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in these lecture notes we review the various relations between intersection theory on the moduli space of riemann surfaces, integrable hierarchies of kdv type, matrix models, and topological quantum field theories. we explain in particular why matrix integrals of the type considered by kontsevich naturally appear as tau - functions associated to minimal models. our starting point is the extremely simple form of the string equation for the topological ( p, 1 ) models, where the so - called baker - akhiezer function is given by a ( generalized ) airy function.
arxiv:hep-th/9201003
since the 1960s i proposed that we could understand and replicate the highest level of intelligence seen in the brain, by building ever more capable and general systems for adaptive dynamic programming ( adp ), which is like reinforcement learning but based on approximating the bellman equation and allowing the controller to know its utility function. growing empirical evidence on the brain supports this approach. adaptive critic systems now meet tough engineering challenges and provide a kind of first - generation model of the brain. lewis, prokhorov and myself have early second - generation work. mammal brains possess three core capabilities, creativity / imagination and ways to manage spatial and temporal complexity, even beyond the second generation. this paper reviews previous progress, and describes new tools and approaches to overcome the spatial complexity gap.
arxiv:q-bio/0612045
mathematical logic is the study of formal logic within mathematics. major subareas include model theory, proof theory, set theory, and recursion theory ( also known as computability theory ). research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. however, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. this study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. in the early 20th century it was shaped by david hilbert ' s program to prove the consistency of foundational theories. results of kurt godel, gerhard gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems ( as in reverse mathematics ) rather than trying to find theories in which all of mathematics can be developed. = = subfields and scope = = the handbook of mathematical logic in 1977 makes a rough division of contemporary mathematical logic into four areas : set theory model theory recursion theory, and proof theory and constructive mathematics ( considered as parts of a single area ). additionally, sometimes the field of computational complexity theory is also included together with mathematical logic. each area has a distinct focus, although many techniques and results are shared among multiple areas. the borderlines amongst these fields, and the lines separating mathematical logic and other fields of mathematics, are not always sharp. godel ' s incompleteness theorem marks not only a milestone in recursion theory and proof theory, but has also led to lob ' s theorem in modal logic. the method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics. the mathematical field of category theory uses many formal axiomatic methods, and includes the study of categorical logic, but category theory is not ordinarily considered a subfield of mathematical logic. because of its applicability in diverse fields of mathematics, mathematicians including saunders mac lane have proposed category theory as a foundational system for mathematics, independent of
https://en.wikipedia.org/wiki/Mathematical_logic
we consider the maximum coding rate achievable by uniformly - random codes for the deletion channel. we prove an upper bound that ' s within 0. 1 of the best known lower bounds for all values of the deletion probability $ d, $ and much closer for small and large $ d. $ we give simulation results which suggest that our upper bound is within 0. 05 of the exact value for all $ d $, and within $ 0. 01 $ for $ d > 0. 75 $. despite our upper bounds, based on simulations, we conjecture that a positive rate is achievable with uniformly - random codes for all deletion probabilities less than 1. our results imply impossibility results for the ( equivalent ) problem of compression of i. i. d. sources correlated via the deletion channel, a relevant model for dna storage.
arxiv:2210.07437
we consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest - plane algorithm, due to babai. two distinct communication models, centralized and interactive, are considered. the importance of proper basis selection is addressed. assuming a reduced basis for a two - dimensional lattice, we determine the approximation error of the nearest plane algorithm. the communication cost for determining the babai point, or equivalently, for constructing the rectangular nearest - plane partition, is calculated in the interactive setting. for the centralized model, an algorithm is presented for reducing the communication cost of the nearest plane algorithm in an arbitrary number of dimensions.
arxiv:1701.08456
in the field of soft dielectric elastomers, the notion electrostriction indicates the dependency of the permittivity on strain. the present paper is aimed at investigating the effects of electrostriction onto the stability behaviour of homogeneous electrically activated dielectric elastomer actuators. in particular, three objectives are pursued and achieved : i ) the description of the phenomenon within the general nonlinear theory of electroelasticity ; ii ) the application of the recently proposed theory of bifurcation for electroelastic bodies in order to determine its role on the onset of electromechanical and diffuse - mode instabilities in prestressed or prestretched dielectric layers ; iii ) the analysis of band - localization instability in homogeneous dielectric elastomers. results for a typical soft acrylic elastomer show that electrostriction is responsible for an enhancement towards diffuse - mode instability, while it represents a crucial property - necessarily to be taken into account - in order to provide a solution to the problem of electromechanical band - localization, that can be interpreted as a possible reason of electric breakdown. a comparison between the buckling stresses of a mechanical compressed slab and the electrically activated counterpart concludes the paper.
arxiv:1310.0332
a long - term sublimation model to explain how phaethon could provide the geminid stream is proposed. we find that it would take $ \ sim6 $ myr or more for phaethon to lose all of its internal ice ( if ever there was ) in its present orbit. thus, if the asteroid moved from the region of a 5 : 2 or 8 : 3 mean motion resonance with jupiter to its present orbit less than $ 1 $ myr ago, it may have retained much of its primordial ice. the dust mantle on the sublimating body should have a thickness of at least $ 15 $ m but the mantle could have been less than $ 1 $ m thick $ 1000 $ years ago. we find that the total gas production rate could have been as large as $ 10 ^ { 27 } \ rm ~ s ^ { - 1 } $ then, and the gas flow could have been capable of lifting dust particles of up to a few centimeters in size. therefore, gas production during the past millennium could have been sufficient to blow away enough dust particles to explain the entire geminid stream. for present - day phaethon, the gas production is comparatively weak. but strong transient gas release with a rate of $ \ sim4. 5 \ times10 ^ { 19 } \ rm ~ m ^ { - 2 } s ^ { - 1 } $ is expected for its south polar region when phaethon moves from $ 0 ^ \ circ $ to $ 2 ^ \ circ $ mean anomaly near perihelion. consequently, dust particles with radii of $ < \ sim260 ~ \ mu m $ can be blown away to form a dust tail. in addition, we find that the large surface temperature variation of $ > 600 $ k near perihelion can generate sufficiently large thermal stress to cause fracture of rocks or boulders and provide an efficient mechanism to produce dust particles on the surface. the time scale for this process should be several times longer than the seasonal thermal cycle, thereby dominating the cycle of appearance of the dust tail.
arxiv:1811.00759
this paper presents a novel decentralized control strategy for a multi - robot system that enables parallel multi - target exploration while ensuring a time - varying connected topology in cluttered 3d environments. flexible continuous connectivity is guaranteed by building upon a recent connectivity maintenance method, in which limited range, line - of - sight visibility, and collision avoidance are taken into account at the same time. completeness of the decentralized multi - target exploration algorithm is guaranteed by dynamically assigning the robots with different motion behaviors during the exploration task. one major group is subject to a suitable downscaling of the main traveling force based on the traveling efficiency of the current leader and the direction alignment between traveling and connectivity force. this supports the leader in always reaching its current target and, on a larger time horizon, that the whole team realizes the overall task in finite time. extensive monte ~ carlo simulations with a group of several quadrotor uavs show the scalability and effectiveness of the proposed method and experiments validate its practicability.
arxiv:1505.05441
polaritons enable the resonant coupling of excitons and photons to vibrations in the application - relevant super high frequency ( shf, 3 - 30 ghz ) domain. we introduce a novel platform for coherent optomechanics based on the coupling of exciton - polaritons and electrically driven shf longitudinal acoustic phonons confined within the spacer region of a planar bragg microcavity. an intrinsic property of the microcavity platform is the back - feeding of phonons via reflections at the sample boundaries, which enables frequency x quality factors products exceeding 10 ^ 14 hz as well as huge modulation amplitudes of the optical transition energies ( up to 8 mev ). we show that the modulation is dominated by the phonon - induced energy shifts of the excitonic polariton component, thus leading to an oscillatory transition between the regimes of weak and strong light - matter coupling. these results open the way for polariton - based coherent optomechanics in the non - adiabatic, side - band - resolved regime of coherent control.
arxiv:2003.01051
we identify the scaling region of a width o ( n ^ { - 1 } ) in the vicinity of the accumulation points $ t = \ pm 1 $ of the real roots of a random kac - like polynomial of large degree n. we argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c _ i, as long as the second moment \ sigma = e ( c _ i ^ 2 ) is finite. in particular, we reveal a gradual ( in contrast to the previously reported abrupt ) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value \ mu _ n = e ( c _ i ) scaled as \ mu _ n \ sim n ^ { - 1 / 2 }.
arxiv:math-ph/0309014
image compression aims to reduce the information redundancy in images. most existing neural image compression methods rely on side information from hyperprior or context models to eliminate spatial redundancy, but rarely address the channel redundancy. inspired by the mask sampling modeling in recent self - supervised learning methods for natural language processing and high - level vision, we propose a novel pretraining strategy for neural image compression. specifically, cube mask sampling module ( cmsm ) is proposed to apply both spatial and channel mask sampling modeling to image compression in the pre - training stage. moreover, to further reduce channel redundancy, we propose the learnable channel mask module ( lcmm ) and the learnable channel completion module ( lccm ). our plug - and - play cmsm, lcmm, lccm modules can apply to both cnn - based and transformer - based architectures, significantly reduce the computational cost, and improve the quality of images. experiments on the public kodak and tecnick datasets demonstrate that our method achieves competitive performance with lower computational complexity compared to state - of - the - art image compression methods.
arxiv:2306.05704
the paper studies the limiting behavior of spectral measures of random jacobi matrices of gaussian, wishart and manova beta ensembles. we show that the spectral measures converge weakly to a limit distribution which is the semicircle distribution, marchenko - pastur distributions or kesten - mckey distributions, respectively. the gaussian fluctuation around the limit is then investigated.
arxiv:1601.01146
we test our knowledge of the atomic opacity in the solar uv spectrum. using the atomic data compiled in paper i from modern, publicly available, databases, we perform calculations that are confronted with space - based observations of the sun. at wavelengths longer than about 260 nm, lte modeling can reproduce quite closely the observed fluxes ; uncertainties in the atomic line data account fully for the differences between calculated and observed fluxes. at shorter wavelengths, departures from lte appear to be important, as our lte and restricted nlte calculations differ. analysis of visible - near infrared na i and o i lines, two species that produce a negligible absorption in the uv, shows that observed departures from lte for theses species can be reproduced very accurately with restricted ( fixed atmospheric structure ) nlte calculations.
arxiv:astro-ph/0303560
privacy is a concept found throughout human history and opinion polls suggest that the public value this principle. however, while many individuals claim to care about privacy, they are often perceived to express behaviour to the contrary. this phenomenon is known as the privacy paradox and its existence has been validated through numerous psychological, economic and computer science studies. several contributory factors have been suggested including user interface design, risk salience, social norms and default configurations. we posit that the further proliferation of the internet - of - things ( iot ) will aggravate many of these factors, posing even greater risks to individuals ' privacy. this paper explores the evolution of both the paradox and the iot, discusses how privacy risk might alter over the coming years, and suggests further research required to address a reasonable balance. we believe both technological and socio - technical measures are necessary to ensure privacy is protected in a world of ubiquitous technology.
arxiv:1807.05754
we investigate the geometry near the horizon of a generic, four - dimensional extremal black hole. when the cosmological constant is negative, we show that ( in almost all cases ) tidal forces diverge as one crosses the horizon, and this singularity is stronger for larger black holes. in particular, this applies to generic nonspherical black holes, such as those satisfying inhomogeneous boundary conditions. nevertheless, all scalar curvature invariants remain finite. moreover, we show that nonextremal black holes have tidal forces that diverge in the extremal limit. holographically, this singularity is reflected in anomalous scaling of the specific heat with temperature. similar ( albeit weaker ) effects are present when the cosmological constant is positive, but not when it vanishes.
arxiv:2210.02473
we present a numerical model which allows us to investigate thermonuclear flames in type ia supernova explosions. the model is based on a finite - volume explicit hydrodynamics solver employing ppm. using the level - set technique combined with in - cell reconstruction and flux - splitting schemes we are able to describe the flame in the discontinuity approximation. we apply our implementation to flame propagation in chandrasekhar - mass type ia supernova models. in particular we concentrate on intermediate scales between the flame width and the gibson - scale, where the burning front is subject to the landau - darrieus instability. we are able to reproduce the theoretical prediction on the growth rates of perturbations in the linear regime and observe the stabilization of the flame in a cellular shape. the increase of the mean burning velocity due to the enlarged flame surface is measured. results of our simulation are in agreement with semianalytical studies.
arxiv:astro-ph/0211202
the cross - industry working team ( xiwt ), with the support of the stanford university consortium for research on information security and policy ( crisp ), sponsored a symposium on cross - industry activities aimed at improving the reliability, dependability, and robustness of the information infrastructure. held 3 - 4 november 1998 in crystal city, virginia, the symposium engaged representatives from industry, academia, and government in discussion of current and potential cross - industry, cross - sector activities including information exchange, collaborative operations, and cooperative research and development. this proceedings summarizes the discussions and results of the meeting.
arxiv:cs/9902014
integer - valued elements of an integral submodular flow polyhedron $ q $ are investigated which are decreasingly minimal ( dec - min ) in the sense that their largest component is as small as possible, within this, the second largest component is as small as possible, and so on. as a main result, we prove that the set of dec - min integral elements of $ q $ is the set of integral elements of another integral submodular flow polyhedron arising from $ q $ by intersecting a face of $ q $ with a box. based on this description, we develop a strongly polynomial algorithm for computing not only a dec - min integer - valued submodular flow but even a cheapest one with respect to a linear cost - function. a special case is the problem of finding a strongly connected ( or $ k $ - edge - connected ) orientation of a mixed graph whose in - degree vector is decreasingly minimal.
arxiv:2012.07325
systems with a first integral ( i. e., constant of motion ) or a lyapunov function can be written as ` ` linear - gradient systems ' ' $ \ dot x = l ( x ) \ nabla v ( x ) $ for an appropriate matrix function $ l $, with a generalization to several integrals or lyapunov functions. the discrete - time analogue, $ \ delta x / \ delta t = l \ bar \ nabla v $ where $ \ bar \ nabla $ is a ` ` discrete gradient, ' ' preserves $ v $ as an integral or lyapunov function, respectively.
arxiv:math-ph/9805021
several examples of non - compact manifolds $ m _ 0 $ whose geometry at infinity is described by lie algebras of vector fields $ v \ subset \ gamma ( tm ) $ ( on a compactification of $ m _ 0 $ to a manifold with corners $ m $ ) were studied by melrose and his collaborators. in math. dg / 0201202 and math. oa / 0211305, the geometry of manifolds described by lie algebras of vector fields - - baptised " manifolds with a lie structure at infinity " there - - was studied from an axiomatic point of view. in this paper, we define and study the algebra $ \ psi _ { 1, 0, \ vv } ^ \ infty ( m _ 0 ) $, which is an algebra of pseudodifferential operators canonically associated to a manifold $ m _ 0 $ with the lie structure at infinity $ v \ subset \ gamma ( tm ) $. we show that many of the properties of the usual algebra of pseudodifferential operators on a compact manifold extend to $ \ psi _ { 1, 0, v } ^ \ infty ( m _ 0 ) $. we also consider the algebra $ \ diffv { * } ( m _ 0 ) $ of differential operators on $ m _ 0 $ generated by $ v $ and $ \ ci ( m ) $, and show that $ \ psi _ { 1, 0, v } ^ \ infty ( m _ 0 ) $ is a ` ` microlocalization ' ' of $ \ diffv { * } ( m _ 0 ) $. finally, we introduce and study semi - classical and ` ` suspended ' ' versions of the algebra $ \ psi _ { 1, 0, v } ^ \ infty ( m _ 0 ) $. our construction solves a problem posed by melrose in his talk at the icm in kyoto.
arxiv:math/0304044
a restrictive assumption in change point analysis is " stationarity under the null hypothesis of no change - point ", which is crucial for asymptotic theory but not very realistic from a practical point of view. for example, if change point analysis for correlations is performed, it is not necessarily clear that the mean, marginal variance or higher order moments are constant, even if there is no change in the correlation. this paper develops change point analysis for the correlation structures under less restrictive assumptions. in contrast to previous work, our approach does not require that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. moreover, we also address the problem of detecting relevant change points.
arxiv:1801.10478
opensesame is a program for generating tabular equations of state ( eos ), with capabilities for multiphase eos construction. in this tutorial, we provide an overview of how to run opensesame to construct a multiphase eos. we discuss some general features of opensesame, followed by a description of sample input files required for multiphase eos construction. we also discuss how to extract data from eos tables in order to compare to experimental data, with an example using the opensesame gui. lastly, we provide a description of how to generate ascii - formatted eos tables most often used by hydro code users.
arxiv:2109.08254
we consider the inverse problem of multi - armed bandits ( imab ) that are widely used in neuroscience and psychology research for behavior modelling. we first show that the imab problem is not convex in general, but can be relaxed to a convex problem via variable transformation. based on this result, we propose a two - step sequential heuristic for ( approximately ) solving the imab problem. we discuss a condition where our method provides global solution to the imab problem with certificate, as well as approximations to further save computing time. numerical experiments indicate that our heuristic method is more robust than directly solving the imab problem via repeated local optimization, and can achieve the performance of monte carlo methods within a significantly decreased running time. we provide the implementation of our method based on cvxpy, which allows straightforward application by users not well versed in convex optimization.
arxiv:2501.18945
this paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. three approaches are examined : residual assessment, the method of modified equations, and shadowing. we investigate how these methods explain the success of numerical simulations in capturing the behavior of chaotic systems, even when facing issues like spurious chaos introduced by numerical methods or suppression of chaos by numerical methods. finally, we point out an open problem, namely to explain why the statistics of long orbits are usually correct, even though we do not have a theoretical guarantee why this should be so.
arxiv:2501.06123
we present preliminary results for the static quark potential computed on some of the dwf lattice configurations generated by the rbc - ukqcd collaborations. most of these results were obtained using wilson lines joining spatial planes fixed into the coulomb gauge. we compare the results from this method with the earlier ones on $ 16 ^ 3 \ times 32 $ lattices using bresenham spatial paths with ape smeared link variables. some preliminary results on $ 24 ^ 3 \ times 64 $ lattices are also presented.
arxiv:hep-lat/0610106
we simulate an individual - based model that represents both the phenotype and genome of digital organisms with predator - prey interactions. we show how open - ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non - equilibrium critical point. the mechanism is analogous to the development of the cascade in fluid turbulence.
arxiv:0707.4533
a full off - diagonal asymptotic expansion is established for the generalized bergman kernels of the renormalized bochner laplacians associated with high tensor powers of a positive line bundle over a compact symplectic manifold. as an application, the algebra of toeplitz operators on the symplectic manifold associated with the renormalized bochner laplacian is constructed.
arxiv:1703.04107
let $ q \ in ( 1, 2 ) $ and $ x \ in [ 0, \ frac1 { q - 1 } ] $. we say that a sequence $ ( \ epsilon _ i ) _ { i = 1 } ^ { \ infty } \ in \ { 0, 1 \ } ^ { \ mathbb { n } } $ is an expansion of $ x $ in base $ q $ ( or a $ q $ - expansion ) if x = \ sum _ { i = 1 } ^ { \ infty } \ epsilon _ iq ^ { - i }. let $ \ mathcal { b } _ { \ aleph _ { 0 } } $ denote the set of $ q $ for which there exists $ x $ with exactly $ \ aleph _ { 0 } $ expansions in base $ q $. in \ cite { ehj } it was shown that $ \ min \ mathcal { b } _ { \ aleph _ { 0 } } = \ frac { 1 + \ sqrt { 5 } } { 2 }. $ in this paper we show that the smallest element of $ \ mathcal { b } _ { \ aleph _ { 0 } } $ strictly greater than $ \ frac { 1 + \ sqrt { 5 } } { 2 } $ is $ q _ { \ aleph _ { 0 } } \ approx1. 64541 $, the appropriate root of $ x ^ 6 = x ^ 4 + x ^ 3 + 2x ^ 2 + x + 1 $. this leads to a full dichotomy for the number of possible $ q $ - expansions for $ q \ in ( \ frac { 1 + \ sqrt { 5 } } { 2 }, q _ { \ aleph _ { 0 } } ) $. we also prove some general results regarding $ \ mathcal { b } _ { \ aleph _ { 0 } } \ cap [ \ frac { 1 + \ sqrt { 5 } } { 2 }, q _ { f } ], $ where $ q _ { f } \ approx 1. 75488 $ is the appropriate root of $ x ^ { 3 } = 2x ^ { 2 } - x + 1. $ moreover, the techniques developed in this paper imply that if $ x \ in [ 0, \ frac { 1 } { q - 1 } ] $ has uncountably many $ q $ -
arxiv:1305.3850
the chandra multiwavelength plane ( champlane ) survey is a comprehensive effort to constrain the population of accretion - powered and coronal low - luminosity x - ray sources ( l _ x < 10 ^ 33 erg s ^ - 1 ) in the galaxy. champlane incorporates x - ray, optical, and infrared observations of fields in the galactic plane imaged with chandra in the past six years. we present the results of a population study of the brightest x - ray sources in champlane. we use x - ray spectral fitting, x - ray lightcurve analysis, and optical photometry of candidate counterparts to determine the properties of 21 sources. our sample includes a previously unreported quiescent low - mass x - ray binary or cataclysmic variable ( r = 20. 9 ) and ten stellar sources ( 12. 5 < r < 15 ), including one flare star ( r = 17. 3 ). we find that quantile analysis, a new technique developed for constraining the x - ray spectral properties of low - count sources, is largely consistent with spectral fitting.
arxiv:0803.2565
we computed linguistic information at the lexical, syntactic, and semantic levels for recognizing inference in text ( rite ) tasks for both traditional and simplified chinese in ntcir - 9 and ntcir - 10. techniques for syntactic parsing, named - entity recognition, and near synonym recognition were employed, and features like counts of common words, statement lengths, negation words, and antonyms were considered to judge the entailment relationships of two statements, while we explored both heuristics - based functions and machine - learning approaches. the reported systems showed robustness by simultaneously achieving second positions in the binary - classification subtasks for both simplified and traditional chinese in ntcir - 10 rite - 2. we conducted more experiments with the test data of ntcir - 9 rite, with good results. we also extended our work to search for better configurations of our classifiers and investigated contributions of individual features. this extended work showed interesting results and should encourage further discussion.
arxiv:1504.02150
in this paper we define an action by the symplectomorphisms on a symplectic manifold on the space of real singular polarizations. it is then shown that under some topological conditions, this action preserves quantization by a fixed prequantum line bundle.
arxiv:2106.15484
a local deformation property for uniform embeddings in metric manifolds ( ld ) is formulated and its behaviour is studied in a formal view point. it is shown that any metric manifold with a geometric group action, typical metric spaces ( euclidean space, hyperbolic space and cylinders ) and for \ kappa \ leq 0 the \ kappa - cone ends over any compact lipschitz metric manifolds, all of them have the property ( ld ). we also formulate a notion of end deformation property for uniform embeddings over proper product ends ( ed ). for example, the 0 - cone end over a compact metric manifold has the property ( ed ) if it has the property ( ld ). it is shown that if a metric manifold m has finitely many proper product ends with the property ( ed ), then the group of bounded uniform homeomorphisms of m endowed with the uniform topology admits a strong deformation retraction onto the subgroup of bounded uniform homeomorphisms which are identity over those ends. we also study a role of uniform isotopies in deformation of uniform homeomorphisms and show that alexander isotopies in \ kappa - cones induce contractions of some subgroups of groups of bounded uniform homeomorphisms.
arxiv:1301.3265
we study lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. we consider them as invariants on the space of hitchin representations and show that there is a gap between any two consecutive lyapunov exponents. moreover we characterize the uniformizing representation of the riemann surface as the one with the extremal gaps. the strategy of the proof is to relate lyapunov exponents in the case of anosov representations to other invariants, where the gap result is already available or where we can directly show it. in particular, firstly we relate lyapunov exponents to a foliated lyapunov exponent associated to a foliation h \ " older isomorphic to the unstable foliation on the unitary tangent bundle of a riemann surface. secondly, we relate them to the renormalized intersection product in the setting of the thermodynamic formalism developed by bridgeman, canary, labourie and sambarino.
arxiv:2211.03651
a controlling factor in the seasonal and climatological evolution of the sea ice cover is its albedo $ \ alpha $. here we analyze arctic data from the advanced very high resolution radiometer ( avhrr ) polar pathfinder and assess the seasonality and variability of broadband albedo from a 23 year daily record. we produce a histogram of daily albedo over ice covered regions in which the principal albedo transitions are seen ; high albedo in late winter and spring, the onset of snow melt and melt pond formation in the summer, and fall freeze up. the bimodal late summer distribution demonstrates the combination of the poleward progression of the onset of melt with the coexistence of perennial bare ice with melt ponds and open water, which then merge to a broad peak at $ \ alpha \ gtrsim $ 0. 5. we find the interannual variability to be dominated by the low end of the $ \ alpha $ distribution, highlighting the controlling influence of the ice thickness distribution and large - scale ice edge dynamics. the statistics obtained provide a simple framework for model studies of albedo parameterizations and sensitivities.
arxiv:1109.3058
fields such that φ ( e1 + e2 ) = φ ( e1 ) + φ ( e2 ), φ ( e1e2 ) = φ ( e1 ) φ ( e2 ), and φ ( 1e ) = 1f, where e1 and e2 are arbitrary elements of e. all field homomorphisms are injective. if φ is also surjective, it is called an isomorphism ( or the fields e and f are called isomorphic ). a field is called a prime field if it has no proper ( i. e., strictly smaller ) subfields. any field f contains a prime field. if the characteristic of f is p ( a prime number ), the prime field is isomorphic to the finite field fp introduced below. otherwise the prime field is isomorphic to q. = = finite fields = = finite fields ( also called galois fields ) are fields with finitely many elements, whose number is also referred to as the order of the field. the above introductory example f4 is a field with four elements. its subfield f2 is the smallest field, because by definition a field has at least two distinct elements, 0 and 1. the simplest finite fields, with prime order, are most directly accessible using modular arithmetic. for a fixed positive integer n, arithmetic " modulo n " means to work with the numbers z / nz = { 0, 1,..., n − 1 }. the addition and multiplication on this set are done by performing the operation in question in the set z of integers, dividing by n and taking the remainder as result. this construction yields a field precisely if n is a prime number. for example, taking the prime n = 2 results in the above - mentioned field f2. for n = 4 and more generally, for any composite number ( i. e., any number n which can be expressed as a product n = r ⋅ s of two strictly smaller natural numbers ), z / nz is not a field : the product of two non - zero elements is zero since r ⋅ s = 0 in z / nz, which, as was explained above, prevents z / nz from being a field. the field z / pz with p elements ( p being prime ) constructed in this way is usually denoted by fp. every finite field f has q = pn elements, where p is prime and n ≥ 1. this statement holds since f may be viewed as a vector space over its prime field
https://en.wikipedia.org/wiki/Field_(mathematics)
we present a ` global ' description of the wide variety of high energy elastic and diffractive data that are presently available, particularly from the lhc experiments. the model is based on only one pomeron pole, but includes multi - pomeron interactions and, significantly, includes the transverse momentum dependence of intermediate partons as a function of their rapidity, which provides the rapidity dependence of the multi - pomeron vertices. we give predictions for diffractive observables at lhc energies.
arxiv:1312.3851
we use perron ' s method to construct viscosity solutions of fully nonlinear degenerate parabolic pathwise ( rough ) partial differential equations. this provides an intrinsic method for proving the existence of solutions that relies only on a comparison principle, rather than considering equations driven by smooth approximating paths. the result covers the case of multidimensional geometric rough path noise, where the noise coefficients depend nontrivially on space and on the gradient of the solution. also included in this note is a discussion of the comparison principle and a summary of the pathwise equations for which one has been proved.
arxiv:1605.01108
task allocation in heterogeneous multi - agent teams often requires reasoning about multi - dimensional agent traits ( i. e., capabilities ) and the demands placed on them by tasks. however, existing methods tend to ignore the fact that not all traits equally contribute to a given task. ignoring such inherent preferences or relative importance can lead to unintended sub - optimal allocations of limited agent resources that do not necessarily contribute to task success. further, reasoning over a large number of traits can incur a hefty computational burden. to alleviate these concerns, we propose an algorithm to infer task - specific trait preferences implicit in expert demonstrations. we leverage the insight that the consistency with which an expert allocates a trait to a task across demonstrations reflects the trait ' s importance to that task. inspired by findings in psychology, we account for the fact that the inherent diversity of a trait in the dataset influences the dataset ' s informativeness and, thereby, the extent of the inferred preference or the lack thereof. through detailed numerical simulations and evaluations of a publicly - available soccer dataset ( fifa 20 ), we demonstrate that we can successfully infer implicit trait preferences and that accounting for the inferred preferences leads to more computationally efficient and effective task allocation, compared to a baseline approach that treats all traits equally.
arxiv:2302.10817
we develop a constitutive model allowing for the description of the rheology of two - dimensional soft dense suspensions above jamming. starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a non - linear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain - rate and vorticity tensors. the coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle - level parameters. this constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. more complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.
arxiv:2102.05938
nowadays deep learning - based methods have achieved a remarkable progress at the image classification task among a wide range of commonly used datasets ( imagenet, cifar, svhn, caltech 101, sun397, etc. ). sota performance on each of the mentioned datasets is obtained by careful tuning of the model architecture and training tricks according to the properties of the target data. although this approach allows setting academic records, it is unrealistic that an average data scientist would have enough resources to build a sophisticated training pipeline for every image classification task he meets in practice. this work is focusing on reviewing the latest augmentation and regularization methods for the image classification and exploring ways to automatically choose some of the most important hyperparameters : total number of epochs, initial learning rate value and it ' s schedule. having a training procedure equipped with a lightweight modern cnn architecture ( like bilenetv3 or efficientnet ), sufficient level of regularization and adaptive to data learning rate schedule, we can achieve a reasonable performance on a variety of downstream image classification tasks without manual tuning of parameters to each particular task. resulting models are computationally efficient and can be deployed to cpu using the openvino toolkit. source code is available as a part of the openvino training extensions ( https : / / github. com / openvinotoolkit / training _ extensions ).
arxiv:2108.07049
recent work in deep reinforcement learning ( rl ) has produced algorithms capable of mastering challenging games such as go, chess, or shogi. in these works the rl agent directly observes the natural state of the game and controls that state directly with its actions. however, when humans play such games, they do not just reason about the moves but also interact with their physical environment. they understand the state of the game by looking at the physical board in front of them and modify it by manipulating pieces using touch and fine - grained motor control. mastering complicated physical systems with abstract goals is a central challenge for artificial intelligence, but it remains out of reach for existing rl algorithms. to encourage progress towards this goal we introduce a set of physically embedded planning problems and make them publicly available. we embed challenging symbolic tasks ( sokoban, tic - tac - toe, and go ) in a physics engine to produce a set of tasks that require perception, reasoning, and motor control over long time horizons. although existing rl algorithms can tackle the symbolic versions of these tasks, we find that they struggle to master even the simplest of their physically embedded counterparts. as a first step towards characterizing the space of solution to these tasks, we introduce a strong baseline that uses a pre - trained expert game player to provide hints in the abstract space to an rl agent ' s policy while training it on the full sensorimotor control task. the resulting agent solves many of the tasks, underlining the need for methods that bridge the gap between abstract planning and embodied control. see illustrating video at https : / / youtu. be / rwhihlym _ 1k.
arxiv:2009.05524
in this paper we uses an i. i. hirschman - w. beckner entropy argument to give an uncertainty inequality for the $ q $ - bessel fourier transform : $ $ \ mathcal { f } _ { q, v } f ( x ) = c _ { q, v } \ int _ { 0 } ^ { \ infty } f ( t ) j _ { v } ( xt, q ^ { 2 } ) t ^ { 2v + 1 } d _ { q } t, $ $ where $ j _ v ( x, q ) $ is the normalized hahn - exton $ q $ - bessel function.
arxiv:0707.1494
for arrays $ ( s _ { i, j } ) _ { 1 \ leq i \ leq j } $ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $ ( s _ { 1, n } ) _ { n = 1 } ^ { \ infty } $ can be bounded in terms of a measure of the ` ` mean subadditivity ' ' of the process $ ( s _ { i, j } ) _ { 1 \ leq i \ leq j } $. we derive universal upcrossing inequalities with exponential decay for kingman ' s subadditive ergodic theorem, the shannon - - macmillan - - breiman theorem and for the convergence of the kolmogorov complexity of a stationary sample.
arxiv:math/0608311
we show how solution concepts from cooperative game theory can be used to tackle the problem of pruning neural networks. the ever - growing size of deep neural networks ( dnns ) increases their performance, but also their computational requirements. we introduce a method called game theory assisted pruning ( gtap ), which reduces the neural network ' s size while preserving its predictive accuracy. gtap is based on eliminating neurons in the network based on an estimation of their joint impact on the prediction quality through game theoretic solutions. specifically, we use a power index akin to the shapley value or banzhaf index, tailored using a procedure similar to dropout ( commonly used to tackle overfitting problems in machine learning ). empirical evaluation of both feedforward networks and convolutional neural networks shows that this method outperforms existing approaches in the achieved tradeoff between the number of parameters and model accuracy.
arxiv:2311.10468
in this work, we present a hybrid numerical method for solving evolution partial differential equations ( pdes ) by merging the time finite element method with deep neural networks. in contrast to the conventional deep learning - based formulation where the neural network is defined on a spatiotemporal domain, our methodology utilizes finite element basis functions in the time direction where the space - dependent coefficients are defined as the output of a neural network. we then apply the galerkin or collocation projection in the time direction to obtain a system of pdes for the space - dependent coefficients which is approximated in the framework of pinn. the advantages of such a hybrid formulation are twofold : statistical errors are avoided for the integral in the time direction, and the neural network ' s output can be regarded as a set of reduced spatial basis functions. to further alleviate the difficulties from high dimensionality and low regularity, we have developed an adaptive sampling strategy that refines the training set. more specifically, we use an explicit density model to approximate the distribution induced by the pde residual and then augment the training set with new time - dependent random samples given by the learned density model. the effectiveness and efficiency of our proposed method have been demonstrated through a series of numerical experiments.
arxiv:2409.02810
recent lhcb measurements of the $ j / \ psi $ meson production in jets is analyzed using fragmentation jet function formalism. it is shown that disagreement with theoretical predictions for distribution over the fraction of $ j / \ psi $ transverse momentum $ z ( j / \ psi ) $ in the cases of prompt production can be explained if one takes into account evolution of the fragmentation function and contributions from double parton scattering mechanism.
arxiv:1703.09081
bent - tailed ( bt ) radio sources have long been known to trace over densities in the universe up to z ~ 1 and there is increasing evidence this association persists out to redshifts of 2. the morphology of the jets in bt galaxies is primarily a function of the environment that they have resided in and so bts provide invaluable clues as to their local conditions. thus, not only can samples of bt galaxies be used as signposts of large - scale structure, but are also valuable for obtaining a statistical measurement of properties of the intra - cluster medium including the presence of cluster accretion shocks & winds, and as historical anemometers, preserving the dynamical history of their surroundings in their jets. we discuss the use of bts to unveil large - scale structure and provide an example in which a bt was used to unlock the dynamical history of its host cluster. in addition to their use as density and dynamical indicators, bts are useful probes of the magnetic field on their environment on scales which are inaccessible to other methods. here we discuss a novel way in which a particular sub - class of bts, the so - called ` corkscrew ' galaxies might further elucidate the coherence lengths of the magnetic fields in their vicinity. given that bts are estimated to make up a large population in next generation surveys we posit that the use of jets in this way could provide a unique source of environmental information for clusters and groups up to z = 2.
arxiv:1412.8596
modern particle accelerators and their applications increasingly rely on precisely coordinated interactions of intense charged particle and laser beams. femtosecond - scale synchronization alongside micrometre - scale spatial precision are essential e. g. for pump - probe experiments, seeding and diagnostics of advanced light sources and for plasma - based accelerators. state - of - the - art temporal or spatial diagnostics typically operate with low - intensity beams to avoid material damage at high intensity. as such, we present a plasma - based approach, which allows measurement of both temporal and spatial overlap of high - intensity beams directly at their interaction point. it exploits amplification of plasma afterglow arising from the passage of an electron beam through a laser - generated plasma filament. the corresponding photon yield carries the spatiotemporal signature of the femtosecond - scale dynamics, yet can be observed as a visible light signal on microsecond - millimetre scales.
arxiv:1908.09263
brihadeeswarar temple of thanjavur, among many others, stand as a testament to the ingenuity and skill of ancient civil and military engineers. other monuments, no longer standing, such as the hanging gardens of babylon and the pharos of alexandria, were important engineering achievements of their time and were considered among the seven wonders of the ancient world. the six classic simple machines were known in the ancient near east. the wedge and the inclined plane ( ramp ) were known since prehistoric times. the wheel, along with the wheel and axle mechanism, was invented in mesopotamia ( modern iraq ) during the 5th millennium bc. the lever mechanism first appeared around 5, 000 years ago in the near east, where it was used in a simple balance scale, and to move large objects in ancient egyptian technology. the lever was also used in the shadoof water - lifting device, the first crane machine, which appeared in mesopotamia c. 3000 bc, and then in ancient egyptian technology c. 2000 bc. the earliest evidence of pulleys date back to mesopotamia in the early 2nd millennium bc, and ancient egypt during the twelfth dynasty ( 1991 – 1802 bc ). the screw, the last of the simple machines to be invented, first appeared in mesopotamia during the neo - assyrian period ( 911 – 609 ) bc. the egyptian pyramids were built using three of the six simple machines, the inclined plane, the wedge, and the lever, to create structures like the great pyramid of giza. the earliest civil engineer known by name is imhotep. as one of the officials of the pharaoh, djoser, he probably designed and supervised the construction of the pyramid of djoser ( the step pyramid ) at saqqara in egypt around 2630 – 2611 bc. the earliest practical water - powered machines, the water wheel and watermill, first appeared in the persian empire, in what are now iraq and iran, by the early 4th century bc. kush developed the sakia during the 4th century bc, which relied on animal power instead of human energy. hafirs were developed as a type of reservoir in kush to store and contain water as well as boost irrigation. sappers were employed to build causeways during military campaigns. kushite ancestors built speos during the bronze age between 3700 and 3250 bc. bloomeries and blast furnaces were also created during the 7th centuries bc in kush. ancient greece developed machines in both civilian and military domains. the antikythera
https://en.wikipedia.org/wiki/Engineering
we will show that every element of a finitely generated abelian group is automorphically equivalent what we will define to be a { \ em representative element } in a { \ em repeat - free subgroup }, and for finite abelian groups we can count the number of automorphism classes of elements.
arxiv:1109.2106
large language models ( llms ) have performed well on several reasoning benchmarks, including ones that test analogical reasoning abilities. however, it has been debated whether they are actually performing humanlike abstract reasoning or instead employing less general processes that rely on similarity to what has been seen in their training data. here we investigate the generality of analogy - making abilities previously claimed for llms ( webb, holyoak, & lu, 2023 ). we take one set of analogy problems used to evaluate llms and create a set of " counterfactual " variants - versions that test the same abstract reasoning abilities but that are likely dissimilar from any pre - training data. we test humans and three gpt models on both the original and counterfactual problems, and show that, while the performance of humans remains high for all the problems, the gpt models ' performance declines sharply on the counterfactual set. this work provides evidence that, despite previously reported successes of llms on analogical reasoning, these models lack the robustness and generality of human analogy - making.
arxiv:2402.08955
the large attention - based encoder - decoder network ( transformer ) has become prevailing recently due to its effectiveness. but the high computation complexity of its decoder raises the inefficiency issue. by examining the mathematic formulation of the decoder, we show that under some mild conditions, the architecture could be simplified by compressing its sub - layers, the basic building block of transformer, and achieves a higher parallelism. we thereby propose compressed attention network, whose decoder layer consists of only one sub - layer instead of three. extensive experiments on 14 wmt machine translation tasks show that our model is 1. 42x faster with performance on par with a strong baseline. this strong baseline is already 2x faster than the widely used standard baseline without loss in performance.
arxiv:2101.00542
a decoherence mechanism caused by spacetime curvature is discussed. the spin state of a particle is shown to decohere if only the particle moves in a curved spacetime. in particular, when a particle is near the event horizon of a black hole, an extremely rapid spin decoherence occurs for an observer who is static in a killing time, however slow the particle ' s motion is.
arxiv:quant-ph/0312064
graphical passwords ( gpws ) are convenient for mobile equipments with touch screen. topological graphic passwords ( topsnut - gpws ) can be saved in computer by classical matrices and run quickly than the existing gpws. we research topsnut - gpws by the matching of view, since they have many advantages. we discuss : configuration matching partition, coloring / labelling matching partition, set matching partition, matching chain, etc. and, we introduce new graph labellings for enriching topsnut - matchings and show that these labellings can be realized for trees or spanning trees of networks. in theoretical works we explore graph labelling analysis, and show that every graph admits our extremal labellings and set - type labellings in graph theory. many of the graph labellings mentioned are related with problems of set matching partitions to number theory, and yield new objects and new problems to graph theory.
arxiv:1808.03324
direct simulations of two - dimensional plane channel flow of a viscoelastic fluid at reynolds number re = 3000 reveal the existence of a family of attractors whose structure closely resembles the linear tollmien - schlichting ( ts ) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the ts mode. at the parameter values chosen, this solution branch is not connected to the nonlinear ts solution branch found for newtonian flow, and thus represents a solution family that is nonlinearly self - sustained by viscoelasticity. the ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear ts mode, and increases strongly with weissenberg number, wi. for the latter, there is a transition in the scaling of this ratio as wi increases, and the wi at which the nonlinear solution family comes into existence is just above this transition. finally, evidence indicates that this branch is connected through an unstable solution branch to two - dimensional elastoinertial turbulence ( eit ). these results suggest that, in the parameter range considered here, the bypass transition leading to eit is mediated by nonlinear amplification and self - sustenance of perturbations that excite the tollmien - schlichting mode.
arxiv:1910.11419
a strong connection between cluster algebras and representation theory was established by the cluster category. cluster characters, like the original caldero - chapoton ( cc ) map, are maps from certain triangulated categories to cluster algebras and they have generated much interest. holm and j { \ o } rgensen constructed a modified cc map from a sufficiently nice triangulated category to a commutative ring, which is a generalised frieze under some conditions. in their construction, a quotient $ k _ { 0 } ^ { sp } ( \ mathcal { t } ) / m $ of a grothendieck group of a cluster tilting subcategory $ \ mathcal { t } $ is used. in this article, we show that this quotient is the grothendieck group of a certain extriangulated category, thereby exposing the significance of it and the relevance of extriangulated structures. we use this to define another modified cc map that recovers the one of holm - - j { \ o } rgensen. we prove our results in a higher homological context. suppose $ \ mathcal { s } $ is a $ ( d + 2 ) $ - angulated category with subcategories $ \ mathcal { x } \ subseteq \ mathcal { t } \ subseteq \ mathcal { s } $, where $ \ mathcal { x } $ is functorially finite and $ \ mathcal { t } $ is $ 2d $ - cluster tilting, satisfying some mild conditions. we show there is an isomorphism between the grothendieck group $ k _ { 0 } ( \ mathcal { s }, \ mathbb { e } _ { \ mathcal { x } }, \ mathfrak { s } _ { \ mathcal { x } } ) $ of the category $ \ mathcal { s } $, equipped with the $ d $ - exangulated structure induced by $ \ mathcal { x } $, and the quotient $ k _ { 0 } ^ { sp } ( \ mathcal { t } ) / n $, where $ n $ is the higher analogue of $ m $ above. when $ \ mathcal { x } = \ mathcal { t } $ the isomorphism is induced by the higher index with respect to $ \ mathcal { t } $ introduced recently by j { \ o } rgensen.
arxiv:2106.02142
in this article, we study the fluctuation of linear eigenvalue statistics of symmetric circulant matrices $ ( sc _ n ) $ with independent entries which satisfy some moment conditions. we show that $ \ frac { 1 } { \ sqrt { n } } \ tr \ phi ( sc _ n ) $ obey the central limit theorem ( clt ) type result, where $ \ phi $ is a nice test function.
arxiv:2004.11294
one of the aims of aether scalar tensor theory ( aest ) is to reproduce the successes of modified newtonian dynamics ( mond ) on galactic scales. indeed, the quasi - static limit of aest achieves precisely this, assuming that the vector field $ \ vec { a } $ vanishes and that the so - called ghost condensate can be neglected. the effects of the ghost condensate were investigated in detail in previous studies. here, we focus on the assumption of a vanishing vector field. we argue that this assumption is not always justified and show how to correctly take into account the vector field, finding that the quasi - static limit depends on a model parameter $ m _ \ times $. in the limit $ m _ \ times \ to 0 $, one recovers the quasi - static limit with a vanishing vector field. in particular, one finds a two - field version of mond. in the opposite limit, $ m _ \ times \ to \ infty $, one finds a single - field version of mond. we show that, in practice, much of the phenomenology of the quasi - static limit depends only very little on the value of $ m _ \ times $. still, for some observational tests, such as those involving wide binaries, $ m _ \ times $ has percent - level effects that may be important.
arxiv:2305.07742
we investigate whether the affleck - dine mechanism can produce sufficient baryon number of the universe in the gauge - mediated susy breaking models, while evading the cosmological moduli problem by late - time entropy production. we find that the q - ball formation makes the scenario difficult, irrespective of the detail mechanism of the entropy production.
arxiv:hep-ph/0202014
to exist today? almost certainly no, given the chain of circumstances that led to our existence. these considerations suggest that we are unique not just on our planet but in the whole milky way. and if our planet is so special, it becomes all the more important to preserve this unique world for ourselves, our descendants and the many creatures that call earth home. " ( p. 99. )
https://en.wikipedia.org/wiki/Technology
game - like programs have become increasingly popular in many software engineering domains such as mobile apps, web applications, or programming education. however, creating tests for programs that have the purpose of challenging human players is a daunting task for automatic test generators. even if test generation succeeds in finding a relevant sequence of events to exercise a program, the randomized nature of games means that it may neither be possible to reproduce the exact program behavior underlying this sequence, nor to create test assertions checking if observed randomized game behavior is correct. to overcome these problems, we propose neatest, a novel test generator based on the neuroevolution of augmenting topologies ( neat ) algorithm. neatest systematically explores a program ' s statements, and creates neural networks that operate the program in order to reliably reach each statement - - that is, neatest learns to play the game in a way to reliably cover different parts of the code. as the networks learn the actual game behavior, they can also serve as test oracles by evaluating how surprising the observed behavior of a program under test is compared to a supposedly correct version of the program. we evaluate this approach in the context of scratch, an educational programming environment. our empirical study on 25 non - trivial scratch games demonstrates that our approach can successfully train neural networks that are not only far more resilient to random influences than traditional test suites consisting of static input sequences, but are also highly effective with an average mutation score of more than 65 %.
arxiv:2208.13632
high - resolution inputs enable large vision - language models ( lvlms ) to discern finer visual details, enhancing their comprehension capabilities. to reduce the training and computation costs caused by high - resolution input, one promising direction is to use sliding windows to slice the input into uniform patches, each matching the input size of the well - trained vision encoder. although efficient, this slicing strategy leads to the fragmentation of original input, i. e., the continuity of contextual information and spatial geometry is lost across patches, adversely affecting performance in cross - patch context perception and position - specific tasks. to overcome these shortcomings, we introduce hires - llava, a novel framework designed to efficiently process any size of high - resolution input without altering the original contextual and geometric information. hires - llava comprises two innovative components : ( i ) a slicerestore adapter that reconstructs sliced patches into their original form, efficiently extracting both global and local features via down - up - sampling and convolution layers, and ( ii ) a self - mining sampler to compresses the vision tokens based on themselves, preserving the original context and positional information while reducing training overhead. to assess the ability of handling context fragmentation, we construct a new benchmark, entitygrid - qa, consisting of edge - related and position - related tasks. our comprehensive experiments demonstrate the superiority of hires - llava on both existing public benchmarks and on entitygrid - qa, particularly on document - oriented tasks, establishing new standards for handling high - resolution inputs.
arxiv:2407.08706
we show that the edges of every 3 - connected planar graph except $ k _ 4 $ can be colored with two colors in such a way that the graph has no color preserving automorphisms. also, we characterize all graphs which have the property that their edges can be $ 2 $ - colored so that no matter how the graph is embedded in any orientable surface, there is no homeomorphism of the surface which induces a non - trivial color preserving automorphism of the graph.
arxiv:1206.1945
in economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. in some applications such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. our work is motivated by a dataset consisting of time series of industry - to - industry transactions. in this example, pairwise relationships between standard industrial classification ( sic ) codes can be represented using a network, with sic codes as nodes and pairwise transactions between sic codes as edges, while the observed time series of the amounts of the transactions for each pair of sic codes can be regarded as time - varying weights on the edges. inspired by knight et al. ( 2020 ), we introduce the gnar - edge model which allows modelling of multiple time series utilising the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. the method is validated through simulations. results from the implementation of the gnar - edge model on the real industry - to - industry data show good fitting and predictive performance of the model. the predictive performance is improved when sparsifying the network using a lead - lag analysis and thresholding edges according to a lead - lag score.
arxiv:2305.16097
we present a technically simple treatment of self - trapping of bose - einstein condensates in double well traps based on intuitive semi - classical approximations. our analysis finally leads to a convenient closed form approximation for the time - averaged population imbalance valid in both the mean - field case and in the case of finite particle numbers for short times.
arxiv:1112.4721
lhcb is one of the four experiments at the large hadron collider ( cern ), dedicated to the study of b - hadrons. throughout my research, i studied in particular b - baryons which are abundantly produced at the lhcb. my habilitation summarises the studies of fundamental properties of these particles within the standard model. in particular, i discuss both lifetime and mass measurements. this work is followed by a search of new physics using a lepton universality test. finally, i discuss my contribution to the upgrade detectors of the lhcb experiment in particular those related to the calorimeter and the scintillator fibre tracker.
arxiv:2005.11226
we consider the nonlinear schrodinger equation with cubic ( focusing or defocusing ) nonlinearity on the multidimensional torus. for special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. the proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two - dimensional discrete dynamical system.
arxiv:1010.5173
people leverage avatars to communicate nonverbal behaviors in immersive virtual reality ( vr ), like interpersonal distance [ 2, 6 ] and virtual touch [ 5 ]. however, violations of appropriate physical distancing and unsolicited intimate touching behavior in social virtual worlds represent potential social and psychological virtual harm to older adolescent users [ 4, 8 ]. obtaining peer acceptance and social rewards, while avoiding social rejection can drive older adolescent behavior even in simulated virtual spaces [ 1, 3 ], and while " the beginning of adolescence is largely defined by a biological event, [... ] the end of adolescence is often defined socially " [ 3 ] ( p. 912 ). avatar crossing, the phenomenon of avatars walking through each other in virtual environments, is a unique capability of virtual embodiment, and others intriguing possibilities and ethical concerns for older adolescents experiencing social virtual spaces. for example, the ability to cross through and share positions with other avatars in a virtual classroom helps students concentrate on accessing and comprehending information without concerns about blocking others when navigating for better viewpoints [ 10 ]. however, the ability to cross through others in virtual spaces has been associated with a reduction in perceived presence and avatar realism, coupled with a greater level of discomfort and intimidation in comparison to avatar collisions [ 12 ]. in this article, we consider the potential benefits and harms of utilizing avatar crossing with adolescent users.
arxiv:2405.05933
we calculate the tidal torque on a uniformly rotating 1 msun star at various stages of core hydrogen burning by an orbiting companion. we apply the ` traditional approximation ' and solve the radial part of the tidal perturbations by matrix inversion of the set of finite difference equations on a very fine grid. we have identified resonances with gravity - and quasi - toroidal modes with up to 1000 radial nodes in the more evolved stellar models. for low forcing frequencies we find significant tidal response due to viscous damping of inertial modes in the convective envelope of the solar - type star. we conclude that effects due to stellar rotation ( including resonance locking ) may considerably enhance the speed of tidal evolution in solar - type stars.
arxiv:astro-ph/0202276
two types of approximation to the paradoxical russell set are presented, one approximating it from below, one from above. it is shown that any lower approximation gives rise to a better approximation containing it, and that any upper approximation contains a distinct better approximation. the russell paradox is then seen to be the claim that two of these processes of better approximations stop, and at the same set. this suggests that the unrestricted axiom of comprehension is, not a coherent intuition worthy of rescue from a mysterious paradox, but simply wishful thinking, a confusion of sets as extensional objects with classes defined by a property.
arxiv:2103.00090
fluorescence spectroscopy is an image correlation technique to analyze and characterize the molecular dynamics from a sequence of fluorescence images. many image correlation techniques have been developed for different applications [ 1 ]. but in practice the use of these techniques is often limited to a manually selected region of analysis where it is assumed that the observed molecules have homogeneous and constant behavior over time. due to the spatial and temporal complexity of biological objects, this assumption is frequently at fault. it is then necessary to propose a robust method for discriminating the different behaviors over time from experience, as well as identification of the type of dynamics ( diffusion or flow ). this paper presents an original system of automatic discrimination and identification of spatially and temporally uniform regions for the analysis of molecular different dynamics over time by calculating stics ( spatio - temporal image correlation spectroscopy ) at different time lags. an evaluation of system performance is presented on simulated images and images acquired by fluorescence microscopy on actin cytoskeleton.
arxiv:1710.08186
molecular hydrogen clouds are a key component of the interstellar medium because they are the birthplaces for stars. they are embedded in atomic gas that pervades the interstellar space. however, the details of how molecular clouds assemble from and interact with the atomic gas are still largely unknown. as a result of new observations of the 158 ~ $ \ mu $ m line of ionized carbon cii in the cygnus region within the feedback program on sofia ( stratospheric observatory for infrared astronomy ), we present compelling evidence that cii unveils dynamic interactions between cloud ensembles. this process is neither a head - on collision of fully molecular clouds nor a gentle merging ofonly atomic clouds. moreover, we demonstrate that the dense molecular clouds associated with the dr21 and w75n star - forming regions and a cloud at higher velocity are embedded in atomic gas and all components interact over a large range of velocities ( 20 km / s ). the atomic gas has a density of 100 cm $ ^ { - 3 } $ and a temperature of 100 k. we conclude that the cii 158 $ \ mu $ m line is an excellent tracer to witness the processes involved in cloud interactions and anticipate further detections of this phenomenon in other regions
arxiv:2302.09266
we aim to estimate the contribution of the radial component of the lorentz force to the gas rotation in several types of galaxies. using typical parameters for the exponential scale of synchrotron emission and the scale length of hi gas, under the assumption of equipartition between the energies of cosmic rays and total magnetic fields, we derive the lorentz force and compare it to the gravitational force in the radial component of the momentum equation. we distinguish the different contributions between the large - scale and the small - scale turbulent fields by reynolds averaging. we compare these findings with a dynamical dynamo model. we find a possible reduction of circular gas velocity in the very outer parts and an increase inside a radius of four times the synchrotron scale length. sufficiently localized radial reversals of the magnetic field may cause characteristic modulations in the gas rotation curve with typical amplitudes of 10 - 20 km / s. it is unlikely that the magnetic field contributes to the flat rotation in the outer parts of galaxies. if anything, it will \ emph { impede } the gravitationally supported rotation, demanding for an even higher halo mass to explain the observed rotation profile. we speculate that this may have consequences for ram pressure stripping and the truncation of the stellar disc.
arxiv:1407.6998
we report the first experimental study of cluster size distributions in electrostatically driven granular submonolayers. the cluster size distribution in this far - from - equilibrium process exhibits dynamic scaling behavior characteristic of the ( nearly equilibrium ) ostwald ripening, controlled by the attachment and detachment of the " gas " particles. the scaled size distribution, however, is different from the classical wagner distribution obtained in the limit of a vanishingly small area fraction of the clusters. a much better agreement is found with the theory of conti et al. [ phys. rev. e 65, 046117 ( 2002 ) ] which accounts for the cluster merger.
arxiv:cond-mat/0411522
distance - based approaches in phylogenetics such as neighbor - joining are a fast and popular approach for building trees. these methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic model of site substitution. most models assume a distribution of rates across sites, often based on a gamma distribution. provided the ( shape ) parameter of this distribution is known, the method can correctly reconstruct the tree. however, if the shape parameter is not known then we show that topologically different trees, with different shape parameters and associated positive branch lengths, can lead to exactly matching distributions on pairwise site patterns between all pairs of taxa. thus, one could not distinguish between the two trees using pairs of sequences without some prior knowledge of the shape parameter. more surprisingly, this can happen for { \ em any } choice of distinct shape parameters on the two trees, and thus the result is not peculiar to a particular or contrived selection of the shape parameters. on a positive note, we point out known conditions where identifiability can be restored ( namely, when the branch lengths are clocklike, or if methods such as maximum likelihood are used ).
arxiv:0808.2660
we investigate the efficiency of interstellar polarization $ p _ \ lambda / a _ \ lambda $ where $ p _ \ lambda $ is the fractional linear polarization and $ a _ \ lambda $ is extinction, in 16 lines of sight as a function of wavelength $ \ lambda $. we have used the data obtained with the low - dispersion spectropolarimeter hbs as well as those in literature. it is found that the polarization efficiency $ p _ \ lambda / a _ \ lambda $ is proportional to $ \ exp ( - \ beta / \ lambda ) $ in wavelength $ \ lambda \ approx 0. 4 - 0. 8 \ micron $, where $ \ beta $ is a parameter which varies from 0. 5 to 1. 2 $ \ micron $. we find that $ \ beta $ is negatively correlated with the dust temperature deduced from infrared data by schlegel et al., suggesting that the polarization efficiency is higher in short wavelength for higher temperature. according to the alignment theory by radiative torques ( rats ), if the radiation is stronger and bluer, rats will make small grains align better, and the polarization efficiency will increase in short wavelength. our finding of the correlation between $ \ beta $ and the temperature is consistent with what is expected with the alignment mechanism by rats.
arxiv:1101.4253
for a perfectoid ring $ r $, we compute the full $ \ mathrm { ro } ( \ mathbb t ) $ - graded ring $ \ mathrm { tf } _ \ bigstar ( r ; \ mathbf z _ p ) $. this extends and simplifies work of gerhardt and angeltveit - gerhardt. in even degrees, we find an $ \ mathrm { ru } ( \ mathbb t ) $ - graded version of b \ " okstedt periodicity, with some additional classes in the case of perfect $ \ mathbf f _ p $ - algebras. in odd degrees, we find extremely intricate and rather mysterious torsion. we also discuss the $ \ mathrm { ro } ( \ mathbb t ) $ - graded homotopy tambara functors $ \ underline \ pi _ \ bigstar \ mathrm { thh } ( r ; \ mathbf z _ p ) $.
arxiv:2205.12151
we say that a finite metric space $ x $ can be embedded almost isometrically into a class of metric spaces $ c $, if for every $ \ epsilon > 0 $ there exists an embedding of $ x $ into one of the elements of $ c $ with the bi - lipschitz distortion less then $ 1 + \ epsilon $. we show that almost isometric embeddability conditions are equal for following classes of spaces ( a ) quotients of euclidean spaces by isometric actions of finite groups, ( b ) $ l _ 2 $ - wasserstein spaces over euclidean spaces, ( c ) compact flat manifolds, ( d ) compact flat orbifolds, ( e ) quotients of connected compact bi - invariant lie groups by isometric actions of compact lie groups. ( this one is the most surprising. ) we call spaces which satisfy this conditions finite flat spaces. the question about synthetic definition naturally arises. since markov type constants depend only on finite subsets we can conclude that connected compact bi - invariant lie groups and their quotients have markov type $ 2 $ with constant $ 1 $.
arxiv:1712.08177
we propose a continuous feedback control strategy that steers a point - mass vehicle safely to a desired destination, in a quasi - optimal manner, from almost all initial conditions in an n - dimensional euclidean space cluttered with spherical obstacles. the main idea consists in avoiding each obstacle via the shortest path within the cone enclosing the obstacle, and moving straight towards the target when the vehicle has a clear line of sight to the target location. the proposed control strategy ensures safe navigation with almost global asymptotic stability of the equilibrium point at the target location. simulation results, illustrating the effectiveness of the proposed approach, are presented.
arxiv:2302.12309
in this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test observables. the method is based on the bayesian inversion framework, which provides a platform for analyzing the posterior distribution and naturally leads to an efficient numerical sampling algorithm. we highlight that, the stability estimate is obtained by treating the potential functions as intermediate variables in the following way : the discrepancy between two sets of observation data of training observables can bound the distance between corresponding posterior distributions of potential functions, while the latter naturally leads to a bound of the discrepancies between corresponding thermal averages of test observables. besides, the training observables can be more flexible than finite samples of the local density function, which are mostly used in previous researches. the method also applies to the multi - level quantum systems in the non - adiabatic regime. in addition, we provide extensive numerical tests to verify the accuracy and efficiency of the proposed algorithm.
arxiv:1910.02116
the object of this paper is to introduce and study the concept of quasi - geometric infinite divisibility for distributions on $ \ bf r _ + $. these distributions arise as mixing distributions of ( discrete ) geometric infinitely divisible poisson mixtures. several characterizations and closure properties are presented. a connection between quasi - geometric infinite divisibility and log - convex ( log - concave ) distributions is established. a generalized notion of quasi - infinite divisibility is also discussed.
arxiv:2112.04105
the coupling of $ n = 1 $ scft of type $ ( 4m, 2 ) $ to two - dimensional supergravity can be formulated non - perturbatively in terms of a discrete super - eigenvalue model proposed by alvarez - gaum \ ' e, et al. we derive the superloop equations that describe, in the double scaling limit, the non - perturbative solution of this model. these equations are equivalent to the double scaled super - virasoro constraints satisfied by the partition function. they are formulated in terms of a $ \ widehat c = 1 $ theory, with a $ \ iz _ 2 $ - twisted scalar field and a weyl - majorana fermion in the ramond sector. we have solved the superloop equations to all orders in the genus expansion and obtained the explicit expressions for the correlation functions of gravitationally dressed scaling operators in the ns - and r - sector. in the double scaling limit, we obtain a formulation of the model in terms of a new supersymmetric extension of the kdv hierarchy.
arxiv:hep-th/9403129
platooning involves a set of vehicles moving in a cooperative fashion at equal inter - vehicular distances. taking advantage of wireless communication technology, this paper aims to show the impact of network protocols on a platoon using a controller, based on the cooperative adaptive cruise control ( cacc ) principles. the network protocols used in this work are dsrc ( dedicated short range communication ) and lte - v2v sidelink ( mode 4 ). the main focus of this work is to showcase the ability of the controller to maintain platoon stability despite having uncertainties in both, the platoon and the message delivery rates over the network protocols. the controller interacts with all vehicles using messages transmitted over the network protocols. the controller is designed to be responsible for micro - managing every vehicle in the platoon and to ensure that the platoon does not break under any circumstances. sumo ( simulation of urban mobility ) is used as the simulation platform. results indicate, that the controller manages to achieve platoon stability in all scenarios, unless a set number of consecutive messages are not transmitted, in which case it leads to collisions. this work also presents certain bottlenecks pertaining to wireless communication with vehicles.
arxiv:1905.02395
multi - robot task planning and collaboration are critical challenges in robotics. while behavior trees ( bts ) have been established as a popular control architecture and are plannable for a single robot, the development of effective multi - robot bt planning algorithms remains challenging due to the complexity of coordinating diverse action spaces. we propose the multi - robot behavior tree planning ( mrbtp ) algorithm, with theoretical guarantees of both soundness and completeness. mrbtp features cross - tree expansion to coordinate heterogeneous actions across different bts to achieve the team ' s goal. for homogeneous actions, we retain backup structures among bts to ensure robustness and prevent redundant execution through intention sharing. while mrbtp is capable of generating bts for both homogeneous and heterogeneous robot teams, its efficiency can be further improved. we then propose an optional plugin for mrbtp when large language models ( llms ) are available to reason goal - related actions for each robot. these relevant actions can be pre - planned to form long - horizon subtrees, significantly enhancing the planning speed and collaboration efficiency of mrbtp. we evaluate our algorithm in warehouse management and everyday service scenarios. results demonstrate mrbtp ' s robustness and execution efficiency under varying settings, as well as the ability of the pre - trained llm to generate effective task - specific subtrees for mrbtp.
arxiv:2502.18072
the recent progress on image recognition and language modeling is making automatic description of image content a reality. however, stylized, non - factual aspects of the written description are missing from the current systems. one such style is descriptions with emotions, which is commonplace in everyday communication, and influences decision - making and interpersonal relationships. we design a system to describe an image with emotions, and present a model that automatically generates captions with positive or negative sentiments. we propose a novel switching recurrent neural network with word - level regularization, which is able to produce emotional image captions using only 2000 + training sentences containing sentiments. we evaluate the captions with different automatic and crowd - sourcing metrics. our model compares favourably in common quality metrics for image captioning. in 84. 6 % of cases the generated positive captions were judged as being at least as descriptive as the factual captions. of these positive captions 88 % were confirmed by the crowd - sourced workers as having the appropriate sentiment.
arxiv:1510.01431
a classical result owing to mancini and sandeep [ ann. sc. norm. super. pisa cl. sci. 7 ( 2008 ) ] asserts that all positive solutions of the poincar \ ' e - sobolev equation on the hyperbolic space $ $ - \ delta _ { \ mathbb { b } ^ n } u - \ lambda u = | u | ^ { p - 1 } u, \ quad u \ in h ^ 1 ( \ mathbb { b } ^ n ), $ $ are unique up to hyperbolic isometries where $ n \ geq 3, $ $ 1 < p \ leq \ frac { n + 2 } { n - 2 } $ and $ \ lambda \ leq \ frac { ( n - 1 ) ^ 2 } { 4 }. $ we prove under certain bounds on $ \ | \ nabla u \ | _ { l ^ 2 ( \ mathbb { b } ^ n ) } $ the inequality $ $ \ delta ( u ) \ lesssim \ | \ delta _ { \ mathbb { b } ^ n } u + \ lambda u + u ^ { p } \ | _ { h ^ { - 1 } }, $ $ holds whenever $ p > 2 $ and hence forcing the dimensional restriction $ 3 \ leq n \ leq 5, $ where $ \ delta ( u ) $ denotes the $ h ^ 1 $ distance of $ u $ from the manifold of sums of hyperbolic bubbles. moreover, it fails for any $ n \ geq 3 $ and $ p \ in ( 1, 2 ]. $ this strengthens the phenomenon observed in the euclidean case that the ( linear ) quantitative stability estimate depends only on whether the exponent $ p $ is $ > 2 $ or $ \ leq 2 $. in the critical case, our dimensional constraint coincides with the seminal result of figalli and glaudo [ arch. ration. mech. anal, 237 ( 2020 ) ] but we notice a striking dependence on the exponent $ p $ in the subcritical regime as well which is not present in the flat case. our technique is an amalgamation of figalli and glaudo ' s method and builds upon a series of new and novel estimates on the interaction of hyperbolic bubbles and their derivatives and improved eigenfunction integrability estimates. since the conformal group coincides with the isometry group of the hyperbolic space, we perceive
arxiv:2211.14618
we derive and analyze a class of spherically symmetric cosmological models whose source is an interactive mixture of inhomogeneous cold dark matter ( dm ) and a generic homogeneous dark energy ( de ) fluid. if the de fluid corresponds to a quintessense scalar field, the interaction term can be associated with a well motivated non - - minimal coupling to the dm component. by constructing a suitable volume average of the dm component we obtain a friedman evolution equation relating this average density with an average hubble scalar, with the de component playing the role of a repulsive and time - dependent $ \ lambda $ term. once we select an ` ` equation of state ' ' linking the energy density ( $ \ mu $ ) and pressure ( $ p $ ) of the de fluid, as well as a free function governing the radial dependence, the models become fully determinate and can be applied to known specific de sources, such as quintessense scalar fields or tachyonic fluids. considering the simple equation of state $ p = ( \ gamma - 1 ) \ mu $ with $ 0 \ leq \ gamma < 2 / 3 $, we show that the free parameters and boundary conditions can be selected for an adequate description of a local dm overdensity evolving in a suitable cosmic background that accurately fits current observational data. while a de dominated scenario emerges in the asymptotic future, with total $ \ omega $ and $ q $ tending respectively to 1 and - 1 / 2 for all cosmic observers, the effects of inhomogeneity and anisotropy yield different local behavior and evolution rates for these parameters in the local overdense region. we suggest that the models presented can be directly applied to explore the effects of various de formalisms on local dm cosmological inhomogeneities.
arxiv:astro-ph/0503609
we explore cp - violating ( cpv ) effects of heavy new physics in flavour - changing quark dipole transitions, within the framework of standard model effective field theory ( smeft ). first, we establish the relevant dimension six operators and consider the renormalisation group ( rg ) evolution of the appropriate wilson coefficients. we investigate rg - induced correlations between different flavour - violating processes and electric dipole moments ( edms ) within the minimal flavour violating and $ u ( 2 ) ^ 3 $ quark flavour models. at low energies, we set bounds on the wilson coefficients of the dipole operators using cpv induced contributions to observables in non - leptonic and radiative $ b $, $ d $ and $ k $ decays as well as the neutron and electron edms. this enables us to connect observable cpv effects at low energies and general np appearing at high scales. we present bounds on the wilson coefficients of the relevant smeft operators at the high scale $ \ lambda = 5 ~ { \ rm tev } $, and discuss most sensitive cpv observables for future experimental searches.
arxiv:2306.16471
background : the numerical solution of few - body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. this strongly limits the possibility of accurate treatments for many important few - particle problems in different branches of quantum physics. purpose : to develop a new general highly effective approach for the practical solution of few - body scattering equations that can be implemented on a graphics processing unit. methods : the general approach is realized in three steps : ( i ) the reformulation of the scattering equations using a convenient analytical form for the channel resolvent operator ; ( ii ) a complete few - body continuum discretization and projection of all operators and wave functions onto a $ l _ 2 $ basis constructed from stationary wave packets and ( iii ) the ultra - fast solution of the resulting matrix equations using graphics processor. results : the whole approach is illustrated by a calculation of the neutron - deuteron elastic scattering cross section below and above the three - body breakup threshold with a realistic $ nn $ potential which is performed on a standard pc using a graphics processor with an extremely short runtime. conclusions : the general technique proposed in this paper opens a new way for a fast practical solution of quantum few - body scattering problems both in non - relativistic and relativistic formulations in hadronic, nuclear and atomic physics.
arxiv:1404.5253
let $ \ mathrm { \ mathbf { l } \ rightarrow \ mathbf { x } } $ be a base point free $ \ mathrm { \ mathbb { t } = t ^ { \ mathbb { c } } } $ - linearized hermitian line bundle over a compact variety $ \ mathrm { \ mathbf { x } } $ where $ \ mathrm { t = \ left ( s ^ { 1 } \ right ) ^ { m } } $ is a real torus. the main focus of this paper is to describe the asymptotic behavior of a certain class of sequences $ \ mathrm { \ left ( s _ { n } \ right ) _ { n } } $ of $ \ mathrm { \ mathbb { t } } $ - eigensections $ \ mathrm { s _ { n } \ in h ^ { 0 } \ left ( \ mathbf { x }, \ mathbf { l } ^ { n } \ right ) } $ as $ \ mathrm { n \ rightarrow \ infty } $, introduced by shiffman, tate and zelditch, and its connection to the geometry of the hilbert quotient $ \ mathrm { \ pi \! : \! \ bf { x } ^ { ss } _ { \ xi } \ rightarrow \ mathbf { x } ^ { ss } _ { \ xi } / \! \! / \ mathbb { t } } $ where $ \ mathrm { \ xi \ in \ mathfrak { t } ^ { * } } $.
arxiv:1503.01550
we report a systematic investigation on c - axis point - contact andreev reflection ( pcar ) in bafe $ _ { 2 - x } $ ni $ _ x $ as $ _ 2 $ superconducting single crystals from underdoped to overdoped regions ( 0. 075 $ \ leq x \ leq 0. 15 $ ). at optimal doping ( $ x = 0. 1 $ ) the pcar spectrum feature the structures of two superconducting gap and electron - boson coupling mode. in the $ s \ pm $ scenario, quantitative analysis using a generalized blonder - tinkham - klapwijk ( btk ) formalism with two gaps : one isotropic and another angle dependent, suggest a nodeless state in strong - coupling limit with gap minima on the fermi surfaces. upon crossing above the optimal doping ( $ x > 0. 1 $ ), the pcar spectrum show an in - gap sharp narrow peak at low bias, in contrast to the case of underdoped samples ( $ x < 0. 1 $ ), signaling the onset of deepened gap minima or nodes in the superconducting gap. this result provides evidence of the modulation of the gap amplitude with doping concentration, consistent with the calculations for the orbital dependent pair interaction mediated by the antiferromagnetic spin fluctuations.
arxiv:1106.2891
sorted l - one penalized estimation ( slope ) has shown the nice theoretical property as well as empirical behavior recently on the false discovery rate ( fdr ) control of high - dimensional feature selection by adaptively imposing the non - increasing sequence of tuning parameters on the sorted $ \ ell _ 1 $ penalties. this paper goes beyond the previous concern limited to the fdr control by considering the stepdown - based slope to control the probability of $ k $ or more false rejections ( $ k $ - fwer ) and the false discovery proportion ( fdp ). two new slopes, called $ k $ - slope and f - slope, are proposed to realize $ k $ - fwer and fdp control respectively, where the stepdown procedure is injected into the slope scheme. for the proposed stepdown slopes, we establish their theoretical guarantees on controlling $ k $ - fwer and fdp under the orthogonal design setting, and also provide an intuitive guideline for the choice of regularization parameter sequence in much general setting. empirical evaluations on simulated data validate the effectiveness of our approaches on controlled feature selection and support our theoretical findings.
arxiv:2302.10610
the integration of natural language processing ( nlp ) technologies into educational applications has shown promising results, particularly in the language learning domain. recently, many spoken open - domain chatbots have been used as speaking partners, helping language learners improve their language skills. however, one of the significant challenges is the high word - error - rate ( wer ) when recognizing non - native / non - fluent speech, which interrupts conversation flow and leads to disappointment for learners. this paper explores the use of gpt4 for asr error correction in conversational settings. in addition to wer, we propose to use semantic textual similarity ( sts ) and next response sensibility ( nrs ) metrics to evaluate the impact of error correction models on the quality of the conversation. we find that transcriptions corrected by gpt4 lead to higher conversation quality, despite an increase in wer. gpt4 also outperforms standard error correction methods without the need for in - domain training data.
arxiv:2307.09744
the cosmological moduli problem ( cmp ) comes in three parts : 1. potential violation of bbn constraints from late decaying moduli fields, 2. the moduli - induced gravitino problem wherein gravitinos are overproduced and 3. the moduli - induced lightest susy particle ( lsp ) overproduction problem. we examine the cosmological moduli problem and its connection to electroweak naturalness. we calculate the various two - body decay widths of a light modulus field into mssm particles and gravitinos within general supersymmetric models. we include both phase space and mixing effects. we examine cases without and with helicity suppression of modulus decays to gravitinos ( cases 1 & 2 ) and / or gauginos ( cases a & b ). for case b1, we evaluate regions of gravitino mass m _ { 3 / 2 } vs. modulus mass m _ \ phi parameter space constrained by bbn, by overproduction of gravitinos and by overproduction of neutralino dark matter, along with connections to naturalness. for this case, essentially all of parameter space is excluded unless m _ \ phi > ~ 2. 5 \ times 10 ^ 3 tev with m _ \ phi < 2m _ { 3 / 2 }. for a potentially most propitious case b2 with \ phi decay to higgs and matter turned off, then modulus branching fractions to susy and to gravitinos become highly suppressed at large m _ \ phi. but since the modulus number density increases faster than the branching fractions decrease, there is still gross overproduction of neutralino dark matter. we also show that in this scenario the thermally produced gravitino problem is fixed by huge entropy dilution, but non - thermal gravitino production from moduli decay remains a huge problem unless it is kinematically suppressed with m _ \ phi < 2m _ { 3 / 2 }. in a pedagogical appendix, we present detailed calculations of modulus field two - body decay widths.
arxiv:2201.06633
in natural auditory environments, acoustic signals originate from the temporal superimposition of different sound sources. the problem of inferring individual sources from ambiguous mixtures of sounds is known as blind source decomposition. experiments on humans have demonstrated that the auditory system can identify sound sources as repeating patterns embedded in the acoustic input. source repetition produces temporal regularities that can be detected and used for segregation. specifically, listeners can identify sounds occurring more than once across different mixtures, but not sounds heard only in a single mixture. however, whether such a behaviour can be computationally modelled has not yet been explored. here, we propose a biologically inspired computational model to perform blind source separation on sequences of mixtures of acoustic stimuli. our method relies on a somatodendritic neuron model trained with a hebbian - like learning rule which can detect spatio - temporal patterns recurring in synaptic inputs. we show that the segregation capabilities of our model are reminiscent of the features of human performance in a variety of experimental settings involving synthesized sounds with naturalistic properties. furthermore, we extend the study to investigate the properties of segregation on task settings not yet explored with human subjects, namely natural sounds and images. overall, our work suggests that somatodendritic neuron models offer a promising neuro - inspired learning strategy to account for the characteristics of the brain segregation capabilities as well as to make predictions on yet untested experimental settings.
arxiv:2201.06123
estimating the data density is one of the challenging problems in deep learning. in this paper, we present a simple yet effective method for estimating the data density using a deep neural network and the donsker - varadhan variational lower bound on the kl divergence. we show that the optimal critic function associated with the donsker - varadhan representation on the kl divergence between the data and the uniform distribution can estimate the data density. we also present the deep neural network - based modeling and its stochastic learning. the experimental results and possible applications of the proposed method demonstrate that it is competitive with the previous methods and has a lot of possibilities in applied to various applications.
arxiv:2104.06612
cu is an ubiquitous material used in industry for its great thermal and electrical properties. studying the high - pressure high temperature properties of copper ( cu ) is relevant for nuclear fusion research as projectiles and flyers used in hypervelocity impacts are generally made of copper, where it is used also in the design of the nuclear fusion targets. recently, a solid ( fcc ) - solid ( bcc ) phase transition has been detected in shock compressed cu with x - ray diffraction. here, we present a study on shock compressed copper up to 300 gpa and 7100 k probed by single pulse ( 100 ps fwhm ) x - ray absorption spectroscopy ( xas ). based on the analysis of the xas spectra, we provide structural identification and bulk temperature measurements along the hugoniot up to the melting. the collection of xas spectra under release conditions, i. e. at later times than the breakout time of the shock wave, helped constraining the experimental fcc - bcc and solid - liquid phase boundaries. in particular, we report the first bulk temperature measurement in shock compressed copper on the melting plateau located between 237 ( 40 ) gpa and 5750 ( 1130 ) k and 261 ( 27 ) gpa and 6240 ( 1155 ) k and on liquid copper at 300 gpa and 7100 k.
arxiv:2503.01939
we report an investigation into random - jet - stirred homogeneous turbulence generated in a vertical octagonal prism shaped tank where there are jet arrays on four of the eight vertical faces. we show that the turbulence is homogeneous at all scales in the central region of the tank that spans multiple integral scales in all directions. the jet forcing from four sides in the horizontal direction guarantees isotropy in horizontal planes but leads to more energy in the horizontal fluctuations compared with the vertical fluctuations. this anisotropy between the horizontal and vertical fluctuations decreases at smaller scales, so that the inertial and dissipation range statistics show isotropic behaviour. using four jet arrays allows us to achieve higher turbulence intensity and reynolds number with a shorter jet merging distance compared to two facing arrays. we show that we are able to vary the turbulence scales and reynolds number by adding attachments to the exits of each jet and changing the parameters of the algorithm that drives random - jet stirring. by linking how the flow from each jet influences the random - jet - stirred turbulence, we provide recommendations on how to select the parameters of the jet driving algorithm.
arxiv:2305.19430
by studying an effective action description of the coupling of charged gauge fields in n = 2 su ( n ) supersymmetric yang - mills theories, we can describe regions of moduli space where one or more of these fields becomes unphysical. we discuss subtleties in the structure of the moduli space for su ( 3 ).
arxiv:hep-th/9508043
purpose : since the recent covid - 19 outbreak, there has been an avalanche of research papers applying deep learning based image processing to chest radiographs for detection of the disease. to test the performance of the two top models for cxr covid - 19 diagnosis on external datasets to assess model generalizability. methods : in this paper, we present our argument regarding the efficiency and applicability of existing deep learning models for covid - 19 diagnosis. we provide results from two popular models - covid - net and coronet evaluated on three publicly available datasets and an additional institutional dataset collected from emory hospital between january and may 2020, containing patients tested for covid - 19 infection using rt - pcr. results : there is a large false positive rate ( fpr ) for covid - net on both chexpert ( 55. 3 % ) and mimic - cxr ( 23. 4 % ) dataset. on the emory dataset, covid - net has 61. 4 % sensitivity, 0. 54 f1 - score and 0. 49 precision value. the fpr of the coronet model is significantly lower across all the datasets as compared to covid - net - emory ( 9. 1 % ), chexpert ( 1. 3 % ), chestx - ray14 ( 0. 02 % ), mimic - cxr ( 0. 06 % ). conclusion : the models reported good to excellent performance on their internal datasets, however we observed from our testing that their performance dramatically worsened on external data. this is likely from several causes including overfitting models due to lack of appropriate control patients and ground truth labels. the fourth institutional dataset was labeled using rt - pcr, which could be positive without radiographic findings and vice versa. therefore, a fusion model of both clinical and radiographic data may have better performance and generalization.
arxiv:2006.13262