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in this work, we thoroughly investigate the impact process on the granular media in the limit when the ratio of the impact velocity to the acoustic speed becomes of the order of 0. 01 - 1, which is far greater than the existing literature ( 0. 0001 - 0. 001 ). we show that the energy dissipation is largely due to the energy cost associated with the exploration between different metastable states via large scale reorganization of the force chain network. in this regime, the conventional drag force models break down, and the drag force can not be decomposed into a depth dependent static pressure and a depth independent inertial drag as proposed in the existing literature. the high dynamical stress generates acoustic pulses, which propagate longer distances rather than decaying exponentially, as observed in the previous works. in the latter stage of the impact process, the boundary also plays an essential role in the reorganization of the force chains as the reflected acoustic pulses interact with the original impact pulses. furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling. | arxiv:2305.11269 |
3d object detection has recently become popular due to many applications in robotics, augmented reality, autonomy, and image retrieval. we introduce the objectron dataset to advance the state of the art in 3d object detection and foster new research and applications, such as 3d object tracking, view synthesis, and improved 3d shape representation. the dataset contains object - centric short videos with pose annotations for nine categories and includes 4 million annotated images in 14, 819 annotated videos. we also propose a new evaluation metric, 3d intersection over union, for 3d object detection. we demonstrate the usefulness of our dataset in 3d object detection tasks by providing baseline models trained on this dataset. our dataset and evaluation source code are available online at http : / / www. objectron. dev | arxiv:2012.09988 |
within the euclidean path integral and mass perturbation theory we derive, from the dyson - schwinger equations of the massive schwinger model, a general formula that incorporates, for sufficiently small fermion mass, all the bound - state mass poles of the massive schwinger model. as an illustration we perturbatively compute the masses of the three lowest bound states. | arxiv:hep-th/9602175 |
it is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. this contrasts with the case of the full elementary theory of the finitely generated free algebras which is known to be undecidable. as a by - product, a description of the pseudocomplemented distributive lattices that can be embedded into the free algebra is also obtained. | arxiv:2409.03640 |
this article proposes and evaluates a new safety concept called backup plan safety for path planning of autonomous vehicles under mission uncertainty using model predictive control ( mpc ). backup plan safety is defined as the ability to complete an alternative mission when the primary mission is aborted. to include this new safety concept in control problems, we formulate a feasibility maximization problem aiming to maximize the feasibility of the primary and alternative missions. the feasibility maximization problem is based on multi - objective mpc, where each objective ( cost function ) is associated with a different mission and balanced by a weight vector. furthermore, the feasibility maximization problem incorporates additional control input horizons toward the alternative missions on top of the control input horizon toward the primary mission, denoted as multi - horizon inputs, to evaluate the cost for each mission. we develop the backup plan constrained mpc algorithm, which designs the weight vector that ensures asymptotic stability of the closed - loop system, and generates the optimal control input by solving the feasibility maximization problem with computational efficiency. the performance of the proposed algorithm is validated through simulations of a uav path planning problem. | arxiv:2306.06102 |
plausible ratios of deuterium to hydrogen d / h as a function of metallicity, time, and redshift are investigated. guided by the heavy element abundance patterns observed locally in galactic dwarf stars and at large redshift in quasi - stellar object absorption line systems, empirical evolution of the relative abundance ratios li / d, b / d, n / d, o / d, and f / d for qso absorption line systems are given for the possible evolutionary patterns in d / h. shortened abstract. | arxiv:astro-ph/9701243 |
given a target distribution $ \ mu $ and a proposal chain with generator $ q $ on a finite state space, in this paper we study two types of metropolis - hastings ( mh ) generator $ m _ 1 ( q, \ mu ) $ and $ m _ 2 ( q, \ mu ) $ in a continuous - time setting. while $ m _ 1 $ is the classical mh generator, we define a new generator $ m _ 2 $ that captures the opposite movement of $ m _ 1 $ and provide a comprehensive suite of comparison results ranging from hitting time and mixing time to asymptotic variance, large deviations and capacity, which demonstrate that $ m _ 2 $ enjoys superior mixing properties than $ m _ 1 $. to see that $ m _ 1 $ and $ m _ 2 $ are natural transformations, we offer an interesting geometric interpretation of $ m _ 1 $, $ m _ 2 $ and their convex combinations as $ \ ell ^ 1 $ minimizers between $ q $ and the set of $ \ mu $ - reversible generators, extending the results by billera and diaconis ( 2001 ). we provide two examples as illustrations. in the first one we give explicit spectral analysis of $ m _ 1 $ and $ m _ 2 $ for metropolised independent sampling, while in the second example we prove a laplace transform order of the fastest strong stationary time between birth - death $ m _ 1 $ and $ m _ 2 $. | arxiv:1810.11763 |
let k be a commutative ring with unit. we endow the categories of filtered complexes and of bicomplexes of k - modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi - isomorphism at a certain fixed stage of the associated spectral sequence. for filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and d \ ' ecalage. | arxiv:1805.00374 |
sample efficiency remains a key challenge in multi - agent reinforcement learning ( marl ). a promising approach is to learn a meaningful latent representation space through auxiliary learning objectives alongside the marl objective to aid in learning a successful control policy. in our work, we present mapo - lso ( multi - agent policy optimization with latent space optimization ) which applies a form of comprehensive representation learning devised to supplement marl training. specifically, mapo - lso proposes a multi - agent extension of transition dynamics reconstruction and self - predictive learning that constructs a latent state optimization scheme that can be trivially extended to current state - of - the - art marl algorithms. empirical results demonstrate mapo - lso to show notable improvements in sample efficiency and learning performance compared to its vanilla marl counterpart without any additional marl hyperparameter tuning on a diverse suite of marl tasks. | arxiv:2406.02890 |
for locally compact groups amenability and kazhdan ' s property ( t ) are mutually exclusive in the sense that a group having both properties is compact. this is no longer true for more general polish groups. however, a weaker result still holds for sin groups ( topological groups admitting a basis of conjugation - invariant neighbourhoods of identity ) : if such a group admits sufficiently many unitary representations, then it is precompact as soon as it is amenable and has the strong property ( t ) ( i. e. admits a finite kazhdan set ). if an amenable topological group with property ( t ) admits a faithful uniformly continuous representation, then it is maximally almost periodic. in particular, an extremely amenable sin group never has strong property ( t ), and an extremely amenable subgroup of unitary operators in the uniform topology is never a kazhdan group. this leads to first examples distinguishing between property ( t ) and property ( fh ) in the class of polish groups. disproving a 2003 conjecture by bekka, we construct a complete, separable, minimally almost periodic topological group with property ( t ), having no finite kazhdan set. finally, as a curiosity, we observe that the class of topological groups with property ( t ) is closed under arbitrary infinite products with the usual product topology. | arxiv:1512.01572 |
understanding the late - time acceleration of the universe is one of the major challenges in cosmology today. in this paper, we present a new scalar field model corresponding to a generalised axion - like potential. in fact, this model can be framed as a quintessence model based on physically motivated considerations. this potential is capable of alleviating the coincidence problem through a tracking regime. we will as well prove that this potential allows for a late - time acceleration period induced by an effective cosmological constant, which is reached without fine - tuning the initial conditions of the scalar field. in our model, the generalised axion field fuels the late - time acceleration of the universe rather than fuelling an early dark energy era. additionally, we will show how the late - time transition to dark energy dominance could be favoured in this model, since the density parameter of the scalar field will rapidly grow in the late phase of the tracking regime. | arxiv:2409.18184 |
we describe a new representation of hankel operators $ h $ as pseudo - differential operators $ a $ in the space of functions defined on the whole axis. the amplitudes of such operators $ a $ have a very special structure : they are products of functions of a one variable only. this representation has numerous spectral consequences both for compact hankel operators and for operators with the continuous spectrum. | arxiv:1801.00706 |
it is well known that the long - term evolution of the photospheric magnetic field plays an important role in building up free energy to power solar eruptions. observations, despite being controversial, have also revealed a rapid and permanent variation of the photospheric magnetic field in response to the coronal magnetic field restructuring during the eruption. the helioseismic and magnetic imager instrument ( hmi ) on board the newly launched solar dynamics observatory ( sdo ) produces seeing - free full - disk vector magnetograms at consistently high resolution and high cadence, which finally makes possible an unambiguous and comprehensive study of this important back - reaction process. in this study, we present a near disk - center, goes - class x2. 2 flare, which occurred in noaa ar 11158 on 2011 february 15. using the magnetic field measurements made by hmi, we obtained the first solid evidence of a rapid ( in about 30 minutes ) and irreversible enhancement in the horizontal magnetic field at the flaring magnetic polarity inversion line ( pil ) by a magnitude of ~ 30 %. it is also shown that the photospheric field becomes more sheared and more inclined. this field evolution is unequivocally associated with the flare occurrence in this sigmoidal active region, with the enhancement area located in between the two chromospheric flare ribbons and the initial conjugate hard x - ray footpoints. these results strongly corroborate our previous conjecture that the photospheric magnetic field near the pil must become more horizontal after eruptions, which could be related to the newly formed low - lying fields resulted from the tether - cutting reconnection. | arxiv:1112.3948 |
we consider the photon field between an unusual configuration of infinite parallel plates : a perfectly conducting plate $ ( \ epsilon \ to \ infty ) $ and an infinitely permeable one $ \ mu \ to \ infty ) $. after quantizing the vector potential in the coulomb gauge, we obtain explicit expressions for the vacuum expectation values of field operators of the form $ < { \ hat e } _ i { \ hat e } _ j > _ 0 $ and $ < { \ hat b } _ i { \ hat b } _ j > _ 0 $. these field correlators allow us to reobtain the casimir effect for this set up and to discuss the light velocity shift caused by the presence of plates ( scharnhorst effect \ cite { scharnhorst, barton, barscharn } ) for both scalar and spinor qed. | arxiv:hep-th/9811062 |
the way spacetime behaves as one approaches a spacelike singularity is re - investigated. we find a simple twistorial presentation that includes and simplifies the classic work of belinskii, khalatnikov and lifshitz as well as the more recent results of damour, henneaux and nicolai. we speculate on the application of our technique to the e { 10 } programme of m - theory. | arxiv:2301.03443 |
selecting the right journal for your research paper is a pivotal decision in the academic publishing journey. this paper aims to guide researchers through the process of choosing a suitable journal for their work by discussing key criteria and offering practical tips. | arxiv:2312.04573 |
new estimates are derived concerning the behavior of self - dual hamonic 2 - forms on a compact riemannian 4 - manifold with non - trivial seiberg - witten invariants. applications include a vanishing theorem for certain seiberg - witten invariants on compact 4 - manifolds of constant negative sectional curvature. | arxiv:math/0111265 |
we study the convergence of multigrid schemes for the helmholtz equation, focusing in particular on the choice of the coarse scale operators. let g _ c denote the number of points per wavelength at the coarse level. if the coarse scale solutions are to approximate the true solutions, then the oscillatory nature of the solutions implies the requirement g _ c > 2. however, in examples the requirement is more like g _ c > = 10, in a trade - off involving also the amount of damping present and the number of multigrid iterations. we conjecture that this is caused by the difference in phase speeds between the coarse and fine scale operators. standard 5 - point finite differences in 2 - d are our first example. a new coarse scale 9 - point operator is constructed to match the fine scale phase speeds. we then compare phase speeds and multigrid performance of standard schemes with a scheme using the new operator. the required g _ c is reduced from about 10 to about 3. 5, with less damping present so that waves propagate over > 100 wavelengths in the new scheme. next we consider extensions of the method to more general cases. in 3 - d comparable results are obtained with standard 7 - point differences and optimized 27 - point coarse grid operators, leading to an order of magnitude reduction in the number of unknowns for the coarsest scale linear system. finally we show how to include pml boundary layers, using a regular grid finite element method. matching coarse scale operators can easily be constructed for other discretizations. the method is therefore potentially useful for a large class of discretized high - frequency helmholtz equations. | arxiv:1304.4103 |
this paper presents a framework to incorporate ride - pooling from a mesoscopic point of view, within time - invariant network flow models of mobility - on - demand systems. the resulting problem structure remains identical to a standard network flow model, a linear problem, which can be solved in polynomial time for a given ride - pooling request assignment. in order to compute such a ride - pooling assignment, we devise a polynomial - time knapsack - like algorithm that is optimal w. r. t. the minimum user travel time instance of the original problem. finally, we conduct two case studies of sioux falls and manhattan, where we validate our models against state - of - the - art time - varying results, and we quantitatively highlight the effects that maximum waiting time and maximum delay thresholds have on the vehicle hours traveled, overall pooled rides and actual delay experienced. we show that for a sufficient number of requests, with a maximum waiting time and delay of 5 minutes, it is possible to ride - pool more than 80 % of the requests for both case studies. last, allowing for four people ride - pooling can significantly boost the performance of the system. | arxiv:2311.06035 |
we present and compare the predictions of various cosmic - ray monte carlo models for the energy ( de / deta ) and particle ( dn / deta ) flows in p - p, p - pb and pb - pb collisions at sqrt ( s ) = 14, 8. 8, and 5. 5 tev respectively, in the range covered by forward lhc detectors like castor or totem ( 5. 2 < | eta | < 6. 6 ) and zdc or lhcf ( | eta | > 8. 1 for neutrals ). | arxiv:0806.0944 |
the conventional treatment of the bethe - bloch equation for protons accounts for electron capture at the end of the projectile track by the small barkas correction. this is only a possible way for protons, whereas for light and heavier charged nuclei the exchange of energy and charge along the track has to be accounted for by regarding the projectile charge q as a function of the residual energy. this leads to a significant modification of the bethe - bloch equation, otherwise the range in a medium is incorrectly determined. the let in the bragg peak domain and distal end is significantly influenced by the electron capture. a rather significant result is that in the domain of the bragg peak the superiority of carbon ions is reduced compared to protons. | arxiv:1109.2509 |
eris, the enhanced resolution imager and spectrograph, is an instrument that both extends and enhances the fundamental diffraction limited imaging and spectroscopy capability for the vlt. it replaces two instruments that were being maintained beyond their operational lifetimes, combines their functionality on a single focus, provides a new wavefront sensing module for natural and laser guide stars that makes use of the adaptive optics facility, and considerably improves on their performance. the observational modes eris provides are integral field spectroscopy at 1 - 2. 5 { \ mu } m, imaging at 1 - 5 { \ mu } m with several options for high contrast imaging, and longslit spectroscopy at 3 - 4 { \ mu } m, the instrument is installed at the cassegrain focus of ut4 at the vlt and, following its commissioning during 2022, has been made available to the community. | arxiv:2304.02343 |
we show that for any set of primes $ \ mathcal { p } $ there exists a space $ m _ { \ mathcal { p } } $ which is a homology and cohomology 3 - manifold with coefficients in $ \ mathbb { z } _ { p } $ for $ p \ in \ mathcal { p } $ and is not a homology or cohomology 3 - manifold with coefficients in $ \ mathbb { z } _ q $ for $ q \ not \ in \ mathcal { p } $. moreover, $ m _ { \ mathcal { p } } $ is neither a homology nor cohomology 3 - manifold with coefficients in $ \ mathbb { z } $ or $ \ mathbb { q } $. | arxiv:1606.05835 |
we examine charge fractionalization by chiral separation in a one - dimensional fermion system described by luttinger liquid theory. the focus is on the question of whether the fractional charges are quantum mechanically sharp, and in the analysis we make a distinction between the global charge, which is restricted by boundary conditions, and the local charge where a background contribution is subtracted. we show, by way of examples, that fractional charges of arbitrary values, all which are quantum mechanically sharp, can be introduced by different initial conditions. since the system is gapless, excitations of arbitrary low frequency contribute to the fluctuations, it is important to make a precise definition of sharp charges, and this we we do by subtraction of the ground state contribution. we very briefly comment on the relevance of our analysis for proposed experiments. | arxiv:0906.0811 |
the moduli space of flat connections for maximally supersymmetric yang - mills theories, in a space - time of the form t ^ 3xr, contains isolated points, corresponding to normalizable zero energy states, for certain simple gauge groups g. we consider the low energy effective field theories in the weak coupling limit supported on such isolated points and find that when quantized they consist of an infinite set of harmonic oscillators whose angular frequencies are completely determined by the lie algebra of g. we then proceed to find the isolated flat connections for all simple g and subsequently specify the corresponding effective field theories. | arxiv:0804.0503 |
we investigate the properties of the event horizon and static limit for a charged rotating black hole solution of minimal supergravity theory in ( 1 + 4 ) dimension. unlike the four - dimensional case, there are in general two rotations, and they couple to both mass and charge. this gives rise to much richer structure to ergosphere leading to energy extraction even for axial fall. another interesting feature is that the metric in this case is sensitive to the sign of the maxwell charge. | arxiv:0902.3079 |
it is well known that the optical properties of spherical metal particles can be described with the rayleigh approximation or rigorous mie theory. but for the single metallic nanorods, a theory well capturing the fundamental resonance and scattering features is still absent. in this study, an analytical model is developed for the metallic nanorod, considering the longitudinally non - uniform conduction current and surface charges. with the circuit parameters deduced from the kinetic and electromagnetic energy of the nanorod, a formula which agrees well with the simulations has been suggested for the resonance wavelength of the fundamental longitudinal mode. moreover, by introducing the radiative resistance to the circuit theory, the dipole moment, extinction spectrum, and near - field enhancement of the nanorod have been derived analytically and confirmed numerically. the results are important for understanding the optical properties of the metallic nanorods and provide a guideline for designing the light scattering and absorption. | arxiv:2205.00912 |
due to the sparse connectivity of superconducting quantum computers, qubit communication via swap gates accounts for the vast majority of overhead in quantum programs. we introduce a method for improving the speed and reliability of swaps at the level of the superconducting hardware ' s native gateset. our method relies on four techniques : 1 ) swap orientation, 2 ) cross - gate pulse cancellation, 3 ) commutation through cross - resonance, and 4 ) cross - resonance polarity. importantly, our optimized swap is bootstrapped from the pre - calibrated gates, and therefore incurs zero calibration overhead. we experimentally evaluate our optimizations with qiskit pulse on ibm hardware. our optimized swap is 11 % faster and 13 % more reliable than the standard swap. we also experimentally validate our optimizations on application - level benchmarks. due to ( a ) the multiplicatively compounding gains from improved swaps and ( b ) the frequency of swaps, we observe typical improvements in success probability of 10 - 40 %. the optimized swap is available through the superstaq platform. | arxiv:2109.13199 |
we prove that for any automorphism $ \ phi $ of the restricted wreath product $ \ mathbb { z } _ 2 \ mathrm { wr } \ mathbb { z } ^ k $ and $ \ mathbb { z } _ 3 \ mathrm { wr } \ mathbb { z } ^ { 2d } $ the reidemeister number $ r ( \ phi ) $ is infinite, i. e. these groups have the property $ r _ \ infty $. for $ \ mathbb { z } _ 3 \ mathrm { wr } \ mathbb { z } ^ { 2d + 1 } $ and $ \ mathbb { z } _ p \ mathrm { wr } \ mathbb { z } ^ k $, where $ p > 3 $ is prime, we give examples of automorphisms with finite reidemeister numbers. so these groups do not have the property $ r _ \ infty $. for these groups and $ \ mathbb { z } _ m \ mathrm { wr } \ mathbb { z } $, where $ m $ is relatively prime to $ 6 $, we prove the twisted burnside - frobenius theorem ( tbft $ _ f $ ) : if $ r ( \ phi ) < \ infty $, then it is equal to the number of equivalence classes of finite - dimensional irreducible unitary representations fixed by the action $ [ \ rho ] \ mapsto [ \ rho \ circ \ phi ] $. | arxiv:1711.09371 |
we describe a new method to construct laplacians on fractals using a peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain julia sets. the peano curve allows us to visualize eigenfunctions of the laplacian by graphing the pullback to the circle. we study in detail three fractals : the pentagasket, the octagasket and the magic carpet. we also use the method for two nonfractal self - similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. in contrast to the many familiar pictures of approximations to standard peano curves, that do no show self - intersections, our descriptions of approximations to the peano curves have self - intersections that play a vital role in constructing graph approximations to the fractal with explicit graph laplacians that give the fractal laplacian in the limit. | arxiv:1402.2106 |
this paper concerns with the conversion of a spoken english language query into sql for retrieving data from rdbms. a user submits a query as speech signal through the user interface and gets the result of the query in the text format. we have developed the acoustic and language models using which a speech utterance can be converted into english text query and thus natural language processing techniques can be applied on this english text query to generate an equivalent sql query. for conversion of speech into english text htk and julius tools have been used and for conversion of english text query into sql query we have implemented a system which uses rule based translation to translate english language query into sql query. the translation uses lexical analyzer, parser and syntax directed translation techniques like in compilers. jflex and byacc tools have been used to build lexical analyzer and parser respectively. system is domain independent i. e. system can run on different database as it generates lex files from the underlying database. | arxiv:1308.3106 |
property technology ( also known as by the portmanteaus proptech, proptech, prop - tech and also known as real estate technology ) is used to refer to the application of information technology and platform economics to the real estate industry. property technology overlaps with financial technology, including uses like online payment and booking systems. = = overview = = property technology encompasses any application of digital technology or platform economics in the real estate industry. some examples of property technology include property management using digital dashboards, smart home technology, research and analytics, listing services / tech - enabled brokerages, mobile applications, residential and commercial lending, 3d - modeling for online portals, automation, crowdfunding real estate projects, shared spaces management, as well as organizing, analyzing, and extracting key data from lengthy rental documents. according to economist richard reed, the real estate industry has historically been conservative in its approach to technology, and is slower to adopt new technologies than other industries. advances in the residential side of real estate technology encompass some target areas, but generally aim to reduce friction in the purchase, sale, or rental of a property. areas of focus include finding a home, selling a home, financing a purchase, closing on a property ( including valuation, title & escrow, and title insurance ), managing a property, managing loans, and mortgage lending software. many proptech companies have seen a spike in demand for these solutions as the covid - 19 pandemic has jolted management companies from their " business as usual " routine. = = history of real estate technology = = the history of property technology is often divided into three stages of development. these stages broadly correspond to the period from 1980 to 2000, from 2000 to 2008, and from 2008 to the present. digital technology began to be adopted by the real estate industry during the 1980s, when personal computing became more common. spreadsheet and accounting software like microsoft excel began to be used by real estate companies when they were first introduced. advancements in the area of investment analysis also allowed real estate investors to more accurately assess the value of commercial real estate using larger databases of information. the second stage began as real estate technology first targeted consumers during the dot - com bubble. at a time when most sales and residential listings were on print media and real estate offices, companies began to focus on moving listings onto the digital media. from 2008 onwards, the widespread availability of high speed internet meant that real estate companies could move more of their data and services online. real estate databases such as zillow are an example | https://en.wikipedia.org/wiki/Property_technology |
for positive $ q \ neq1 $, the $ q $ - exchangeability of an infinite random word is introduced as quasi - invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. this framework allows us to extend the $ q $ - analog of de finetti ' s theorem for binary sequences - - - see gnedin and olshanski [ electron. j. combin. 16 ( 2009 ) r78 ] - - - to general real - valued sequences. in contrast to the classical case of exchangeability ( $ q = 1 $ ), the order on $ \ mathbb { r } $ plays a significant role for the $ q $ - analogs. an explicit construction of ergodic $ q $ - exchangeable measures involves random shuffling of $ \ mathbb { n } = \ { 1, 2,... \ } $ by iteration of the geometric choice. connections are established with transient markov chains on $ q $ - pascal pyramids and invariant random flags over the galois fields. | arxiv:0907.3275 |
given an array a of $ n $ elements, we wish to support queries for the most frequent and least frequent element in a subrange $ [ l, r ] $ of $ a $. we also wish to support updates that change a particular element at index $ i $ or insert / delete an element at index $ i $. for the range mode problem, our data structure supports all operations in $ o ( n ^ { 2 / 3 } ) $ deterministic time using only $ o ( n ) $ space. this improves two results by chan et al. \ cite { c14 } : a linear space data structure supporting update and query operations in $ \ tilde { o } ( n ^ { 3 / 4 } ) $ time and an $ o ( n ^ { 4 / 3 } ) $ space data structure supporting update and query operations in $ \ tilde { o } ( n ^ { 2 / 3 } ) $ time. for the range least frequent problem, we address two variations. in the first, we are allowed to answer with an element of $ a $ that may not appear in the query range, and in the second, the returned element must be present in the query range. for the first variation, we develop a data structure that supports queries in $ \ tilde { o } ( n ^ { 2 / 3 } ) $ time, updates in $ o ( n ^ { 2 / 3 } ) $ time, and occupies $ o ( n ) $ space. for the second variation, we develop a monte carlo data structure that supports queries in $ o ( n ^ { 2 / 3 } ) $ time, updates in $ \ tilde { o } ( n ^ { 2 / 3 } ) $ time, and occupies $ \ tilde { o } ( n ) $ space, but requires that updates are made independently of the results of previous queries. the monte carlo data structure is also capable of answering $ k $ - frequency queries ; that is, the problem of finding an element of given frequency in the specified query range. previously, no dynamic data structures were known for least frequent element or $ k $ - frequency queries. | arxiv:1807.03827 |
nowadays, engineers have to develop software often without even knowing which hardware it will eventually run on in numerous mobile phones, tablets, desktops, laptops, data centers, supercomputers and cloud services. unfortunately, optimizing compilers are not keeping pace with ever increasing complexity of computer systems anymore and may produce severely underperforming executable codes while wasting expensive resources and energy. we present our practical and collaborative solution to this problem via light - weight wrappers around any software piece when more than one implementation or optimization choice available. these wrappers are connected with a public collective mind autotuning infrastructure and repository of knowledge ( c - mind. org / repo ) to continuously monitor various important characteristics of these pieces ( computational species ) across numerous existing hardware configurations together with randomly selected optimizations. similar to natural sciences, we can now continuously track winning solutions ( optimizations for a given hardware ) that minimize all costs of a computation ( execution time, energy spent, code size, failures, memory and storage footprint, optimization time, faults, contentions, inaccuracy and so on ) of a given species on a pareto frontier along with any unexpected behavior. the community can then collaboratively classify solutions, prune redundant ones, and correlate them with various features of software, its inputs ( data sets ) and used hardware either manually or using powerful predictive analytics techniques. our approach can then help create a large, realistic, diverse, representative, and continuously evolving benchmark with related optimization knowledge while gradually covering all possible software and hardware to be able to predict best optimizations and improve compilers and hardware depending on usage scenarios and requirements. | arxiv:1506.06256 |
we study cfts at finite temperature and derive explicit sum rules for one - point functions of operators by imposing the kms condition. in the case of a large gap between light and heavy operators, we explicitly compute one - point functions for light operators. turning to heavy operators we employ tauberian theorems and compute the asymptotic ope density for heavy operators, from which we extract the leading terms of the ope coefficients associated with heavy operators. furthermore, we approximate and establish bounds for the two - point functions. | arxiv:2312.13030 |
polycyclic aromatic hydrocarbons ( pahs ) have been detected throughout the universe where they play essential roles in the evolution of their environments. for example, they are believed to affect atmospheric loss rates of close - in planets and might contribute to the pre - biotic chemistry and emergence of life. despite their importance, the study of pahs in exoplanet atmospheres has been limited. we aim to evaluate the possibility of detecting pahs on exoplanets considering future observations using jwst ' s nirspec prism mode. the hot saturn wasp - 6 b shows properties that are consistent with a potential pah presence and is thus used as a case study for this work. here, we compare the likelihoods of various synthetic haze species and their combinations with the influence of pahs on the transmission spectrum of wasp - 6 b. this is possible by applying the atmospheric retrieval code petitradtrans to a collection of data from previous observations. subsequently, by exploring synthetic, single transit jwst spectra of this planet that include pahs, we assess if these molecules can be detected in the near future. previous observations support the presence of cloud / haze species in the spectrum of wasp - 6 b. while this may include pahs, the current data do not confirm their existence unambiguously. our research suggests that utilizing the jwst for future observations could lead to a notable advancement in the study of pahs. employing this telescope, we find that a pah abundance of approximately 0. 1 per cent of the ism value could be robustly detectable. | arxiv:2411.07861 |
we calculate the new physics contributions to the rare semileptonic decay $ b \ to x _ s l ^ + l ^ - $ $ ( l = e, \ mu ) $ induced by the charged - higgs loop diagrams appeared in the top quark two - higgs doublet model ( t2hdm ). within the considered parameter space, we found that ( a ) the effective wilson coefficients $ \ widetilde { c } _ { i } ^ { eff } ( m _ b ) $ ( $ i = 7 \ gamma, 9v $ and $ 10a $ ) in the t2hdm are always standard model like ; ( b ) the new physics contributions to $ \ widetilde { c } _ { 7 \ gamma } ^ { eff } $ and $ \ widetilde { c } _ { 9v } ^ { eff } $ can be significant, but they tend to cancel each other ; and ( c ) the t2hdm predictions for $ br ( b \ to x _ s l ^ + l ^ - ) $ agree well with the measured value within one standard deviation. | arxiv:hep-ph/0605076 |
in this work, we explore all possible scenarios in the evaporation process of a spherical neutral ads black hole in four - dimensional conformal gravity, where the equations of states are branched. in one branch, the final states correspond to the extremal black hole where the total decay time is divergent given any initial mass. in the other branch, the black holes always evaporate completely with in a finite time ; the total decay time depends linearly on the ads radius, when the mass is taken to be infinity. | arxiv:1811.07309 |
the distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. the hierarchical distribution of the universe, with its galaxies, clusters and super - clusters of galaxies indicates the absence of a natural length scale. in the newtonian formulation, numerical simulations of a one - dimensional system permit us to precisely follow the evolution of an ensemble of particles starting with an initial perturbation in the hubble flow. the limitation of the investigation to one dimension removes the necessity to make approximations in calculating the gravitational field and, on the whole, the system dynamics. it is then possible to accurately follow the trajectories of particles for a long time. the simulations show the emergence of a self - similar hierarchical structure in both the phase space and the configuration space and invites the implementation of a multifractal analysis. here, after showing that symmetry considerations leads to the construction of a family of equations of motion of the one - dimensional gravitational system, we apply four different methods for computing generalized dimensions $ d _ q $ of the distribution of particles in configuration space. we first employ the conventional box counting and correlation integral methods based on partitions of equal size and then the less familiar nearest - neighbor and k - neighbor methods based on partitions of equal mass. we show that the latter are superior for computing generalized dimensions for indices $ q < - 1 $ which characterize regions of low density. | arxiv:1501.04674 |
it has been observed \ citep { zhang2016understanding } that deep neural networks can memorize : they achieve 100 \ % accuracy on training data. recent theoretical results explained such behavior in highly overparametrized regimes, where the number of neurons in each layer is larger than the number of training samples. in this paper, we show that neural networks can be trained to memorize training data perfectly in a mildly overparametrized regime, where the number of parameters is just a constant factor more than the number of training samples, and the number of neurons is much smaller. | arxiv:1909.11837 |
we study the minimal supersymmetric standard model derived from $ z _ n \ times z _ m $ orbifold models. moduli dependent threshold corrections of the gauge couplings are investigated to explain the measured values of the coupling constants. also we study yukawa couplings of the models. we find that the $ z _ 2 \ times z _ 6 ' $, $ z _ 2 \ times z _ 6 $, $ z _ 3 \ times z _ 6 $ and $ z _ 6 \ times z _ 6 $ orbifold models have the possibility to derive yukawa couplings for the second and third generations as well as the measured gauge coupling constants. allowed models are shown explicitly by combinations of modular weights for the matter fields. | arxiv:hep-ph/9406238 |
we introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. this approach is based on a new dual representation for divergences. we treat point estimation and tests for simple and composite hypotheses, extending maximum likelihood technique. an other view at the maximum likelihood approach, for estimation and test, is given. we prove existence and consistency of the proposed estimates. the limit laws of the estimates and test statistics ( including the generalized likelihood ratio one ) are given both under the null and the alternative hypotheses, and approximation of the power functions is deduced. a new procedure of construction of confidence regions, when the parameter may be a boundary value of the parameter space, is proposed. also, a solution to the irregularity problem of the generalized likelihood ratio test pertaining to the number of components in a mixture is given, and a new test is proposed, based on $ \ chi ^ { 2 } $ - divergence on signed finite measures and duality technique. | arxiv:0811.3705 |
we report $ ^ { 121 / 123 } $ sb nuclear quadrupole resonance ( nqr ) and $ ^ { 51 } $ v nuclear magnetic resonance ( nmr ) measurements on kagome metal csv $ _ 3 $ sb $ _ 5 $ with $ t _ { \ rm c } = 2. 5 $ k. both $ ^ { 51 } $ v nmr spectra and $ ^ { 121 / 123 } $ sb nqr spectra split after a charge density wave ( cdw ) transition, which demonstrates a commensurate cdw state. the coexistence of the high temperature phase and the cdw phase between $ 91 $ k and $ 94 $ k manifests that it is a first order phase transition. at low temperature, electric - field - gradient fluctuations diminish and magnetic fluctuations become dominant. superconductivity emerges in the charge order state. knight shift decreases and $ 1 / t _ { 1 } t $ shows a hebel - - slichter coherence peak just below $ t _ { \ rm c } $, indicating that csv $ _ 3 $ sb $ _ 5 $ is an s - wave superconductor. | arxiv:2104.06698 |
in this article, we solve the equivalence problem for 2 - - nondegenerate cr geometries that have ( at every point ) a homogeneous space $ g / h $ as a maximally symmetric model for $ g $ simple real lie group of cr automorphisms. this completes the classification of real submanifolds in complex space that are maximally symmetric models with a real simple cr automorphism group. in particular, we construct ( local ) embeddings of these models into complex space. | arxiv:1906.00848 |
this paper proposes a novel non - orthogonal multiple access ( noma ) - assisted orthogonal time - frequency space ( otfs ) - integrated sensing and communication ( isac ) network, which uses unmanned aerial vehicles ( uavs ) as air base stations to support multiple users. by employing isac, the uav extracts position and velocity information from the user ' s echo signals, and non - orthogonal power allocation is conducted to achieve a superior achievable rate. a 3d motion prediction topology is used to guide the noma transmission for multiple users, and a robust power allocation solution is proposed under perfect and imperfect channel estimation for maxi - min fairness ( mmf ) and maximum sum - rate ( sr ) problems. simulation results demonstrate the superiority of the proposed noma - assisted otfs - isac system over other systems in terms of achievable rate under both perfect and imperfect channel conditions with the aid of 3d motion prediction topology. | arxiv:2310.13984 |
recent advances in graph learning have paved the way for innovative retrieval - augmented generation ( rag ) systems that leverage the inherent relational structures in graph data. however, many existing approaches suffer from rigid, fixed settings and significant engineering overhead, limiting their adaptability and scalability. additionally, the rag community has largely overlooked the decades of research in the graph database community regarding the efficient retrieval of interesting substructures on large - scale graphs. in this work, we introduce the rag - on - graphs library ( rgl ), a modular framework that seamlessly integrates the complete rag pipeline - from efficient graph indexing and dynamic node retrieval to subgraph construction, tokenization, and final generation - into a unified system. rgl addresses key challenges by supporting a variety of graph formats and integrating optimized implementations for essential components, achieving speedups of up to 143x compared to conventional methods. moreover, its flexible utilities, such as dynamic node filtering, allow for rapid extraction of pertinent subgraphs while reducing token consumption. our extensive evaluations demonstrate that rgl not only accelerates the prototyping process but also enhances the performance and applicability of graph - based rag systems across a range of tasks. | arxiv:2503.19314 |
let $ \ mathcal { m } _ 1 $ denote the space of solutions $ z ( x, y ) $ to an elliptic, real analytic monge - amp \ ` ere equation $ { \ rm det } ( d ^ 2 z ) = \ varphi ( x, y, z, dz ) > 0 $ whose graphs have a non - removable isolated singularity at the origin. we prove that $ \ mathcal { m } _ 1 $ is in one - to - one correspondence with $ \ mathcal { m } _ 2 \ times z _ 2 $, where $ \ mathcal { m } _ 2 $ is a suitable subset of the class of regular, real analytic strictly convex jordan curves in $ r ^ 2 $. we also describe the asymptotic behavior of solutions of the monge - amp \ ` ere equation in the $ c ^ k $ - smooth case, and a general existence theorem for isolated singularities of analytic solutions of the more general equation $ { \ rm det } ( d ^ 2 z + \ mathcal { a } ( x, y, z, dz ) ) = \ varphi ( x, y, z, dz ) > 0 $. | arxiv:1210.5362 |
while parity transformation represents a fundamental symmetry operation in physics, its implications remain underexplored in metamaterial science. here, we introduce a framework leveraging parity transformation to construct parity - inverted counterparts of arbitrary three - dimensional meta - atoms, enabling the creation of parity - engineered metamaterial slabs. we demonstrate that the synergy between reciprocity and parity transformation, distinct from mirror operation, guarantees undistorted wave transmission across exceptional bandwidths, independent of structural configuration or meta - atom design specifics. furthermore, these metamaterials exhibit dynamic acoustic mimicry capability, enabling adaptive blending of reflected signatures into surrounding environments while preserving transmitted wavefront integrity. validated through numerical simulations and experimental prototypes, this breakthrough offers transformative potential for acoustic camouflage applications, particularly for sonar systems. our findings reveal fundamental implications of parity transformation in artificial materials, establishing parity engineering as a paradigm for designing ultra - broadband functional materials with unprecedented operational versatility. | arxiv:2503.17369 |
we study the effect of film density on the uniaxial compression of thin elastic films at a liquid - - fluid interface. using a combination of experiments and theory, we show that dense films first wrinkle and then fold as the compression is increased, similarly to what has been reported when the film density is neglected. however, we highlight the changes in the shape of the fold induced by the film ' s own weight and extend the model of diamant and witten [ phys. rev. lett. 2011, 107, 164302, arxiv : 1107. 5505 ] to understand these changes. in particular, we suggest that it is the weight of the film that breaks the up - down symmetry apparent from previous models, but elusive experimentally. we then compress the film beyond the point of self - contact and observe a new behaviour dependent on the film density : the single fold that forms after wrinkling transitions into a closed loop after self - contact, encapsulating a cylindrical droplet of the upper fluid. the encapsulated drop either causes the loop to bend upward or to sink deeper as compression is increased, depending on the relative buoyancy of the drop - film combination. we propose a model to qualitatively explain this behaviour. finally, we discuss the relevance of the different buckling modes predicted in previous theoretical studies and highlight the important role of surface tension in the shape of the fold that is observed from the side - - an aspect that is usually neglected in theoretical analyses. | arxiv:1609.03366 |
optimal sample path properties of stochastic processes often involve generalized h \ " { o } lder - or variation norms. following a classical result of taylor, the exact variation of brownian motion is measured in terms of $ \ psi ( x ) \ equiv $ $ x ^ { 2 } / \ log \ log ( 1 / x ) $ near $ 0 + $. such $ \ psi $ - variation results extend to classes of processes with values in abstract metric spaces. ( no gaussian or markovian properties are assumed. ) to establish integrability properties of the $ \ psi $ - variation we turn to a large class of gaussian rough paths ( e. g. brownian motion and l \ ' { e } vy ' s area viewed as a process in a lie group ) and prove gaussian integrability properties using borell ' s inequality on abstract wiener spaces. the interest in such results is that they are compatible with rough path theory and yield certain sharp regularity and integrability properties ( for iterated stratonovich integrals, for example ) which would be difficult to obtain otherwise. at last, $ \ psi $ - variation is identified as robust regularity property of solutions to ( random ) rough differential equations beyond semimartingales. | arxiv:0711.0163 |
in many cosmological models, including the $ \ lambda $ cdm concordance model, there exist a theoretical upper bounds on the size of collapsing structures. the most common formulations in the literature refer to a turnaround radius in spherical symmetry or a turnaround surface, defined as the zero - expansion boundary separating the outer hubble flow from the inner flow of a collapsing fluid. in order to access a generic scenario, we propose an improvement of this cosmological test in terms of the maximum volume of the cosmological structures, which is equivalent to a zero - averaged expansion - - instead of the zero - local expansion. by combining the lagrangian perturbations method and the scalar averaging of einstein ' s equations, we obtain a maximum volume for a collapse model without any restricting symmetries. we compare this result with some exact, inhomogeneous solutions and discuss further potential developments. | arxiv:2112.05245 |
a novel approach for estimating the lower end of the $ \ mathrm { su } ( 3 ) $ conformal window is presented through the study of center vortex geometry and its dependence on the number of fermion flavors $ n _ f $. values ranging from $ n _ f = 2 $ - - $ 8 $ are utilized to infer an upper limit for vortex behavior in the low $ n _ f $ phase, which may inform the transition to the conformal window. the simulations are performed at a single lattice spacing and pion mass, both fixed for all $ n _ f $. visualizations of the center vortex structure in three - dimensional slices of the lattice reveal a growing roughness in the vortex matter as a function of $ n _ f $, embodied by an increase in the density of vortex matter in the percolating cluster and a simultaneous reduction in secondary clusters disconnected from the percolating cluster in 3d slices. this is quantified by various bulk properties, including the vortex and branching point densities. a correlation of the vortex structure reveals a turning point near $ n _ f \ simeq 5 $ past which a randomness in the vortex field becomes the dominant aspect of its evolution with $ n _ f $. as a byproduct, extrapolations to the vortex content of a uniform - random gauge field provide a critical point at which there must be a drastic shift in vacuum field structure. a precise estimate for the critical value is extracted as $ n _ f ^ * = 11. 43 ( 16 ) ( 17 ) $, close to various other estimates. | arxiv:2501.11279 |
geometry projection is a powerful depth estimation method in monocular 3d object detection. it estimates depth dependent on heights, which introduces mathematical priors into the deep model. but projection process also introduces the error amplification problem, in which the error of the estimated height will be amplified and reflected greatly at the output depth. this property leads to uncontrollable depth inferences and also damages the training efficiency. in this paper, we propose a geometry uncertainty projection network ( gup net ) to tackle the error amplification problem at both inference and training stages. specifically, a gup module is proposed to obtains the geometry - guided uncertainty of the inferred depth, which not only provides high reliable confidence for each depth but also benefits depth learning. furthermore, at the training stage, we propose a hierarchical task learning strategy to reduce the instability caused by error amplification. this learning algorithm monitors the learning situation of each task by a proposed indicator and adaptively assigns the proper loss weights for different tasks according to their pre - tasks situation. based on that, each task starts learning only when its pre - tasks are learned well, which can significantly improve the stability and efficiency of the training process. extensive experiments demonstrate the effectiveness of the proposed method. the overall model can infer more reliable object depth than existing methods and outperforms the state - of - the - art image - based monocular 3d detectors by 3. 74 % and 4. 7 % ap40 of the car and pedestrian categories on the kitti benchmark. | arxiv:2107.13774 |
dust grains absorb half of the radiation emitted by stars throughout the history of the universe, re - emitting this energy at infrared wavelengths. polycyclic aromatic hydrocarbons ( pahs ) are large organic molecules that trace millimeter - size dust grains and regulate the cooling of the interstellar gas within galaxies. observations of pah features in very distant galaxies have been difficult due to the limited sensitivity and wavelength coverage of previous infrared telescopes. here we present jwst observations that detect the 3. 3um pah feature in a galaxy observed less than 1. 5 billion years after the big bang. the high equivalent width of the pah feature indicates that star formation, rather than black hole accretion, dominates the infrared emission throughout the galaxy. the light from pah molecules, large dust grains, and stars and hot dust are spatially distinct from one another, leading to order - of - magnitude variations in the pah equivalent width and the ratio of pah to total infrared luminosity across the galaxy. the spatial variations we observe suggest either a physical offset between the pahs and large dust grains or wide variations in the local ultraviolet radiation field. our observations demonstrate that differences in the emission from pah molecules and large dust grains are a complex result of localized processes within early galaxies. | arxiv:2306.03152 |
conversational query generation aims at producing search queries from dialogue histories, which are then used to retrieve relevant knowledge from a search engine to help knowledge - based dialogue systems. trained to maximize the likelihood of gold queries, previous models suffer from the data hunger issue, and they tend to both drop important concepts from dialogue histories and generate irrelevant concepts at inference time. we attribute these issues to the over - association phenomenon where a large number of gold queries are indirectly related to the dialogue topics, because annotators may unconsciously perform reasoning with their background knowledge when generating these gold queries. we carefully analyze the negative effects of this phenomenon on pretrained seq2seq query producers and then propose effective instance - level weighting strategies for training to mitigate these issues from multiple perspectives. experiments on two benchmarks, wizard - of - internet and dusinc, show that our strategies effectively alleviate the negative effects and lead to significant performance gains ( 2 % - 5 % across automatic metrics and human evaluation ). further analysis shows that our model selects better concepts from dialogue histories and is 10 times more data efficient than the baseline. the code is available at https : / / github. com / deeplearnxmu / qg - overasso. | arxiv:2409.19572 |
the possibility of ferromagnetic ordering is revisited in the band model. the coherent potential approximation decoupling has been used for the strong on - site coulomb interaction. the driving forces towards the ferromagnetism are the on - site and inter - site molecular fields coming from different coulomb interactions. another driving force is the lowering of the kinetic energy with growing magnetic moment coming from the dependence of the hopping integrals on occupation of the neighboring sites involved in hopping. this effect is described by the hopping interaction, $ \ delta t $, and by what we call the exchange - hopping interaction, $ t _ { ex } $. the exchange - hopping interaction, which is the difference in hopping integrals for different occupation of neighboring lattice sites, acts in analogous way to the hund ' s magnetic exchange interaction. the results are calculated for semi - elliptic density of states ( dos ) and for the distorted semi - elliptic dos with the maximum around the fermi energy. they show a natural tendency towards the magnetic ordering at the end of the 3d row for the dos with maximum density around the fermi energy, when the hopping integrals grow with the occupation of the neighboring lattice sites. | arxiv:cond-mat/0410394 |
the nielsen - olesen flux tube in the su ( 2 ) yang - mills - higgs theory dressed with the color electric $ e ^ a _ { \ rho, \ phi } $ and magnetic $ h ^ a _ { \ rho, \ phi } $ fields is derived. on the next step it is argued that this flux tube can be considered as a result of the nonperturbatuve analytical calculations in the su ( 3 ) quantum theory. | arxiv:hep-ph/0306203 |
methodological contributions : this paper introduces a family of kernels for analyzing ( anatomical ) trees endowed with vector valued measurements made along the tree. while state - of - the - art graph and tree kernels use combinatorial tree / graph structure with discrete node and edge labels, the kernels presented in this paper can include geometric information such as branch shape, branch radius or other vector valued properties. in addition to being flexible in their ability to model different types of attributes, the presented kernels are computationally efficient and some of them can easily be computed for large datasets ( n of the order 10. 000 ) of trees with 30 - 600 branches. combining the kernels with standard machine learning tools enables us to analyze the relation between disease and anatomical tree structure and geometry. experimental results : the kernels are used to compare airway trees segmented from low - dose ct, endowed with branch shape descriptors and airway wall area percentage measurements made along the tree. using kernelized hypothesis testing we show that the geometric airway trees are significantly differently distributed in patients with chronic obstructive pulmonary disease ( copd ) than in healthy individuals. the geometric tree kernels also give a significant increase in the classification accuracy of copd from geometric tree structure endowed with airway wall thickness measurements in comparison with state - of - the - art methods, giving further insight into the relationship between airway wall thickness and copd. software : software for computing kernels and statistical tests is available at http : / / image. diku. dk / aasa / software. php. | arxiv:1303.7390 |
we examine the mass loss rates and lifetimes of tev - scale extra dimensional black holes ( bh ) in add - like models with lovelock higher - curvature terms present in the action. in particular we focus on the predicted differences between the canonical and microcanonical ensemble statistical mechanics descriptions of the hawking radiation that results in the decay of these bh. in even numbers of extra dimensions the employment of the microcanonical approach is shown to generally lead to a significant increase in the bh lifetime as in case of the einstein - hilbert action. for odd numbers of extra dimensions, stable bh remnants occur when employing either description provided the highest order allowed lovelock invariant is present. however, in this case, the time dependence of the mass loss rates obtained employing the two approaches will be different. these effects are in principle measurable at future colliders. | arxiv:hep-ph/0601029 |
density functional calculations are performed to study the effect of epitaxial strain on pbzro3. we find a remarkably small energy difference between the epitaxially strained polar r3c and nonpolar pbam structures over the full range of experimentally accessible epitaxial strains - 3 % < \ eta < 4 %. while ferroelectricity is favored for all compressive strains, for tensile strains the small energy difference between the nonpolar ground state and the alternative polar phase yields a robust antiferroelectric ground state. the coexistence of ferroelectricity and antiferroelectricity observed in thin films is attributed to a combination of strain and depolarization field effects. | arxiv:1307.7645 |
a survey article that presents some recent algebraic and model - theoretic results on the automorphism groups of relatively free groups of infinite rank. the topics include topological aspects, generating sets, descripition of automorpisms and expressive power of the first - order theories. | arxiv:0807.4343 |
we prove that the klr algebra associated with the cyclic quiver of length $ e $ is a subquotient of the klr algebra associated with the cyclic quiver of length $ e + 1 $. we also give a geometric interpretation of this fact. this result has an important application in the theory of categorical representations. we prove that a category with an action of $ \ widetilde { \ mathfrak { sl } } _ { e + 1 } $ contains a subcategory with an action of $ \ widetilde { \ mathfrak { sl } } _ { e } $. we also give generalizations of these results to more general quivers and lie types. | arxiv:1901.11026 |
a characterization of $ n $ - dimensional spaces via continuous selections avoiding $ z _ n $ - sets is given, and a selection theorem for strongly countable - dimensional spaces is established. we apply these results to prove a generalized ostrand ' s theorem and to obtain a new alternative proof of the hurewicz formula. | arxiv:math/0111254 |
we investigate the possible ground states of qcd at asymptotic densities, where the theory is expected to exhibit color superconductivity. we characterize the color - flavor structure of possible diquark condensates, and find those that are energy extrema by solving the weak - coupling dyson - schwinger equations, including landau damping and the meissner effect. we show that, as previously anticipated, in the two flavor case the vacuum breaks su ( 3 ) color to su ( 2 ) and in the three flavor case the vacua with color - flavor locking ( cfl ) have the lowest energy. we identify a number of relatively flat directions in the potential along which the pattern of gauge symmetry breaking changes and parity is violated. we discuss possible phenomenological consequences of our results. | arxiv:hep-ph/9910313 |
image reconstruction by algebraic methods ( am ) outperforms the transform methods in situations where the data collection procedure is constrained by time, space, and radiation dose. am algorithms can also be applied for the cases where these constraints are not present but their high computational and storage requirement prohibit their actual breakthrough in such cases. in the present work, we propose a novel uniformly sampled polar / cylindrical grid ( uspg / uscg ) discretization scheme to reduce the computational and storage burden of algebraic methods. the symmetries of uspg / uscg are utilized to speed up the calculations of the projection coefficients. in addition, we also offer an efficient approach for uspg to cartesian grid ( cg ) transformation for the visualization. the multiplicative algebraic reconstruction technique ( mart ) has been used to determine the field function of the suggested grids. experimental projections data of a frog and cu - lump have been exercised to validate the proposed approach. a variety of image quality measures have been evaluated to check the accuracy of the reconstruction. results indicate that the current strategies speed up ( when compared to cg - based algorithms ) the reconstruction process by a factor of 2. 5 and reduce the memory requirement by the factor p, the number of projections used in the reconstruction. | arxiv:2208.12964 |
gamow - teller ( gt ) resonances in finite nuclei are studied in a fully consistent relativistic random phase approximation ( rpa ) framework. a relativistic form of the landau - migdal contact interaction in the spin - isospin channel is adopted. this choice ensures that the gt excitation energy in nuclear matter is correctly reproduced in the non - relativistic limit. the gt response functions of doubly magic nuclei $ ^ { 48 } $ ca, $ ^ { 90 } $ zr and $ ^ { 208 } $ pb are calculated using the parameter set nl3 and $ g _ 0 ' $ = 0. 6. it is found that effects related to dirac sea states account for a reduction of 6 - 7 % in the gt sum rule. | arxiv:nucl-th/0308021 |
with deep reinforcement learning ( rl ) systems like autonomous driving being wildly deployed but remaining largely opaque, developers frequently use explainable rl ( xrl ) tools to better understand and work with deep rl agents. however, previous xrl works employ a techno - centric research approach, ignoring how rl developers perceive the generated explanations. through a pilot study, we identify major goals for rl practitioners to use xrl methods and four pitfalls that widen the gap between existing xrl methods and these goals. the pitfalls include inaccessible reasoning processes, inconsistent or unintelligible explanations, and explanations that cannot be generalized. to fill the discovered gap, we propose a counterfactual - inference - based explanation method that discovers the details of the reasoning process of rl agents and generates natural language explanations. surrounding this method, we build an interactive xrl system where users can actively explore explanations and influential information. in a user study with 14 participants, we validated that developers identified 20. 9 % more abnormal behaviors and limitations of rl agents with our system compared to the baseline method, and using our system helped end users improve their performance in actionability tests by 25. 1 % in an auto - driving task and by 16. 9 % in a starcraft ii micromanagement task. | arxiv:2212.00888 |
we define and study a generalization of sobol sensitivity indices for the case of a vector output. | arxiv:1303.3574 |
we tackle the problem of computing counterfactual explanations - - minimal changes to the features that flip an undesirable model prediction. we propose a solution to this question for linear support vector machine ( svms ) models. moreover, we introduce a way to account for weighted actions that allow for more changes in certain features than others. in particular, we show how to find counterfactual explanations with the purpose of increasing model interpretability. these explanations are valid, change only actionable features, are close to the data distribution, sparse, and take into account correlations between features. we cast this as a mixed integer programming optimization problem. additionally, we introduce two novel scale - invariant cost functions for assessing the quality of counterfactual explanations and use them to evaluate the quality of our approach with a real medical dataset. finally, we build a support vector machine model to predict whether law students will pass the bar exam using protected features, and used our algorithms to uncover the inherent biases of the svm. | arxiv:2212.07432 |
i review the principal theories that have been proposed for the superconducting phases of upt $ _ 3 $. the detailed h - t phase diagram places constraints on any theory for the multiple superconducting phases. i comment on the limitations of the models proposed so far for the superconducting phases of upt $ _ 3 $. i also find that a theory in which the order parameter belongs to an orbital 2d representation coupled to a sbf is a viable model for the phases of upt $ _ 3 $, based on the existing body of experimental data. specifically, i show that ( 1 ) the existing phase diagram ( including an apparent tetracritical point for all field orientations ), ( 2 ) the anisotropy of the upper critical field over the full temperature range, ( 3 ) the correlation between superconductivity and basal plane antiferromagnetism and ( 4 ) low - temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd - parity, e $ _ { 2u } $ order parameter with a pair spin projection of zero along the $ { \ bf c } $ - axis. the coupling of an afm moment to the superconducting order parameter acts as a symmetry breaking field ( sbf ) which is responsible for the apparent tetracritical point, in addition to the zero - field double transition. the results presented here for the e $ _ { 2u } $ representation are based on an analysis of the material parameters calculated within bcs theory for the 2d representations, and a refinement of the sbf model of hess, et al. [ j. phys. condens. matter, 1, 8135 ( 1989 ) ]. i also discuss possible experiments to test the symmetry of the order parameter. | arxiv:1812.09984 |
we show that strictly convex surfaces expanding by the inverse gauss curvature flow converge to infinity in finite time. after appropriate rescaling, they converge to spheres. we describe the algorithm to find our main test function. | arxiv:math/0412297 |
using the direct relation between the gegenbauer polynomials and the ferrers function of the first kind, we compute interrelations between certain jacobi polynomials, meixner polynomials, and the ferrers function of the first kind. we then compute rodrigues - type and orthogonality relations for ferrers functions of the first and second kinds. in the remainder of the paper using the relation between gegenbauer polynomials and the ferrers function of the first kind we derive connection and linearization relations, some definite integral and series expansions, some asymptotic expansions of mehler - heine type, christoffel - darboux summation formulas, and infinite series closure relations ( dirac delta distribution ). | arxiv:2108.03276 |
the form factor equations are solved for an su ( n ) invariant s - matrix under the assumption that the anti - particle is identified with the bound state of n - 1 particles. the solution is obtained explicitly in terms of the nested off - shell bethe ansatz where the contribution from each level is written in terms of multiple contour integrals. | arxiv:hep-th/0611012 |
we analyse exhaustively the structure of \ emph { non - degenerate } cauchy horizons in gowdy space - times, and we establish existence of a large class of non - polarized gowdy space - times with such horizons. added in proof : our results here, together with deep new results of h. ringstr \ " om ( talk at the miami waves conference, january 2004 ), establish strong cosmic censorship in ( toroidal ) gowdy space - times. | arxiv:gr-qc/0307088 |
we present a symbolic perturbation scheme for arbitrary polynomial geometric predicates which combines the benefits of emiris and canny ' s simple randomized linear perturbation scheme with yap ' s multiple infinitesimal scheme for general predicates. like the randomized scheme, our method accepts black box polynomial functions as input. for nonmaliciously chosen predicates, our method is as fast as the linear scheme, scaling reasonably with the degree of the polynomial even for fully degenerate input. like yap ' s scheme, the computed sign is deterministic, never requiring an algorithmic restart ( assuming a high quality pseudorandom generator ), and works for arbitrary predicates with no knowledge of their structure. we also apply our technique to exactly or nearly exactly rounded constructions that work correctly for degenerate input, using l ' hopital ' s rule to compute the necessary singular limits. we provide an open source prototype implementation including example algorithms for delaunay triangulation and boolean operations on polygons and circular arcs in the plane. | arxiv:1308.1986 |
we construct the most general effective lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non - minimal coupling terms respecting both diffeomorphism and gauge invariance. in all, there are only two unique terms after field re - definitions ; one is known to arise from loop effects in qed while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. we show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of general relativity are useful probes of these terms. these non - minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future. | arxiv:1007.3992 |
we propose an extensive report on the simulation of electronic transport in 2d graphene in presence of structural defects. amongst the large variety of such defects in sp $ ^ 2 $ carbon - based materials, we focus on the stone - wales defect and on two divacancy - type reconstructed defects. first, based on ab initio calculations, a tight - binding model is derived to describe the electronic structure of these defects. then, semiclassical transport properties including the elastic mean free paths, mobilities and conductivities are computed using an order - n real - space kubo - greenwood method. a plateau of minimum conductivity ( $ \ sigma ^ { min } _ { sc } = 4e ^ 2 / \ pi h $ ) is progressively observed as the density of defects increases. this saturation of the decay of conductivity to $ \ sigma ^ { min } _ { sc } $ is associated with defect - dependent resonant energies. finally, localization phenomena are captured beyond the semiclassical regime. an anderson transition is predicted with localization lengths of the order of tens of nanometers for defect densities around 1 %. | arxiv:1204.4574 |
in the last years, several variants of transformers have emerged. in this paper, we compare different transformer - based models for solving the reverse dictionary task and explore their use in the context of a serious game called the dictionary game. | arxiv:2311.02985 |
we analyze ge - related defects in ge - doped sio _ 2 using first - principles density functional techniques. ge is incorporated at the level of ~ 1 mol % and above. the growth conditions of ge : sio _ 2 naturally set up oxygen deficiency, with vacancy concentration increasing by a factor 10 ^ 5 over undoped sio _ 2, and o vacancies binding strongly to ge impurities. all the centers considered exhibit potentially epr - active states, candidates for the identification of the ge ( n ) centers. substitutional ge produces an apparent gap shrinking via its extrinsic levels. | arxiv:cond-mat/0202497 |
the main topics that cognitive science is concerned with ; see list of cognitive science topics for a more exhaustive list. = = = artificial intelligence = = = artificial intelligence ( ai ) involves the study of cognitive phenomena in machines. one of the practical goals of ai is to implement aspects of human intelligence in computers. computers are also widely used as a tool with which to study cognitive phenomena. computational modeling uses simulations to study how human intelligence may be structured. ( see § computational modeling. ) there is some debate in the field as to whether the mind is best viewed as a huge array of small but individually feeble elements ( i. e. neurons ), or as a collection of higher - level structures such as symbols, schemes, plans, and rules. the former view uses connectionism to study the mind, whereas the latter emphasizes symbolic artificial intelligence. one way to view the issue is whether it is possible to accurately simulate a human brain on a computer without accurately simulating the neurons that make up the human brain. = = = attention = = = attention is the selection of important information. the human mind is bombarded with millions of stimuli and it must have a way of deciding which of this information to process. attention is sometimes seen as a spotlight, meaning one can only shine the light on a particular set of information. experiments that support this metaphor include the dichotic listening task ( cherry, 1957 ) and studies of inattentional blindness ( mack and rock, 1998 ). in the dichotic listening task, subjects are bombarded with two different messages, one in each ear, and told to focus on only one of the messages. at the end of the experiment, when asked about the content of the unattended message, subjects cannot report it. the psychological construct of attention is sometimes confused with the concept of intentionality due to some degree of semantic ambiguity in their definitions. at the beginning of experimental research on attention, wilhelm wundt defined this term as " that psychical process, which is operative in the clear perception of the narrow region of the content of consciousness. " his experiments showed the limits of attention in space and time, which were 3 - 6 letters during an exposition of 1 / 10 s. because this notion develops within the framework of the original meaning during a hundred years of research, the definition of attention would reflect the sense when it accounts for the main features initially attributed to this term – it is a process of controlling thought that continues over time. while intentionality is the power of minds to be about something, attention | https://en.wikipedia.org/wiki/Cognitive_science |
despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample - efficient way. we propose active learning strategies that leverage information - theoretical properties arising naturally during gaussian process regression, while respecting constraints on the sampling process imposed by the system dynamics. sample points are selected in regions with high uncertainty, leading to exploratory behavior and data - efficient training of the model. all results are finally verified in an extensive numerical benchmark. | arxiv:1911.09946 |
in this paper, we proposed an identification and data encrypt key manage protocol that can be used in some security system based on such secure devices as secure usb memories or rfids, which are widely used for identifying persons or other objects recently. in general, the default functions of the security system using a mobile device are the authentication for the owner of the device and secure storage of data stored on the device. we proposed a security model that consists of the server and mobile devices in order to realize these security features. in this model we defined the secure communication protocol for the authentication and management of data encryption keys using a private key encryption algorithm with the public key between the server and mobile devices. in addition, we was performed the analysis for the attack to the communication protocol between the mobile device and server. using the communication protocol, the system will attempt to authenticate the mobile device. the data decrypt key is transmitted only if the authentication process is successful. the data in the mobile device can be decrypted using the key. our analysis proved that this protocol ensures anonymity, prevents replay attacks and realizes the interactive identification between the security devices and the authentication server. | arxiv:1304.6241 |
we have studied thermally driven magnon spin transport ( spin seebeck effect, sse ) in heterostructures of antiferromagnetic $ \ alpha $ - $ \ mathrm { cr _ 2o _ 3 } $ and pt at low temperatures. monitoring the amplitude of the local and nonlocal sse signals as a function of temperature, we found that both decrease with increasing temperature and disappear above 100 k and 20 k, respectively. additionally, both sse signals show a tendency to saturate at low temperatures. the nonlocal sse signal decays exponentially for intermediate injector - detector separation, consistent with magnon spin current transport in the relaxation regime. we estimate the magnon relaxation length of our $ \ alpha $ - $ \ mathrm { cr _ 2o _ 3 } $ films to be around 500 nm at 3 k. this short magnon relaxation length along with the strong temperature dependence of the sse signal indicates that temperature - dependent inelastic magnon scattering processes play an important role in the intermediate range magnon transport. our observation is relevant to low - dissipation antiferromagnetic magnon memory and logic devices involving thermal magnon generation and transport. | arxiv:2011.08885 |
high quality graphene nanoribbons ( gnrs ) grown by on - surface synthesis strategies with atomic precision can be controllably doped by inserting heteroatoms or chemical groups in the molecular precursors. here, we study the electronic structure of armchair gnrs substitutionally doped with di - boron moieties at the center, through a combination of scanning tunneling spectroscopy, angle - resolved photoemission, and density functional theory simulations. boron atoms appear with a small displacement towards the surface signaling their stronger interaction with the metal. we find two boron - rich flat bands emerging as impurity states inside the gnr band gap, one of them particularly broadened after its hybridization with the gold surface states. in addition, the boron atoms shift the conduction and valence bands of the pristine gnr away from the gap edge, and leave unaffected the bands above and below, which become the new frontier bands and have negligible boron character. this is due to the selective mixing of boron states with gnr bands according to their symmetry. our results depict that the gnrs band structure can be tuned by modifying the separation between di - boron moieties. | arxiv:1806.02385 |
we consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. every node has two states : it is either active or inactive. we assume that to each node is assigned a nonnegative ( integer ) threshold. the diffusion process is initiated by a subset of nodes with threshold zero which consists of initially activated nodes, whereas every other node is inactive. subsequently, in each round, if an inactive node with threshold $ \ theta $ has at least $ \ theta $ of its neighbours activated, then it also becomes active and remains so forever. this is repeated until no more nodes become activated. the main result of this paper provides a central limit theorem for the final size of activated nodes. namely, under suitable assumptions on the degree and threshold distributions, we show that the final size of activated nodes has asymptotically gaussian fluctuations. | arxiv:2103.00357 |
this paper presents our linked open data ( lod ) infrastructures for genomic and experimental data related to microrna biomolecules. legacy data from two well - known microrna databases with experimental data and observations, as well as change and version information about microrna entities, are fused and exported as lod. our lod server assists biologists to explore biological entities and their evolution, and provides a sparql endpoint for applications and services to query historical mirna data and track changes, their causes and effects. | arxiv:1205.2320 |
we study distinguished subalgebras and automorphisms of boundary quotients arising from algebraic dynamical systems $ ( g, p, \ theta ) $. our work includes a complete solution to the problem of extending bogolubov automorphisms from the cuntz algebra in $ 2 \ leq p < \ infty $ generators to the $ p $ - adic ring $ c ^ * $ - algebra. for the case where $ p $ is abelian and $ c ^ * ( g ) $ is a maximal abelian subalgebra, we establish a picture for the automorphisms of the boundary quotient that fix $ c ^ * ( g ) $ pointwise. this allows us to show that they form a maximal abelian subgroup of the entire automorphism group. the picture also leads to the surprising outcome that, for integral dynamics, every automorphism that fixes one of the natural cuntz subalgebras pointwise is necessarily a gauge automorphism. many of the automorphisms we consider are shown to be outer. | arxiv:1709.08839 |
prospects of the two future e ^ + e ^ - flavour factories are discussed. the detector designs and the technical challenges are described together with the motivating physics background. | arxiv:0808.0096 |
for a commutative ring $ r, $ with non - zero zero divisors $ z ^ { \ ast } ( r ) $. the zero divisor graph $ \ gamma ( r ) $ is a simple graph with vertex set $ z ^ { \ ast } ( r ) $, and two distinct vertices $ x, y \ in v ( \ gamma ( r ) ) $ are adjacent if and only if $ x \ cdot y = 0. $ in this note, we provide counter examples to the eigenvalues, the energy and the second zagreb index related to zero divisor graphs of rings obtained in [ johnson and sankar, j. appl. math. comp. ( 2023 ), \ cite { johnson } ]. we correct the eigenvalues ( energy ) and the zagreb index result for the zero divisor graphs of ring $ \ mathbb { z } _ { p } [ x ] / \ langle x ^ { 4 } \ rangle. $ we show that for any prime $ p $, $ \ gamma ( \ mathbb { z } _ { p } [ x ] / \ langle x ^ { 4 } \ rangle ) $ is non - hyperenergetic and for prime $ p \ geq 3 $, $ \ gamma ( \ mathbb { z } _ { p } [ x ] / \ langle x ^ { 4 } \ rangle ) $ is hypoenergetic. we give a formulae for the topological indices of $ \ gamma ( \ mathbb { z } _ { p } [ x ] / \ langle x ^ { 4 } \ rangle ) $ and show that its zagreb indices satisfy hansen and vuki $ \ check { c } $ cevi \ ' c conjecture \ cite { hansen }. | arxiv:2401.02554 |
a method is presented which makes considerably more transparent possible patterns behind low - energy scattering data. in particular, structures associated with resonances, such as locations, widths and heights, become visible with a naked eye. the method is illustrated with a study of the $ p $ - wave $ k \ pi $ amplitude. | arxiv:1404.4111 |
in spite of anderson ' s theorem, disorder is known to affect superconductivity in conventional s - wave superconductors. in most superconductors, the degree of disorder is fixed during sample preparation. here we report measurements of the superconducting properties of the two - dimensional gas that forms at the interface between laalo $ _ 3 $ ( lao ) and srtio $ _ 3 $ ( sto ) in the ( 111 ) crystal orientation, a system that permits \ emph { in situ } tuning of carrier density and disorder by means of a back gate voltage $ v _ g $. like the ( 001 ) oriented lao / sto interface, superconductivity at the ( 111 ) lao / sto interface can be tuned by $ v _ g $. in contrast to the ( 001 ) interface, superconductivity in these ( 111 ) samples is anisotropic, being different along different interface crystal directions, consistent with the strong anisotropy already observed other transport properties at the ( 111 ) lao / sto interface. in addition, we find that the ( 111 ) interface samples " remember " the backgate voltage $ v _ f $ at which they are cooled at temperatures near the superconducting transition temperature $ t _ c $, even if $ v _ g $ is subsequently changed at lower temperatures. the low energy scale and other characteristics of this memory effect ( $ < 1 $ k ) distinguish it from charge - trapping effects previously observed in ( 001 ) interface samples. | arxiv:1704.01203 |
we consider fractional quantum hall states in systems where two flat chern number $ c = \ pm 1 $ bands are labeled by an approximately conserved ' valley ' index and interchanged by time reversal symmetry. at filling factor $ \ nu = 1 $ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle - hole pair excitations of a fully valley - polarized ` orbital ferromagnet ' parent state where all electrons occupy a single valley. excitons experience an effective magnetic field due to the chern numbers of the underlying bands. this obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. all these have the same quantized charge hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. we explore the relevance of this scenario for moir \ ' e heterostructures of bilayer graphene on a hexagonal boron nitride substrate. | arxiv:2003.11559 |
mutually unbiased bases ( mubs ), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1 / sqrt { d ), with d the dimension of the finite hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the heisenberg - weil group of quantum optics. complete sets of mubs of cardinality d + 1 have been derived for prime power dimensions d = p ^ m using the tools of abstract algebra. presumably, for non prime dimensions the cardinality is much less. here we reinterpret mubs as quantum phase states, i. e. as eigenvectors of hermitean phase operators generalizing those introduced by pegg & barnett in 1989. we relate mub states to additive characters of galois fields ( in odd characteristic p ) and to galois rings ( in characteristic 2 ). quantum fourier transforms of the components in vectors of the bases define a more general class of mubs with multiplicative characters and additive ones altogether. we investigate the complementary properties of the above phase operator with respect to the number operator. we also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the gauss sums, which are sums over all elements of the field ( or of the ring ) of the product of multiplicative and additive characters. finally, we relate the concepts of mutual unbiasedness and maximal entanglement. this allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects | arxiv:quant-ph/0506128 |
post - hoc explanations for black box models have been studied extensively in classification and regression settings. however, explanations for models that output similarity between two inputs have received comparatively lesser attention. in this paper, we provide model agnostic local explanations for similarity learners applicable to tabular and text data. we first propose a method that provides feature attributions to explain the similarity between a pair of inputs as determined by a black box similarity learner. we then propose analogies as a new form of explanation in machine learning. here the goal is to identify diverse analogous pairs of examples that share the same level of similarity as the input pair and provide insight into ( latent ) factors underlying the model ' s prediction. the selection of analogies can optionally leverage feature attributions, thus connecting the two forms of explanation while still maintaining complementarity. we prove that our analogy objective function is submodular, making the search for good - quality analogies efficient. we apply the proposed approaches to explain similarities between sentences as predicted by a state - of - the - art sentence encoder, and between patients in a healthcare utilization application. efficacy is measured through quantitative evaluations, a careful user study, and examples of explanations. | arxiv:2202.01153 |
we present a novel fitting formula for the halo concentration enhancement in chameleon $ f ( r ) $ gravity relative to general relativity ( gr ). the formula is derived by employing a large set of $ n $ - body simulations of the hu - sawicki $ f ( r ) $ model which cover a wide range of model and cosmological parameters, resolutions and simulation box sizes. the complicated dependence of the concentration on halo mass $ m $, redshift $ z $, and the $ f ( r ) $ and cosmological parameters can be combined into a simpler form that depends only on a rescaled mass $ m / 10 ^ { p _ 2 } $, with $ p _ 2 \ equiv1. 5 \ log _ { 10 } \ left [ | { \ bar { f } _ r ( z ) } | / ( 1 + z ) \ right ] + 21. 64 $ and $ \ bar { f } _ r ( z ) $ the background scalar field at $ z $, irrespective of the $ f ( r ) $ model parameter. our fitting formula can describe the concentration enhancement well for redshifts $ z \ leq3 $, nearly 7 orders of magnitude in $ m / 10 ^ { p _ 2 } $ and five decades in halo mass. this is part of a series of works which aims to provide a general framework for self - consistent and unbiased tests of gravity using present and upcoming galaxy cluster surveys. the fitting formula, which is the first quantitative model for the concentration enhancement due to chameleon type modified gravity, is an important part in this framework and will allow continuous exploration of the parameter space. it can also be used to model other statistics such as the matter power spectrum. | arxiv:1901.06392 |
reconstructing two - hand interactions from a single image is a challenging problem due to ambiguities that stem from projective geometry and heavy occlusions. existing methods are designed to estimate only a single pose, despite the fact that there exist other valid reconstructions that fit the image evidence equally well. in this paper we propose to address this issue by explicitly modeling the distribution of plausible reconstructions in a conditional normalizing flow framework. this allows us to directly supervise the posterior distribution through a novel determinant magnitude regularization, which is key to varied 3d hand pose samples that project well into the input image. we also demonstrate that metrics commonly used to assess reconstruction quality are insufficient to evaluate pose predictions under such severe ambiguity. to address this, we release the first dataset with multiple plausible annotations per image called multihands. the additional annotations enable us to evaluate the estimated distribution using the maximum mean discrepancy metric. through this, we demonstrate the quality of our probabilistic reconstruction and show that explicit ambiguity modeling is better - suited for this challenging problem. | arxiv:2210.01692 |
a wide variety of higher - order symmetry protected topological phase ( hospt ) with gapless corners or hinges had been proposed as a descendant of topological crystalline insulator protected by spatial symmetry. in this work, we address a new class of higher - order topological state which does not require crystalline symmetries but instead relies on subsystem symmetry for protection. we propose several strong interacting models with gapless hinge or corner based on a ` decorated hinge - wall condensate ' picture. the hinge - wall, which appears as the defect configuration of $ z _ 2 $ paramagnet is decorated with lower - dim spt state. such unique hinge - wall decoration structure leads to gapped surfaces separated by gapless hinges. the non - trivial nature of the hinge modes can be captured by a $ 1 + 1 $ d conformal field theory with a wess - zumino - witten term. besides, we establish a no - go theorem to demonstrate the ungappable nature of the hinge by making a connection between generalized lieb - schultz - mattis theorem and the boundary anomaly of hospt state. this universal correspondence engenders a comprehensive criterion to determine the existence of hospt under certain symmetry regardless of the microscopic hamiltonian. | arxiv:1908.04299 |
we derive formulae for neutrino masses and mixing angles in a type i seesaw framework with an underlying a4 flavor symmetry. in particular, the majorana neutrino mass matrix includes contributions from an a4 triplet, 1, 1 ', and 1 " flavon fields. using these formulae, we constrain the general a4 parameter space using the updated global fits on neutrino mixing angles and mass squared differences, including results from the daya bay and reno experiments, and we find predictive relations among the mixing parameters for certain choices of the triplet vacuum expectation value. in the normal hierarchy case, sizable deviation from maximal atmospheric mixing is predicted, and such deviation is strongly correlated with the value of theta13 in the range of ~ ( 8 - 10 ) degrees. on the other hand, such deviation is negligible and insensitive to theta13 in the inverted mass hierarchy case. we also show expectations for the dirac cp phase resulting from the parameter scan. future refined measurements of neutrino mixing angles will test these predicted correlations and potentially show evidence for particular triplet vev patterns. | arxiv:1210.6982 |
this paper is the third in an investigation begun in arxiv : 1906. 05602 and arxiv : 1907. 07571 of extending the t1 theorem of david and journ \ ' e, and optimal cancellation conditions, to more general weight pairs. the main result here is that the familiar t1 testing conditions over indicators of cubes, together with the one - tailed a2 conditions, imply polynomial testing. analogous results for fractional singular integrals hold as well. applications include a t1 theorem for fractional czo ' s t in the case of doubling measures when one of the weights is a infinity, and then to optimal cancellation conditions for such czo ' s in similar situations. | arxiv:1907.10734 |
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