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we analyse the violations of lepton - flavour universality in the ratios b ( p - > l nu ) / b ( p - > l ' nu ) using a general effective theory approach, discussing various flavour - symmetry breaking patterns of physics beyond the sm. we find that in models with minimal lepton flavour violation the effects are too small to be observed in the next generations of experiments in all relevant meson systems ( p = pi, k, b ). in a grand unified framework with a minimal breaking of the flavour symmetry, the effects remain small in pi and k decays while large violations of lepton - flavour universality are possible in b - > l nu decays. | arxiv:0906.3024 |
current evaluations of defenses against prompt attacks in large language model ( llm ) applications often overlook two critical factors : the dynamic nature of adversarial behavior and the usability penalties imposed on legitimate users by restrictive defenses. we propose d - sec ( dynamic security utility threat model ), which explicitly separates attackers from legitimate users, models multi - step interactions, and expresses the security - utility in an optimizable form. we further address the shortcomings in existing evaluations by introducing gandalf, a crowd - sourced, gamified red - teaming platform designed to generate realistic, adaptive attack. using gandalf, we collect and release a dataset of 279k prompt attacks. complemented by benign user data, our analysis reveals the interplay between security and utility, showing that defenses integrated in the llm ( e. g., system prompts ) can degrade usability even without blocking requests. we demonstrate that restricted application domains, defense - in - depth, and adaptive defenses are effective strategies for building secure and useful llm applications. | arxiv:2501.07927 |
we use quantum monte carlo simulations to study a dimer - diluted $ s = 1 / 2 $ heisenberg model on a bilayer square lattice with intralayer interaction $ j _ { 1 } $ and interlayer interaction $ j _ { 2 } $. below the classical percolation threshold $ p _ c $, the system has three phases reachable by tuning the interaction ratio $ g = j _ { 2 } / j _ { 1 } $ : a n $ \ acute { e } $ el ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. we present the ground - state phase diagram in the plane of dilution $ p $ and interaction ratio $ g $. the quantum glass phase is certified to be of the gapless mott glass type, having a uniform susceptibility vanishing at zero temperature $ t $ and following a stretched exponential form at $ t > 0 $ ; $ \ chi _ u \ sim \ exp ( - b / t ^ { \ alpha } ) $ with $ \ alpha < 1 $. at the phase transition point from n $ \ acute { e } $ el ordered to mott glass, we find that the critical exponents are different from those of the clean system described by the standard $ o ( 3 ) $ universality class in 2 + 1 dimensions. | arxiv:1511.07895 |
the direct measurements of the meridional flow velocities on stars are impossible today. to evaluate the meridional flow velocities on solar - like stars with stable activity periods, we supposed that during the stellar hale cycle the matter on surfaces of stars passes the meridional way equivalent to $ 2 \ pi r _ \ star $. we present here the dependence of the mean meridional flow velocity on rossby number, which is an effective parameter of the stellar magnetic dynamo. | arxiv:1406.2085 |
i review the prospects for measuring the properties of the top quark at the tevatron, with an integrated luminosity of 2 fb $ ^ { - 1 } $ or more, and at lhc in the early running at instantaneous luminosities of $ 10 ^ { 32 } - 10 ^ { 33 } ~ cm ^ { - 2 } ~ s ^ { - 1 } $. | arxiv:hep-ph/9510274 |
a finite range density and momentum dependent effective interaction is used to calculate the density and temperature dependence of the symmetry energy coefficient csym ( rho, t ) of infinite nuclear matter. this symmetry energy is then used in the local density approximation to evaluate the excitation energy dependence of the symmetry energy coefficient of finite nuclei in a microcanonical formulation that accounts for thermal and expansion effects. the results are in good harmony with the recently reported experimental data from energetic nucleus - nucleus collisions. | arxiv:0706.3385 |
we consider the effective potential v in the massless wess - zumino model. by using the renormalization group equation, we show that the explicit dependence of v on the renormalization mass scale mu cancels. if v has an extremum at some non - vanishing value of the background field, then it follows that v is " flat ", independent of the background field. this is consistent with the general requirement that v be complex. the consequences for supersymmetric gauge theories are briefly considered. | arxiv:1805.10069 |
let $ k \ leq h $ be two finite groups and let $ c \ leq a $ be two finite abelian groups, with $ h $ acting on $ a $ as a group of isomorphisms admitting $ c $ as a $ k $ - invariant subgroup. we study the homogeneous space $ x \ coloneqq \ left ( h \ ltimes a \ right ) / \ left ( k \ ltimes c \ right ) $ and determine the decomposition of the permutation representation of $ h \ ltimes a $ acting on $ x $. we then characterize when this is multiplicity - free, that is, when $ \ left ( h \ ltimes a, k \ ltimes c \ right ) $ is a gelfand pair. if this is the case, we explicitly calculate the corresponding spherical functions. from our general construction and related analysis, we recover dunkl ' s results on the $ q $ - analog of the nonbinary johnson scheme. | arxiv:2405.08371 |
in this work, we developed a deep learning model - based approach to forecast the spreading trend of sars - cov - 2 in the united states. we implemented the designed model using the united states to confirm cases and state demographic data and achieved promising trend prediction results. the model incorporates demographic information and epidemic time - series data through a gated recurrent unit structure. the identification of dominating demographic factors is delivered in the end. | arxiv:2008.05644 |
we study the problem of revising specifications with preferences for automata based control synthesis problems. in this class of revision problems, the user provides a numerical ranking of the desirability of the subgoals in their specifications. when the specification cannot be satisfied on the system, then our algorithms automatically revise the specification so that the least desirable user goals are removed from the specification. we propose two different versions of the revision problem with preferences. in the first version, the algorithm returns an exact solution while in the second version the algorithm is an approximation algorithm with non - constant approximation ratio. finally, we demonstrate the scalability of our algorithms and we experimentally study the approximation ratio of the approximation algorithm on random problem instances. | arxiv:1402.3611 |
this paper addresses the problem of single - target tracker performance evaluation. we consider the performance measures, the dataset and the evaluation system to be the most important components of tracker evaluation and propose requirements for each of them. the requirements are the basis of a new evaluation methodology that aims at a simple and easily interpretable tracker comparison. the ranking - based methodology addresses tracker equivalence in terms of statistical significance and practical differences. a fully - annotated dataset with per - frame annotations with several visual attributes is introduced. the diversity of its visual properties is maximized in a novel way by clustering a large number of videos according to their visual attributes. this makes it the most sophistically constructed and annotated dataset to date. a multi - platform evaluation system allowing easy integration of third - party trackers is presented as well. the proposed evaluation methodology was tested on the vot2014 challenge on the new dataset and 38 trackers, making it the largest benchmark to date. most of the tested trackers are indeed state - of - the - art since they outperform the standard baselines, resulting in a highly - challenging benchmark. an exhaustive analysis of the dataset from the perspective of tracking difficulty is carried out. to facilitate tracker comparison a new performance visualization technique is proposed. | arxiv:1503.01313 |
let m be a closed manifold. wodzicki shows that, in the stable range, the cyclic cohomology of the associative algebra of pseudodifferential symbols of order \ leq 0 is isomorphic to the homology of the cosphere bundle of m. in this article we develop a formalism which allows to calculate that, under this isomorphism, the radul cocycle corresponds to the poincar \ ' e dual of the todd class. as an immediate corollary we obtain a purely algebraic proof of the atiyah - singer index theorem for elliptic pseudodifferential operators on closed manifolds. | arxiv:1112.1850 |
within linear response theory using pauli master equation approach, we have investigated the thermoelectric properties of quantum dots ( qds ) embedded in an aharonov - bohm ( ab ) ring weakly coupled to two metallic electrodes. this study explores the impact of magnetic flux on thermoelectric transport, emphasizing the role of quantum interference induced by the flux. when the magnetic flux is varied from 0 to one quantum of flux $ \ phi = \ phi _ { 0 } = \ frac { h } { e } $, both the electrical conductance and the thermoelectric figure of merit ( $ zt $ ) significantly increase by two order of magnitude. moreover, our investigation into the effects of onsite and inter - site coulomb interactions in this nanojunction indicates that an optimal $ zt $ is attained with moderate onsite coulomb interaction and minimal inter - site coulomb interaction. we briefly discussed the effects of asymmetric arrangements of triple qds within an ab ring. however, within our parameter regime, a symmetric arrangement offers superior thermoelectric performance compared to asymmetric configurations. furthermore, we explored how increasing the number of qds in the ring enhances the thermoelectric properties, resulting in a potential $ zt $ value of around $ 0. 43 $. this study shows that arranging multiple qds symmetrically in an ab ring can result in significant thermoelectric performance in nanostructured system at low temperatures. | arxiv:2504.15813 |
this is the first part of an halpha kinematics follow - up survey of the sings sample. the data for 28 galaxies are presented. the observations were done on three different telescopes with fantomm, an integral field photon counting spectrometer, installed in the respective focal reducer of each telescope. the data reduction was done through a newly built pipeline with the aim of producing the most homogenous data set possible. adaptive spatial binning was applied to the data cubes in order to get a constant signal - to - noise ratio across the field of view. radial velocity and monochromatic maps were generated using a new algorithm and the kinematical parameters were derived using tilted - ring models. | arxiv:astro-ph/0601376 |
it was shown recently that the 2 - user interference channel with a cognitive relay ( ic - cr ) has full degrees of freedom ( dof ) almost surely, that is, 2 dof. the purpose of this work is to check whether the dof of the $ k $ - user ic - cr, consisting of $ k $ user pairs and a cognitive relay, follow as a straight forward extension of the 2 - user case. as it turns out, this is not the case. the $ k $ - user ic - cr is shown to have $ 2k / 3 $ dof if $ k > 2 $ for the when the channel is time varying, achievable using interference alignment. thus, while the basic $ k $ - user ic with time varying channel coefficients has 1 / 2 dof per user for all $ k $, the $ k $ - user ic - cr with varying channels has 1 dof per user if k = 2 and 2 / 3 dof per user if $ k > 2 $. furthermore, the dof region of the 3 - user ic - cr with constant channels is characterized using interference neutralization, and a new upper bound on the sum - capacity of the 2 - user ic - cr is given. | arxiv:1207.0337 |
in this mainly expository note, we state a criterion for when a left kan extension of a lax monoidal functor along a strong monoidal functor can itself be equipped with a lax monoidal structure, in a way that results in a left kan extension in moncat. this belongs to the general theory of algebraic kan extensions, as developed by melli \ ` es - tabareau, koudenburg and weber, and is very close to an instance of a theorem of koudenburg. we find this special case particularly important due to its connections with the theory of graded monads. | arxiv:1809.10481 |
in a recent paper ( math. dg / 0701278 ) we constructed a series of new moishezon twistor spaces which is a kind of variant of the famous lebrun twistor spaces. in this paper we explicitly give projective models of another series of moishezon twistor spaces on ncp ^ 2 for arbitrary n > 2, which can be regarded as a generalization of the twistor spaces of a ' double solid type ' on 3cp ^ 2 studied by kreussler, kurke, poon and the author. similarly to the twistor spaces of ' double solid type ' on 3cp ^ 2, projective models of present twistor spaces have a natural structure of double covering of a cp ^ 2 - bundle over cp ^ 1. we explicitly give a defining polynomial of the branch divisor of the double covering whose restriction to fibers are degree four. if n > 3 these are new twistor spaces, to the best of the author ' s knowledge. we also compute the dimension of the moduli space of these twistor spaces. differently from math. dg / 0701278, the present investigation is based on analysis of pluri - ( half - ) anticanonical systems of the twistor spaces. | arxiv:0705.0060 |
in this study, the proton is taken as an ensemble of quark - gluon fock states. using the principle of balance that every fock state should be balanced with all of the nearby fock states ( denoted as the balance model ), instead of the principle of detailed balance that any two nearby fock states should be balanced with each other ( denoted as the detailed balance model ), the probabilities of finding every fock state of the proton are obtained. the balance model can be taken as a revised version of the detailed balance model, which can give an excellent description of the light flavor sea asymmetry ( i. e., $ \ bar { u } \ not = \ bar { d } $ ) without any parameter. in case of $ g \ leftrightarrow gg $ sub - processes not considered, the balance model and the detailed balance model give the same results. in case of $ g \ leftrightarrow gg $ sub - processes considered, there is about 10 percent difference between the results of these models. we also calculate the strange content of the proton using the balance model under the equal probability assumption. | arxiv:hep-ph/0204344 |
non - linear transport effects in response to external magnetic fields, i. e. electrical magnetochiral anisotropy ( emcha ), have attracted much attention for their importance to study quantum and spin - related phenomena. indeed, they have permitted the exploration of topological surface states and charge - to - spin conversion processes in low - symmetry systems. nevertheless, despite the inherent correlation between the symmetry of the material under examination and its non - linear transport characteristics, there is a lack of experimental demonstration to delve into this relationship and to unveil their microscopic mechanisms. here, we study emcha in chiral elemental tellurium ( te ) along different crystallographic directions, establishing the connection between the different emcha components and the crystal symmetry of te. we observed different longitudinal emcha components with collinear current and magnetic field, demonstrating experimentally the radial angular momentum texture of te. we also measured a transverse non - linear resistance which, as the longitudinal counterpart, scales bilinearly with current and magnetic fields, illustrating that they are different manifestations of the same effect. finally, we study the scaling law of the emcha, evidencing that extrinsic scattering from dynamic sources is the dominant microscopic mechanism. these findings underscore the efficacy of symmetry - based investigations in understanding and predicting non - linear transport phenomena, with potential applications in spintronics and energy harvesting. | arxiv:2406.17389 |
let $ x $ be a smooth projective variety over $ \ overline { \ mathbb q } $, and $ f : x - rightarrow x $ be a dominant rational map. let $ \ delta _ { f } $ be the first dynamical degree of $ f $ and $ h _ { x } : x ( \ overline { \ mathbb q } ) \ to [ 1, \ infty ) $ be a weil height function on $ x $ associated with an ample divisor on $ x $. we prove several inequalities which give upper bounds of the sequence $ ( h _ x ( f ^ n ( p ) ) ) _ { n \ geq0 } $ where $ p $ is a point of $ x ( \ overline { \ mathbb q } ) $ whose forward orbit by $ f $ is well - defined. as a corollary, we prove that the upper arithmetic degree is less than or equal to the first dynamical degree ; $ \ overline { \ alpha } _ { f } ( p ) \ leq \ delta _ { f } $. furthermore, if the picard number of $ x $ is one, $ f $ is algebraically stable and $ \ delta _ { f } > 1 $, we prove that the limit defining canonical height $ \ lim _ { n \ to \ infty } h _ { x } ( f ^ { n } ( p ) ) \ big / \ delta _ f ^ n $ converges. | arxiv:1606.00598 |
matrix forms of the representation of the multi - level system of molecular - genetic alphabets have revealed algebraic properties of this system. families of genetic ( 4 * 4 ) - and ( 8 * 8 ) - matrices show unexpected connections of the genetic system with walsh functions and hadamard matrices, which are known in theory of noise - immunity coding, digital communication and digital holography. dyadic - shift decompositions of such genetic matrices lead to sets of sparse matrices. each of these sets is closed in relation to multiplication and defines relevant algebra of hypercomplex numbers. it is shown that genetic hadamard matrices are identical to matrix representations of hamilton quaternions and its complexification in the case of unit coordinates. the diversity of known dialects of the genetic code is analyzed from the viewpoint of the genetic algebras. an algebraic analogy with punnett squares for inherited traits is shown. our results are used in analyzing genetic phenomena. the statement about existence of the geno - logic code in dna and epigenetics on the base of the spectral logic of systems of boolean functions is put forward. our results show promising ways to develop algebraic - logical biology, in particular, in connection with the logic holography on walsh functions. | arxiv:1102.3596 |
we derive general static spherically symmetric solutions in the horava theory of gravity with nonzero shift field. these represent " hedgehog " versions of black holes with radial " hair " arising from the shift field. for the case of the standard de witt kinetic term ( lambda = 1 ) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. special solutions also arise in the anisotropic conformal point lambda = 1 / 3. | arxiv:0911.1535 |
in this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints. under such constraints, the raw data $ ( x _ 1, y _ 1 ), \ ldots, ( x _ n, y _ n ) $, taking values in $ \ mathbb { r } ^ d \ times \ mathbb { r } $, cannot be directly observed, and all estimators are functions of the randomised output from a suitable privacy mechanism. the statistician is free to choose the form of the privacy mechanism, and here we add laplace distributed noise to a discretisation of the location of a feature vector $ x _ i $ and to the value of its response variable $ y _ i $. based on this randomised data, we design a novel estimator of the regression function, which can be viewed as a privatised version of the well - studied partitioning regression estimator. the main result is that the estimator is strongly universally consistent. our methods and analysis also give rise to a strongly universally consistent binary classification rule for locally differentially private data. | arxiv:2011.00216 |
let $ \ left \ lbrace f _ { k } \ right \ rbrace _ { k \ geq0 } $ be the fibonacci sequence defined by $ f _ { k } = f _ { f - 1 } + f _ { k - 2 } $ for all $ n \ geq2 $ with initials $ f _ { 0 } = 0 \ ; f _ { 1 } = 1 $. let $ \ left \ lbrace j _ { n } \ right \ rbrace _ { n \ geq0 } $ be the jacobsthal sequence defined by $ j _ n = 2j _ { n - 1 } + j _ { n - 2 } $ for all $ n \ geq2 $ with initials $ j _ 0 = 0 $, $ j _ 1 = 1 $. in this paper we find all the solutions of the two diophantine equations $ j _ n + j _ m = f _ a $, $ f _ n + f _ m = j _ a $ in the non - negative integer variables ( n, m, a ), i. e we determine all fibonacci numbers which are sum of two jacobsthal numbers, and also determine all jacobsthal numbers which are sum of two fibonacci numbers. | arxiv:2209.14809 |
how to extract instance - level masks without instance - level supervision is the main challenge of weakly supervised instance segmentation ( wsis ). popular wsis methods estimate a displacement field ( df ) via learning inter - pixel relations and perform clustering to identify instances. however, the resulting instance centroids are inherently unstable and vary significantly across different clustering algorithms. in this paper, we propose boundary - assisted instance segmentation ( baiseg ), which is a novel paradigm for wsis that realizes instance segmentation with pixel - level annotations. baiseg comprises an instance - aware boundary detection ( iabd ) branch and a semantic segmentation branch. the iabd branch identifies instances by predicting class - agnostic instance boundaries rather than instance centroids, therefore, it is different from previous df - based approaches. in particular, we proposed the cascade fusion module ( cfm ) and the deep mutual attention ( dma ) in the iabd branch to obtain rich contextual information and capture instance boundaries with weak responses. during the training phase, we employed pixel - to - pixel contrast to enhance the discriminative capacity of the iabd branch. this further strengthens the continuity and closedness of the instance boundaries. extensive experiments on pascal voc 2012 and ms coco demonstrate the effectiveness of our approach, and we achieve considerable performance with only pixel - level annotations. the code will be available at https : / / github. com / wsis - seg / baiseg. | arxiv:2406.18558 |
the orion ob1 association, at a distance of roughly 400 pc and spanning over ~ 200 deg ^ 2 on the sky, is one of the largest and nearest ob associations. with a wide range of ages and environmental conditions, orion is an ideal laboratory for investigating fundamental questions related to the birth of stars and planetary systems. this rich region exhibits all stages of the star formation process, from very young, embedded clusters, to older, fully exposed young stars ; it also harbors dense clusters and widely spread populations in vast, low stellar density areas. this review focuses on the later, namely, the low - mass ( m ~ < 2 mo ), pre - main sequence population spread over wide spatial scales in orion ob1, mostly in the off - cloud areas. as ongoing studies yield more complete censa it becomes clearer that this " distributed " or non - clustered population, is as numerous as that located in the molecular clouds ; modern studies of star formation in orion would be incomplete if they did not include this widely spread population. | arxiv:0810.2294 |
we study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a liouville - like equation driven density. the reason for this discrepancy seems to be that the liouville - like equation is unable to reproduce the multi - scaling properties emerging from trajectory dynamics. we argue that this conflict between density and trajectory might help us to define the uncertain border between dynamics and thermodynamics, and that between quantum and classical physics as well. | arxiv:cond-mat/0112205 |
we present the near - infrared and optical properties of the peculiar galaxy eso 235 - g58, which resembles a late - type ringed barred spiral seen close to face - on. however, the apparent bar of eso 235 - g58 is in reality an edge - on disk galaxy of relatively low luminosity. we have analyzed the light and color distributions of eso 235 - g58 in the nir and optical bands and compared them with the typical properties observed for other morphological galaxy types, including polar ring galaxies. similar properties are observed for eso 235 - g58, polar ring galaxies, and spiral galaxies, which leads us to conclude that this peculiar system is a polar - ring - related galaxy, characterized by a low inclined ring / disk structure, as pointed out by buta & crocker in an earlier study, rather than a barred galaxy. | arxiv:astro-ph/0402126 |
crystal structures connected by continuous phase transitions are linked through mathematical relations between crystallographic groups and their subgroups. in the present study, we introduce group - subgroup machine learning ( gs - ml ) and show that including materials with small unit cells in the training set decreases out - of - sample prediction errors for materials with large unit cells. gs - ml incurs the least training cost to reach 2 - 3 % target accuracy compared to other ml approaches. since available materials datasets are heterogeneous providing insufficient examples for realizing the group - subgroup structure, we present the " friezermq1d " dataset with 8393 q1d organometallic materials uniformly distributed across 7 frieze groups. furthermore, by comparing the performances of fchl and 1 - hot representations, we show gs - ml to capture subgroup information efficiently when the descriptor encodes structural information. the proposed approach is generic and extendable to symmetry abstractions such as spin -, valency -, or charge order. | arxiv:2012.15619 |
in this paper, we study the equivariant coarse novikov conjectures for spaces that equivariantly and coarsely embed into admissible hilbert - hadamard spaces, which are a type of infinite - dimensional nonpositively curved spaces. the paper is split into two parts. we prove in the first part that for any metric space $ x $ with bounded geometry and with a proper isometric action $ \ alpha $ by a countable discrete group $ \ gamma $, if $ x $ admits an equivariant coarse embedding into an admissible hilbert - hadamard space and $ \ gamma $ is torsion - free, then the equivariant coarse strong novikov conjecture holds rationally for $ ( x, \ gamma, \ alpha ) $. in the second part, we drop the torsion - free assumption for $ \ gamma $ in the first part. we introduce a miscenko - kasparov assembly map for a proper $ \ gamma $ - space $ x $ with equivariant bounded geometry, which leads to a new novikov - type conjecture that we call the analytic equivariant coarse novikov conjecture. we show that for a proper $ \ gamma $ - space $ x $ with equivariant bounded geometry, the rational analytic equivariant coarse novikov conjecture holds for $ ( x, \ gamma, \ alpha ) $ if $ x $ admits an equivariant coarse embedding into an admissible hilbert - hadamard space, i. e., the miscenko - kasparov assembly map is a rational injection. | arxiv:2411.18538 |
grammar error correction ( gec ) systems have become ubiquitous in a variety of software applications, and have started to approach human - level performance for some datasets. however, very little is known about how to efficiently personalize these systems to the user ' s characteristics, such as their proficiency level and first language, or to emerging domains of text. we present the first results on adapting a general - purpose neural gec system to both the proficiency level and the first language of a writer, using only a few thousand annotated sentences. our study is the broadest of its kind, covering five proficiency levels and twelve different languages, and comparing three different adaptation scenarios : adapting to the proficiency level only, to the first language only, or to both aspects simultaneously. we show that tailoring to both scenarios achieves the largest performance improvement ( 3. 6 f0. 5 ) relative to a strong baseline. | arxiv:2006.02964 |
a stable single - photon source working at high temperatures with high brightness and covering full band emission from one host material is critically important for quantum technologies. here, we find that the certain hbn single - photon emissions ( spes ) can be significantly enhanced by lasers with special wavelengths, which largely broaden the wavelength range of the hbn emitters, down to ultraviolet ( 357 nm ) and up to near - infrared ( 912 nm ). importantly, these hbn spes are still stable even at the temperature up to 1100 kelvin. the decoupling between single - photon and acoustic phonon is observed at high temperatures. our work suggests that hbn can be a good host material for generating single - photon sources with ultrabroad wavelength range. | arxiv:1908.06578 |
in the distributed remote ( ceo ) source coding problem, many separate encoders observe independently noisy copies of an underlying source. the rate loss is the difference between the rate required in this distributed setting and the rate that would be required in a setting where the encoders can fully cooperate. in this sense, the rate loss characterizes the price of distributed processing. we survey and extend the known results on the rate loss in various settings, with a particular emphasis on the case where the noise in the observations is gaussian, but the underlying source is general. | arxiv:2202.01489 |
ethics is probably the most - cited dataset for testing the ethical capabilities of language models. drawing on moral theory, psychology, and prompt evaluation, we interrogate the validity of the ethics benchmark. adding to prior work, our findings suggest that having a clear understanding of ethics and how it relates to empirical phenomena is key to the validity of ethics evaluations for ai. | arxiv:2410.13009 |
we generalise a result of bykovskii to the gaussian integers and prove an asymptotic formula for the prime geodesic theorem in short intervals on the picard manifold. previous works show that individually the remainder is bounded by $ o ( x ^ { 13 / 8 + \ epsilon } ) $ and $ o ( x ^ { 3 / 2 + \ theta + \ epsilon } ) $, where $ \ theta $ is the subconvexity exponent for quadratic dirichlet $ l $ - functions over $ \ mathbb { q } ( i ) $. by combining arithmetic methods with estimates for a spectral exponential sum and a smooth explicit formula, we obtain an improvement for both of these exponents. moreover, by assuming two standard conjectures on $ l $ - functions, we show that it is possible to reduce the exponent below the barrier $ 3 / 2 $ and get $ o ( x ^ { 34 / 23 + \ epsilon } ) $ conditionally. we also demonstrate a dependence of the remainder in the short interval estimate on the classical gauss circle problem for shifted centres. | arxiv:1911.01800 |
recognizing objects in low - resolution images is a challenging task due to the lack of informative details. recent studies have shown that knowledge distillation approaches can effectively transfer knowledge from a high - resolution teacher model to a low - resolution student model by aligning cross - resolution representations. however, these approaches still face limitations in adapting to the situation where the recognized objects exhibit significant representation discrepancies between training and testing images. in this study, we propose a cross - resolution relational contrastive distillation approach to facilitate low - resolution object recognition. our approach enables the student model to mimic the behavior of a well - trained teacher model which delivers high accuracy in identifying high - resolution objects. to extract sufficient knowledge, the student learning is supervised with contrastive relational distillation loss, which preserves the similarities in various relational structures in contrastive representation space. in this manner, the capability of recovering missing details of familiar low - resolution objects can be effectively enhanced, leading to a better knowledge transfer. extensive experiments on low - resolution object classification and low - resolution face recognition clearly demonstrate the effectiveness and adaptability of our approach. | arxiv:2409.02555 |
we consider the nls system of the third - harmonic generation, which was introduced by sammut. our interest is in solitary wave solutions and their stability properties. the recent work of oliveira and pastor, discussed global well - posedness vs. finite time blow - up, as well as other aspects of the dynamics. these authors have also constructed solitary wave solutions, via the method of mountain pass / nehari manifold, in an appropriate range of parameters. specifically, the waves exist only in spatial dimensions $ n = 1, 2, 3 $. they have also established some stability / instability results for these waves. in this work, we systematically build and study solitary waves for this important model. we construct the waves in the largest possible parameter space, and we provide a complete classification of their stability. in dimension one, we show stability, whereas, in $ n = 2, 3 $, they are generally spectrally unstable, except for a small region, where they do enjoy an extra pseudo - conformal symmetry. finally, we discuss instability by a blow - up. in the case $ n = 3 $, and for a more restrictive set of parameters, we use virial identities methods to derive the strong instability, in the spirit of ohta ' s approach. in $ n = 2 $, the virial identities reduce matters, via conservation of mass and energy, to the initial data. our conclusions mirror closely the well - known results for the scalar cubic focusing nls, while the proofs are much more involved. | arxiv:2304.01867 |
large language models ( llms ) are revolutionizing various domains, yet verifying their answers remains a significant challenge, especially for intricate open - ended tasks such as consolidation, summarization, and extraction of knowledge. in this work, we propose checkembed : an accurate, scalable, and simple llm verification approach. checkembed is driven by a straightforward yet powerful idea : in order to compare llm solutions to one another or to the ground - truth, compare their corresponding answer - level embeddings obtained with a model such as gpt text embedding large. this reduces a complex textual answer to a single embedding, facilitating straightforward, fast, and meaningful verification. we develop a comprehensive verification pipeline implementing the checkembed methodology. the checkembed pipeline also comes with metrics for assessing the truthfulness of the llm answers, such as embedding heatmaps and their summaries. we show how to use these metrics for deploying practical engines that decide whether an llm answer is satisfactory or not. we apply the pipeline to real - world document analysis tasks, including term extraction and document summarization, showcasing significant improvements in accuracy, cost - effectiveness, and runtime performance compared to existing token -, sentence -, and fact - level schemes such as bertscore or selfcheckgpt. | arxiv:2406.02524 |
we report on a c - band double layer graphene electro - absorption modulator on a passive soi platform showing 29ghz 3db - bandwith and nrz eye - diagrams extinction ratios ranging from 1. 7 db at 10 gb / s to 1. 3 db at 50 gb / s. such high modulation speed is achieved thanks to the quality of the cvd pre - patterned single crystal growth and transfer on wafer method that permitted the integration of high - quality scalable graphene and low contact resistance. by demonstrating this high - speed cvd graphene eam modulator integrated on si photonics and the scalable approach, we are confident that graphene can satisfy the main requirements to be a competitive technology for photonics. | arxiv:2003.11896 |
extreme event are sudden large - amplitude changes in the state or observables of chaotic nonlinear systems, which characterize many scientific phenomena. because of their violent nature, extreme events typically have adverse consequences, which call for methods to prevent the events from happening. in this work, we introduce the control - aware echo state network ( ca - esn ) to seamlessly combine esns and control strategies, such as proportional - integral - derivative and model predictive control, to suppress extreme events. the methodology is showcased on a chaotic - turbulent flow, in which we reduce the occurrence of extreme events with respect to traditional methods by two orders of magnitude. this works opens up new possibilities for the efficient control of nonlinear systems with neural networks. | arxiv:2308.03095 |
the evolution of complex transport networks is investigated under three strategies of link removal : random, intentional attack and " pseudo - darwinian " strategy. at each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. we study how the network structure and the total flux between randomly chosen source and drain nodes evolve. we discover a universal power - law decrease of the total flux, followed by an abrupt transport collapse. the time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations. | arxiv:2007.15307 |
automated wireless spectrum monitoring across frequency, time and space will be essential for many future applications. manual and fine - grained spectrum analysis is becoming impossible because of the large number of measurement locations and complexity of the spectrum use landscape. detecting unexpected behaviors in the wireless spectrum from the collected data is a crucial part of this automated monitoring, and the control of detected anomalies is a key functionality to enable interaction between the automated system and the end user. in this paper we look into the wireless spectrum anomaly detection problem for crowdsourced sensors. we first analyze in detail the nature of these anomalies and design effective algorithms to bring the higher dimensional input data to a common feature space across sensors. anomalies can then be detected as outliers in this feature space. in addition, we investigate the importance of user feedback in the anomaly detection process to improve the performance of unsupervised anomaly detection. furthermore, schemes for generalizing user feedback across sensors are also developed to close the anomaly detection loop. | arxiv:1903.05408 |
we stretch the spectral bound equal growth bound condition along with a generalized lyapunov stability theorem, known to hold for $ c _ 0 $ - semigroups of normal operators on complex hilbert spaces, to $ c _ 0 $ - semigroups of scalar type spectral operators on complex banach spaces. for such semigroups, we obtain exponential estimates with the best stability constants. we also extend to a banach space setting a celebrated characterization of uniform exponential stability for $ c _ 0 $ - semigroups on complex hilbert spaces and thereby acquire a characterization of uniform exponential stability for scalar type spectral and eventually norm - continuous $ c _ 0 $ - semigroups. | arxiv:2107.02832 |
the notion of strong structural controllability ( s - controllability ) allows for determining controllability properties of large linear time - invariant systems even when numerical values of the system parameters are not known a priori. the s - controllability guarantees controllability for all numerical realizations of the system parameters. we address the optimization problem of minimal cardinality input selection for s - controllability. previous work shows that not only the optimization problem is np - hard, but finding an approximate solution is also hard. we propose a randomized algorithm using the notion of zero forcing sets to obtain an optimal solution with high probability. we compare the performance of the proposed algorithm with a known heuristic [ 1 ] for synthetic random systems and five real - world networks, viz. ieee 39 - bus system, re - tweet network, protein - protein interaction network, us airport network, and a network of physicians. it is found that our algorithm performs much better than the heuristic in each of these cases. | arxiv:1810.07220 |
out of about 500 lithium - rich rosat counterparts, which are presumed to be low - mass pre - main sequence stars, 21 stars have been observed by hipparcos. we study their parallaxes, proper motions, and photometric data. for 7 out of 10 taurus and lupus stars in our sample, proper motions and parallaxes are not inconsistent with membership to these associations, while most of the stars in chamaeleon and scorpius appear to be young foreground stars. combined with ground based photometry and spectroscopy, hipparcos parallaxes allow us to place 15 stars on an h - r diagram. all these 15 stars are indeed pre - main sequence stars with ages from 1 to 15 myr. only two of the stars are located on the hayashi - tracks, whereas the other 13 are post - t tauri stars located on radiative tracks. although this sample is admittedly small, containing only 3 % of the total sample of lithium - rich rosat counterparts, it does not confirm recent predictions by other authors : we find no stars in the age range from 20 to 100 myr. the foreground pre - main sequence stars may have been ejected towards us, or they belong to the gould belt system, a plane filled with young stars. | arxiv:astro-ph/9712045 |
a tessellation or tiling is a collection of sets, called tiles, that cover a plane without gaps and overlaps. the present note is an invitation to get to know the beauty and majesty of tessellations and triangulation of orientable surfaces. | arxiv:2303.17263 |
the paris agreement is the first - ever universally accepted and legally binding agreement on global climate change. it is a bridge between today ' s and climate - neutrality policies and strategies before the end of the century. critical to this endeavor is energy system modeling, which, while adept at devising cost - effective carbon - neutral strategies, often overlooks the broader environmental and social implications. this study introduces an innovative methodology that integrates life - cycle impact assessment indicators into energy system modeling, enabling a comprehensive assessment of both economic and environmental outcomes. focusing on switzerland ' s energy system as a case study, our model reveals that optimizing key environomic indicators can lead to significant economic advantages, with system costs potentially decreasing by 15 % to 47 % by minimizing potential impacts from operating fossil technologies to the indirect impact related to the construction of the renewable infrastructure. however, a system optimized solely for economic efficiency, despite achieving 63 % reduction in carbon footprint compared to 2020, our results show a potential risk of burden shift to other environmental issues. the adoption of multi - objective optimization in our approach nuances the exploration of the complex interplay between environomic objectives and technological choices. our results illuminate pathways towards more holistically optimized energy systems, effectively addressing trade - offs across environmental problems and enhancing societal acceptance of the solutions to this century ' s defining challenge. | arxiv:2402.12973 |
recent xmm - newton observations have measured the hard ( 2. 5 - 12 kev ) x - ray spectrum of the well - known seyfert galaxy ngc 4151 with a signal - to - noise unprecedented for this source. we find that a spectral model, developed to fit previous beppo - sax and asca observations of ngc 4151, provides an excellent description of the xmm - newton epic data. the results support the view that it is the level of the continuum that is the main driver of the complex spectral variability exhibited by ngc 4151. we focus on the iron k features in the ngc 4151 spectrum. there is no requirement for a relativistically broadened iron ka line, in contrast to several earlier studies. the iron ka line profile is well modelled by a narrow gaussian, the intensity of which varies by ~ 25 % on timescales of about a year. there is also a strong suggestion that the cold media present in the active nucleus of ngc 4151 have an iron abundance that is at least twice the solar value. | arxiv:astro-ph/0306540 |
the goal of this paper is to deal with a data scarcity scenario where deep learning techniques use to fail. we compare the use of two well established techniques, restricted boltzmann machines and variational auto - encoders, as generative models in order to increase the training set in a classification framework. essentially, we rely on markov chain monte carlo ( mcmc ) algorithms for generating new samples. we show that generalization can be improved comparing this methodology to other state - of - the - art techniques, e. g. semi - supervised learning with ladder networks. furthermore, we show that rbm is better than vae generating new samples for training a classifier with good generalization capabilities. | arxiv:1903.09030 |
a model for domain wall motion in ferromagnets is analyzed. long - range magnetic dipolar interactions are shown to give rise to self - similar dynamics when the external magnetic field is increased adiabatically. the power spectrum of the resultant barkhausen noise is of the form $ 1 / \ omega ^ \ alpha $, where $ \ alpha \ approx 1. 5 $ can be estimated from the critical exponents for interface depinning in random media. | arxiv:cond-mat/9610053 |
the application of digital twin ( dt ) technology to the nuclear field is one of the challenges in the future development of nuclear energy. possible applications of dt technology in the nuclear field are expected to be very wide : operate commercial nuclear reactors, monitor spent fuel storage and disposal facilities, and develop new nuclear systems. as u. s. nuclear regulatory committee ( nrc ) recently announced, machine learning ( ml ) and artificial intelligence ( ai ) will be new domains in the nuclear field. considering the data science perspective, gaussian process ( gp ) has proven to be an ml algorithm for modeling and simulation components of the digital twin framework, specifically for the accident tolerant fuel ( atf ) concepts. atf is one of the high - priority areas for both the u. s. department of energy ( doe ) and nrc. gp ' s inherent treatment of lack of data, missing data, and data inconsistencies ( noisy / erroneous data ) present in the atf concepts make it an attractive machine learning algorithm for implementation in the dt framework. this chapter focuses on the practical demonstration of gp and its applicability to the dt framework for predicting atf. | arxiv:2210.07495 |
we investigate the importance of dynamical spin effects in the holographic light - front wavefunctions of the pseudoscalar mesons. we find that these effects are crucial to describe the pion data while they are not necessary to describe the available kaon data. for $ \ eta - \ eta ^ \ prime $ system, we find that dynamical spin effects are required to describe their transition form factors data. | arxiv:1811.12886 |
intelligent metasurfaces are one of the favorite technologies for integrating sixth - generation ( 6g ) networks, especially the reconfigurable intelligent surface ( ris ) that has been extensively researched in various applications. in this context, a feature that deserves further exploration is the frequency scattering that occurs when the elements are periodically switched, referred to as space - time - coding metasurface ( stcm ) topology. this type of topology causes impairments to the established communication methods by generating undesirable interference both in frequency and space, which is worsened when using wideband signals. nevertheless, it has the potential to bring forward useful features for sensing and localization. this work exploits stcm sensing capabilities in target detection, localization, and classification using narrowband downlink pilot signals at the base station ( bs ). the results of this novel approach reveal the ability to retrieve a scattering point ( sp ) localization within the sub - centimeter and sub - decimeter accuracy depending on the sp position in space. we also analyze the associated detection and classification probabilities, which show reliable detection performance in the whole analyzed environment. in contrast, the classification is bounded by physical constraints, and we conclude that this method presents a promising approach for future integrated sensing and communications ( isac ) protocols by providing a tool to perform sensing and localization services using legacy communication signals. | arxiv:2401.03189 |
the distribution of bases spacing in human genome was investigated. an analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution has no self - similar ( fractal ) structure. the results nevertheless revealed several characteristic features : ( i ) the distribution for short - range spacing is quite similar to the purely stochastic sequences ; ( ii ) the distribution for long - range spacing essentially deviates from the random sequence distribution, showing strong long - range correlations ; ( iii ) the differences between ( a, t ) and ( c, g ) bases are quite significant ; ( iv ) the spacing distribution displays tiny oscillations. | arxiv:1904.07860 |
the asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. the long - time limit of this distribution is shown to exist and to depend on the initial conditions, and it also determines the asymptotic value of the entanglement between the coin and the position. it is shown that for given asymptotic values of both the entanglement and the chirality distribution it is possible to find the corresponding initial conditions within a particular class of spatially extended gaussian distributions. moreover it is shown that the entanglement also measures the degree of markovian randomness of the distribution of chirality. | arxiv:1004.1134 |
deep neural networks ( dnns ) are vulnerable to adversarial noise. a range of adversarial defense techniques have been proposed to mitigate the interference of adversarial noise, among which the input pre - processing methods are scalable and show great potential to safeguard dnns. however, pre - processing methods may suffer from the robustness degradation effect, in which the defense reduces rather than improving the adversarial robustness of a target model in a white - box setting. a potential cause of this negative effect is that adversarial training examples are static and independent to the pre - processing model. to solve this problem, we investigate the influence of full adversarial examples which are crafted against the full model, and find they indeed have a positive impact on the robustness of defenses. furthermore, we find that simply changing the adversarial training examples in pre - processing methods does not completely alleviate the robustness degradation effect. this is due to the adversarial risk of the pre - processed model being neglected, which is another cause of the robustness degradation effect. motivated by above analyses, we propose a method called joint adversarial training based pre - processing ( jatp ) defense. specifically, we formulate a feature similarity based adversarial risk for the pre - processing model by using full adversarial examples found in a feature space. unlike standard adversarial training, we only update the pre - processing model, which prompts us to introduce a pixel - wise loss to improve its cross - model transferability. we then conduct a joint adversarial training on the pre - processing model to minimize this overall risk. empirical results show that our method could effectively mitigate the robustness degradation effect across different target models in comparison to previous state - of - the - art approaches. | arxiv:2106.05453 |
we present a novel form of collective oscillatory behavior in the kinetics of irreversible coagulation with a constant input of monomers and removal of large clusters. for a broad class of collision rates, this system reaches a non - equilibrium stationary state at large times and the cluster size distribution tends to a universal form characterised by a constant flux of mass through the space of cluster sizes. universality, in this context, means that the stationary state becomes independent of the cut - off as the cut - off grows. this universality is lost, however, if the aggregation rate between large and small clusters increases sufficiently steeply as a function of cluster sizes. we identify a transition to a regime in which the stationary state vanishes as the cut - off grows. this non - universal stationary state becomes unstable, however, as the cut - off is increased and undergoes a hopf bifurcation. after this bifurcation, the stationary kinetics are replaced by persistent and periodic collective oscillations. these oscillations carry pulses of mass through the space of cluster sizes. as a result, the average mass flux remains constant. furthermore, universality is partially restored in the sense that the scaling of the period and amplitude of oscillation is inherited from the dynamical scaling exponents of the universal regime. the implications of this new type of long - time asymptotic behaviour for other driven non - equilibrium systems are discussed. | arxiv:1205.4445 |
game publishers and anti - cheat companies have been unsuccessful in blocking cheating in online gaming. we propose a novel, vision - based approach that captures the final state of the frame buffer and detects illicit overlays. to this aim, we train and evaluate a dnn detector on a new dataset, collected using two first - person shooter games and three cheating software. we study the advantages and disadvantages of different dnn architectures operating on a local or global scale. we use output confidence analysis to avoid unreliable detections and inform when network retraining is required. in an ablation study, we show how to use interval bound propagation to build a detector that is also resistant to potential adversarial attacks and study its interaction with confidence analysis. our results show that robust and effective anti - cheating through machine learning is practically feasible and can be used to guarantee fair play in online gaming. | arxiv:2103.10031 |
we report ope predictions for hadronic mass and q ^ 2 moments in inclusive semileptonic b decays without charm, taking into account experimental cuts on the charged lepton energy and on the hadronic invariant mass, and address the related theoretical uncertainty. | arxiv:hep-ph/0505091 |
using diffusion monte carlo ( dmc ) and density functional theory ( dft ) calculations, we examined the structural stability and interlayer binding properties of ptse $ _ 2 $, a representative transition metal dichalcogenide ( tmd ) with strong interlayer interaction. our dmc results for the bilayer revealed that aa and ab - r stacking modes are nearly degenerate, highlighting the significant role of interlayer hybridization in offsetting the energy cost due to larger interlayer separations in the ab - r mode. additionally, our dmc - benchmarked dft studies with the r $ ^ 2 $ scan + rvv10 functional demonstrated pronounced stacking polymorphism in few - layer ptse $ _ 2 $, suggesting the potential for stacking faults and the formation of grain boundaries between different stacking domains which could develop metallic electronic structures. thus this polymorphism, along with selenium vacancies, influences a layer - dependent metal - insulator transition observed in few - layer ptse $ _ 2 $. our findings emphasize the importance of both van der waals interactions and interlayer hybridization in determining the phase stability and electronic properties of tmds, advancing our understanding of their fundamental properties and refining theoretical models for practical applications in nanoelectronic devices. | arxiv:2408.10156 |
in this paper we propose an energy - efficient camera - based gesture recognition system powered by light energy for " always on " applications. low energy consumption is achieved by directly extracting gesture features from the compressed measurements, which are the block averages and the linear combinations of the image sensor ' s pixel values. the gestures are recognized using a nearest - neighbour ( nn ) classifier followed by dynamic time warping ( dtw ). the system has been implemented on an analog devices black fin ulp vision processor and powered by pv cells whose output is regulated by ti ' s dc - dc buck converter with maximum power point tracking ( mppt ). measured data reveals that with only 400 compressed measurements ( 768x compression ratio ) per frame, the system is able to recognize key wake - up gestures with greater than 80 % accuracy and only 95mj of energy per frame. owing to its fully self - powered operation, the proposed system can find wide applications in " always - on " vision systems such as in surveillance, robotics and consumer electronics with touch - less operation. | arxiv:1605.08313 |
this note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction - diffusion models. the approach is differential in nature. it proceeds from classical tools of contraction analysis and recent extensions to differential dissipativity. | arxiv:2005.00940 |
in this paper we examine the inverse problem of determining the twisting function for the dynamicschrodinger operator in a quantum waveguide from some suitable localized, either interior or boundary. | arxiv:1512.07762 |
constructing accurate and generalizable approximators for complex physico - chemical processes exhibiting highly non - smooth dynamics is challenging. in this work, we propose new developments and perform comparisons for two promising approaches : manifold - based polynomial chaos expansion ( m - pce ) and the deep neural operator ( deeponet ), and we examine the effect of over - parameterization on generalization. we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2d time - dependent brusselator reaction - diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. we first propose an extension of the m - pce by constructing a mapping between latent spaces formed by two separate embeddings of input functions and output qois. to enhance the accuracy of the deeponet, we introduce weight self - adaptivity in the loss function. we demonstrate that the performance of m - pce and deeponet is comparable for cases of relatively smooth input - output mappings. however, when highly non - smooth dynamics is considered, deeponet shows higher accuracy. we also find that for m - pce, modest over - parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over - parameterization leads to over - fitting. in contrast, an even highly over - parameterized deeponet leads to better generalization for both smooth and non - smooth dynamics. furthermore, we compare the performance of the above models with another operator learning model, the fourier neural operator, and show that its over - parameterization also leads to better generalization. our studies show that m - pce can provide very good accuracy at very low training cost, whereas a highly over - parameterized deeponet can provide better accuracy and robustness to noise but at higher training cost. in both methods, the inference cost is negligible. | arxiv:2203.05071 |
perhaps standard effective field theory arguments are right, and vacuum fluctuations really do generate a huge cosmological constant. i show that if one does not assume homogeneity and an arrow of time at the planck scale, a very large class of general relativistic initial data exhibit expansions, shears, and curvatures that are enormous at small scales, but quickly average to zero macroscopically. subsequent evolution is more complex, but i argue that quantum fluctuations may preserve these properties. the resulting picture is a version of wheeler ' s ` spacetime foam, ' in which the cosmological constant produces high curvature at the planck scale but is nearly invisible at observable scales. | arxiv:1809.08277 |
in a recent paper, we investigated the effects of the massive charged gauge bosons ( bileptons ) predicted by the minimal 331 model on the off - shell vertex wwv ^ * ( v = gamma, z ) using a su _ l ( 2 ) x u _ y ( 1 ) covariant gauge - fixing term for the bileptons. we proceed along the same lines and calculate the effects of the gauge bosons predicted by the 331 model with right - handed neutrinos. it is found that the bilepton effects on the wwv ^ * vertex are of the same order of magnitude than those arising from the sm and several of its extensions, provided that the bilepton mass is of the order of a few hundred of gevs. for heavier bileptons, their effects on the wwv ^ * vertex are negligible. the behavior of the form factors at high energies is also discussed as it is a reflect of the gauge invariance and gauge independence of the wwv ^ * green function obtained via our quantization method. | arxiv:hep-ph/0702081 |
the main objective of this paper is to present a general mathematical model and an associated numerical algorithm applicable to an arbitrary fixed - wing fixed - mass aircraft undergoing an arbitrary maneuver, based on the 3d nonlinear coupled differential - algebraic equations of motion, including force, moment, kinematic and constraint equations. the model is formulated to address the inverse simulation problem where a target maneuver is prescribed and the corresponding time dependent patterns of the control variables are solved for to meet this maneuver. the model utilizes two different moving frames of references, namely the body axes and the wind axes. the numerical algorithm features sequential solution of equations in a fully explicit manner. it is straightforward to use the model in a reverse mode, namely the direct simulation problem. the inverse problem may be summarized as follows : inputs : time history of desired - trajectory rectangular coordinates relative to the ground - fixed axes. a constraint should be specified, which we arbitrarily chose it to be the bank angle. also, certain geometric and aerodynamic aircraft data are needed. outputs : time history of the control variables ( thrust magnitude, elevator angle, rudder angle, ailerons angle ), which will satisfy the aimed trajectory. the paper finally applies the presented numerical algorithm to a roll maneuver for the mirage - iii fighter. | arxiv:2411.00834 |
we consider galton - watson trees associated with a critical offspring distribution and conditioned to have exactly $ n $ vertices. these trees are embedded in the real line by affecting spatial positions to the vertices, in such a way that the increments of the spatial positions along edges of the tree are independent variables distributed according to a symmetric probability distribution on the real line. we then condition on the event that all spatial positions are nonnegative. under suitable assumptions on the offspring distribution and the spatial displacements, we prove that these conditioned spatial trees converge as $ n \ to \ infty $, modulo an appropriate rescaling, towards the conditioned brownian tree that was studied in previous work. applications are given to asymptotics for random quadrangulations. | arxiv:math/0503263 |
quantum field theory is the application of quantum physics to fields. it provides a theoretical framework widely used in particle physics and condensed matter physics. one of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. in quantum fields, observables restricted to a region of space define a subsystem. while there are proofs on the existence of local observables that would allow a violation of bell ' s inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine - tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. the introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial ( mathematical ) points but rather smeared over finite volumes. we first give explicit collective observables whose correlations reveal vacuum entanglement in the klein - gordon field. we then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the compton wavelength of the particle corresponding to the massive klein - gordon field. | arxiv:1003.3354 |
a supersymmetric formulation of the classical action of interacting charged and neutral fermions with arbitrary anomalous magnetic moment is considered. this formulation generalizes the known action for scalar charged particles investigated in papers by fokker, schwarzschild, tetrode, wheeler and feynman. the superfield formulation of the electrodynamics of the maxwell supermultiplet, constructed from the world coordinates of charged or neutral fermions is carried out basing on the proposed action. | arxiv:hep-th/9602128 |
we study a finite spin - $ \ frac { 1 } { 2 } $ ising chain with a spatially alternating transverse field of period 2. by means of a jordan - wigner transformation for even and odd sites, we are able to map it into a one - dimensional model of free fermions. we determine the ground - state energies in the positive - and negative - parity subspaces ( subspaces with an even or odd total number of down spins, respectively ) and compare them in order to establish the ground - state energy for the entire hamiltonian. we derive closed - form expressions for this energy gap between the different parity subspaces and analyze its behavior and dependence on the system size in the various regimes of the applied field. finally, we suggest an expression for the correlation length of such a model that is consistent with the various values found in the literature for its behavior in the vicinity of critical points. | arxiv:1903.09468 |
let $ l / k $ be a finite galois extension of $ p $ - adic fields and let $ l _ { \ infty } $ be the unramified $ \ mathbb z _ p $ - extension of $ l $. then $ l _ { \ infty } / k $ is a one - dimensional $ p $ - adic lie extension. in the spirit of the main conjectures of equivariant iwasawa theory, we formulate a conjecture which relates the equivariant local epsilon constants attached to the finite galois intermediate extensions $ m / k $ of $ l _ { \ infty } / k $ to a natural arithmetic invariant arising from the \ ' etale cohomology of the constant sheaf $ \ mathbb q _ p / \ mathbb z _ p $ on the spectrum of $ l _ { \ infty } $. we give strong evidence of the conjecture including a full proof in the case that $ l / k $ is at most tamely ramified. | arxiv:1803.05743 |
entity alignment ( ea ) aims to match equivalent entities in different knowledge graphs ( kgs ), which is essential for knowledge fusion and integration. recently, embedding - based ea has attracted significant attention and many approaches have been proposed. early approaches primarily focus on learning entity embeddings from the structural features of kgs, defined by relation triples. later methods incorporated entities ' names and attributes as auxiliary information to enhance embeddings for ea. however, these approaches often used different techniques to encode structural and attribute information, limiting their interaction and mutual enhancement. in this work, we propose a dense entity retrieval framework for ea, leveraging language models to uniformly encode various features of entities and facilitate nearest entity search across kgs. alignment candidates are first generated through entity retrieval, which are subsequently reranked to determine the final alignments. we conduct comprehensive experiments on both cross - lingual and monolingual ea datasets, demonstrating that our approach achieves state - of - the - art performance compared to existing ea methods. | arxiv:2408.01154 |
the localization of fast radio bursts ( frbs ) has been hindered by the poor angular resolution of the detection observations and inconclusive identification of transient or variable counterparts. recently a $ \ gamma $ - ray pulse of $ 380 $ s duration has been associated with the fast radio burst frb 131104. we report on radio - continuum imaging observations of the original localization region of the frb, beginning three days after the event and comprising 25 epochs over 2. 5 yr. besides probabilistic arguments that suggest that the association between the $ \ gamma $ - ray transient and the frb is not compelling, we provide upper limits on a putative radio afterglow of this transient that are at odds with standard models for its progenitor. we further report the discovery of an unusual variable radio source spatially and temporally coincident with frb 131104, but not spatially coincident with the $ \ gamma $ - ray event. the radio variable flares by a factor of $ 3 $ above its long term average within $ 10 $ d of the frb at 7. 5 ghz, with a factor - of - $ 2 $ increase at $ 5. 5 $ ghz. within our observations, the variable has persisted with only modest modulation and never approached the flux density observed in the days after the frb. we identify an optical counterpart to the variable. optical and infrared photometry, and deep optical spectroscopy, suggest that the object is a narrow - line radio agn. | arxiv:1611.05580 |
we present the first x - ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the kerr solution. we employ the formalism of the transfer function proposed by cunningham. the calculations of the reflection spectrum of a thin accretion disk are split into two parts : the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. the transfer function only depends on the background metric and takes into account all the relativistic effects ( gravitational redshift, doppler boosting, and light bending ). our code computes the transfer function for a spacetime described by the johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. transfer functions and single line shapes in the kerr metric are compared with those calculated from existing codes to check that we reach the necessary accuracy. we also simulate some observations with nustar and lad / extp and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the kerr metric. | arxiv:1607.00596 |
we study a bijective map from integer partitions to the prime factorizations of integers that we call the " supernorm " of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors of natural numbers. the supernorm is connected to a family of maps we define, which suggests the potential to apply techniques from partition theory to identify and prove multiplicative properties of integers. we make a brief study of pertinent analytic aspects of the supernorm. then, as an application of " supernorma " ' mappings ( i. e., pertaining to the supernorm statistic ), we prove an analogue of a formula of kural - mcdonald - sah to give arithmetic densities of subsets of $ \ mathbb n $ instead of natural densities in $ \ mathbb p $ like previous formulas of this type ; this builds on works of alladi, ono, wagner, and the first and third authors. finally, using a table of " supernormal " additive - multiplicative correspondences, we conjecture abelian - type formulas that specialize to our main theorem and other known results. | arxiv:2107.14284 |
in the category of semisimple hopf algebras the hopf kernels introduced by andruskiewitsch and devoto in \ cite { ad } coincide with kernels of representation as introduced in \ cite { bker }. some new results concerning the normality of kernels are also presented. it is proven that the property for hopf algebras to have all kernels normal hopf subalgebras is a self dual property. | arxiv:1010.2096 |
identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. many applications require methods capable of handling complex systems while providing strong learning guarantees for safe and reliable performance. however, existing approaches often focus on simplified scenarios, such as deterministic models, known diffusion, discrete systems, one - dimensional dynamics, or systems constrained by strong structural assumptions such as linearity. this work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations with non - uniform diffusion. we assume regularity of the coefficients within a sobolev space, allowing for broad applicability to various dynamical systems in robotics, finance, climate modeling, and biology. leveraging the fokker - planck equation, we split the estimation into two tasks : ( a ) estimating system dynamics for a finite set of controls, and ( b ) estimating coefficients that govern those dynamics. we provide strong theoretical guarantees, including finite - sample bounds for \ ( l ^ 2 \ ), \ ( l ^ \ infty \ ), and risk metrics, with learning rates adaptive to coefficients ' regularity, similar to those in nonparametric least - squares regression literature. the practical effectiveness of our approach is demonstrated through extensive numerical experiments. our method is available as an open - source python library. | arxiv:2411.01982 |
dp - coloring ( also called correspondence coloring ) is a generalization of list coloring introduced by dvo \ v { r } \ ' { a } k and postle in 2015. in 2019, bernshteyn, kostochka, and zhu introduced a fractional version of dp - coloring. they showed that unlike the fractional list chromatic number, the fractional dp - chromatic number of a graph $ g $, denoted $ \ chi _ { _ { dp } } ^ * ( g ) $, can be arbitrarily larger than $ \ chi ^ * ( g ) $, the graph ' s fractional chromatic number. we generalize a result of alon, tuza, and voigt ( 1997 ) on the fractional list chromatic number of odd cycles, and, in the process, show that for each $ k \ in \ mathbb { n } $, $ \ chi _ { _ { dp } } ^ * ( c _ { 2k + 1 } ) = \ chi ^ * ( c _ { 2k + 1 } ) $. we also show that for any $ n \ geq 2 $ and $ m \ in \ mathbb { n } $, if $ p ^ * $ is the solution in $ ( 0, 1 ) $ to $ p = ( 1 - p ) ^ n $ then $ \ chi _ { _ { dp } } ^ * ( k _ { n, m } ) \ leq1 / p ^ * $, and we prove a generalization of this result for multipartite graphs. finally, we determine a lower bound on $ \ chi _ { _ { dp } } ^ * ( k _ { 2, m } ) $ for any $ m \ geq 3 $. | arxiv:1910.03416 |
we ( re ) cosider the propagation of small disturbances ( sound waves ) in the presence of a pinned irrotational vortex in a superfluid with the help of the formalism of acoustic spacetimes. we give closed formulas for the scattering angle for sound rays, formulate the sound - propagation problem in the hamiltonian form, and discuss the form of boundary conditions at the core of the vortex, where the hamiltonian has a singular point. the wave equation is simplified to a single ordinary differential equation of mathieu type. we give an extensive discussion of perturbations localized close to the core, which are similar to what is known as the kelvin waves. the spectra of modes depend strongly on the type of boundary condition employed close to the vortex core. the existence of the gapless kelvin mode, which is one of the modes with angular number - 1, is usually discussed in the context of unpinned vortices in superfluid helium or rotating bose - einstein condensates. we prove that this particular mode is absent if the vortex is pinned, and consequently one must discuss the full family of modes in this case. the question of whether or not the acoustic spacetime admits an ergoregion turns out to have a decisive ( qualitative ) influence on many aspects of sound - propagation phenomena. | arxiv:1110.0115 |
let $ \ mathcal { x } $ be a ( projective, non - singular, geometrically irreducible ) curve of even genus $ g ( \ mathcal { x } ) \ geq 2 $ defined over an algebraically closed field $ k $ of odd characteristic $ p $. if the $ p $ - rank $ \ gamma ( \ mathcal { x } ) $ equals $ g ( \ mathcal { x } ) $, then $ \ mathcal { x } $ is \ emph { ordinary }. in this paper, we deal with \ emph { large } automorphism groups $ g $ of ordinary curves of even genus. we prove that $ | g | < 821. 37g ( \ mathcal { x } ) ^ { 7 / 4 } $. the proof of our result is based on the classification of automorphism groups of curves of even genus in positive characteristic, see \ cite { giulietti - korchmaros - 2017 }. according to this classification, for the exceptional cases $ { \ rm aut } ( \ mathcal { x } ) \ cong { \ rm alt } _ 7 $ and $ { \ rm aut } ( \ mathcal { x } ) \ cong \ rm { m } _ { 11 } $ we show that the classical hurwitz bound $ | { \ rm aut } ( \ mathcal { x } ) | < 84 ( g ( \ mathcal { x } ) - 1 ) $ holds, unless $ p = 3 $, $ g ( \ mathcal { x } ) = 26 $ and $ { \ rm aut } ( \ mathcal { x } ) \ cong \ rm { m } _ { 11 } $ ; an example for the latter case being given by the modular curve $ x ( 11 ) $ in characteristic $ 3 $. | arxiv:1908.04684 |
in a quantum computer, creating superpositions of quantum bits ( qubits ) in different states can lead to a speed - up over classical computers [ 1 ], but quantum mechanics also allows for the superposition of quantum circuits [ 2 ]. in fact, it has recently been theoretically predicted that superimposing quantum circuits, each with a different gate order, could provide quantum computers with an even further computational advantage [ 3 - 5 ]. here, we experimentally demonstrate this enhancement by applying two quantum gates in a superposition of both possible orders to determine whether the two gates commute or anti - commute. we are able to make this determination with only a single use ( or query ) of each gate, while all quantum circuits with a fixed order of gates would require at least two uses of one of the gates [ 3 ]. remarkably, when the problem is scaled to n gates, creating a superposition of quantum circuits is likely to provide an exponential advantage over classical algorithms, and a linear advantage over quantum algorithms with fixed gate order [ 4 ]. the new resource that we exploit in our experiment can be interpreted as a " superposition of causal orders ". we demonstrate such a superposition could allow some quantum algorithms to be implemented with an efficiency that is unlikely to be achieved on a quantum computer with a fixed gate order. | arxiv:1412.4006 |
current studies of large - scale asymmetries ( i. e. lopsidedness ) in the stellar density distribution of disk galaxies have mainly focused on the local universe. recent observations have found a significant fraction ( over 60 % ) of lopsided galaxies at high - redshift ( $ 1. 5 < z < 3 $ ), which is significantly larger than the fraction ( ~ 30 % ) observed in the nearby universe. we aim to understand whether the more widespread lopsidedness at high - than low - redshift can be associated to environmental mechanisms being more effective in producing lopsided perturbations at high - redshift. at each redshift between $ 0 < z < 2 $, we independently select a sample of disk - like galaxies from the illustristng simulations. we then characterize lopsidedness in the disks of galaxies at each redshift, study the relevant mechanisms generating lopsidedness, as well as the correlation between such perturbation, the local environment and the galaxy internal properties as a function of redshift. consistent with previous and new observational results, we find that : 1 ) simulations predict a significant fraction ( ~ 60 % ) of lopsided galaxies at high - redshift ( $ 1. 5 < z < 2 $ ), 2 ) the fraction of lopsided galaxies, as well as the lopsided amplitude, decreases from high - to low - redshift, and 3 ) there is not a significant dependence of lopsidedness on the local environment, but there is a strong correlation between the lopsided amplitude and basic galaxies ' structural properties at all redshift between $ 0 < z < 2 $. this means that, independent of the mechanisms on - setting lopsidedness, galaxies with low central stellar mass density and more extended disks are more susceptible of developing strong lopsidedness. we find that both recent interactions with mass - ratio > 1 : 10 and gas accretion with subsequent star formation can produce lopsided perturbations at all redshift, but they are both significantly more effective at high - redshift. | arxiv:2411.19426 |
we report on the bepposax observations of the gamma - ray blazar pks 0528 + 134 performed in feb and mar 1997, during a multiwavelength campaign involving egret and ground based telescopes. the source was in a faint and hard state, with energy spectral index alpha = 0. 48 + - 0. 04 between 0. 1 and 10 kev, and [ 2 - 10 ] kev flux of 2. 7e - 12 erg / cm2 / s. no significant variability was observed. the source was detected in the 20 - 120 kev band by the pds, with a flux lying slightly above the extrapolation from lower x - ray energies. comparing this low state with previous higher states of the source, there is an indication that the x - ray spectrum hardens and the gamma - ray spectrum steepens when the source is fainter. | arxiv:astro-ph/9712285 |
interpolation - based trust - region methods are an important class of algorithms for derivative - free optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations between variables are negligible, implying, in the smooth case, a sparse structure in the hessian matrix. to be able to exploit hessian sparsity, existing optimization approaches require the knowledge of the sparsity structure. the goal of this paper is to develop and analyze a method where the sparse models are constructed automatically. the sparse recovery theory developed recently in the field of compressed sensing characterizes conditions under which a sparse vector can be accurately recovered from few random measurements. such a recovery is achieved by minimizing the l1 - norm of a vector subject to the measurements constraints. we suggest an approach for building sparse quadratic polynomial interpolation models by minimizing the l1 - norm of the entries of the model hessian subject to the interpolation conditions. we show that this procedure recovers accurate models when the function hessian is sparse, using relatively few randomly selected sample points. motivated by this result, we developed a practical interpolation - based trust - region method using deterministic sample sets and minimum l1 - norm quadratic models. our computational results show that the new approach exhibits a promising numerical performance both in the general case and in the sparse one. | arxiv:1306.5729 |
in this paper we classify all blocks with defect group $ c _ { 2 ^ n } \ times c _ 2 \ times c _ 2 $ up to morita equivalence. together with a recent paper of wu, zhang and zhou, this completes the classification of morita equivalence classes of $ 2 $ - blocks with abelian defect groups of rank at most $ 3 $. the classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. the case considered in this paper is significant because it involves comparison of morita equivalence classes between a group and a normal subgroup of index $ 2 $, so requires novel reduction techniques which we hope will be of wider interest. we note that this also completes the classification of blocks with abelian defect groups of order dividing $ 16 $ up to morita equivalence. a consequence is that broue ' s abelian defect group conjecture holds for all blocks mentioned above. | arxiv:1709.04331 |
the superallowed beta - decay rates that provide stringent constraints on physics beyond the standard model of particle physics are affected by nuclear structure effects through isospin - breaking corrections. the self - consistent isospin - and angular - momentum - projected nuclear density functional theory is used for the first time to compute those corrections for a number of fermi transitions in nuclei from a = 10 to a = 74. the resulting leading element of the ckm matrix, | v _ { ud } | = 0. 97447 ( 23 ), agrees well with the recent result by towner and hardy [ phys. rev. c { \ bf 77 }, 025501 ( 2008 ) ]. | arxiv:1101.0939 |
in this article the wells - dawson polyoxometalate k6 [ p2w18o62 ] is grown as an interfacial layer between indium tin oxide and bulk heterojunction of poly ( 3 - hexylthiophene ) ( p3ht ) and [ 6, 6 ] - phenyl - c61 - butyric acid methyl ester ( pcbm ). the structure of the pom layers depends on the thickness and shows a highly anisotropic surface organization. the films have been characterized by atomic force microscopy and x - ray photoelectron spectroscopy ( xps ) to gain insight into their macroscopic organization and better understand their electronic properties. then, they were put at the anodic interface of a p3ht : pcbm organic solar cell and characterized on an optical bench. the photovoltaic efficiency is discussed in terms of the benefit of the polyoxometalate at the anodic interface of an organic photovoltaic cell. | arxiv:1806.02650 |
we extend the classical heisenberg uncertainty principle to a fractional $ l ^ p $ setting by investigating a novel class of uncertainty inequalities derived from the fractional schr \ " odinger equation. in this work, we establish the existence of extremal functions for these inequalities, characterize their structure as fractional analogues of gaussian functions, and determine the sharp constants involved. moreover, we prove a quantitative stability result showing that functions nearly attaining the equality in the uncertainty inequality must be close - - in an appropriate norm - - to the set of extremizers. our results provide new insights into the fractional analytic framework and have potential applications in the analysis of fractional partial differential equations. | arxiv:2504.16245 |
we consider the gut - like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. in this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly - generated propagating conformal factor of the metric and the usual dimensional scalar field. this interaction leads to the renormalization group flow from the conformal point. in the supersymmetric conformal invariant model such an effect produces a very weak violation of sypersymmetry at lower energies. | arxiv:hep-th/9804119 |
we numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. the systems investigated are sparse random matrix hamiltonians and disordered lattices. in the former case, the quench consists of sudden switching - on the off - diagonal elements of the hamiltonian. in the latter case, it is sudden switching - on of the hopping between adjacent lattice sites. the quench - induced ensembles are compared with the so - called " quantum micro - canonical " ( qmc ) ensemble describing quantum superpositions with fixed energy expectation values. our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the qmc ensemble. away from the qmc condensation regime, the overall agreement with the qmc predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. in the case of disordered lattices, the qmc ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate. | arxiv:1209.2954 |
spatial awareness in mammals is based on internalized representations of the environment - - - cognitive maps - - - encoded by networks of spiking neurons. although behavioral studies suggest that these maps can remain stable for long periods, it is also well - known that the underlying networks of synaptic connections constantly change their architecture due to various forms of neuronal plasticity. this raises a principal question : how can a dynamic network encode a stable map of space? in the following, we discuss some recent results obtained in this direction using an algebro - topological modeling approach, which demonstrate that emergence of stable cognitive maps produced by networks with transient architectures is not only possible, but may be a generic phenomenon. | arxiv:1909.07540 |
the work initially started as a test to retrace the shen & ho ( 2014 ) quasar main sequence diagram where they ( and references therein ) claimed that the parameter rfeii, which defines the eigenvector 1 ( ev1 ) is driven by the eddington ratio alone. we subsequently construct a refined ( error and redshift limited ) sample from the original shen et. al ( 2011 ) qso catalogue. based on our hypothesis - the main driver of the quasar main sequence is the maximum of the accretion disk temperature defined by the big blue bump on the spectral energy distribution. we select five extreme sources that have rfeii > = 4. 0 and use the sed modelling code cigale to fit the multi - band photometric data for these sources. incorporating the prescription for broad emission - line species dependent virial factors, we derive the black hole masses for the entire shen + 11 catalogue and compare their distribution with the black hole masses in the original catalogue. here, we show the results of our analysis for one of the 5 extreme sources, sdssj082358. 30 + 213545. 2. we also show the detailed modelling, including the fe ii pseudo - continuum to estimate and compare the value of rfeii for this object. | arxiv:1804.09954 |
first order invariants of generic immersions of manifolds of dimension nm - 1 into manifolds of dimension n ( m + 1 ) - 1, m, n > 1 are constructed using the geometry of self - intersections. the range of one of these invariants is related to bernoulli numbers. as by - products some geometrically defined invariants of regular homotopy are found. | arxiv:math/9904031 |
federated learning is a newly emerging distributed learning framework that facilitates the collaborative training of a shared global model among distributed participants with their privacy preserved. however, federated learning systems are vulnerable to byzantine attacks from malicious participants, who can upload carefully crafted local model updates to degrade the quality of the global model and even leave a backdoor. while this problem has received significant attention recently, current defensive schemes heavily rely on various assumptions, such as a fixed byzantine model, availability of participants ' local data, minority attackers, iid data distribution, etc. to relax those constraints, this paper presents robust - fl, the first prediction - based byzantine - robust federated learning scheme where none of the assumptions is leveraged. the core idea of the robust - fl is exploiting historical global model to construct an estimator based on which the local models will be filtered through similarity detection. we then cluster local models to adaptively adjust the acceptable differences between the local models and the estimator such that byzantine users can be identified. extensive experiments over different datasets show that our approach achieves the following advantages simultaneously : ( i ) independence of participants ' local data, ( ii ) tolerance of majority attackers, ( iii ) generalization to variable byzantine model. | arxiv:2210.01437 |
the possible interpretations of a new continuum model for the two - dimensional quantum gravity for $ d > 1 $ ( $ d $ = matter central charge ), obtained by carefully treating both diffeomorphism and weyl symmetries, are discussed. in particular we note that an effective field theory is achieved in low energy ( large area ) expansion, that may represent smooth self - avoiding random surfaces embedded in a $ d $ - dimensional flat space - time for arbitrary $ d $. moreover the values of some critical exponents are computed, that are in agreement with some recent numerical results. | arxiv:hep-lat/9402004 |
since the seminal paper by breiman in 2001, who pointed out a potential harm of prediction multiplicities from the view of explainable ai, global analysis of a collection of all good models, also known as a ` rashomon set, ' has been attracted much attention for the last years. since finding such a set of good models is a hard computational problem, there have been only a few algorithms for the problem so far, most of which are either approximate or incomplete. to overcome this difficulty, we study efficient enumeration of all good models for a subclass of interpretable models, called rule lists. based on a state - of - the - art optimal rule list learner, corels, proposed by angelino et al. in 2017, we present an efficient enumeration algorithm corelsenum for exactly computing a set of all good models using polynomial space in input size, given a dataset and a error tolerance from an optimal model. by experiments with the compas dataset on recidivism prediction, our algorithm corelsenum successfully enumerated all of several tens of thousands of good rule lists of length at most $ \ ell = 3 $ in around 1, 000 seconds, while a state - of - the - art top - $ k $ rule list learner based on lawler ' s method combined with corels, proposed by hara and ishihata in 2018, found only 40 models until the timeout of 6, 000 seconds. for global analysis, we conducted experiments for characterizing the rashomon set, and observed large diversity of models in predictive multiplicity and fairness of models. | arxiv:2204.11285 |
we propose a qubit implementation based on exciton condensation in capacitively coupled josephson junction chains. the qubit is protected in the sense that all unwanted terms in its effective hamiltonian are exponentially suppressed as the chain length increases. we also describe an implementation of a universal set of quantum gates. most gates also offer exponential error suppression. the only gate that is not intrinsically fault - tolerant needs to be realized with about 50 % precision, provided the other gates are exact. | arxiv:cond-mat/0609441 |
in this article we show analytic properties of certain rankin - selberg type dirichlet series for holomorphic jacobi cusp forms of integral weight and of half - integral weight. the numerators of these dirichlet series are the inner products of fourier - jacobi coefficients of two jacobi cusp forms. the denominators and the range of summation of these dirichlet series are like the ones of the koecher - maass series. the meromorphic continuations and functional equations of these dirichlet series are obtained. moreover, an identity between the petersson norms of jacobi forms with respect to linear isomorphism between jacobi forms of integral weight and half - integral weight is also obtained. | arxiv:1804.04319 |
in the past three years, there has been significant interest in hyperspectral imagery ( hsi ) classification using vision transformers for analysis of remotely sensed data. previous research predominantly focused on the empirical integration of convolutional neural networks ( cnns ) to augment the network ' s capability to extract local feature information. yet, the theoretical justification for vision transformers out - performing cnn architectures in hsi classification remains a question. to address this issue, a unified hierarchical spectral vision transformer architecture, specifically tailored for hsi classification, is investigated. in this streamlined yet effective vision transformer architecture, multiple mixer modules are strategically integrated separately. these include the cnn - mixer, which executes convolution operations ; the spatial self - attention ( ssa ) - mixer and channel self - attention ( csa ) - mixer, both of which are adaptations of classical self - attention blocks ; and hybrid models such as the ssa + cnn - mixer and csa + cnn - mixer, which merge convolution with self - attention operations. this integration facilitates the development of a broad spectrum of vision transformer - based models tailored for hsi classification. in terms of the training process, a comprehensive analysis is performed, contrasting classical cnn models and vision transformer - based counterparts, with particular attention to disturbance robustness and the distribution of the largest eigenvalue of the hessian. from the evaluations conducted on various mixer models rooted in the unified architecture, it is concluded that the unique strength of vision transformers can be attributed to their overarching architecture, rather than being exclusively reliant on individual multi - head self - attention ( msa ) components. | arxiv:2409.09244 |
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