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reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. its defining method can briefly be described as " going backwards from the theorems to the axioms ", in contrast to the ordinary mathematical practice of deriving theorems from axioms. it can be conceptualized as sculpting out necessary conditions from sufficient ones. the reverse mathematics program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and zorn ' s lemma are equivalent over zf set theory. the goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory. reverse mathematics is usually carried out using subsystems of second - order arithmetic, where many of its definitions and methods are inspired by previous work in constructive analysis and proof theory. the use of second - order arithmetic also allows many techniques from recursion theory to be employed ; many results in reverse mathematics have corresponding results in computable analysis. in higher - order reverse mathematics, the focus is on subsystems of higher - order arithmetic, and the associated richer language. the program was founded by harvey friedman and brought forward by steve simpson. = = general principles = = in reverse mathematics, one starts with a framework language and a base theory β a core axiom system β that is too weak to prove most of the theorems one might be interested in, but still powerful enough to develop the definitions necessary to state these theorems. for example, to study the theorem β every bounded sequence of real numbers has a supremum β it is necessary to use a base system that can speak of real numbers and sequences of real numbers. for each theorem that can be stated in the base system but is not provable in the base system, the goal is to determine the particular axiom system ( stronger than the base system ) that is necessary to prove that theorem. to show that a system s is required to prove a theorem t, two proofs are required. the first proof shows t is provable from s ; this is an ordinary mathematical proof along with a justification that it can be carried out in the system s. the second proof, known as a reversal, shows that t itself implies s ; this proof is carried out in the base system. the reversal establishes that no axiom system s β² that extends the base system can be weaker than s while still proving t. = = = use of second - order arithmetic =
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https://en.wikipedia.org/wiki/Reverse_mathematics
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we present \ textbf { symbioticrag }, a novel framework that fundamentally reimagines retrieval - augmented generation ~ ( rag ) systems by establishing a bidirectional learning relationship between humans and machines. our approach addresses two critical challenges in current rag systems : the inherently human - centered nature of relevance determination and users ' progression from " unconscious incompetence " in query formulation. symbioticrag introduces a two - tier solution where level 1 enables direct human curation of retrieved content through interactive source document exploration, while level 2 aims to build personalized retrieval models based on captured user interactions. we implement level 1 through three key components : ( 1 ) ~ a comprehensive document processing pipeline with specialized models for layout detection, ocr, and extraction of tables, formulas, and figures ; ( 2 ) ~ an extensible retriever module supporting multiple retrieval strategies ; and ( 3 ) ~ an interactive interface that facilitates both user engagement and interaction data logging. we experiment level 2 implementation via a retriever strategy incorporated llm summarized user intention from user interaction logs. to maintain high - quality data preparation, we develop a human - on - the - loop validation interface that improves pipeline output while advancing research in specialized extraction tasks. evaluation across three scenarios ( literature review, geological exploration, and education ) demonstrates significant improvements in retrieval relevance and user satisfaction compared to traditional rag approaches. to facilitate broader research and further advancement of symbioticrag level 2 implementation, we will make our system openly accessible to the research community.
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arxiv:2505.02418
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assume that $ \ omega _ { 1 } $ and $ \ omega _ { 2 } $ are two smooth bounded pseudoconvex domains in $ \ mathbb { c } ^ { 2 } $ that intersect ( real ) transversely, and that $ \ omega _ { 1 } \ cap \ omega _ { 2 } $ is a domain ( i. e. is connected ). if the $ \ overline { \ partial } $ - neumann operators on $ \ omega _ { 1 } $ and on $ \ omega _ { 2 } $ are compact, then so is the $ \ overline { \ partial } $ - neumann operator on $ \ omega _ { 1 } \ cap \ omega _ { 2 } $. the corresponding result holds for the $ \ overline { \ partial } $ - neumann operators on $ ( 0, n - 1 ) $ - forms on domains in $ \ mathbb { c } ^ { n } $.
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arxiv:1408.6134
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big data applications and analytics are employed in many sectors for a variety of goals : improving customers satisfaction, predicting market behavior or improving processes in public health. these applications consist of complex software stacks that are often run on cloud systems. predicting execution times is important for estimating the cost of cloud services and for effectively managing the underlying resources at runtime. machine learning ( ml ), providing black box solutions to model the relationship between application performance and system configuration without requiring in - detail knowledge of the system, has become a popular way of predicting the performance of big data applications. we investigate the cost - benefits of using supervised ml models for predicting the performance of applications on spark, one of today ' s most widely used frameworks for big data analysis. we compare our approach with \ textit { ernest } ( an ml - based technique proposed in the literature by the spark inventors ) on a range of scenarios, application workloads, and cloud system configurations. our experiments show that ernest can accurately estimate the performance of very regular applications, but it fails when applications exhibit more irregular patterns and / or when extrapolating on bigger data set sizes. results show that our models match or exceed ernest ' s performance, sometimes enabling us to reduce the prediction error from 126 - 187 % to only 5 - 19 %.
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arxiv:2108.12214
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relative drone - to - drone localization is a fundamental building block for any swarm operations. we address this task in the context of miniaturized nano - drones, i. e., 10cm in diameter, which show an ever - growing interest due to novel use cases enabled by their reduced form factor. the price for their versatility comes with limited onboard resources, i. e., sensors, processing units, and memory, which limits the complexity of the onboard algorithms. a traditional solution to overcome these limitations is represented by lightweight deep learning models directly deployed aboard nano - drones. this work tackles the challenging relative pose estimation between nano - drones using only a gray - scale low - resolution camera and an ultra - low - power system - on - chip ( soc ) hosted onboard. we present a vertically integrated system based on a novel vision - based fully convolutional neural network ( fcnn ), which runs at 39hz within 101mw onboard a crazyflie nano - drone extended with the gwt gap8 soc. we compare our fcnn against three state - of - the - art ( soa ) systems. considering the best - performing soa approach, our model results in an r - squared improvement from 32 to 47 % on the horizontal image coordinate and from 18 to 55 % on the vertical image coordinate, on a real - world dataset of 30k images. finally, our in - field tests show a reduction of the average tracking error of 37 % compared to a previous soa work and an endurance performance up to the entire battery lifetime of 4 minutes.
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arxiv:2402.13756
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the randomly pivoted partial cholesky algorithm ( rpcholesky ) computes a factorized rank - k approximation of an n x n positive - semidefinite ( psd ) matrix. rpcholesky requires only ( k + 1 ) n entry evaluations and o ( k ^ 2 n ) additional arithmetic operations, and it can be implemented with just a few lines of code. the method is particularly useful for approximating a kernel matrix. this paper offers a thorough new investigation of the empirical and theoretical behavior of this fundamental algorithm. for matrix approximation problems that arise in scientific machine learning, experiments show that rpcholesky matches or beats the performance of alternative algorithms. moreover, rpcholesky provably returns low - rank approximations that are nearly optimal. the simplicity, effectiveness, and robustness of rpcholesky strongly support its use in scientific computing and machine learning applications.
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arxiv:2207.06503
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one of the main sources of a background in underground physics experiments ( such as the investigation of solar neutrino flux, neutrino oscillations, neutrinoless double beta decay, and the search for annual and daily cold dark matter particle flux modulation ) are fast neutrons originating from the surrounding rocks. the measurements of fast neutron flux in the new dulb laboratory situated at a depth of 4900 m w. e. in the baksan neutrino observatory have been performed. the relative neutron shielding properties of several commonly available natural materials were investigated too. the preliminary results obtained with a high - sensitive fast neutron spectrometer at the level of sensitivity of about 10 ^ ( - 7 ) neutron / ( cm ^ 2 sec ) are presented and discussed.
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arxiv:physics/0001007
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unlike 2d object detection where all roi features come from grid pixels, the roi feature extraction of 3d point cloud object detection is more diverse. in this paper, we first compare and analyze the differences in structure and performance between the two state - of - the - art models pv - rcnn and voxel - rcnn. then, we find that the performance gap between the two models does not come from point information, but structural information. the voxel features contain more structural information because they do quantization instead of downsampling to point cloud so that they can contain basically the complete information of the whole point cloud. the stronger structural information in voxel features makes the detector have higher performance in our experiments even if the voxel features don ' t have accurate location information. then, we propose that structural information is the key to 3d object detection. based on the above conclusion, we propose a self - attention roi feature extractor ( sarfe ) to enhance structural information of the feature extracted from 3d proposals. sarfe is a plug - and - play module that can be easily used on existing 3d detectors. our sarfe is evaluated on both kitti dataset and waymo open dataset. with the newly introduced sarfe, we improve the performance of the state - of - the - art 3d detectors by a large margin in cyclist on kitti dataset while keeping real - time capability.
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arxiv:2111.00931
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investigations of dynamic and thermodynamic properties for a molecular crystal tris - hexafluoroacetylacetonate - iron $ fe ( o _ 2c _ 5hf _ 6 ) _ 3 $ are presented. heat capacity $ c _ p ( t ) $ has been measured by adiabatic calorimetry method in the temperature range $ 4. 8 - 321 k $. an anomaly with a maximum at $ t _ c = 44. 6 k $ has been discovered. intermolecular vibrations spectrum was calculated by lattice dynamics method in quasiharmonic approximation. intramolecular frequencies are found by solving the schr \ " odinger equation in approach of small harmonic oscillations. in the frequency interval $ \ approx 30 - 70 cm ^ { - 1 } $ overlapping the spectrums intra - and intermolecular oscillations has been found. the good agreement for calculated and experimental $ c _ p ( t ) $ occurred to be possible for two sets of the force constants. these sets describe two phases above and below $ t _ c $. the difference between phases is connected with freezing of rotation $ cf _ 3 $ groups. it has been concluded that the interaction between different modes leads to phase transition and anomaly in heat capacity.
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arxiv:cond-mat/0410428
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periodic signatures in time - domain observations of quasars have been used to search for binary supermassive black holes. these searches, across existing time - domain surveys, have produced several hundred candidates. the general stochastic variability of quasars, however, can masquerade as a false - positive periodic signal, especially when monitoring cadence and duration are limited. in this work, we predict the detectability of binary supermassive black holes in the upcoming rubin observatory legacy survey of space and time ( lsst ). we apply computationally inexpensive sinusoidal curve fits to millions of simulated lsst deep drilling field light curves of both single, isolated quasars and binary quasars. period and phase of simulated binary signals can generally be disentangled from quasar variability. binary amplitude is overestimated and poorly recovered for two - thirds of potential binaries due to quasar accretion variability. quasars with strong intrinsic variability can obscure a binary signal too much for recovery. we also find that the most luminous quasars mimic current binary candidate light curves and their properties : false positive rates are 60 \ % for these quasars. the reliable recovery of binary period and phase for a wide range of input binary lsst light curves is promising for multi - messenger characterization of binary supermassive black holes. however, pure electromagnetic detections of binaries using photometric periodicity with amplitude greater than 0. 1 magnitude will result in samples that are overwhelmed by false positives. this paper represents an important and computationally inexpensive way forward for understanding the true and false positive rates for binary candidates identified by rubin.
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arxiv:2311.10851
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we calculate the full asymptotic expansion of boundary blow - up solutions, for any nonlinearity f. our approach enables us to state sharp qualitative results regarding uniqueness and ra - dial symmetry of solutions, as well as a characterization of nonlinearities for which the blow - up rate is universal. lastly, we study in more detail the standard nonlinearities f ( u ) = u ^ p, p > 1.
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arxiv:1003.3578
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morse theory relates algebraic topology invariants and the dynamics of the gradient flow of a morse function, allowing to derive information about one out of the other. in the case of the homology, the construction extends to much more general settings, and in particular to the infinite dimensional setting of the celebrated floer homology in symplectic geometry. the case of the fundamental group is quiet different however, and the object of this paper is to provide a dynamical description of the fundamental group in the stable morse setting, which can be thought of as an intermediate case between the morse and the floer settings.
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arxiv:2410.07802
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unsupervised image - to - image translation aims at learning the mapping from the source to target domain without using paired images for training. an essential yet restrictive assumption for unsupervised image translation is that the two domains are aligned, e. g., for the selfie2anime task, the anime ( selfie ) domain must contain only anime ( selfie ) face images that can be translated to some images in the other domain. collecting aligned domains can be laborious and needs lots of attention. in this paper, we consider the task of image translation between two unaligned domains, which may arise for various possible reasons. to solve this problem, we propose to select images based on importance reweighting and develop a method to learn the weights and perform translation simultaneously and automatically. we compare the proposed method with state - of - the - art image translation approaches and present qualitative and quantitative results on different tasks with unaligned domains. extensive empirical evidence demonstrates the usefulness of the proposed problem formulation and the superiority of our method.
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arxiv:2109.11736
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testing plays a pivotal role in ensuring software quality, yet conventional search based software testing ( sbst ) methods often struggle with complex software units, achieving suboptimal test coverage. recent works using large language models ( llms ) for test generation have focused on improving generation quality through optimizing the test generation context and correcting errors in model outputs, but use fixed prompting strategies that prompt the model to generate tests without additional guidance. as a result llm - generated testsuites still suffer from low coverage. in this paper, we present symprompt, a code - aware prompting strategy for llms in test generation. symprompt ' s approach is based on recent work that demonstrates llms can solve more complex logical problems when prompted to reason about the problem in a multi - step fashion. we apply this methodology to test generation by deconstructing the testsuite generation process into a multi - stage sequence, each of which is driven by a specific prompt aligned with the execution paths of the method under test, and exposing relevant type and dependency focal context to the model. our approach enables pretrained llms to generate more complete test cases without any additional training. we implement symprompt using the treesitter parsing framework and evaluate on a benchmark challenging methods from open source python projects. symprompt enhances correct test generations by a factor of 5 and bolsters relative coverage by 26 % for codegen2. notably, when applied to gpt - 4, symprompt improves coverage by over 2x compared to baseline prompting strategies.
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arxiv:2402.00097
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we study the nontrivial solutions of the qcd fermionic gap equation including the contribution of dynamically massive gluons and the confining propagator proposed by cornwall. without the confining propagator, in the case of non - running gluon mass ( mg ), we found the multivacuum solutions ( replicas ) reported in the literature and we were able to define limits on mg for dynamical chiral symmetry breaking. on the other side, when considering the running in the gluon mass the vacuum replicas are absent in the limits on mg where the chiral symmetry is broken. in the pure confining sector, the multivacuum states are always absent so it is said that only one stable solution for the gap equation is found as claimed in previous analysis using different approaches. finally in the case of the complete gap equation i. e. with both contributions, the vacuum replicas are also absent in both cases ; with constant and with running gluon mass.
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arxiv:1410.3184
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we introduce a new machine learning approach for image segmentation that uses a neural network to model the conditional energy of a segmentation given an image. our approach, combinatorial energy learning for image segmentation ( celis ) places a particular emphasis on modeling the inherent combinatorial nature of dense image segmentation problems. we propose efficient algorithms for learning deep neural networks to model the energy function, and for local optimization of this energy in the space of supervoxel agglomerations. we extensively evaluate our method on a publicly available 3 - d microscopy dataset with 25 billion voxels of ground truth data. on an 11 billion voxel test set, we find that our method improves volumetric reconstruction accuracy by more than 20 % as compared to two state - of - the - art baseline methods : graph - based segmentation of the output of a 3 - d convolutional neural network trained to predict boundaries, as well as a random forest classifier trained to agglomerate supervoxels that were generated by a 3 - d convolutional neural network.
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arxiv:1506.04304
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in this paper we prove the existence of extreme value laws for dynamical systems perturbed by instrument - like - error, also called observational noise. an orbit perturbed with observational noise mimics the behavior of an instrumentally recorded time series. instrument characteristics - defined as precision and accuracy - act both by truncating and randomly displacing the real value of a measured observable. here we analyze both these effects from a theoretical and numerical point of view. first we show that classical extreme value laws can be found for orbits of dynamical systems perturbed with observational noise. then we present numerical experiments to support the theoretical findings and give an indication of the order of magnitude of the instrumental perturbations which cause relevant deviations from the extreme value laws observed in deterministic dynamical systems. finally, we show that the observational noise preserves the structure of the deterministic attractor. this goes against the common assumption that random transformations cause the orbits asymptotically fill the ambient space with a loss of information about any fractal structures present on the attractor.
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arxiv:1308.5624
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in 2 + 1 - dimensional conformal field theories with a global u ( 1 ) symmetry, monopoles can be introduced through a background gauge field that couples to the u ( 1 ) conserved current. we use the state - operator correspondence to calculate scaling dimensions of such monopoles. we obtain the next - to - leading term in the 1 / n _ b expansion of the wilson - fisher fixed point in the theory of n _ b complex bosons.
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arxiv:1303.3006
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we study the two weight quantitative estimates for the commutator of maximal functions and the maximal commutators with respect to the symbol in weighted bmo space on spaces of homogeneous type. these commutators turn out to be controlled by the sparse operators in the setting of space of homogeneous type. the lower bound of the maximal commutator is also obtained.
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arxiv:2012.00575
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an exposition on spivakovsky ' s dual graphs of valuations on function fields of dimension two is first given, leading to a proof of minimal generating sequences for the non - divisorial valuations. it should be noted that the definition of generating sequence used in this paper is different from spivakovsky ' s original usage. this change leads to an explicit formulation of generating sequence values for the non - divisorial cases in terms of data from their dual graphs. the proofs are elementary in the sense that only continued fractions and the linear diophantine frobenius problem from classical number theory are used.
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arxiv:1311.1542
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several new families of multi - memory classical convolutional bose - chaudhuri - hocquenghem ( bch ) codes as well as families of unit - memory quantum convolutional codes are constructed in this paper. our unit - memory classical and quantum convolutional codes are optimal in the sense that they attain the classical ( quantum ) generalized singleton bound. the constructions presented in this paper are performed algebraically and not by computational search.
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arxiv:1212.4654
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state - of - the - art deep reading comprehension models are dominated by recurrent neural nets. their sequential nature is a natural fit for language, but it also precludes parallelization within an instances and often becomes the bottleneck for deploying such models to latency critical scenarios. this is particularly problematic for longer texts. here we present a convolutional architecture as an alternative to these recurrent architectures. using simple dilated convolutional units in place of recurrent ones, we achieve results comparable to the state of the art on two question answering tasks, while at the same time achieving up to two orders of magnitude speedups for question answering.
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arxiv:1711.04352
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we consider the variant of mirror symmetry conjecture for k3 surfaces which relates " geometry " of curves of a general member of a family of k3 with " algebraic functions " on the moduli of the mirror family. lorentzian kac - - moody algebras are involved in this construction. we give several examples when this conjecture is valid.
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arxiv:alg-geom/9510008
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graph neural networks ( gnns ) have been shown to achieve competitive results to tackle graph - related tasks, such as node and graph classification, link prediction and node and graph clustering in a variety of domains. most gnns use a message passing framework and hence are called mpnns. despite their promising results, mpnns have been reported to suffer from over - smoothing, over - squashing and under - reaching. graph rewiring and graph pooling have been proposed in the literature as solutions to address these limitations. however, most state - of - the - art graph rewiring methods fail to preserve the global topology of the graph, are neither differentiable nor inductive, and require the tuning of hyper - parameters. in this paper, we propose diffwire, a novel framework for graph rewiring in mpnns that is principled, fully differentiable and parameter - free by leveraging the lov \ ' asz bound. the proposed approach provides a unified theory for graph rewiring by proposing two new, complementary layers in mpnns : ct - layer, a layer that learns the commute times and uses them as a relevance function for edge re - weighting ; and gap - layer, a layer to optimize the spectral gap, depending on the nature of the network and the task at hand. we empirically validate the value of each of these layers separately with benchmark datasets for graph classification. we also perform preliminary studies on the use of ct - layer for homophilic and heterophilic node classification tasks. diffwire brings together the learnability of commute times to related definitions of curvature, opening the door to creating more expressive mpnns.
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arxiv:2206.07369
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motivated by the observation of light surface states in smb6, we examine the effects of surface kondo breakdown in topological kondo insulators. we present both numerical and analytic results which show that the decoupling of the localized moments at the surface disturbs the compensation between light and heavy electrons and dopes the dirac cone. dispersion of these uncompensated surface states are dominated by inter - site hopping, which leads to a much lighter quasiparticles. these surface states are also highly durable against the effects of surface magnetism and decreasing thickness of the sample.
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arxiv:1501.03031
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in the vertex connectivity survivable network design problem we are given an undirected graph g = ( v, e ) and connectivity requirement r ( u, v ) for each pair of vertices u, v. we are also given a cost function on the set of edges. our goal is to find the minimum cost subset of edges such that for every pair ( u, v ) of vertices we have r ( u, v ) vertex disjoint paths in the graph induced by the chosen edges. recently, chuzhoy and khanna presented a randomized algorithm that achieves a factor of o ( k ^ 3 log n ) for this problem where k is the maximum connectivity requirement. in this paper we derandomize their algorithm to get a deterministic o ( k ^ 3 log n ) factor algorithm. another problem of interest is the single source version of the problem, where there is a special vertex s and all non - zero connectivity requirements must involve s. we also give a deterministic o ( k ^ 2 log n ) algorithm for this problem.
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arxiv:1004.1208
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we explicitly evaluate the heat kernel for the laplacian of arbitrary spin tensor fields on the thermal quotient of ( euclidean ) $ ads _ n $ for $ n \ geq 3 $ using the group theoretic techniques employed for $ ads _ 3 $ in arxiv : 0911. 5085. our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.
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arxiv:1103.3627
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let $ s $ be a set of dominant rational self - maps on $ \ mathbb { p } ^ n $. we study the arithmetic and dynamical degrees of infinite sequences of $ s $ obtained by sequentially composing elements of $ s $ on the right and left. we then apply this insight to dynamical galois theory.
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arxiv:2002.09798
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we present ch and cn index analysis and c and n abundance calculations based on the low - resolution blue spectra of red giant branch ( rgb ) stars in the galactic globular cluster ngc 7089 ( m 2 ). our main goal is to investigate the c - n anticorrelation for this intermediate metallicity cluster. the data were collected with dolores, the multiobject, low - resolution facility at the telescopio nazionale galileo. spectroscopic data were coupled with uv photometry obtained during the spectroscopic run. we found a considerable star - to - star variation in both a ( c ) and a ( n ) at all luminosities for our sample of 35 targets. these abundances appear to be anticorrelated, with a hint of bimodality in the c content for stars with luminosities below the rbg bump ( v ~ 15. 7 ), while the range of variations in n abundances is very large and spans almost ~ 2 dex. we find additional c depletion as the stars evolve off the rgb bump, in fairly good agreement with theoretical predictions for metal - poor stars in the course of normal stellar evolution. we isolated two groups with n - rich and n - poor stars and found that n abundance variations correlate with the ( u - v ) color in the dolores color - magnitude diagram ( cmd ). the v, ( u - v ) cmd for this cluster shows an additional rgb sequence, located at the red of the main rgb and amounting to a small fraction of the total giant population. we identified two ch stars detected in previous studies in our u, v images. these stars, which are both cluster members, fall on this redder sequence, suggesting that the anomalous rgb should have a peculiar chemical pattern. unfortunately, no additional spectra were obtained for stars in this previously unknown rgb branch.
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arxiv:1210.2566
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quantum teleportation of a squeezed state is demonstrated experimentally. due to some inevitable losses in experiments, a squeezed vacuum necessarily becomes a mixed state which is no longer a minimum uncertainty state. we establish an operational method of evaluation for quantum teleportation of such a state using fidelity, and discuss the classical limit for the state. the measured fidelity for the input state is 0. 85 $ \ pm $ 0. 05 which is higher than the classical case of 0. 73 $ \ pm $ 0. 04. we also verify that the teleportation process operates properly for the nonclassical state input and its squeezed variance is certainly transferred through the process. we observe the smaller variance of the teleported squeezed state than that for the vacuum state input.
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arxiv:quant-ph/0311056
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as xr technology continues to advance rapidly, 3d generation and editing are increasingly crucial. among these, stylization plays a key role in enhancing the appearance of 3d models. by utilizing stylization, users can achieve consistent artistic effects in 3d editing using a single reference style image, making it a user - friendly editing method. however, recent nerf - based 3d stylization methods encounter efficiency issues that impact the user experience, and their implicit nature limits their ability to accurately transfer geometric pattern styles. additionally, the ability for artists to apply flexible control over stylized scenes is considered highly desirable to foster an environment conducive to creative exploration. to address the above issues, we introduce stylizedgs, an efficient 3d neural style transfer framework with adaptable control over perceptual factors based on 3d gaussian splatting ( 3dgs ) representation. we propose a filter - based refinement to eliminate floaters that affect the stylization effects in the scene reconstruction process. the nearest neighbor - based style loss is introduced to achieve stylization by fine - tuning the geometry and color parameters of 3dgs, while a depth preservation loss with other regularizations is proposed to prevent the tampering of geometry content. moreover, facilitated by specially designed losses, stylizedgs enables users to control color, stylized scale, and regions during the stylization to possess customization capabilities. our method achieves high - quality stylization results characterized by faithful brushstrokes and geometric consistency with flexible controls. extensive experiments across various scenes and styles demonstrate the effectiveness and efficiency of our method concerning both stylization quality and inference speed.
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arxiv:2404.05220
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we tackle the problem of learning complex, general behaviors directly in the real world. we propose an approach for robots to efficiently learn manipulation skills using only a handful of real - world interaction trajectories from many different settings. inspired by the success of learning from large - scale datasets in the fields of computer vision and natural language, our belief is that in order to efficiently learn, a robot must be able to leverage internet - scale, human video data. humans interact with the world in many interesting ways, which can allow a robot to not only build an understanding of useful actions and affordances but also how these actions affect the world for manipulation. our approach builds a structured, human - centric action space grounded in visual affordances learned from human videos. further, we train a world model on human videos and fine - tune on a small amount of robot interaction data without any task supervision. we show that this approach of affordance - space world models enables different robots to learn various manipulation skills in complex settings, in under 30 minutes of interaction. videos can be found at https : / / human - world - model. github. io
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arxiv:2308.10901
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we provide a library to facilitate the implementation of new models in codes such as matrix element and event generators or codes for computing dark matter observables. the library contains a slha reader routine as well as diagonalisation routines. this library is available in calchep and micromegas. the implementation of models based on this library is supported by lanhep and feynrules.
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arxiv:1008.0181
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word embeddings aims to map sense of the words into a lower dimensional vector space in order to reason over them. training embeddings on domain specific data helps express concepts more relevant to their use case but comes at a cost of accuracy when data is less. our effort is to minimise this by infusing syntactic knowledge into the embeddings. we propose a graph based embedding algorithm inspired from node2vec. experimental results have shown that our algorithm improves the syntactic strength and gives robust performance on meagre data.
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arxiv:1808.05907
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we study schemes for interpolating functions that take values in the special orthogonal group $ so ( n ) $. our focus is on interpolation schemes obtained by embedding $ so ( n ) $ in a linear space, interpolating in the linear space, and mapping the result onto $ so ( n ) $ via the closest point projection. the resulting interpolants inherit both the order of accuracy and the regularity of the underlying interpolants on the linear space. the values and derivatives of the interpolants admit efficient evaluation via either explicit formulas or iterative algorithms, which we detail for two choices of embeddings : the embedding of $ so ( n ) $ in the space of $ n \ times n $ matrices and, when $ n = 3 $, the identification of $ so ( 3 ) $ with the set of unit quaternions. along the way, we point out a connection between these interpolation schemes and geodesic finite elements. we illustrate the utility of these interpolation schemes by numerically computing minimum acceleration curves on $ so ( n ) $, a task which is handled naturally with $ so ( n ) $ - valued finite elements having $ c ^ 1 $ - continuity.
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arxiv:1608.05738
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we apply a physical based model to describe the clothes fashion market. every time a new outlet appears on the market, it can invade the market under certain specific conditions. hence, the " old ' ' outlet can be completely dominated and disappears. each creator competes for a finite population of agents. fashion phenomena are shown to result from a collective phenomenon produced by local individual imitation effects. we assume that, in each step of the imitation process, agents only interact with a subset rather than with the whole set of agents. people are actually more likely to influence ( and be influenced by ) their close ' ' neighbours ' '. accordingly we discuss which strategy is best fitted for new producers when people are either simply organised into anonymous reference groups or when they are organised in social groups hierarchically ordered. while counterfeits are shown to reinforce the first strategy, creating social leaders can permit to avoid them.
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arxiv:cond-mat/0410483
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reinforcement learning and recently deep reinforcement learning are popular methods for solving sequential decision making problems modeled as markov decision processes. rl modeling of a problem and selecting algorithms and hyper - parameters require careful considerations as different configurations may entail completely different performances. these considerations are mainly the task of rl experts ; however, rl is progressively becoming popular in other fields where the researchers and system designers are not rl experts. besides, many modeling decisions, such as defining state and action space, size of batches and frequency of batch updating, and number of timesteps are typically made manually. for these reasons, automating different components of rl framework is of great importance and it has attracted much attention in recent years. automated rl provides a framework in which different components of rl including mdp modeling, algorithm selection and hyper - parameter optimization are modeled and defined automatically. in this article, we explore the literature and present recent work that can be used in automated rl. moreover, we discuss the challenges, open questions and research directions in autorl.
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arxiv:2201.05000
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we show that the cofinalities of both the miller ideal m ^ 0 ( the sigma - ideal naturally related to miller forcing ) and the laver ideal ell ^ 0 ( related to laver forcing ) are larger than the size of the continuum in zfc.
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arxiv:1611.08143
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among ( regular, normal ) parabolic geometries of type $ ( g, p ) $, there is a locally unique maximally symmetric structure and it has symmetry dimension $ \ dim ( g ) $. the symmetry gap problem concerns the determination of the next realizable ( submaximal ) symmetry dimension. when $ g $ is a complex or split - real simple lie group of rank at least three or when $ ( g, p ) = ( g _ 2, p _ 2 ) $, we establish a local uniqueness result for submaximally symmetric structures of type $ ( g, p ) $.
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arxiv:2107.10500
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the geometrical construction of rational maps using a cubic grid has led to many new skyrmion solutions, with baryon numbers up to 108. energy spectra of some of the new skyrmions are calculated here by semi - classical quantization. quantization of the b = 20 t _ d - symmetric skyrmion, which is one of the newly found skyrmions, is considered, and this leads to the development of a new approach to solving finkelstein - rubinstein ( f - r ) constraints. matrix equations are simplified by introducing a cartesian version of angular momentum basis states, and the computations are easier. the quantum states of all t _ d - symmetric skyrmions, constructed from the cubic grid, are classified into three classes, depending on the contribution of vertex points of the cubic grid to the rational maps. the analysis is extended to the larger symmetry group o _ h. quantum states of o _ h - symmetric skyrmions, constructed from the cubic grid, form a subset of the t _ d - symmetric quantum states.
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arxiv:1402.6994
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gray wolves were reintroduced to yellowstone national park ( ynp ) in 1995. the population initially flourished, but since 2003 the population has experience significant reductions due to factors that may include disease - induced mortality, illegal hunting, park control pro - grams, vehicle induced deaths and intra - species aggression. despite facing similar conditions, and interference competition with the wolves, the coyote population at ynp has persisted. in this paper we introduce an epidemiological framework that incorporates natural, human - caused and disease - induced mortality as well as interference competition between two species of predators. the outcomes generated by this theoretical framework are used to explore the impact of competition and death - induced mechanisms on predators coexistence. it is the hope that these results on the competitive dynamics of carnivores in yellowstone national park will provide park management insights that result in policies that keep the reintroduction of wolves successful.
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arxiv:1408.6819
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the rarefied flow and multi - scale flow are crucial for the aerodynamic design of spacecraft, ultra - low orbital vehicles and plumes. by introducing a discrete velocity space, the boltzmann method, such as the discrete velocity method and unified methods, can capture complex and non - equilibrium velocity distribution functions ( vdfs ) and describe flow behaviors exactly. however, the extremely steep slope and high concentration of the gas vdfs in a local particle velocity space make it very difficult for the boltzmann method with structured velocity space to describe high speed flow. therefore, the adaptive velocity space ( avs ) is required for the boltzmann solvers to be practical in complex rarefied flow and multi - scale flow. this paper makes two improvements to the avs approach, which is then incorporated into a general discrete velocity framework, such as the unified gas - kinetic scheme. firstly, a global velocity mesh is used to prevent the interpolation of the vdfs at the physical interface during the calculation of the microscopic fluxes, maintaining the program ' s high level of parallelism. secondly, rather than utilizing costly interpolation, the vdfs on a new velocity space were reconstruction using the ` ` consanguinity " relationship. in other words, a split child node ' s vdf is the same as its parent ' s vdf, and a merged parent ' s vdf is the average of its children ' s vdfs. additionally, the discrete deviation of the equilibrium distribution functions is employed to maintain the proposed method ' s conservation. moreover, an appropriate set of adaptive parameters is established to enhance the automation of the proposed method. finally, a number of numerical tests are carried out to validate the proposed method.
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arxiv:2212.05645
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the dynamic characteristics of near - field levitation bearings have been investigated in this study. through theoretical analysis, two different types of system stiffness are defined and derived analytically. the dynamic stiffness relates the excitation amplitude to the dynamic force amplitude, while the effective stiffness governs the time - averaged force - displacement relationship. the results indicate two non - linear and asymmetric spring constants that can effectively predict levitation force and height. the models are verified with a carefully designed experimental setup to eliminate the structural resonance effect. besides, some unique dynamic behaviors are investigated and predicted based on the proposed stiffness model.
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arxiv:2110.01125
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generating audio from a video ' s visual context has multiple practical applications in improving how we interact with audio - visual media - for example, enhancing cctv footage analysis, restoring historical videos ( e. g., silent movies ), and improving video generation models. we propose a novel method to generate audio from video using a sequence - to - sequence model, improving on prior work that used cnns and wavenet and faced sound diversity and generalization challenges. our approach employs a 3d vector quantized variational autoencoder ( vq - vae ) to capture the video ' s spatial and temporal structures, decoding with a custom audio decoder for a broader range of sounds. trained on the youtube8m dataset segment, focusing on specific domains, our model aims to enhance applications like cctv footage analysis, silent movie restoration, and video generation models.
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arxiv:2404.17608
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we notice that haynes - hedetniemi - slater conjecture is true ( i. e. $ \ gamma ( g ) \ leq \ frac { \ delta } { 3 \ delta - 1 } n $ for every graph $ g $ of size $ n $ with minimum degree $ \ delta \ geq 4 $, where $ \ gamma ( g ) $ is the domination number of $ g $ ). because the conjecture for $ \ delta = 6 $ follows from the estimate n ( 1 - \ prod _ { i = 1 } ^ [ \ delta + 1 } ( \ delta i ) / ( \ delta i + 1 ) by w. e. clark, b. shekhtman, s. suen [ upper bounds of the domination number of a graph, congressus numerantium, 132 ( 1998 ), pp. 99 - 123. ]
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arxiv:1011.3383
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we prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of ` dark ' subspaces, where the time evolution is unitary.
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arxiv:quant-ph/0505084
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in mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. the underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. the larger set is then said to be generated by the smaller set. it is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. it is usually the case that properties of the generating set are in some way preserved by the act of generation ; likewise, the properties of the generated set are often reflected in the generating set. = = list of generators = = a list of examples of generating sets follow. generating set or spanning set of a vector space : a set that spans the vector space generating set of a group : a subset of a group that is not contained in any subgroup of the group other than the entire group generating set of a ring : a subset s of a ring a generates a if the only subring of a containing s is a generating set of an ideal in a ring generating set of a module a generator, in category theory, is an object that can be used to distinguish morphisms in topology, a collection of sets that generate the topology is called a subbase generating set of a topological algebra : s is a generating set of a topological algebra a if the smallest closed subalgebra of a containing s is a generating a Ο - algebra by a collection of subsets = = differential equations = = in the study of differential equations, and commonly those occurring in physics, one has the idea of a set of infinitesimal displacements that can be extended to obtain a manifold, or at least, a local part of it, by means of integration. the general concept is of using the exponential map to take the vectors in the tangent space and extend them, as geodesics, to an open set surrounding the tangent point. in this case, it is not unusual to call the elements of the tangent space the generators of the manifold. when the manifold possesses some sort of symmetry, there is also the related notion of a charge or current, which is sometimes also called the generator, although, strictly speaking, charges are not elements of the tangent space. elements of the lie algebra to a lie group are sometimes referred to as " generators of the group, " especially by physicists. the lie algebra can be thought
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https://en.wikipedia.org/wiki/Generator_(mathematics)
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chiral effective field theory ( $ \ chi $ eft ) has proved to be a powerful microscopic framework for predicting the properties of neutron - rich nuclear matter with quantified theoretical uncertainties up to about twice the nuclear saturation density. tests of $ \ chi $ eft predictions are typically performed at low densities using nuclear experiments, with neutron star ( ns ) constraints only being considered at high densities. in this work, we discuss how asteroseismic quasi - normal modes within nss could be used to constrain specific matter properties at particular densities, not just the integrated quantities to which bulk ns observables are sensitive. we focus on the crust - core interface mode, showing that measuring this mode ' s frequency would provide a meaningful test of $ \ chi $ eft at densities around half the saturation density. conversely, we use nuclear matter properties predicted by $ \ chi $ eft to estimate that this mode ' s frequency is around 185 $ \ pm $ 50 hz. asteroseismic observables such as resonant phase shifts in gravitational - wave signals and multimessenger resonant shattering flare timings, therefore, have the potential to provide useful tests of $ \ chi $ eft.
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arxiv:2410.19971
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when implementing a non - continuous controller for a cyber - physical system, it may happen that the evolution of the closed - loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. this may lead to some unwanted chattering effects than may damage the system. this behavior is difficult to observe even in simulation. in this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. we show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set - membership uncertainties. an application to the verification of the controller of a child swing is considered to illustrate the principle of the approach.
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arxiv:2101.05418
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evasion attacks against machine learning models often succeed via iterative probing of a fixed target model, whereby an attack that succeeds once will succeed repeatedly. one promising approach to counter this threat is making a model a moving target against adversarial inputs. to this end, we introduce morphence - 2. 0, a scalable moving target defense ( mtd ) powered by out - of - distribution ( ood ) detection to defend against adversarial examples. by regularly moving the decision function of a model, morphence - 2. 0 makes it significantly challenging for repeated or correlated attacks to succeed. morphence - 2. 0 deploys a pool of models generated from a base model in a manner that introduces sufficient randomness when it responds to prediction queries. via ood detection, morphence - 2. 0 is equipped with a scheduling approach that assigns adversarial examples to robust decision functions and benign samples to an undefended accurate models. to ensure repeated or correlated attacks fail, the deployed pool of models automatically expires after a query budget is reached and the model pool is seamlessly replaced by a new model pool generated in advance. we evaluate morphence - 2. 0 on two benchmark image classification datasets ( mnist and cifar10 ) against 4 reference attacks ( 3 white - box and 1 black - box ). morphence - 2. 0 consistently outperforms prior defenses while preserving accuracy on clean data and reducing attack transferability. we also show that, when powered by ood detection, morphence - 2. 0 is able to precisely make an input - based movement of the model ' s decision function that leads to higher prediction accuracy on both adversarial and benign queries.
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arxiv:2206.07321
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large language models ( llms ) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. exploiting the heterogeneous capabilities of edge llms is crucial for diverse emerging applications, as it enables greater cost - effectiveness and reduced latency. in this work, we introduce \ textit { mixture - of - edge - experts ( moe $ ^ 2 $ ) }, a novel collaborative inference framework for edge llms. we formulate the joint gating and expert selection problem to optimize inference performance under energy and latency constraints. unlike conventional moe problems, llm expert selection is significantly more challenging due to the combinatorial nature and the heterogeneity of edge llms across various attributes. to this end, we propose a two - level expert selection mechanism through which we uncover an optimality - preserving property of gating parameters across expert selections. this property enables the decomposition of the training and selection processes, significantly reducing complexity. furthermore, we leverage the objective ' s monotonicity and design a discrete monotonic optimization algorithm for optimal expert selection. we implement edge servers with nvidia jetson agx orins and nvidia rtx 4090 gpus, and perform extensive experiments. our results validate that performance improvements of various llm models and show that our moe $ ^ 2 $ method can achieve optimal trade - offs among different delay and energy budgets, and outperforms baselines under various system resource constraints.
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arxiv:2501.09410
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we discuss the photoproduction processes of light vector mesons ( $ \ rho $, $ \ omega $, and $ \ phi $ ) from the nucleon near threshold. we first develop a simple model based on meson exchanges which is modified by the nucleon pole terms. we then extend this model to study other physically interesting topics. as examples, we discuss the missing nucleon resonances problem in $ \ omega $ photoproduction and the direct $ \ phi nn $ coupling constant in $ \ phi $ photoproduction. the calculated cross sections are compared with the recent experimental data. various spin observables are discussed, which may be measured at current photon / electron facilities such as tjnaf and spring - 8 of rcnp. precise measurements of such quantities would provide very useful information to understand the production mechanism.
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arxiv:nucl-th/0301011
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a virtual private network ( vpn ) helps to mitigate security and privacy risks of data transmitting on unsecured network such as public wi - fi. however, despite awareness of public wi - fi risks becoming increasingly common, the use of vpn when using public wi - fi is low. to increase adoption, understanding factors driving user decision to adopt a vpn app is an important first step. this study is the first to achieve this objective using discrete choice experiments ( dces ) to elicit individual preferences of specific attributes of a vpn app. the experiments were run in the united kingdom ( uk ) and japan ( jp ). we first interviewed participants ( 15 uk, 17 jp ) to identify common attributes of a vpn app which they considered important. the results were used to design and run a dce in each country. participants ( 149 uk, 94 jp ) were shown a series of two hypothetical vpn apps, varying in features, and were asked to choose one which they preferred. customer review rating, followed by price of a vpn app, significantly affected the decision to choose which vpn app to download and install. a change from a rating of 3 to 4 - 5 stars increased the probability of choosing an app by 33 % in the uk and 14 % in japan. unsurprisingly, price was a deterrent. recommendations by friends, source of product reviews, and the presence of in - app ads also played a role but to a lesser extent. to actually use a vpn app, participants considered internet speed, connection stability, battery level on mobile devices, and the presence of in - app ads as key drivers. participants in the uk and in japan prioritized these attributes differently, suggesting possible influences from cultural differences.
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arxiv:2008.06813
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thermal fluctuations are important for amphiphilic bilayer membranes since typical bending stiffnesses can be a few $ k _ b t $. the rod - like constituent molecules are generically tilted with respect to the local normal for packing reasons. we study the effects of fluctuations on membranes with nematic order, a simplified idealization with the same novel features as realistic tilt order. we find that nematic membranes lie in the same universality class as hexatic membranes, { \ it i. e. } the couplings that distinguish nematic from hexatic order are marginally irrelevant. our calculation also illustrates the advantages of conformal gauge, which brings great conceptual and technical simplifications compared to the more popular monge gauge.
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arxiv:cond-mat/9504073
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micro - expressions are typically regarded as unconscious manifestations of a person ' s genuine emotions. however, their short duration and subtle signals pose significant challenges for downstream recognition. we propose a multi - task learning framework named the adaptive motion magnification and sparse mamba ( ammsm ) to address this. this framework aims to enhance the accurate capture of micro - expressions through self - supervised subtle motion magnification, while the sparse spatial selection mamba architecture combines sparse activation with the advanced visual mamba model to model key motion regions and their valuable representations more effectively. additionally, we employ evolutionary search to optimize the magnification factor and the sparsity ratios of spatial selection, followed by fine - tuning to improve performance further. extensive experiments on two standard datasets demonstrate that the proposed ammsm achieves state - of - the - art ( sota ) accuracy and robustness.
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arxiv:2503.24057
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in this article i explain in detail a method for making small amounts of liquid oxygen in the classroom if there is no access to a cylinder of compressed oxygen gas. i also discuss two methods for identifying the fact that it is liquid oxygen as opposed to liquid nitrogen.
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arxiv:1010.5774
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the topologically nontrivial and chemically functional distorted octahedral ( t ' ) transition metal dichalcogenides ( tmdcs ) are a type of layered semimetal that has attracted significant recent attention. however, the properties of monolayer ( 1l ) t ' - tmdc, a fundamental unit of the system, is still largely unknown due to rapid sample degradation in air. here we report that well - protected 1l cvd t ' - mote2 exhibits sharp and robust intrinsic raman bands, with intensities about one order of magnitude stronger than those from bulk t ' - mote2. the high - quality samples enabled us to reveal the set of all nine even - parity zone - center optical phonons, providing reliable fingerprints for the previously elusive crystal. by performing light polarization and crystal orientation resolved scattering analysis, we can effectively distinguish the intrinsic modes from te - metalloid - like modes a ( ~ 122 cm - 1 ) and b ( ~ 141 cm - 1 ) which are related to the sample degradation. our studies offer a powerful non - destructive method for assessing sample quality and for monitoring sample degradation in situ, representing a solid advance in understanding the fundamental properties of 1l - t ' - tmdcs.
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arxiv:1612.04027
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this work describes the investigation of neuromorphic computing - based spiking neural network ( snn ) models used to filter data from sensor electronics in high energy physics experiments conducted at the high luminosity large hadron collider. we present our approach for developing a compact neuromorphic model that filters out the sensor data based on the particle ' s transverse momentum with the goal of reducing the amount of data being sent to the downstream electronics. the incoming charge waveforms are converted to streams of binary - valued events, which are then processed by the snn. we present our insights on the various system design choices - from data encoding to optimal hyperparameters of the training algorithm - for an accurate and compact snn optimized for hardware deployment. our results show that an snn trained with an evolutionary algorithm and an optimized set of hyperparameters obtains a signal efficiency of about 91 % with nearly half as many parameters as a deep neural network.
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arxiv:2307.11242
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infrared and nebular lines provide some of our best probes of the physics regulating the properties of the interstellar medium ( ism ) at high - redshift. however, interpreting the physical conditions of high - redshift galaxies directly from emission lines remains complicated due to inhomogeneities in temperature, density, metallicity, ionisation parameter, and spectral hardness. we present a new suite of cosmological, radiation - hydrodynamics simulations, each centred on a massive lyman - break galaxy that resolves such properties in an inhomogeneous ism. many of the simulated systems exhibit transient but well defined gaseous disks that appear as velocity gradients in [ cii ] ~ 158. 6 $ \ mu $ m emission. spatial and spectral offsets between [ cii ] ~ 158. 6 $ \ mu $ m and [ oiii ] ~ 88. 33 $ \ mu $ m are common, but not ubiquitous, as each line probes a different phase of the ism. these systems fall on the local [ cii ] - sfr relation, consistent with newer observations that question previously observed [ cii ] ~ 158. 6 $ \ mu $ m deficits. our galaxies are consistent with the nebular line properties of observed $ z \ sim2 - 3 $ galaxies and reproduce offsets on the bpt and mass - excitation diagrams compared to local galaxies due to higher star formation rate ( sfr ), excitation, and specific - sfr, as well as harder spectra from young, metal - poor binaries. we predict that local calibrations between h $ \ alpha $ and [ oii ] ~ 3727 $ \ aa $ luminosity and galaxy sfr apply up to $ z > 10 $, as do the local relations between certain strong line diagnostics ( r23 and [ oiii ] ~ 5007 $ \ aa $ / h $ \ beta $ ) and galaxy metallicity. our new simulations are well suited to interpret the observations of line emission from current ( alma and hst ) and upcoming facilities ( jwst and ngvla ).
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arxiv:1901.01272
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viscoelastic flows through microscale porous arrays exhibit complex path - selection and switching phenomena. however, understanding this process is limited by a lack of studies linking between a single object and large arrays. here, we report experiments on viscoelastic flow past side - by - side microcylinders with variable intercylinder gap. with increasing flow rate, a sequence of two imperfect symmetry - breaking bifurcations forces selection of either one or two of the three possible flow paths around the cylinders. tuning the gap length through the value where the first bifurcation becomes perfect reveals regions of bi and tristability in a dimensionless flow rate - gap length ` phase ' diagram.
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arxiv:2010.14749
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asymmetric current sheets are likely to be prevalent in both astrophysical and laboratory plasmas with complex three dimensional ( 3d ) magnetic topologies. this work presents kinematic analytical models for spine and fan reconnection at a symmetric 3d null with asymmetric current sheets. asymmetric fan reconnection is characterized by an asymmetric reconnection of flux past each spine line and a bulk flow of plasma across the null point. in contrast, asymmetric spine reconnection is inherently equal and opposite in how flux is reconnected across the fan plane. the higher modes of spine reconnection also include localized wedges of vortical flux transport in each half of the fan. in this situation, two definitions for reconnection rate become appropriate : a local reconnection rate quantifying how much flux is genuinely reconnected across the fan plane and a global rate associated with the net flux driven across each semi - plane. through a scaling analysis it is shown that when the ohmic dissipation in the layer is assumed to be constant, the increase in the local rate bleeds from the global rate as the sheet deformation is increased. both models suggest that asymmetry in the current sheet dimensions will have a profound effect on the reconnection rate and manner of flux transport in reconnection involving 3d nulls.
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arxiv:1306.6476
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if f ( x ) = e ^ g ( x ), where f ( x ) = \ sum f ( n ) x ^ n and $ g ( x ) = \ sum g ( n ) x ^ n, with 0 \ le g ( n ) = o ( n ^ { theta n } / n! ), theta in ( 0, 1 ), and gcd ( n : g ( n ) > 0 ) = 1, then f ( n ) = o ( f ( n - 1 ) ). this gives an answer to compton ' s request in question 8. 3 for an ` ` easily verifiable sufficient condition ' ' to show that an adequate class of structures has a labelled first - order 0 - 1 law, namely it suffices to show that the labelled component count function is o ( n ^ { theta n } ) for some theta in ( 0, 1 ). it also provides the means to recursively construct an adequate class of structures with a labelled 0 - 1 law but not an unlabelled 0 - 1 law, answering compton ' s question 8. 4.
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arxiv:math/0608735
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we find all pairs of real analytic functions $ f $ and $ g $ in $ \ bbr ^ n $ such that $ | \ nabla f | = | \ nabla g | $ and $ ( \ nabla f ) ( \ nabla g ) = 0 $.
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arxiv:math/0605745
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we investigate local and global weighted heights a - la weil for weighted projective spaces via cartier and weil divisors and extend the definition of weighted heights on weighted projective spaces from arxiv : 1902. 06563 to weighted varieties and closed subvarieties. we prove that any line bundle on a weighted variety admits a locally bounded weighted $ m $ - metric. using this fact, we define local and global weighted heights for weighted varieties in weighted projective spaces and their closed subschemes and show their fundamental properties.
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arxiv:2204.01624
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the paper focuses on the numerical stability and accuracy of implicit time - domain integration ( tdi ) methods when applied for the solution of a power system model impacted by time delays. such a model is generally formulated as a set of delay differential algebraic equations ( ddaes ) in non index - 1 hessenberg form. in particular, the paper shows that numerically stable ordinary differential equation ( ode ) methods, such as the trapezoidal and the theta method, can become unstable when applied to a power system that includes a significant number of delayed variables. numerical stability is discussed through a scalar test delay differential equation, as well as through a matrix pencil approach that accounts for the ddaes of any given dynamic power system model. simulation results are presented in a case study based on the ieee 39 - bus system.
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arxiv:2409.04399
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we propose models of twisted multilayer graphene that exhibit exactly flat bloch bands with arbitrary chern numbers and ideal band geometries. the models are constructed by twisting two sheets of bernal - stacked multiple graphene layers with only inter - sublattice couplings. analytically we show that flatband wavefunctions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. we also explicitly demonstrate a generic " wavefunction exchange " mechanism that generates the high chern numbers of these ideal flatbands. the ideal band geometries and high chern numbers of the flatbands imply the possibility of hosting exotic fractional chern insulators which do not have analogues in continuum landau levels. we numerically verify that these exotic fractional chern insulators are model states for short - range interactions, characterized by exact ground - state degeneracies at zero energy and infinite particle - cut entanglement gaps.
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arxiv:2109.10325
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quartic gravity theory is considered with the einstein - hilbert lagrangean $ r + ar ^ { 2 } + br _ { \ mu \ nu } r ^ { \ mu \ nu }, $ $ r _ { \ mu \ nu } $ being ricci \ ' s tensor and r the curvature scalar. the parameters $ a $ and $ b $ are taken of order 1 km $ ^ { 2 }. $ arguments are given which suggest that the effective theory so obtained may be a plausible approximation of a viable theory. a numerical integration is performed of the field equations for a free neutron gas. as in the standard oppenheimer - volkoff calculation the star mass increases with increasing central density until about 1 solar mass and then decreases. however a dramatic difference exists in the behaviour of the baryon number, which increases monotonically. the calculation suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.
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arxiv:1104.2140
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the implementation of an fe buffer layer is a promising way to obtain epitaxial growth of co - doped bafe2as2 ( ba - 122 ). however, the crystalline quality and the superconducting properties of co - doped ba - 122 are influenced by the fe buffer layer thickness, dfe. the well - textured growth of the fe / ba - 122 bilayer with dfe = 15 nm results in a high jc of 0. 45 macm $ ^ { - 2 } $ at 12 k in self - field, whereas a low jc value of 61000 acm $ ^ { - 2 } $ is recorded for the bilayer with dfe = 4 nm at the corresponding reduced temperature due to the presence of grain boundaries.
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arxiv:1011.0035
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let $ k, m, n $ be positive integers with $ k \ geq 2 $. a $ k $ - multiset of $ [ n ] _ m $ is a collection of $ k $ integers from the set $ \ { 1, 2, \ ldots, n \ } $ in which the integers can appear more than once but at most $ m $ times. a family of such $ k $ - multisets is called an intersecting family if every pair of $ k $ - multisets from the family have non - empty intersection. a finite sequence of real numbers $ \ { a _ 1, a _ 2, \ ldots, a _ n \ } $ is said to be unimodal if there is some $ k \ in \ { 1, 2, \ ldots, n \ } $, such that $ a _ 1 \ leq a _ 2 \ leq \ ldots \ leq a _ { k - 1 } \ leq a _ k \ geq a _ { k + 1 } \ geq \ ldots \ geq a _ n $. given $ m, n, k $, denote $ c _ { k, l } $ as the coefficient of $ x ^ k $ in the generating function $ ( \ sum _ { i = 1 } ^ mx ^ i ) ^ l $, where $ 1 \ leq l \ leq n $. in this paper, we first show that the sequence of $ \ { c _ { k, 1 }, c _ { k, 2 }, \ ldots, c _ { k, n } \ } $ is unimodal. then we use this as a tool to prove that the intersecting family in which every $ k $ - multiset contains a fixed element attains the maximum cardinality for $ n \ geq k + \ lceil k / m \ rceil $. in the special case when $ m = 1 $ and $ m = \ infty $, our result gives rise to the famous erd \ h { o } s - ko - rado theorem and an unbounded multiset version for this problem given by meagher and purdy, respectively. the main result in this paper can be viewed as a bounded multiset version of the erd \ h { o } s - ko - rado theorem.
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arxiv:2303.06647
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we study the effect of synthesis temperature on the phase formation in nano ( n ) - sic added bulk mgb2 superconductor. in particular we study : lattice parameters, amount of carbon ( c ) substitution, microstructure, critical temperature ( tc ), irreversibility field ( hirr ), critical current density ( jc ), upper critical field ( hc2 ) and flux pinning. samples of mgb2 + ( n - sic ) x with x = 0. 0, 0. 05 & 0. 10 were prepared at four different synthesis temperatures i. e. 850, 800, 750, and 700oc with the same heating rate as 10oc / min. we found 750oc as the optimal synthesis temperature for n - sic doping in bulk mgb2 in order to get the best superconducting performance in terms of jc, hc2 and hirr. carbon ( c ) substitution enhances the hc2 while the low temperature synthesis is responsible for the improvement in jc due to the smaller grain size, defects and nano - inclusion induced by c incorporation into mgb2 matrix, which is corroborated by elaborative hrtem ( high - resolution transmission electron microscopy ) results. we optimized the the tc ( r = 0 ) of above 15k for the studied n - sic doped and 750 0c synthesized mgb2 under 140 koe field, which is one of the highest values yet obtained for variously processed and nano - particle added mgb2 in literature to our knowledge.
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arxiv:1101.5206
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in the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. however, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. this direction is tied to the conventions used in the quantization procedures. the different possible causal directions have related physics - in this sense they are covariant under time - reversal. however, only one causal direction emerges for a given set of conventions. this causal arrow tells us the direction that scattering reactions proceed. the time direction of scattering in turn tells us the time direction for which entropy increases - the so - called arrow of thermodynamics. this connection is overlooked in most discussions of the arrow of time.
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arxiv:2003.09047
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k - means is a widely used clustering algorithm, but for $ k $ clusters and a dataset size of $ n $, each iteration of lloyd ' s algorithm costs $ o ( kn ) $ time. although there are existing techniques to accelerate single lloyd iterations, none of these are tailored to the case of large $ k $, which is increasingly common as dataset sizes grow. we propose a dual - tree algorithm that gives the exact same results as standard $ k $ - means ; when using cover trees, we use adaptive analysis techniques to, under some assumptions, bound the single - iteration runtime of the algorithm as $ o ( n + k log k ) $. to our knowledge these are the first sub - $ o ( kn ) $ bounds for exact lloyd iterations. we then show that this theoretically favorable algorithm performs competitively in practice, especially for large $ n $ and $ k $ in low dimensions. further, the algorithm is tree - independent, so any type of tree may be used.
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arxiv:1601.03754
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we report a quantum magnetotransport signature of a change in fermi surface topology in the rashba semiconductor bitei with systematic tuning of the fermi level $ e _ f $. beyond the quantum limit, we observe a marked increase / decrease in electrical resistivity when $ e _ f $ is above / below the dirac node that we show originates from the fermi surface topology. this effect represents a measurement of the electron distribution on the low - index ( $ n = 0, - 1 $ ) landau levels and is uniquely enabled by the finite bulk $ k _ z $ dispersion along the $ c $ - axis and strong rashba spin - orbit coupling strength of the system. the dirac node is independently identified by shubnikov - de haas oscillations as a vanishing fermi surface cross section at $ k _ z = 0 $. additionally we find that the violation of kohler ' s rule allows a distinct insight into the temperature evolution of the observed quantum magnetoresistance effects.
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arxiv:1501.00413
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in existing linear response theories for adiabatically driven cyclic heat engines, onsager symmetry is identified only phenomenologically, and a relation between global and local onsager coefficients, defined over one cycle and at any instant of a cycle, respectively, is not derived. to address this limitation, we develop a linear response theory for the speed of adiabatically changing parameters and temperature differences in generic gaussian heat engines obeying fokker - - planck dynamics. we establish a hierarchical relationship between the global linear response relations, defined over one cycle of the heat engines, and the local ones, defined at any instant of the cycle. this yields a detailed expression for the global onsager coefficients in terms of the local onsager coefficients. moreover, we derive an efficiency bound, which is tighter than the carnot bound, for adiabatically driven linear irreversible heat engines based on the detailed global onsager coefficients. finally, we demonstrate the application of the theory using the simplest stochastic brownian heat engine model.
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arxiv:2103.03397
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we consider a two - way half - duplex relaying system where multiple pairs of single antenna users exchange information assisted by a multi - antenna relay. taking into account the practical constraint of imperfect channel estimation, we study the achievable sum spectral efficiency of the amplify - and - forward ( af ) and decode - and - forward ( df ) protocols, assuming that the relay employs simple maximum ratio processing. we derive an exact closed - form expression for the sum spectral efficiency of the af protocol and a large - scale approximation for the sum spectral efficiency of the df protocol when the number of relay antennas, $ m $, becomes sufficiently large. in addition, we study how the transmit power scales with $ m $ to maintain a desired quality - of - service. in particular, our results show that by using a large number of relay antennas, the transmit powers of the user, relay, and pilot symbol can be scaled down proportionally to $ 1 / m ^ \ alpha $, $ 1 / m ^ \ beta $, and $ 1 / m ^ \ gamma $ for certain $ \ alpha $, $ \ beta $, and $ \ gamma $, respectively. this elegant power scaling law reveals a fundamental tradeoff between the transmit powers of the user / relay and pilot symbol. finally, capitalizing on the new expressions for the sum spectral efficiency, novel power allocation schemes are designed to further improve the sum spectral efficiency.
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arxiv:1607.01598
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federated learning ( fl ) is an emerging practical framework for effective and scalable machine learning among multiple participants, such as end users, organizations and companies. however, most existing fl or distributed learning frameworks have not well addressed two important issues together : collaborative fairness and adversarial robustness ( e. g. free - riders and malicious participants ). in conventional fl, all participants receive the global model ( equal rewards ), which might be unfair to the high - contributing participants. furthermore, due to the lack of a safeguard mechanism, free - riders or malicious adversaries could game the system to access the global model for free or to sabotage it. in this paper, we propose a novel robust and fair federated learning ( rffl ) framework to achieve collaborative fairness and adversarial robustness simultaneously via a reputation mechanism. rffl maintains a reputation for each participant by examining their contributions via their uploaded gradients ( using vector similarity ) and thus identifies non - contributing or malicious participants to be removed. our approach differentiates itself by not requiring any auxiliary / validation dataset. extensive experiments on benchmark datasets show that rffl can achieve high fairness and is very robust to different types of adversaries while achieving competitive predictive accuracy.
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arxiv:2011.10464
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this paper presents a cross - lingual sentiment analysis of news articles using zero - shot and few - shot learning. the study aims to classify the croatian news articles with positive, negative, and neutral sentiments using the slovene dataset. the system is based on a trilingual bert - based model trained in three languages : english, slovene, croatian. the paper analyses different setups using datasets in two languages and proposes a simple multi - task model to perform sentiment classification. the evaluation is performed using the few - shot and zero - shot scenarios in single - task and multi - task experiments for croatian and slovene.
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arxiv:2212.07160
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3 - 540 - 34794 - 1 hartshorne, robin ( 1977 ), algebraic geometry, springer - verlag, isbn 978 - 0 - 387 - 90244 - 9, mr 0463157, oclc 13348052 iversen, birger ( 1986 ), cohomology of sheaves, universitext, springer - verlag, isbn 978 - 3 - 540 - 16389 - 3, mr 0842190 joyal, andre ; street, ross ( 1991 ), " an introduction to tannaka duality and quantum groups " ( pdf ), category theory, lecture notes in mathematics, vol. 1488, springer - verlag, pp. 413 β 492, doi : 10. 1007 / bfb0084235, isbn 978 - 3 - 540 - 46435 - 8, mr 1173027 lam, tsit - yuen ( 1999 ), lectures on modules and rings, graduate texts in mathematics, vol. 189, springer - verlag, isbn 978 - 0 - 387 - 98428 - 5, mr 1653294 lang, serge ( 2002 ), algebra, graduate texts in mathematics, vol. 211, springer - verlag, isbn 978 - 0 - 387 - 95385 - 4, mr 1878556 loomis, lynn h. ( 1953 ), an introduction to abstract harmonic analysis, d. van nostrand, pp. x + 190, hdl : 2027 / uc1. b4250788 mac lane, saunders ( 1998 ), categories for the working mathematician ( 2nd ed. ), springer - verlag, isbn 978 - 0 - 387 - 98403 - 2 mazur, barry ( 1973 ), " notes on etale cohomology of number fields ", annales scientifiques de l ' ecole normale superieure, serie 4, 6 ( 4 ) : 521 β 552, doi : 10. 24033 / asens. 1257, issn 0012 - 9593, mr 0344254 milne, james s. ( 1980 ), etale cohomology, princeton university press, isbn 978 - 0 - 691 - 08238 - 7 milne, james s. ( 2006 ), arithmetic duality theorems ( 2nd ed. ), charleston, south carolina : booksurge, llc, isbn 978 - 1 - 4196 - 4274 - 6, mr 2261462 negrepontis,
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https://en.wikipedia.org/wiki/Duality_(mathematics)
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years of post - graduate work experience. a technician can be certified as a registered engineering technician ( tech ) after completion of a two - year ond and two - years of post - graduate work experience. a craftsman can become a registered engineering craftsman after passing the technical exam of the west african examinations council or national business and technical examinations board or a trade test grade 1 from the federal ministry of labour. in addition, two years of work experience are required. = = = south africa = = = engineering training in south africa is typically provided by the universities, universities of technology and colleges for technical and vocational education and training ( previously further education and training ). the qualifications provided by these institutions must have an engineering council of south africa ( ecsa ) accreditation for the qualification for graduates and diplomats of these institutions to be registered as candidate certificated engineers, candidate engineers, candidate engineering technologists and candidate engineering technicians. there are many benefits to these attributes. the academic training performed by the universities is typically in the form of a four - year bsc ( eng ), bing or beng degree. for the degree to be accredited, the course material must conform to the ecsa graduate attributes ( ga ). professional engineers ( pr eng ) are persons that are accredited by ecsa as engineering professionals. legally, a professional engineer ' s sign off is required for any major project to be implemented, in order to ensure the safety and standards of the project. professional engineering technologists ( pr tech eng ) and professional engineering technicians ( pr techni eng ) are other members of the engineering team. professional certificated engineers ( pr cert eng ) are people who hold one of seven government certificates of competency and who have been registered by ecsa as engineering professionals. the categories of professionals are differentiated by the degree of complexity of work carried out, where professional engineers are expected to solve complex engineering problems, professional engineering technologists and professional certificated engineers, broadly defined engineering problems and professional engineering technicians, well - defined engineering problems. = = = tanzania = = = engineering training in tanzania is typically provided by various universities and technical institutions in the country. graduate engineers are registered by the engineers registration board ( erb ) after undergoing three years of practical training. a candidate stands to qualify as a professional engineer, p. eng., if they are a holder of a minimum four years post - secondary engineering education and a minimum of three years of postgraduate work experience. engineers registration board is a statutory body established through an act of the tanzanian parliament in 1968. minor revision was done in 1997
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https://en.wikipedia.org/wiki/Engineering_education
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constraint analysis of the three - dimensional massive gravity, the so - called new massive gravity, is studied in the palatini formalism. we show that amongst 6 components of the metric, 2 are dynamical, which is compatible with the existence of one vector massive graviton in the linearized theory ( fierz - pauli theory ).
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arxiv:1010.2887
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two particle azimuthal correlation functions are presented for charged hadrons produced in au + au collisions at rhic sqrt ( s _ nn ) = 130 gev. the measurements permit determination of elliptic flow without event - by - event estimation of the reaction plane. the extracted elliptic flow values v _ 2 show significant sensitivity to both the collision centrality and the transverse momenta of emitted hadrons, suggesting rapid thermalization and relatively strong velocity fields. when scaled by the eccentricity of the collision zone, epsilon, the scaled elliptic flow shows little or no dependence on centrality for charged hadrons with relatively low p _ t. a breakdown of this epsilon scaling is observed for charged hadrons with p _ t > 1. 0 gev / c for the most central collisions.
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arxiv:nucl-ex/0204005
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black holes, first found as solutions of einstein ' s general relativity, are important in astrophysics, since they result from the gravitational collapse of a massive star or a cluster of stars, and in physics since they reveal properties of the fundamental physics, such as thermodynamic and quantum properties of gravitation. in order to better understand the black hole physics we need exact solutions that describe one or more black holes. in this thesis we study exact solutions in three, four and higher dimensional spacetimes. the study in 3 - dimensions is important due to the simplification of the problem, while the discussion in higher dimensions is essential due to the fact that many theories indicate that extra dimensions exist in our universe. in this thesis, in any of the dimensions mentioned above, we study exact solutions with a single black hole and exact solutions that describe a pair of uniformly accelerated black holes ( c - metric ), with the acceleration source being well identified. this later solutions are then used to study in detail the quantum process of black hole pair creation in an external field. we also compute the gravitational radiation released during this pair creation process. keywords : exact black hole solutions ; pair of accelerated black holes, c - metric, ernst solution ; pair creation of black holes ; gravitational radiation ; d - dimensional spacetimes ; cosmological constant backgrounds.
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arxiv:hep-th/0410294
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achieving versatile robot locomotion requires motor skills which can adapt to previously unseen situations. we propose a multi - expert learning architecture ( mela ) that learns to generate adaptive skills from a group of representative expert skills. during training, mela is first initialised by a distinct set of pre - trained experts, each in a separate deep neural network ( dnn ). then by learning the combination of these dnns using a gating neural network ( gnn ), mela can acquire more specialised experts and transitional skills across various locomotion modes. during runtime, mela constantly blends multiple dnns and dynamically synthesises a new dnn to produce adaptive behaviours in response to changing situations. this approach leverages the advantages of trained expert skills and the fast online synthesis of adaptive policies to generate responsive motor skills during the changing tasks. using a unified mela framework, we demonstrated successful multi - skill locomotion on a real quadruped robot that performed coherent trotting, steering, and fall recovery autonomously, and showed the merit of multi - expert learning generating behaviours which can adapt to unseen scenarios.
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arxiv:2012.05810
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over the last years the tevatron run - ii has extended several limits on higgs boson masses and coupling which were pioneered during the lep accelerator operation between 1989 and 2000. higgs boson searches will also be at the forefront of research at the lhc. this review concisely discusses the experimental constraints set by the cdf and d0 collaborations in summer 2010 at the beginning of the lhc era. model - independent and model - dependent limits on higgs boson masses and couplings have been set and interpretations are discussed both in the standard model and in extended models. recently, the tevatron has extended the excluded sm higgs boson mass range ( 158 - 175 gev ) beyond the lep limit at 95 % cl. the experimental sensitivities are estimated for the completion of the tevatron programme.
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arxiv:1011.0681
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( abridged ) we studied the energy and frequency dependence of the fourier time lags and intrinsic coherence of the khz qpos in the ns lmxbs 4u 1608 - 52 and 4u 1636 - 53 using rxte data. in both sources we confirmed energy - dependent soft lags of 10 - 100 \ mu s for the lower khz qpo. we also found that the time lags of the upper khz qpo are independent of energy and inconsistent with the soft lags of the lower khz qpo. the intrinsic coherence of the lower khz qpo remains constant at 0. 6 from 5 to 12 kev, and then drops to zero, while for the upper khz qpo the intrinsic coherence is consistent with zero across the full energy range. the intrinsic coherence of the upper khz qpo is consistent with zero over the full frequency range of the qpo, except in 4u 1636 - 53 at ~ 780 hz where it increases to 0. 13. in 4u 1636 - 53, for the lower khz qpo the 4 - 12 kev photons lag the 12 - 20 kev ones by 25 \ mu s in the qpo frequency range 500 - 850 hz, with the lags decreasing to 15 \ mu s at higher frequencies. in 4u 1608 - 52 the soft lags of the lower khz qpo remain constant at 40 \ mu s. in 4u 1636 - 53, for the upper khz qpo the 12 - 20 kev photons lag the 4 - 12 kev ones by 11 + / - 3 \ mu s, independent of qpo frequency ; we found consistent results for the time lags of the upper khz qpo in 4u 1608 - 52. the intrinsic coherence of the lower khz qpo increases from ~ 0 - 0. 4 at 600 hz to 1 and 0. 6 at 800 hz in 4u 1636 - 53 and 4u 1608 - 52, respectively. in 4u 1636 - 53 it decreases to 0. 5 at 920 hz, while in 4u 1608 - 52 we do not have data above 800 hz. we discuss our results in the context of scenarios in which the soft lags are either due to reflection off the accretion disc or up - / down - scattering in a hot medium close to the neutron star. we finally explore the connection between, on one hand the time lags and the intrinsic coherence of the
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arxiv:1302.6464
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the voluntary donation of private health information for altruistic purposes, such as supporting research advancements, is a common practice. however, concerns about data misuse and leakage may deter people from donating their information. privacy enhancement technologies ( pets ) aim to alleviate these concerns and in turn allow for safe and private data sharing. this study conducts a vignette survey ( n = 494 ) with participants recruited from prolific to examine the willingness of us - based people to donate medical data for developing new treatments under four general guarantees offered across pets : data expiration, anonymization, purpose restriction, and access control. the study explores two mechanisms for verifying these guarantees : self - auditing and expert auditing, and controls for the impact of confounds including demographics and two types of data collectors : for - profit and non - profit institutions. our findings reveal that respondents hold such high expectations of privacy from non - profit entities a priori that explicitly outlining privacy protections has little impact on their overall perceptions. in contrast, offering privacy guarantees elevates respondents ' expectations of privacy for for - profit entities, bringing them nearly in line with those for non - profit organizations. further, while the technical community has suggested audits as a mechanism to increase trust in pet guarantees, we observe limited effect from transparency about such audits. we emphasize the risks associated with these findings and underscore the critical need for future interdisciplinary research efforts to bridge the gap between the technical community ' s and end - users ' perceptions regarding the effectiveness of auditing pets.
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arxiv:2407.03451
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it is widely known that spin - locking noise - spectroscopy is a powerful technique for the characterization of low - frequency noise mechanisms in superconducting qubits. here we show that the relaxation rate of the driven spin - locking state of a qubit can be significantly affected by the presence of an off - resonant high - frequency two - level - system defect. thus, both low - and high - frequency defects should be taken into account in the interpretation of spin - locking measurements and other types of driven - state noise - spectroscopy.
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arxiv:2006.05820
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utilizing well - trained representations in transfer learning often results in superior performance and faster convergence compared to training from scratch. however, even if such good representations are transferred, a model can easily overfit the limited training dataset and lose the valuable properties of the transferred representations. this phenomenon is more severe in vit due to its low inductive bias. through experimental analysis using attention maps in vit, we observe that the rich representations deteriorate when trained on a small dataset. motivated by this finding, we propose a novel and simple regularization method for vit called guided transfer of spatial attention ( gta ). our proposed method regularizes the self - attention maps between the source and target models. a target model can fully exploit the knowledge related to object localization properties through this explicit regularization. our experimental results show that the proposed gta consistently improves the accuracy across five benchmark datasets especially when the number of training data is small.
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arxiv:2401.02656
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in this paper we investigate fiber - wise linear complex banach sub - poisson structures defined canonically by the structure of a w * - algebra m. in particular we show that these structures are arranged in the short exact sequence of complex banach sub - poisson vb - groupoids with the groupoid of partially invertible elements of m as the side groupoid.
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arxiv:1703.01134
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an integral transformation relating two inequalities in khabibullin ' s conjecture is found. another proof of this conjecture for some special values of its numeric parameters is suggested.
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arxiv:1008.0376
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we extend the theory of holomorphic induction of unitary representations of a possibly infinite - dimensional lie group $ g $ beyond the setting where the representation being induced is required to be norm - continuous. we allow the group $ g $ to be a connected regular bch ( baker - campbell - hausdorff ) fr \ ' echet - lie group. given a smooth $ \ mathbb { r } $ - action $ \ alpha $ on $ g $, we proceed to show that the corresponding class of so - called positive energy representations is intimately related with holomorphic induction. assuming that $ g $ is regular, we in particular show that if $ \ rho $ is a unitary ground - state representation of $ g \ rtimes _ \ alpha \ mathbb { r } $ for which the energy - zero subspace $ \ mathcal { h } _ \ rho ( 0 ) $ admits a dense set of $ g $ - analytic vectors, then $ \ rho \ big | _ g $ is holomorphically induced from the representation of the connected subgroup $ h : = ( g ^ \ alpha ) _ 0 $ of $ \ alpha $ - fixed points on $ \ mathcal { h } _ \ rho ( 0 ) $. as a consequence, we obtain an isomorphism $ \ mathcal { b } ( \ mathcal { h } _ \ rho ) ^ g \ cong \ mathcal { b } ( \ mathcal { h } _ \ rho ( 0 ) ) ^ h $ between the corresponding commutants. we also find that any two such ground - state representations are necessarily unitary equivalent if their energy - zero subspaces are unitarily equivalent as $ h $ - representations. these results were previously only available under the assumption of norm - continuity of the $ h $ - representation on $ \ mathcal { h } _ \ rho ( 0 ) $.
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arxiv:2301.05129
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the assessment of co - movement among metals is crucial to better understand the behaviors of the metal prices and the interactions with others that affect the changes in prices. in this study, both wavelet analysis and varma ( vector autoregressive moving average ) models are utilized. first, multiple wavelet coherence ( mwc ), where wavelet analysis is needed, is utilized to determine dynamic correlation time interval and scales. varma is then used for forecasting which results in reduced errors. the daily prices of steel, aluminium, copper and zinc between 10. 05. 2010 and 29. 05. 2014 are analyzed via wavelet analysis to highlight the interactions. results uncover interesting dynamics between mentioned metals in the time - frequency space. varma ( 1, 1 ) model forecasting is carried out considering the daily prices between 14. 11. 2011 and 16. 11. 2012 where the interactions are quite high and prediction errors are found quite limited with respect to arma ( 1. 1 ). it is shown that dynamic co - movement detection via four variables wavelet coherency analysis in the determination of varma time interval enables to improve forecasting power of arma by decreasing forecasting errors.
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arxiv:1602.01960
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in the context of a left - right extension of the standard model of quarks and leptons with the addition of a gauged $ u ( 1 ) _ d $ dark symmetry, it is shown how the electron may obtain a radiative mass in one loop and two dirac neutrinos obtain masses in three loops.
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arxiv:2012.07964
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} ( c ) $ is the area of the region on the surface $ s $ surrounded by $ c, $ obtained from a special 2 - form $ \ omega _ { ( x, g ) } $ on $ s, $ called an area form $ \ omega _ { ( x, g ) } $ related to $ ( x, g ) $ on $ s. $
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arxiv:1609.06060
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in this paper we present a bottom up procedure for segmentation of text lines written or printed in the latin script. the proposed method uses a combination of image morphology, feature extraction and gaussian mixture model to perform this task. the experimental results show the validity of the procedure.
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arxiv:1710.03027
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we provide an interpretation of the aps index theorem of piazza - schick and zeidler in terms of coarse homotopy theory. on the one hand we propose a motivic version of the boundary value problem, the index theorem, and the associated secondary invariants. on the other hand, we discuss in detail how the abstract version is related with classical case for dirac operators.
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arxiv:1806.03669
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in this note we extend the methods developed by freidel et al. [ arxiv : hep - th / 0612170 ] to derive the form of $ \ phi ^ 4 $ interaction term in the case of scalar field theory on $ \ kappa $ - minkowski space, defined in terms of star product. we present explicit expressions for the $ \ kappa $ - minkowski star product. having obtained the the interaction term we use the resulting deformed conservation rules to investigate if they lead to any threshold anomaly, and we find that in the leading order they do not, as expected.
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arxiv:0904.4036
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the deconfinement phase transition from hadronic matter to quark matter can continuously occur during spins down of neutron stars. it will lead to the release of latent heat if the transition is the first - order one. we have investigated the energy release of such deconfinement phase transition for rotating hybrid stars model which include mixed phase of hadronic matter and quark matter. the release of latent heat per baryon is calculated through studying a randomly process of infinitesimal compressing. finally, we can self - consistently get the heating luminosity of deconfinement phase transition by imputing the eos of mixed phase, and based on the equation of rotation structure of stars.
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arxiv:0708.0900
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the design of phased arrays able to generate arbitrary - shaped beams through a sub - arrayed architecture is addressed here. the synthesis problem is cast in the excitation matching framework, so as to yield clustered phased arrays providing optimal trade - offs between the complexity of the array architecture ( i. e., the minimum number of control points at the sub - array level ) and the matching of a reference pattern. a synthesis tool based on the k - means algorithm is proposed for jointly optimizing the sub - array configuration and the complex sub - array coefficients. selected numerical results, including pencil beams with sidelobe notches and asymmetric lobes as well as shaped main lobes, are reported and discussed to highlight the peculiarities of the proposed approach also in comparison with some extensions to complex excitations of state - of - the - art sub - array design methods.
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arxiv:2102.02258
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twin - field quantum key distribution ( tfqkd ) systems have shown great promise for implementing practical long - distance secure quantum communication due to its measurement - device - independent nature and its ability to offer fundamentally superior rate - loss scaling than point - to - point qkd systems. a surge of research and development effort in the last two years has produced many variants of protocols and experimental demonstrations. in terms of hardware topology, tfqkd systems interfering quantum signals from two remotely phase - locked laser sources are in essence giant mach - zehnder interferometers ( mzis ) requiring active phase stabilization. such configurations are inherently unsuitable for a tfqkd network, where more than one user - pair share the common quantum measurement station, because it is practically extremely difficult, if not impossible, to stabilize mzis of largely disparate path lengths, a situation that is inevitable in a multi - user - pair tfqkd network. on the other hand, sagnac interferometer based tfqkd systems exploiting the inherent phase stability of the sagnac ring can implement asymmetric tfqkd, and are therefore eminently suitable for implementing a tfqkd network. in this work, we experimentally demonstrate a proof - of - principle multi - user - pair sagnac tfqkd network where three user pairs sharing the same measurement station can perform pair - wise tfqkd through time multiplexing, with channel losses up to 58 db, and channel loss asymmetry up to 15 db. in some cases, the secure key rates still beat the rate - loss bounds for point - to - point repeaterless qkd systems, even in this network configuration. it is to our knowledge the first multi - user - pair tfqkd network demonstration, an important step in advancing quantum communication network technologies.
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arxiv:2106.07768
|
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