the corotating binary stars of the polytropic equation of state in the first post - newtonian approximation of general relativity. after we calibrate this model by comparing with previous numerical results, we perform the stability analysis by calculating the energy and the angular momentum of the system as a function of the orbital separation. we find that the orbital angular velocity at the energy and / or momentum minimum increases with the increase of the compactness of each star, and this fact holds irrespective of the polytropic index. these features agree with those in previous numerical works. we also show that due to the influence of the tidal field from the companion star, the central density of each star slightly decreases.
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arxiv:gr-qc/9705028
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splitting - type variational problems \ [ \ int _ \ omega \ sum _ { i = 1 } ^ n f _ i ( \ partial _ i w ) dx \ to \ min \ ] with superlinear growth conditions are studied by assuming \ [ h _ i ( t ) \ leq f ' ' _ i ( t ) \ leq h _ i ( t ) \ ] with suitable functions $ h _ i $, $ h _ i $ : $ \ mathbb { r } \ to \ mathbb { r } ^ + $, $ i = 1 $, $ \ dots $, $ n $, measuring the growth and ellipticity of the energy density. here, as the main feature, a symmetric behaviour like $ h _ i ( t ) \ approx h _ i ( - t ) $ and $ h _ i ( t ) \ approx h _ i ( - t ) $ for large $ | t | $ is not supposed. assuming quite weak hypotheses as above, we establish higher integrability of $ | \ nabla u | $ for local minimizers $ u \ in l ^ \ infty ( \ omega ) $ by using a caccioppoli - type inequality with some power weights of negative exponent.
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arxiv:2301.01072
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recently gate - mediated supercurrent suppression in superconducting nano - bridges has been reported in many experiments. this could be either a direct or an indirect gate effect. the microscopic understanding of this observation is not clear till now. using the quasiclassical green ' s function method, we show that a small concentration of magnetic impurities at the surface of the bridges can significantly help to suppress superconductivity and hence the supercurrent inside the systems while applying a gate field. this is because the gate field can enhance the depairing through the exchange interaction between the magnetic impurities at the surface and the superconductor. we also obtain a \ emph { symmetric } suppression of the supercurrent with respect to the gate field, a signature of a direct gate effect. future experiments can verify our predictions by modifying the surface with magnetic impurities.
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arxiv:2303.07801
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many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis ( lda ). to efficiently use them, sparsity of linear classifiers is a prerequisite. however, this might not be readily available in many applications, and rotations of data are required to create the needed sparsity. in this paper, we propose a family of rotations to create the required sparsity. the basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and to then apply an existing high dimensional classifier. this rotate - and - solve procedure can be combined with any existing classifiers, and is robust against the sparsity level of the true model. we show that these rotations do create the sparsity needed for high dimensional classifications and provide theoretical understanding why such a rotation works empirically. the effectiveness of the proposed method is demonstrated by a number of simulated and real data examples, and the improvements of our method over some popular high dimensional classification rules are clearly shown.
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arxiv:1408.4475
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in a recent paper carot et al. considered carefully the definition of cylindrical symmetry as a specialisation of the case of axial symmetry. one of their propositions states that if there is a second killing vector, which together with the one generating the axial symmetry, forms the basis of a two - dimensional lie algebra, then the two killing vectors must commute, thus generating an abelian group. in this comment a similar result, valid under considerably weaker assumptions, is recalled : any two - dimensional lie transformation group which contains a one - dimensional subgroup whose orbits are circles, must be abelian. the method used to prove this result is extended to apply to three - dimensional lie transformation groups. it is shown that the existence of a one - dimensional subgroup with closed orbits restricts the bianchi type of the associated lie algebra to be i ( abelian ), ii, iii, vii _ 0, viii or ix. the relationship between the present approach and that of the original paper is discussed.
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arxiv:gr-qc/0004019
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detection of primordial gravitational - wave backgrounds generated during the early universe phase transitions is a key science goal for future ground - based detectors. the rate of compact binary mergers is so large that their cosmological population produces a confusion background that could masquerade the detection of potential primordial stochastic backgrounds. in this paper we study the ability of current and future detectors to resolve the confusion background to reveal interesting primordial backgrounds. the current detector network of ligo and virgo and the upcoming kagra and ligo - india will not be able to resolve the cosmological compact binary source population and its sensitivity to stochastic background will be limited by the confusion background of these sources. we find that a network of three ( and five ) third generation ( 3g ) detectors of cosmic explorer and einstein telescope will resolve the confusion background produced by binary black holes leaving only about 0. 013 \ % ( respectively, 0. 00075 \ % ) unresolved ; in contrast, as many as 25 \ % ( respectively, 7. 7 \ % ) of binary neutron star sources remain unresolved. consequently, the binary black hole population will likely not limit observation of primordial backgrounds but the binary neutron star population will limit the sensitivity of 3g detectors to $ \ omega _ { \ rm gw } \ sim 10 ^ { - 11 } $ at 10 hz ( respectively, $ \ omega _ { \ rm gw } \ sim 3 \ times 10 ^ { - 12 } $ ).
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arxiv:2002.05365
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we present the first fully - nonlinear numerical study of the dynamics of highly spinning black - hole binaries. we evolve binaries from quasicircular orbits ( as inferred from post - newtonian theory ), and find that the last stages of the orbital motion of black - hole binaries are profoundly affected by their individual spins. in order to cleanly display its effects, we consider two equal mass holes with individual spin parameters s / m ^ 2 = 0. 757, both aligned and anti - aligned with the orbital angular momentum ( and compare with the spinless case ), and with an initial orbital period of 125m. we find that the aligned case completes three orbits and merges significantly after the anti - aligned case, which completes less than one orbit. the total energy radiated for the former case is ~ 7 % while for the latter it is only ~ 2 %. the final kerr hole remnants have rotation parameters a / m = 0. 89 and a / m = 0. 44 respectively, showing the unlikeliness of creating a maximally rotating black hole out of the merger of two spinning holes.
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arxiv:gr-qc/0604012
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we extend the continuum theory of active nematic fluids to study cell flows and tissue dynamics inside multicellular spheroids, spherical, self - assembled aggregates of cells that are widely used as model systems to study tumour dynamics. cells near the surface of spheroids have better access to nutrients and therefore proliferate more rapidly than those in the resource - depleted core. using both analytical arguments and three - dimensional simulations, we find that the proliferation gradients result in flows and in gradients of activity both of which can align the orientation axis of cells inside the aggregates. depending on environmental conditions and the intrinsic tissue properties, we identify three distinct alignment regimes : spheroids in which all the cells align either radially or tangentially to the surface throughout the aggregate and spheroids with angular cell orientation close to the surface and radial alignment in the core. the continuum description of tissue dynamics inside spheroids not only allows us to infer dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.
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arxiv:2208.08258
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we report significant enhancement in superconducting properties of yttrium substituted ce1 - xyxoffeas superconductors. the polycrystalline samples were prepared by two step solid state reaction technique. x - ray diffraction confirmed tetragonal zrcusias structure with decrease in both a and c lattice parameters on increasing yttrium substitution ( with fixed f content ). with smaller ion y in place of ce, the transition temperature increased by 6 k. yttrium doping also lead to higher critical fields as well as stronger inter and intra - granular current density. the magnetization critical current density increased by an order of magnitude at 30 k and 1 t magnetic field.
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arxiv:0908.3372
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