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we generalise the computations of arxiv : 0712. 2456 to generate long wavelength, asymptotically locally ads _ 5 solutions to the einstein - dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. upon demanding regularity, our solutions are dual, under the ads / cft correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. these solutions turn out to be parametrised by four - velocity and temperature fields that are constrained to obey the boundary covariant navier stokes equations with a dilaton dependent forcing term. we explicitly evaluate the stress tensor and lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the weyl covariance of these expressions. we also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. as a check of our constructions we expand the exactly known solutions for rotating black holes in global ads _ 5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. we also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.
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arxiv:0806.0006
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there are some generalizations of the classical eisenbud - levine - khimshashvili formula for the index of a singular point of an analytic vector field on $ r ^ n $ for vector fields on singular varieties. we offer an alternative approach based on the study of indices of 1 - forms instead of vector fields. when the variety under consideration is a real isolated complete intersection singularity ( icis ), we define an index of a ( real ) 1 - form on it. in the complex setting we define an index of a holomorphic 1 - form on a complex icis and express it as the dimension of a certain algebra. in the real setting, for an icis $ v = f ^ { - 1 } ( 0 ) $, $ f : ( c ^ n, 0 ) \ to ( c ^ k, 0 ) $, $ f $ is real, we define a complex analytic family of quadratic forms parameterized by the points $ \ epsilon $ of the image $ ( c ^ k, 0 ) $ of the map $ f $, which become real for real $ \ epsilon $ and in this case their signatures defer from the " real " index by $ \ chi ( v _ \ epsilon ) - 1 $, where $ \ chi ( v _ \ epsilon ) $ is the euler characteristic of the corresponding smoothing $ v _ \ epsilon = f ^ { - 1 } ( \ epsilon ) \ cap b _ \ delta $ of the icis $ v $.
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arxiv:math/0105242
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large language models ( llms ) are increasingly being utilised across a range of tasks and domains, with a burgeoning interest in their application within the field of journalism. this trend raises concerns due to our limited understanding of llm behaviour in this domain, especially with respect to political bias. existing studies predominantly focus on llms undertaking political questionnaires, which offers only limited insights into their biases and operational nuances. to address this gap, our study establishes a new curated dataset that contains 2, 100 human - written articles and utilises their descriptions to generate 56, 700 synthetic articles using nine llms. this enables us to analyse shifts in properties between human - authored and machine - generated articles, with this study focusing on political bias, detecting it using both supervised models and llms. our findings reveal significant disparities between base and instruction - tuned llms, with instruction - tuned models exhibiting consistent political bias. furthermore, we are able to study how llms behave as classifiers, observing their display of political bias even in this role. overall, for the first time within the journalistic domain, this study outlines a framework and provides a structured dataset for quantifiable experiments, serving as a foundation for further research into llm political bias and its implications.
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arxiv:2406.10773
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we present improved coulomb correction formulae for bose - einstein correlations including also exchange term and use them to calculate appropriate correction factors for several source functions. it is found that coulomb correction to the exchange function in the bose - einstein correlations cannot be neglected.
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arxiv:hep-ph/9503232
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dynamics of information flow in adaptively interacting stochastic processes is studied. we give an extended form of game dynamics for markovian processes and study its behavior to observe information flow through the system. examples of the adaptive dynamics for two stochastic processes interacting through matching pennies game interaction are exhibited along with underlying causal structure.
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arxiv:nlin/0611032
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we study the possibility of generating the observed baryon asymmetry via leptogenesis in the decay of heavy standard model singlet fermions which carry lepton number, in a framework without majorana masses above the electroweak scale. such scenario does not contain any source of total lepton number violation besides the standard model sphalerons, and the baryon asymmetry is generated by the interplay of lepton flavour effects and the sphaleron decoupling in the decay epoch.
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arxiv:0909.3518
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let $ m ( 1 ) $ be the vertex operator algebra with the virasoro element $ \ omega $ associated to the heisenberg algebra of rank $ 1 $ and let $ m ( 1 ) ^ { + } $ be the subalgebra of $ m ( 1 ) $ consisting of the fixed points of an automorphism of $ m ( 1 ) $ of order $ 2 $. we classify the simple weak $ m ( 1 ) ^ { + } $ - modules with a non - zero element $ w $ such that for some integer $ s \ geq 2 $, $ \ omega _ i w \ in { \ mathbb c } w $ ( $ i = \ lfloor s / 2 \ rfloor + 1, \ lfloor s / 2 \ rfloor + 2, \ ldots, s - 1 $ ), $ \ omega _ { s } w \ in { \ mathbb c } ^ { \ times } w $, and $ \ omega _ i w = 0 $ for all $ i > s $. the result says that any such simple weak $ m ( 1 ) ^ { + } $ - module is isomorphic to some simple weak $ m ( 1 ) $ - module or to some $ \ theta $ - twisted simple weak $ m ( 1 ) $ - module.
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arxiv:1608.07890
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this paper presents fedalign, a federated learning ( fl ) framework particularly designed for system identification ( sysid ) tasks by aligning state representations. local workers can learn state - space models ( ssms ) with equivalent representations but different dynamics. we demonstrate that directly aggregating these local ssms via fedavg results in a global model with altered system dynamics. fedalign overcomes this problem by employing similarity transformation matrices to align state representations of local ssms, thereby establishing a common parameter basin that retains the dynamics of local ssms. fedalign computes similarity transformation matrices via two distinct approaches : fedalign - a and fedalign - o. in fedalign - a, we represent the global ssm in controllable canonical form ( ccf ). we apply control theory to analytically derive similarity transformation matrices that convert each local ssm into this form. yet, establishing global ssm in ccf brings additional alignment challenges in multi input - multi output sysid as ccf representation is not unique, unlike in single input - single output sysid. in fedalign - o, we address these alignment challenges by reformulating the local parameter basin alignment problem as an optimization task. we determine the parameter basin of a local worker as the common parameter basin and solve least square problems to obtain similarity transformation matrices needed to align the remaining local ssms. through the experiments conducted on synthetic and real - world datasets, we show that fedalign outperforms fedavg, converges faster, and provides improved stability of the global ssm thanks to the efficient alignment of local parameter basins.
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arxiv:2503.12137
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let $ d $ be a square - free integer and $ \ mathbb { z } [ \ sqrt { d } ] $ a quadratic ring of integers. for a given $ n \ in \ mathbb { z } [ \ sqrt { d } ] $, a set of $ m $ non - zero distinct elements in $ \ mathbb { z } [ \ sqrt { d } ] $ is called a diophantine $ d ( n ) $ - $ m $ - tuple ( or simply $ d ( n ) $ - $ m $ - tuple ) in $ \ mathbb { z } [ \ sqrt { d } ] $ if product of any two of them plus $ n $ is a square in $ \ mathbb { z } [ \ sqrt { d } ] $. assume that $ d \ equiv 2 \ pmod 4 $ is a positive integer such that $ x ^ 2 - dy ^ 2 = - 1 $ and $ x ^ 2 - dy ^ 2 = 6 $ are solvable in integers. in this paper, we prove the existence of infinitely many $ d ( n ) $ - quadruples in $ \ mathbb { z } [ \ sqrt { d } ] $ for $ n = 4m + 4k \ sqrt { d } $ with $ m, k \ in \ mathbb { z } $ satisfying $ m \ not \ equiv 5 \ pmod { 6 } $ and $ k \ not \ equiv 3 \ pmod { 6 } $. moreover, we prove the same for $ n = ( 4m + 2 ) + 4k \ sqrt { d } $ when either $ m \ not \ equiv 9 \ pmod { 12 } $ and $ k \ not \ equiv 3 \ pmod { 6 } $, or $ m \ not \ equiv 0 \ pmod { 12 } $ and $ k \ not \ equiv 0 \ pmod { 6 } $. at the end, some examples supporting the existence of quadruples in $ \ mathbb { z } [ \ sqrt { d } ] $ with the property $ d ( n ) $ for the above exceptional $ n $ ' s are provided for $ d = 10 $.
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arxiv:2302.04145
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a simple model based on the divide and conquer rule and tight - binding ( tb ) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon ( gnr ) heterojunctions. in our model, the gnr heterojunction is divided into three parts : a left ( l ) part, middle ( m ) part, and right ( r ) part. the left part is a gnr of width $ w _ { l } $, the middle part is a gnr of width $ w _ { m } $, and the right part is a gnr of width $ w _ { r } $. we assume that the left and right parts of the gnr heterojunction interact with the middle part only. under this approximation, the hamiltonian of the system can be expressed as a block tridiagonal matrix. the matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal tb approximation. the electronic structure of the gnr heterojunction is analyzed by computing the density of states. we demonstrate that for heterojunctions for which $ w _ { l } = w _ { r } $, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in gnrs. our tb results were compared with calculations employing divide and conquer rule in combination with density functional theory ( dft ) and were found to agree nicely.
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arxiv:1508.01488
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the fitzhugh - nagumo equations have been used as a caricature of the hodgkin - huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture, qualitatively, the general properties of an excitable membrane. even though its simplicity allows very valuable insight to be gained, the accuracy of reproducing real experimental results is limited. in this paper, we utilize a modified version of the fitzhugh - nagumo equations to model the spatial propagation of neuron firing ; we assume that this propagation is ( at least, partially ) caused by the cross - diffusion connection between the potential and recovery variables. we show that the cross - diffusion version of the model, besides giving rise to the typical fast traveling wave solution exhibited in the original diffusion fitzhugh - nagumo equations, also gives rise to a slow traveling wave solution. we analyze all possible traveling wave solutions of the fitzhugh - nagumo equations with this cross - diffusion term and show that there exists a threshold of the cross - diffusion coefficient ( the maximum value for a given speed of propagation ), which bounds the area where normal impulse propagation is possible.
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arxiv:q-bio/0505031
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lisa is an upcoming esa mission that will detect gravitational waves in space by interferometrically measuring the separation between free - falling test masses at picometer precision. to reach the desired performance, lisa will employ the noise reduction technique time - delay interferometry ( tdi ), in which multiple raw interferometric readouts are time shifted and combined into the final scientific observables. evaluating the performance in terms of these tdi variables requires careful tracking of how different noise sources propagate through tdi, as noise correlations might affect the performance in unexpected ways. one example of such potentially correlated noise is the relative intensity noise ( rin ) of the six lasers aboard the three lisa satellites, which will couple into the interferometric phase measurements. in this article, we calculate the expected rin levels based on the current mission architecture and the envisaged mitigation strategies. we find that strict requirements on the technical design reduce the effect from approximately 8. 7 pm / rthz per inter - spacecraft interferometer to that of a much lower sub - 1 pm / rthz noise, with typical characteristics of an uncorrelated readout noise after tdi. our investigations underline the importance of sufficient balanced detection of the interferometric measurements.
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arxiv:2212.12052
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we define the secondary hochschild complex for an entwining structure over a commutative $ k $ - algebra $ b $. we show that this complex carries the structure of a weak comp algebra. we obtain two distinct cup product structures for the secondary cohomology groups. we also consider a subcomplex on which the two cup products coincide and which satisfies the axioms for being a comp algebra. the cohomology of this subcomplex then forms a gerstenhaber algebra. we also construct a bicomplex that controls the deformations of the entwining structure over $ b $.
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arxiv:1909.05476
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any $ r \ in \ left ( 0, \ frac { 4 } { n + 2 } \ right ) $ }, \ ] which is derived with the help of new interpolation inequalities in the variable sobolev spaces. the second - order differentiability of the strong solution is proven : \ [ d _ { x _ i } \ left ( \ left ( a \ vert \ nabla u \ vert ^ { p - 2 } + b \ vert \ nabla u \ vert ^ { q - 2 } \ right ) ^ { \ frac { 1 } { 2 } } d _ { x _ j } u \ right ) \ in l ^ 2 ( q _ t ), \ quad i, j = 1, 2, \ ldots, n. \ ]
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arxiv:2109.03597
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using only the britto - cachazo - feng - witten ( bcfw ) on - shell recursion relation we prove color - order reversed relation, $ u ( 1 ) $ - decoupling relation, kleiss - kuijf ( kk ) relation and bern - carrasco - johansson ( bcj ) relation for color - ordered gauge amplitude in the framework of s - matrix program without relying on lagrangian description. our derivation is the first pure field theory proof of the new discovered bcj identity, which substantially reduces the color ordered basis from $ ( n - 2 )! $ to $ ( n - 3 )! $. our proof gives also its physical interpretation as the mysterious bonus relation with $ { 1 \ over z ^ 2 } $ behavior under suitable on - shell deformation for no adjacent pair.
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arxiv:1004.3417
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the use of audio and visual modality for speaker localization has been well studied in the literature by exploiting their complementary characteristics. however, most previous works employ the setting of static sensors mounted at fixed positions. unlike them, in this work, we explore the ego - centric setting, where the heterogeneous sensors are embodied and could be moving with a human to facilitate speaker localization. compared to the static scenario, the ego - centric setting is more realistic for smart - home applications e. g., a service robot. however, this also brings new challenges such as blurred images, frequent speaker disappearance from the field of view of the wearer, and occlusions. in this paper, we study egocentric audio - visual speaker doa estimation and deal with the challenges mentioned above. specifically, we propose a transformer - based audio - visual fusion method to estimate the relative doa of the speaker to the wearer, and design a training strategy to mitigate the problem of the speaker disappearing from the camera ' s view. we also develop a new dataset for simulating the out - of - view scenarios, by creating a scene with a camera wearer walking around while a speaker is moving at the same time. the experimental results show that our proposed method offers promising performance in this new dataset in terms of tracking accuracy. finally, we adapt the proposed method for the multi - speaker scenario. experiments on easycom show the effectiveness of the proposed model for multiple speakers in real scenarios, which achieves state - of - the - art results in the sphere active speaker detection task and the wearer activity prediction task. the simulated dataset and related code are available at https : / / github. com / kawhizhao / egocentric - audio - visual - speaker - localization.
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arxiv:2309.16308
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we study the toroidal dipole moment of the lightest neutralino in the constrained minimal supersymmetric standard model. the toroidal dipole moment is the only electromagnetic property of the neutralino. since the neutralino is the lsp in many versions of the mssm and therefore a candidate for dark matter, its characterization through its electromagnetic properties is important both for particle physics and for cosmology. we perform a scan in the parameter space of the cmssm and find that the toroidal dipole moment is different from zero, albeit very small, in all the parameter space, and reaches a value around $ 10 ^ { - 3 } \ mathrm { gev } ^ { - 2 } $ in a particular region of the parameter space, well below experimental bounds.
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arxiv:1206.5052
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expectation - based minimalist grammars ( e - mgs ) are simplified versions of the ( conflated ) minimalist grammars, ( c ) mgs, formalized by stabler ( stabler, 2011, 2013, 1997 ) and phase - based minimalist grammars, pmgs ( chesi, 2005, 2007 ; stabler, 2011 ). the crucial simplification consists of driving structure building only by relying on lexically encoded categorial top - down expectations. the commitment on a top - down derivation ( as in e - mgs and pmgs, as opposed to ( c ) mgs, chomsky, 1995 ; stabler, 2011 ) allows us to define a core derivation that should be the same in both parsing and generation ( momma & phillips, 2018 ).
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arxiv:2109.13871
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a search for events with one or more isolated leptons in the final state is performed on a data sample collected in e + - p collisions with the h1 and zeus detectors at the hera collider. the data sample corresponds to an integrated luminosity of ~ 1 fb - 1, representing the full hera high - energy data set. the yields of single, di - and tri - lepton events are measured and compared to the standard model predictions, looking for possible deviations. no significant discrepancy with respect to the standard model expectations is observed.
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arxiv:0810.0501
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we investigate the interaction caused by quantum gravitational vacuum fluctuations between a gravitationally polarizable object and a gravitational boundary, and find a position - dependent energy shift of the object, which induces a force in close analogy to the casimir - polder force in the electromagnetic case. for a dirichlet boundary, the explicit form of the quantum gravitational potential for the polarizable object in its ground - state is worked out and is found to behave like $ z ^ { - 5 } $ in the near regime, and $ z ^ { - 6 } $ in the far regime, where $ z $ is the distance to the boundary. taking a bose - einstein condensate as a gravitationally polarizable object, we find that the relative correction to the radius caused by fluctuating quantum gravitational waves in vacuum is of order $ 10 ^ { - 21 } $. although far too small to observe in comparison with its electromagnetic counterpart, it is nevertheless of the order of the gravitational strain caused by a recently detected black hole merger on the arms of the ligo.
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arxiv:1605.02193
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mobile edge computing ( a. k. a. fog computing ) has recently emerged to enable in - situ processing of delay - sensitive applications at the edge of mobile networks. providing grid power supply in support of mobile edge computing, however, is costly and even infeasible ( in certain rugged or under - developed areas ), thus mandating on - site renewable energy as a major or even sole power supply in increasingly many scenarios. nonetheless, the high intermittency and unpredictability of renewable energy make it very challenging to deliver a high quality of service to users in energy harvesting mobile edge computing systems. in this paper, we address the challenge of incorporating renewables into mobile edge computing and propose an efficient reinforcement learning - based resource management algorithm, which learns on - the - fly the optimal policy of dynamic workload offloading ( to the centralized cloud ) and edge server provisioning to minimize the long - term system cost ( including both service delay and operational cost ). our online learning algorithm uses a decomposition of the ( offline ) value iteration and ( online ) reinforcement learning, thus achieving a significant improvement of learning rate and run - time performance when compared to standard reinforcement learning algorithms such as q - learning. we prove the convergence of the proposed algorithm and analytically show that the learned policy has a simple monotone structure amenable to practical implementation. our simulation results validate the efficacy of our algorithm, which significantly improves the edge computing performance compared to fixed or myopic optimization schemes and conventional reinforcement learning algorithms.
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arxiv:1703.06060
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a local realistic theory is presented for mermin ' s special case of the eprb experiment. the theory, which is readily extended to the general eprb experiment, reproduces all the predictions of quantum theory. it also reveals that bell, and also hess and philipp, had made an error in the mathematical formulation of einstein ' s locality or no action at a distance principle.
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arxiv:quant-ph/0309219
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many combinatorial properties of a point set in the plane are determined by the set of possible partitions of the point set by a line. their essential combinatorial properties are well captured by the axioms of oriented matroids. in fact, goodman and pollack ( journal of combinatorial theory, series a, volume 37, pp. 257 - 293, 1984 ) proved that the axioms of oriented matroids of rank $ 3 $ completely characterize the sets of possible partitions arising from a natural topological generalization of configurations of points and lines. in this paper, we introduce a new class of oriented matroids, called degree - $ k $ oriented matroids, which captures essential combinatorial properties of the possible partitions of point sets in the plane by the graphs of polynomial functions of degree $ k $. we prove that the axiom of degree - $ k $ oriented matroids completely characterizes the sets of possible partitions arising from a natural topological generalization of configurations formed by points and the graphs of polynomial functions degree $ k $. it turns out that the axiom of degree - $ k $ oriented matroids coincides with the axiom of ( $ k + 2 $ ) - signotopes, which was introduced by felsner and weil ( discrete applied mathematics, volume 109, pp. 67 - 94, 2001 ) in a completely different context. our result gives a two - dimensional geometric interpretation for ( $ k + 2 $ ) - signotopes and also for single element extensions of cyclic hyperplane arrangements in $ \ mathbb { r } ^ { n - k - 3 } $.
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arxiv:1703.04963
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##olensky result on the approximation of ac $ ^ 0 $ circuits by random low - degree polynomials.
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arxiv:2411.00976
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motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point - masses, determining their spatial locations, and computing their attributes. based on computation of hermite moments that are fourier - invariant, our approach facilitates the processing of both spatial and fourier data in any dimension.
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arxiv:1707.09319
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cell - penetrating peptides ( cpps ) have been widely used for drug - delivery agents ; however, it has not been fully understood how they translocate across cell membranes. the weighted ensemble ( we ) method, one of powerful and flexible path sampling techniques, can be helpful to reveal translocation paths and free energy barriers along those paths. within the we approach we show how arg9 ( nona - arginine ) and tat interact with a dopc / dopg ( 4 : 1 ) model membrane, and we present free energy ( or potential mean of forces, pmfs ) profiles of penetration, although a translocation across the membrane has not been observed in the current simulations. two different compositions of lipid molecules were also tried and compared. our approach can be applied to any cpps interacting with various model membranes, and it will provide useful information regarding the transport mechanisms of cpps.
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arxiv:2112.00507
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we identify the deviation from the straight line error ( dsle ) - - i. e., the spurious non - linearity of the total energy as a function of fractional particle number - - as the main source for the discrepancy between experimental vertical ionization energies and theoretical quasiparticle energies, as obtained from the $ gw $ and $ gw $ + sosex approximations to many - body perturbation theory ( mbpt ). for self - consistent calculations, we show that $ gw $ suffers from a small dsle. conversely, for perturbative $ g _ 0w _ 0 $ and $ g _ 0w _ 0 $ + sosex calculations the dsle depends on the starting point. we exploit this starting - point dependence to reduce ( or completely eliminate ) the dsle. we find that the agreement with experiment increases as the dsle reduces. dsle - minimized schemes, thus, emerge as promising avenues for future developments in mbpt.
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arxiv:1512.02081
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the properties of young massive clusters ( ymcs ) are key to understanding the star formation mechanism in starburst systems, especially mergers. we present alma high - resolution ( $ \ sim $ 10 pc ) continuum ( 100 and 345 ghz ) data of ymcs in the overlap region of the antennae galaxy. we identify 6 sources in the overlap region, including two sources that lie in the same giant molecular cloud ( gmc ). these ymcs correspond well with radio sources in lower resolution continuum ( 100 and 220 ghz ) images at gmc scales ( $ \ sim $ 60 pc ). we find most of these ymcs are bound clusters through virial analysis. we estimate their ages to be $ \ sim $ 1 myr and to be either embedded or just beginning to emerge from their parent cloud. we also compare each radio source with pa $ \ beta $ source and find they have consistent total ionizing photon numbers, which indicates they are tracing the same physical source. by comparing the free - free emission at $ \ sim $ 10 pc scale and $ \ sim $ 60 pc scale, we find that $ \ sim $ 50 % of the free - free emission in gmcs actually comes from these ymcs. this indicates that roughly half of the stars in massive gmcs are formed in bound clusters. we further explore the mass correlation between ymcs and gmcs in the antennae and find it generally agrees with the predictions of the star cluster simulations. the most massive ymc has a stellar mass that is 1 % - 5 % of its host gmc mass.
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arxiv:2202.08077
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this review focuses on the current status of lattice calculations of three observables which are both phenomenologically and experimentally relevant and have been scrutinized recently. these three observables are the nucleon electromagnetic form factors, the momentum fraction, < x >, and the nucleon axial coupling, ga.
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arxiv:hep-lat/0512001
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we have studied the interplay of an anderson impurity in landau quantized graphene, with special emphasis on the influence of the chemical potential. within the slave - boson mean - field theory, we found reentrant kondo behaviour by varying the chemical potential or gate voltage. between landau levels, the density of states is suppressed, and by changing the graphene ' s fermi energy, we cross from metallic to semiconducting regions. hence, the corresponding kondo behaviour is also influenced. the f - level spectral function reveals both the presence of landau levels in the conduction band and the kondo resonance.
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arxiv:0705.1934
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this paper proposes an infeasible interior - point algorithm for the convex optimization problem using arc - search techniques. the proposed algorithm simultaneously selects the centering parameter and the step size, aiming at optimizing the performance in every iteration. analytic formulas for the arc - search are provided to make the arc - search method very efficient. the convergence of the algorithm is proved and a polynomial bound of the algorithm is established. the preliminary numerical test results indicate that the algorithm is efficient and effective.
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arxiv:2201.01214
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we extend the measure - valued fluid model, which tracks residuals of patience and service times, to allow for time - varying arrivals. the fluid model can be characterized by a one - dimensional convolution equation involving both the patience and service time distributions. we also make an interesting connection to the measure - valued fluid model tracking the elapsed waiting and service times. our analysis shows that the two fluid models are actually characterized by the same one - dimensional convolution equation.
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arxiv:1806.00773
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electric grids are traditionally operated as multi - entity systems with each entity managing a geographical region. interest and demand for decarbonization and energy democratization is resulting in growing penetration of controllable energy resources. in turn, this process is increasing the number of grid entities. the paradigm shift is also fueled by increased adoption of intelligent sensors and actuators equipped with advanced processing and computing capabilities. while collaboration among power grid entities ( agents ) reduces energy cost and increases overall reliability, achieving effective collaboration is challenging. the main challenges stem from the heterogeneity of system agents and their collected information. furthermore, the scale of data collection is constantly increasing and many grid entities have strict privacy requirements. another challenge is the energy industry ' s common practice of keeping data in silos. federated computation is an approach well suited to addressing these issues that are increasingly important for multi - agent energy systems. through federated computation, agents collaboratively solve learning and optimization problems while respecting each agent ' s privacy and overcoming barriers of cross - device and cross - organization data isolation. in this paper, we first establish the need for federated computations to achieve energy optimization goals of the future power grid. we discuss practical challenges of performing multi - agent data processing in general. then we address challenges that arise specifically for orchestrating operation of connected distributed energy resources in the internet of things. we conclude this paper by presenting a novel federated computation framework that addresses some of these issues, and we share examples of two initial field test setups in research demonstrations and commercial building applications with grid fruit llc.
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arxiv:2009.10182
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in this paper, based on the user - tag - object tripartite graphs, we propose a recommendation algorithm, which considers social tags as an important role for information retrieval. besides its low cost of computational time, the experiment results of two real - world data sets, \ emph { del. icio. us } and \ emph { movielens }, show it can enhance the algorithmic accuracy and diversity. especially, it can obtain more personalized recommendation results when users have diverse topics of tags. in addition, the numerical results on the dependence of algorithmic accuracy indicates that the proposed algorithm is particularly effective for small degree objects, which reminds us of the well - known \ emph { cold - start } problem in recommender systems. further empirical study shows that the proposed algorithm can significantly solve this problem in social tagging systems with heterogeneous object degree distributions.
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arxiv:1004.3732
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using the method developed by cherkis and hashimoto we construct partially localized d3 / d5 ( 2 ), d4 / d4 ( 2 ) and m5 / m5 ( 3 ) supergravity solutions where one of the harmonic functions is given in an integral form. this is a generalization of the already known near - horizon solutions. the method fails for certain intersections such as d1 / d5 ( 1 ) which is consistent with the previous no - go theorems. we point out some possible ways of bypassing these results.
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arxiv:hep-th/0306040
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in evolutionary robotics an encoding of the control software, which maps sensor data ( input ) to motor control values ( output ), is shaped by stochastic optimization methods to complete a predefined task. this approach is assumed to be beneficial compared to standard methods of controller design in those cases where no a - priori model is available that could help to optimize performance. also for robots that have to operate in unpredictable environments, an evolutionary robotics approach is favorable. we demonstrate here that such a model - free approach is not a free lunch, as already simple tasks can represent unsolvable barriers for fully open - ended uninformed evolutionary computation techniques. we propose here the ' wankelmut ' task as an objective for an evolutionary approach that starts from scratch without pre - shaped controller software or any other informed approach that would force the behavior to be evolved in a desired way. our focal claim is that ' wankelmut ' represents the simplest set of problems that makes plain - vanilla evolutionary computation fail. we demonstrate this by a series of simple standard evolutionary approaches using different fitness functions and standard artificial neural networks as well as continuous - time recurrent neural networks. all our tested approaches failed. we claim that any other evolutionary approach will also fail that does per - se not favor or enforce modularity and does not freeze or protect already evolved functionalities. thus we propose a hard - to - pass benchmark and make a strong statement for self - complexifying and generative approaches in evolutionary computation. we anticipate that defining such a ' simplest task to fail ' is a valuable benchmark for promoting future development in the field of artificial intelligence, evolutionary robotics and artificial life.
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arxiv:1609.07722
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we demonstrate the use of high - q superconducting coplanar waveguide ( cpw ) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power ( 400 nw ). this power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. we also describe the use of adiabatic microwave pulses to overcome microwave magnetic field ( $ b _ { 1 } $ ) inhomogeneities inherent to cpw resonators. this allows for uniform control over a randomly distributed spin ensemble. sensitivity data are reported showing a single shot ( no signal averaging ) sensitivity to $ 10 ^ { 7 } $ spins or $ 3 \ times 10 ^ { 4 } $ spins / $ \ sqrt { hz } $ with averaging.
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arxiv:1403.0018
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measures characterizing the non - markovianity degree of the quantum dynamics have several drawbacks when applied to real devices. they depend on the chosen measurement time interval and are highly sensitive to experimental noise and errors. we propose several techniques to enhance the practical applicability of the measures and verify our findings experimentally on a superconducting transmon and a trapped - ion qubit. the time dependence can be disregarded by introduction of the measure per oscillation, while the sensitivity to noise is reduced by applying a regularization procedure. the results for both types of qubits are compared with theoretical predictions for a simple model of non - markovianity based on qubit - qubit interaction.
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arxiv:2503.23431
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hubble space telescope ' s ( hst ) space telescope imaging spectrograph ( stis ) targeted 556 stars in a long - running program called next generation spectral library ( ngsl ) via proposals go9088, go9786, go10222, and go13776. exposures through three low resolution gratings provide wavelength coverage from 0. 2 $ < \ lambda < $ 1 $ \ mu $ m at $ \ lambda / \ delta \ lambda \ sim $ 1000, providing unique coverage in the ultraviolet ( uv ). the uv grating ( g230lb ) scatters red light and this results in unwanted flux that becomes especially troubling for cool stars. we applied scattered light corrections based on \ cite { 2022stis. rept.... 5w } and flux corrections arising from pointing errors relative to the center of the 0 \ farcs2 slit. we present 514 fully reduced spectra, fluxed, dereddened, and cross - correlated to zero velocity. because of the broad spectral range, we can simultaneously study h $ \ alpha $ and mg ii $ \ lambda $ 2800, indicators of chromospheric activity. their behaviours are decoupled. besides three cool dwarfs and one giant with mild flares in h $ \ alpha $, only be stars show strong h $ \ alpha $ emission. mg2800 emission, however, strongly anti - correlates with temperature such that warm stars show absorption and stars cooler than $ 5000 \ : \! \ rm { k } $ universally show chromospheric emission regardless of dwarf / giant status or metallicity. transformed to mg2800 flux emerging from the stellar surface, we find a correlation with temperature with approximately symmetric astrophysical scatter, in contrast to other workers who find a basal level with asymmetric scatter to strong values. unsurprisingly, we confirm that mg2800 activity is variable.
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arxiv:2301.05335
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economics job market rumors ( ejmr ) is an online forum and clearinghouse for information on the academic job market for economists. it also includes content that is abusive, defamatory, racist, misogynistic, or otherwise " toxic. " almost all of this content is created anonymously by contributors who receive a four - character username when posting on ejmr. using only publicly available data we show that the statistical properties of the scheme by which these usernames were generated allows the ip addresses from which most posts were made to be determined with high probability. we recover 47, 630 distinct ip addresses of ejmr posters and attribute them to 66. 1 % of the roughly 7 million posts made over the past 12 years. we geolocate posts and describe aggregated cross - sectional variation - - particularly regarding toxic, misogynistic, and hate speech - - across sub - forums, geographies, institutions, and ip addresses. our analysis suggests that content on ejmr comes from all echelons of the economics profession, including, but not limited to, its elite institutions.
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arxiv:2409.15948
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we develop a data - driven machine learning approach to identifying parameters with steady - state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems with parameters. our approach first constructs target functions for these tasks, then designs a parameter - solution neural network ( psnn ) that couples a parameter neural network and a solution neural network to approximate the target functions. we further develop efficient algorithms to train the psnn and locate steady - state solutions. an approximation theory for the target functions with psnn is developed based on kernel decomposition. numerical results are reported to show that our approach is robust in finding solutions, identifying phase boundaries, and classifying solution stability across parameter regions. these numerical results also validate our analysis. while this study focuses on steady states of parameterized dynamical systems, our approach is equation - free and is applicable generally to finding solutions for parameterized nonlinear systems of algebraic equations. some potential improvements and future work are discussed.
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arxiv:2312.10315
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in this note, we study non - uniqueness for minimizing harmonic maps from $ b ^ 3 $ to $ \ mathbb { s } ^ 2 $. we show that every boundary map can be modified to a boundary map that admits multiple minimizers of the dirichlet energy by a small $ w ^ { 1, p } $ - change for $ p < 2 $. this strengthens a remark by the second - named author and strzelecki. the main novel ingredient is a homotopy construction, which is the answer to an easier variant of a challenging question regarding the existence of a norm control for homotopies between $ w ^ { 1, p } $ maps.
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arxiv:2403.12662
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in this paper we investigate the role of the electronic correlation on the hole doping dependence of electron - phonon and superconducting properties of cuprates. we introduce a simple analytical expression for the one - particle green ' s function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half - filling. the poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. we show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the $ t _ c $ - $ \ delta $ phase diagram of cuprates. experimental evidences are also discussed.
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arxiv:cond-mat/0311281
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the geometric dimension for proper actions $ \ underline { \ mathrm { gd } } ( g ) $ of a group $ g $ is the minimal dimension of a classifying space for proper actions $ \ underline { e } g $. we construct for every integer $ r \ geq 1 $, an example of a virtually torsion - free gromov - hyperbolic group $ g $ such that for every group $ \ gamma $ which contains $ g $ as a finite index normal subgroup, the virtual cohomological dimension $ \ mathrm { vcd } ( \ gamma ) $ of $ \ gamma $ equals $ \ underline { \ mathrm { gd } } ( \ gamma ) $ but such that the outer automorphism group $ \ mathrm { out } ( g ) $ is virtually torsion - free, admits a cocompact model for $ \ underline e \ mathrm { out } ( g ) $ but nonetheless has $ \ mathrm { vcd } ( \ mathrm { out } ( g ) ) \ le \ underline { \ mathrm { gd } } ( \ mathrm { out } ( g ) ) - r $.
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arxiv:1602.04354
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the two - point gauge correlation function in yang - - mills - - chern - - simons theory in three dimensional euclidean space is analysed by taking into account the non - perturbative effects of the gribov horizon. in this way, we are able to describe the confinement and de - confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.
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arxiv:1312.3308
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the onboarding of iot devices by authorized users constitutes both a challenge and a necessity in a world, where the number of iot devices and the tampering attacks against them continuously increase. commonly used onboarding techniques today include the use of qr codes, pin codes, or serial numbers. these techniques typically do not protect against unauthorized device access - a qr code is physically printed on the device, while a pin code may be included in the device packaging. as a result, any entity that has physical access to a device can onboard it onto their network and, potentially, tamper it ( e. g., install malware on the device ). to address this problem, in this paper, we present a framework, called deep learning - based watermarking for authorized iot onboarding ( dlwiot ), featuring a robust and fully automated image watermarking scheme based on deep neural networks. dlwiot embeds user credentials into carrier images ( e. g., qr codes printed on iot devices ), thus enables iot onboarding only by authorized users. our experimental results demonstrate the feasibility of dlwiot, indicating that authorized users can onboard iot devices with dlwiot within 2. 5 - 3sec.
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arxiv:2010.10334
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both acoustic and visual information influence human perception of speech. for this reason, the lack of audio in a video sequence determines an extremely low speech intelligibility for untrained lip readers. in this paper, we present a way to synthesise speech from the silent video of a talker using deep learning. the system learns a mapping function from raw video frames to acoustic features and reconstructs the speech with a vocoder synthesis algorithm. to improve speech reconstruction performance, our model is also trained to predict text information in a multi - task learning fashion and it is able to simultaneously reconstruct and recognise speech in real time. the results in terms of estimated speech quality and intelligibility show the effectiveness of our method, which exhibits an improvement over existing video - to - speech approaches.
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arxiv:2004.02541
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we argue that the reasonings that underlie a recent comment by gotay and demaret [ 1, gr - qc / 9605025 ] are defective. we maintain that, contrary to what they assert, our previous papers [ 2, 3, 4 ] are correct and indeed disprove their conjecture that quantum cosmological singularities are predetermined on the classical level by the choice of time.
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arxiv:gr-qc/9605043
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we suggest two approaches to a definition of unitarity for pseudonatural transformations between unitary pseudofunctors on pivotal dagger 2 - categories. the first is to require that the 2 - morphism components of the transformation be unitary. the second is to require that the dagger of the transformation be equal to its inverse. we show that the ` inverse ' making these definitions equivalent is the right dual of the transformation in the 2 - category fun ( c, d ) of pseudofunctors c - > d, pseudonatural transformations, and modifications. we show that the subcategory fun _ u ( c, d ) $ \ subset $ fun ( c, d ) whose objects are unitary pseudofunctors and whose 1 - morphisms are unitary pseudonatural transformations is a pivotal dagger 2 - category. we apply these results to obtain a morita - theoretical classification of unitary pseudonatural transformations between fibre functors on the category of representations of a compact quantum group.
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arxiv:2004.12760
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recent measurements from the cmb and from high - redshift galaxy observations have placed rough constraints on the midpoint and duration of the epoch of reionization. detailed measurements of the ionization history remain elusive, although two proposed probes show great promise for this purpose : the 21cm global signal and the kinetic sunyaev - zel ' dovich ( ksz ) effect. we formally confirm the common assumption that these two probes are highly complementary, with the ksz being more sensitive to extended ionization histories and the global signal to rapidly evolving ones. we do so by performing a karhunen - lo \ ` { e } ve ( kl ) transformation, which casts the data in a basis designed to emphasize the information content of each probe. we find that reconstructing the ionization history using both probes gives significantly more precise results than individual constraints, although carefully chosen, physically motivated priors play a crucial part in obtaining a bias - free reconstruction. additionally, in the kl basis, measurements from one probe can be used to detect the presence of residual systematics in the other, providing a safeguard against systematics that would go undetected when data from each probe is analyzed in isolation. once detected, the modes contaminated by systematics can be discarded from the data analysis to avoid biases in reconstruction.
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arxiv:2112.06933
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the creation of disordered hyperuniform materials with potentially extraordinary optical properties requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. motivated by this challenge, we propose a fabrication protocol using binary superparamagnetic colloidal particles confined in a 2d plane. the strong and long - ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuates long - ranged electrostatic interactions in charged colloidal systems. specifically, we find a family of optimal size ratios that makes the two - phase system effectively hyperuniform. we show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to systems with other long - ranged soft interactions, dimensionalities and / or polydispersity. our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials.
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arxiv:2005.09701
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it is widely believed that asphericity in the explosion is the crucial ingredient leading to successful core - collapse ( cc ) supernovae. however, direct observational evidence for the explosion geometry and for the connection with the progenitor properties are still missing. based on the thus - far largest late - phase spectroscopic sample of stripped - envelope cc supernovae, we demonstrate that about half of the explosions exhibit a substantial deviation from sphericity. for these aspherical cc supernovae, the spatial distributions of the oxygen - burning ash and the unburnt oxygen, as traced by the profiles of [ ca ii ] { \ lambda } { \ lambda } 7291, 7323 and [ o i ] { \ lambda } { \ lambda } 6300, 6363 emissions, respectively, appear to be anticorrelated, which can be explained if the explosion is bipolar and the oxygen - rich material burnt into two detached iron - rich bubbles. our combined analysis of the explosion geometry and the progenitor mass further suggests that the degree of asphericity grows with the mass of the carbon - oxygen core, which may be used to guide state - of - the - art simulations of cc supernova explosions.
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arxiv:2310.19280
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the adaptivity and maneuvering capabilities of autonomous underwater vehicles ( auvs ) have drawn significant attention in oceanic research, due to the unpredictable disturbances and strong coupling among the auv ' s degrees of freedom. in this paper, we developed large language model ( llm ) - enhanced reinforcement learning ( rl ) - based adaptive s - surface controller for auvs. specifically, llms are introduced for the joint optimization of controller parameters and reward functions in rl training. using multi - modal and structured explicit task feedback, llms enable joint adjustments, balance multiple objectives, and enhance task - oriented performance and adaptability. in the proposed controller, the rl policy focuses on upper - level tasks, outputting task - oriented high - level commands that the s - surface controller then converts into control signals, ensuring cancellation of nonlinear effects and unpredictable external disturbances in extreme sea conditions. under extreme sea conditions involving complex terrain, waves, and currents, the proposed controller demonstrates superior performance and adaptability in high - level tasks such as underwater target tracking and data collection, outperforming traditional pid and smc controllers.
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arxiv:2503.00527
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the features of a model interpreting the light scalar mesons as diquark - antidiquark bound states and the consequences of its natural extension to include heavy quarks are briefly reviewed.
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arxiv:hep-ph/0501077
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this article focuses on certain variability and emission characteristics of active galactic nuclei ( agn ), especially their radio - loud subset consisting of quasars, bl lacs and $ \ gamma $ - ray detected narrow - line seyfert 1 galaxies, all of which exhibit relativistically beamed jets of nonthermal radiation. several striking trends and correlations, including some that have received scant attention, drawn from the available comparatively recent literature are highlighted. these can provide very useful inputs to models of agn and be probed at a deeper level using the optical telescopes recently set up at devasthal ( nainital ).
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arxiv:1906.11339
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we present results from a set of experiments in this pilot study to investigate the causal influence of user activity on various environmental parameters monitored by occupant carried multi - purpose sensors. hypotheses with respect to each type of measurements are verified, including temperature, humidity, and light level collected during eight typical activities : sitting in lab / cubicle, indoor walking / running, resting after physical activity, climbing stairs, taking elevators, and outdoor walking. our main contribution is the development of features for activity and location recognition based on environmental measurements, which exploit location - and activity - specific characteristics and capture the trends resulted from the underlying physiological process. the features are statistically shown to have good separability and are also information - rich. fusing environmental sensing together with acceleration is shown to achieve classification accuracy as high as 99. 13 %. for building applications, this study motivates a sensor fusion paradigm for learning individualized activity, location, and environmental preferences for energy management and user comfort.
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arxiv:1406.5765
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consider qbf, the quantified boolean formula problem, as a combinatorial game ruleset. the problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. in this paper, three common variations of games are applied to create seven new games : whether each player is restricted to where they may play, which values they may set variables to, or the condition they are shooting for at the end of the game. the complexity for determining which player can win is analyzed for all games. of the seven, two are trivially in p and the other five are pspace - complete. these varying properties are common for combinatorial games ; reductions from these five hard games can simplify the process for showing the pspace - hardness of other games.
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arxiv:1401.3687
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this work addresses the inverse kinematics of serial robots using conformal geometric algebra. classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. in this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed - form resolution of the inverse kinematic problem for manipulators with a spherical wrist. for serial robots of this kind, the inverse kinematics problem can be split in two subproblems : the position and orientation problems. the latter is solved by appropriately splitting the rotor that defines the target orientation into three simpler rotors, while the former is solved by developing a geometric strategy for each combination of prismatic and revolute joints that forms the position part of the robot. finally, the inverse kinematics of 7 dof redundant manipulators with a spherical wrist is solved by extending the geometric solutions obtained in the non - redundant case.
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arxiv:2109.12411
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randomized benchmarking ( rb ) is a widely used strategy to assess the quality of available quantum gates in a computational context. rb involves applying known random sequences of gates to an initial state and using the statistics of a final measurement step to determine an effective depolarizing error per step of the sequence, which is a metric of gate quality. here we investigate the advantages of fully randomized benchmarking, where a new random sequence is drawn for each experimental trial. the advantages of full randomization include smaller confidence intervals on the inferred step error, the ability to use maximum likelihood analysis without heuristics, straightforward optimization of the sequence lengths, and the ability to model and measure behaviors that go beyond the typical assumption of time - independent error rates. we discuss models of time - dependent or non - markovian errors that generalize the basic rb model of a single exponential decay of the success probability. for any of these models, we implement a concrete protocol to minimize the uncertainty of the estimated parameters given a fixed time constraint on the complete experiment, and we implement a maximum likelihood analysis. we consider several previously published experiments and determine the potential for improvements with optimized full randomization. we experimentally observe such improvements in clifford randomized benchmarking experiments on a single trapped ion qubit at the national institute of standards and technology ( nist ). for an experiment with uniform lengths and intentionally repeated sequences the step error was $ 2. 42 ^ { + 0. 30 } _ { - 0. 22 } \ times 10 ^ { - 5 } $, and for an optimized fully randomized experiment of the same total duration the step error was $ 2. 57 ^ { + 0. 07 } _ { - 0. 06 } \ times 10 ^ { - 5 } $. we find a substantial decrease in the uncertainty of the step error as a result of optimized fully randomized benchmarking.
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arxiv:2312.15836
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these lectures describe some of the latest data on particle production in high - energy collisions and compare them with theoretical calculations and models based on qcd. the main topics covered are : fragmentation functions and factorization, small - x fragmentation, hadronization models, differences between quark and gluon fragmentation, current and target fragmentation in deep inelastic scattering, and heavy quark fragmentation.
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arxiv:hep-ph/9912399
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in this work, we have proved a version of the hardy - littlewood - sobolev inequality for variable exponents. after we use the variational method to establish the existence of solution for a class of choquard equations involving the $ p ( x ) $ - laplacian operator.
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arxiv:1609.09558
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given a poset $ p $ we say a family $ \ mathcal { f } \ subseteq p $ is centered if it is obtained by ` taking sets as close to the middle layer as possible '. a poset $ p $ is said to have the centeredness property if for any $ m $, among all families of size $ m $ in $ p $, centered families contain the minimum number of comparable pairs. kleitman showed that the boolean lattice $ \ { 0, 1 \ } ^ n $ has the centeredness property. it was conjectured by noel, scott, and sudakov, and by balogh and wagner, that the poset $ \ { 0, 1, \ ldots, k \ } ^ n $ also has the centeredness property, provided $ n $ is sufficiently large compared to $ k $. we show that this conjecture is false for all $ k \ geq 2 $ and investigate the range of $ m $ for which it holds. further, we improve a result of noel, scott, and sudakov by showing that the poset of subspaces of $ \ mathbb { f } _ q ^ n $ has the centeredness property. several open questions are also given.
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arxiv:1703.05427
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the flavor changing and cp violating phenomena predicted in supersymmetric unified theories as a consequence of the large top quark yukawa coupling, are investigated in the quark sector and compared with related phenomena in the lepton sector, considered previously. in particular we study $ \ varepsilon _ k $, $ \ varepsilon _ k ' / \ varepsilon _ k $, $ \ delta m _ b $, $ b \ to s \ gamma $, the neutron electric dipole moment, $ d _ n $, and cp violation in neutral $ b $ meson decays, both in minimal ~ su ( 5 ) and ~ so ( 10 ) theories. the leptonic signals are generically shown to provide more significant tests of quark - lepton unification. nevertheless, mostly in the ~ so ( 10 ) case, a variety of hadronic signals is also possible, with interesting correlations among them.
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arxiv:hep-ph/9504373
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an l - sequence of a graph $ g $ is a sequence of distinct vertices $ s = \ { v _ 1,..., v _ k \ } $ such that $ n [ v _ i ] \ setminus \ cup _ { j = 1 } ^ { i - 1 } n ( v _ j ) \ neq \ emptyset $. the length of the longest l - sequence is called the l - grundy domination number, denoted $ \ gamma _ { gr } ^ l ( g ) $. in this paper, we prove $ \ gamma _ { gr } ^ l ( g ) \ leq n ( g ) - \ delta ( g ) + 1 $, which was conjectured by bre { \ v { s } } ar, gologranc, henning, and kos. we also prove some early results about characteristics of $ n $ - vertex graphs such $ \ gamma _ { gr } ^ l ( g ) = n $, as well as bounds on the change in l - grundy number under graph operations.
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arxiv:2108.12264
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the measurements of the higgs boson ( h ) production cross sections performed by the cms collaboration in the four - lepton ( 4 $ \ ell $, $ \ ell $ = e, $ \ mu $ ) final state at a center - of - mass energy $ \ sqrt { s } $ = 13. 6 tev are presented. these measurements are based on data collected with the cms detector at the cern lhc in 2022, corresponding to an integrated luminosity of 34. 7 fb $ ^ { - 1 } $. cross sections are measured in a fiducial region closely matching the experimental acceptance, both inclusively and differentially, as a function of the transverse momentum and the absolute value of the rapidity of the four - lepton system. the h $ \ to $ zz $ \ to $ 4 $ \ ell $ inclusive fiducial cross section is measured to be 2. 89 $ ^ { + 0. 53 } _ { - 0. 49 } $ ( stat ) $ ^ { + 0. 29 } _ { - 0. 21 } $ ( syst ) fb, in agreement with the standard model expectation of 3. 09 $ ^ { + 0. 27 } _ { - 0. 24 } $ fb.
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arxiv:2501.14849
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long - time high - resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics ( rmhd ), to understand coronal heating driven by motion of field lines anchored in the photosphere. we unambiguously identify mhd anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. as the loop parameters vary different regimes of turbulence develop : strong turbulence is found for weak axial magnetic fields and long loops, leading to kolmogorov - like spectra in the perpendicular direction, while weaker and weaker regimes ( steeper spectral slopes of total energy ) are found for strong axial magnetic fields and short loops. as a consequence we predict that the scaling of the heating rate with axial magnetic field intensity $ b _ 0 $, which depends on the spectral index of total energy for given loop parameters, must vary from $ b _ 0 ^ { 3 / 2 } $ for weak fields to $ b _ 0 ^ { 2 } $ for strong fields at a given aspect ratio. the predicted heating rate is within the lower range of observed active region and quiet sun coronal energy losses.
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arxiv:astro-ph/0701872
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let $ \ delta $ and $ b $ be the maximum vertex degree and a subset of vertices in a graph $ g $ respectively. in this paper, we study the first ( non - trivial ) steklov eigenvalue $ \ sigma _ 2 $ of $ g $ with boundary $ b $. using metrical deformation via flows, we first show that $ \ sigma _ 2 = \ mathcal { o } \ left ( \ frac { \ delta ( g + 1 ) ^ 3 } { | b | } \ right ) $ for graphs of orientable genus $ g $ if $ | b | \ geq \ max \ { 3 \ sqrt { g }, | v | ^ { \ frac { 1 } { 4 } + \ epsilon }, 9 \ } $ for some $ \ epsilon > 0 $. this can be seen as a discrete analogue of karpukhin ' s bound. secondly, we prove that $ \ sigma _ 2 \ leq \ frac { 8 \ delta + 4x } { | b | } $ based on planar crossing number $ x $. thirdly, we show that $ \ sigma _ 2 \ leq \ frac { | b | } { | b | - 1 } \ cdot \ delta _ b $, where $ \ delta _ b $ denotes the minimum degree for boundary vertices in $ b $. at last, we compare several upper bounds on laplacian eigenvalues and steklov eigenvalues.
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arxiv:2410.22632
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we introduce a training - free framework specifically designed to bring real - world static paintings to life through image - to - video ( i2v ) synthesis, addressing the persistent challenge of aligning these motions with textual guidance while preserving fidelity to the original artworks. existing i2v methods, primarily trained on natural video datasets, often struggle to generate dynamic outputs from static paintings. it remains challenging to generate motion while maintaining visual consistency with real - world paintings. this results in two distinct failure modes : either static outputs due to limited text - based motion interpretation or distorted dynamics caused by inadequate alignment with real - world artistic styles. we leverage the advanced text - image alignment capabilities of pre - trained image models to guide the animation process. our approach introduces synthetic proxy images through two key innovations : ( 1 ) dual - path score distillation : we employ a dual - path architecture to distill motion priors from both real and synthetic data, preserving static details from the original painting while learning dynamic characteristics from synthetic frames. ( 2 ) hybrid latent fusion : we integrate hybrid features extracted from real paintings and synthetic proxy images via spherical linear interpolation in the latent space, ensuring smooth transitions and enhancing temporal consistency. experimental evaluations confirm that our approach significantly improves semantic alignment with text prompts while faithfully preserving the unique characteristics and integrity of the original paintings. crucially, by achieving enhanced dynamic effects without requiring any model training or learnable parameters, our framework enables plug - and - play integration with existing i2v methods, making it an ideal solution for animating real - world paintings. more animated examples can be found on our project website.
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arxiv:2503.23736
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unsupervised domain adaptation ( uda ) attempts to recognize the unlabeled target samples by building a learning model from a differently - distributed labeled source domain. conventional uda concentrates on extracting domain - invariant features through deep adversarial networks. however, most of them seek to match the different domain feature distributions, without considering the task - specific decision boundaries across various classes. in this paper, we propose a novel adversarial dual distinct classifiers network ( ad $ ^ 2 $ cn ) to align the source and target domain data distribution simultaneously with matching task - specific category boundaries. to be specific, a domain - invariant feature generator is exploited to embed the source and target data into a latent common space with the guidance of discriminative cross - domain alignment. moreover, we naturally design two different structure classifiers to identify the unlabeled target samples over the supervision of the labeled source domain data. such dual distinct classifiers with various architectures can capture diverse knowledge of the target data structure from different perspectives. extensive experimental results on several cross - domain visual benchmarks prove the model ' s effectiveness by comparing it with other state - of - the - art uda.
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arxiv:2008.11878
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computational methods are driving high impact microscopy techniques such as ptychography. however, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close - to - the - hardware programming constructs to speed up the reconstruction. in this paper, we present scicompty, a new ptychography software framework aiming at simulating ptychography datasets and testing state - of - the - art and new reconstruction algorithms. despite its simplicity, the software leverages gpu accelerated processing through the pytorch cuda interface. this is essential to design new methods that can readily be employed. as an example, we present an improved position refinement method based on adam and a new version of the rpie algorithm, adapted for partial coherence setups. results are shown on both synthetic and real datasets. the software is released as open - source.
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arxiv:2205.04295
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we present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time - dependent magnetic field. this method successfully circumvents the computational difficulties presented by a direct solution of the liouville - von neumann equation for a long - lived radical pair containing many hyperfine - coupled nuclear spins. using a modified formulation of floquet theory, treating the time - dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yield by considering only nearly - degenerate sub - spaces of the floquet space. within a significant parameter range, the resulting method is found to give product yields in good agreement with exact quantum mechanical results for a variety of simple model radical pairs. moreover it is considerably more efficient than the exact calculation, and it can be applied to radical pairs containing significantly more nuclear spins. this promises to open the door to realistic theoretical investigations of the effect of radiofrequency electromagnetic radiation on the photochemically induced radical pair recombination reactions in the avian retina which are believed to be responsible for the magnetic compass sense of migratory birds.
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arxiv:1610.00490
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understanding the formation and evolution of the first stars and galaxies represents one of the most exciting frontiers in astronomy. since the universe was filled with neutral hydrogen at early times, the most promising method for observing the epoch of the first stars is using the prominent 21 - cm spectral line of the hydrogen atom. current observational efforts are focused on the reionization era ( cosmic age t ~ 500 myr ), with earlier times considered much more challenging. however, the next frontier of even earlier galaxy formation ( t ~ 200 myr ) is emerging as a promising observational target. this is made possible by a recently noticed effect of a significant relative velocity between the baryons and dark matter at early times. the velocity difference suppresses star formation, causing a unique form of early luminosity bias. the spatial variation of this suppression enhances large - scale clustering and produces a prominent cosmic web on 100 comoving mpc scales in the 21 - cm intensity distribution. this structure makes it much more feasible for radio astronomers to detect these early stars, and should drive a new focus on this era, which is rich with little - explored astrophysics.
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arxiv:1304.2046
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the electronic dispersion of a graphene bilayer is highly dependent on rotational mismatch between layers and can be further manipulated by electrical gating. this allows for an unprecedented control over electronic properties and opens up the possibility of flexible band structure engineering. here we present novel magnetotransport data in a twisted bilayer, crossing the energetic border between decoupled monolayers and coupled bilayer. in addition a transition in berry phase between pi and 2pi is observed at intermediate magnetic fields. analysis of fermi velocities and gate induced charge carrier densities suggests an important role of strong layer asymmetry for the observed phenomena.
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arxiv:1603.04806
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the planetary nebulae he 2 - 436 and wray 16 - 423 in the sagittarius dwarf galaxy appear to result from nearly twin stars, except that third - dredge - up carbon is more abundant in he 2 - 436. a thorough photoionization - model analysis implies that ratios ne / o, s / o and ar / o are significantly smaller in he 2 - 436, indicative of third - dredge - up oxygen enrichment. the enrichment of oxygen with respect to carbon is ( 7 + / - 4 ) %. excess nitrogen in wray 16 - 423 suggests third dredge - up of late cn - cycle products even in these low - mass, intermediate - metallicity stars.
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arxiv:astro-ph/0008443
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in this paper we study the enumeration and the construction of particular binary words avoiding the pattern $ 1 ^ { j + 1 } 0 ^ j $. by means of the theory of riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words and then kills those containing the forbidden pattern.
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arxiv:1103.5689
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we establish a threshold for the connectivity of certain random graphs whose ( dependent ) edges are determined by the uniform distributions on generalized orlicz balls, crucially using their negative correlation properties. we also show the existence of a unique giant component for such random graphs.
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arxiv:1806.08201
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we report a numerical evidence of the discontinuous transition of a tethered membrane model which is defined within a framework of the membrane elasticity of helfrich. two kinds of phantom tethered membrane models are studied via the canonical monte carlo simulation on triangulated fixed connectivity surfaces of spherical topology. a surface model is defined by the gaussian term and the bending energy term, and the other, which is tensionless, is defined by the bending energy term and a hard wall potential. the bending energy is defined by using the normal vector at each vertex. both of the models undergo the first - order phase transition characterized by a gap of the bending energy. the phase structure of the models depends on the choice of discrete bending energy.
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arxiv:cond-mat/0411209
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we comment on calculations of the width of the d ' resonance within framework of quark shell models.
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arxiv:nucl-th/9712079
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startups have become in less than 50 years a major component of innovation and economic growth. an important feature of the startup phenomenon has been the wealth created through equity in startups to all stakeholders. these include the startup founders, the investors, and also the employees through the stock - option mechanism and universities through licenses of intellectual property. in the employee group, the allocation to important managers like the chief executive, vice - presidents and other officers, and independent board members is also analyzed. this report analyzes how equity was allocated in more than 400 startups, most of which had filed for an initial public offering. the author has the ambition of informing a general audience about best practice in equity split, in particular in silicon valley, the central place for startup innovation.
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arxiv:1711.00661
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the abundance of oxygen was determined for selected very metal - poor g - k stars ( six giants and one turn - off star ) based on the high s / n and high - resolution spectra observed with keck hires in the red through near - ir region comprising the permitted o i lines ( 7771 - 5, 8446 ) along with the [ o i ] forbidden line at 6363 a. it turned out that both the abundances from the permitted line features, o i 7771 - 5 and o i 8446, agree quite well with each other, while the forbidden line yields somewhat discrepant and divergent abundances with a tendency of being underestimated on the average. the former ( 7773 / 8446 ) solution, which we believe to be more reliable, gives a fairly tight [ o / fe ] vs. [ fe / h ] relation such that increasing steadily from [ o / fe ] = 0. 6 ( at [ fe / h ] = - 1. 5 ) to [ o / fe ] = 1. 0 ( at [ fe / h ] = - 3. 0 ), in reasonable consistency with the trend recently reported based on the analysis of the uv oh lines. we would suspect that some kind of weakening mechanism may occasionally act on the formation of [ o i ] forbidden lines in metal - poor stars. therefore, [ o i ] lines may not be so a reliable abundance indicator as has been generally believed.
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arxiv:astro-ph/0007007
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we present in - plane optical study on tl $ _ { 2 } $ ba $ _ { 2 } $ cuo $ _ { 6 + \ delta } $ single crystals with substantially different $ t _ c $. the study reveals that the overdoping does not lead to a further increase of the carrier density but a decrease of scattering rate. the most significant change occurs at low temperature and in the low frequency. a characteristic spectral feature, seen most clearly for the optimally doped sample and commonly ascribed to the mode coupling effect, weakens with doping and disappears in the heavily overdoped sample. meanwhile, the optical scattering rate evolves from a linear - $ \ omega $ dependence to an upward curvature lineshape. both the temperature and frequency dependence of the scattering rate can be described by a power law relation. we elaborate that the overall decrease of the optical scattering rate originates from the increase of both the quasiparticle life time and the fermi velocity near the ( $ \ pi $, 0 ) region in the fermi surface.
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arxiv:cond-mat/0511643
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we report sub - pc - scale observations of the 321 - ghz h $ _ 2 $ o emission line in the radio galaxy ngc 1052. the h $ _ 2 $ o line emitter size is constrained in $ < 0. 6 $ milliarcsec distributed on the continuum core component. the brightness temperature exceeding $ 10 ^ 6 $ k and the intensity variation indicate certain evidence for maser emission. the maser spectrum consists of redshifted and blueshifted velocity components spanning $ \ sim 400 $ km s $ ^ { - 1 } $, separated by a local minimum around the systemic velocity of the galaxy. spatial distribution of maser components show velocity gradient along the jet direction, implying that the population - inverted gas is driven by the jets interacting with the molecular torus. we identified significant change of the maser spectra between two sessions separated by 14 days. the maser profile showed a radial velocity drift of $ 127 \ pm 13 $ km s $ ^ { - 1 } $ yr $ ^ { - 1 } $ implying inward gravitational acceleration at 5000 schwarzschild radii. the results demonstrate feasibility of future vlbi observations to resolve the jet - torus interacting region.
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arxiv:2402.06166
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i review recent lattice calculations performed with nf = 2 and nf = 2 + 1 dynamical fermions which provide a precise computation of the bk bag parameter. i also report on nf = 2 dynamical quark simulations aiming at the computation of the full basis of the delta _ s = 2 four - fermion operator matrix elements that are relevant to models beyond the standard model.
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arxiv:1101.3069
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we analyze the cross - correlation of 2, 705 unambiguously intervening mg ii ( 2796, 2803a ) quasar absorption line systems with 1, 495, 604 luminous red galaxies ( lrgs ) from the fifth data release of the sloan digital sky survey within the redshift range 0. 36 < = z < = 0. 8. we confirm with high precision a previously reported weak anti - correlation of equivalent width and dark matter halo mass, measuring the average masses to be log m _ h ( m _ [ solar ] h ^ - 1 ) = 11. 29 [ + 0. 36, - 0. 62 ] and log m _ h ( m _ [ solar ] h ^ - 1 ) = 12. 70 [ + 0. 53, - 1. 16 ] for systems with w [ 2796a ] > = 1. 4a and 0. 8a < = w [ 2796a ] < 1. 4a, respectively. additionally, we investigate the significance of a number of potential sources of bias inherent in absorber - lrg cross - correlation measurements, including absorber velocity distributions and the weak lensing of background quasars, which we determine is capable of producing a 20 - 30 % bias in angular cross - correlation measurements on scales less than 2 '. we measure the mg ii - lrg cross - correlation for 719 absorption systems with v < 60, 000 km s ^ - 1 in the quasar rest frame and find that these associated absorbers typically reside in dark matter haloes that are ~ 10 - 100 times more massive than those hosting unambiguously intervening mg ii absorbers. furthermore, we find evidence for evolution of the redshift number density, dn / dz, with 2 - sigma significance for the strongest ( w > 2. 0a ) absorbers in the dr5 sample. this width - dependent dn / dz evolution does not significantly affect the recovered equivalent width - halo mass anti - correlation and adds to existing evidence that the strongest mg ii absorption systems are correlated with an evolving population of field galaxies at z < 0. 8, while the non - evolving dn / dz of the weakest absorbers more closely resembles that of the lrg population.
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arxiv:0902.4003
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we calculate the cmb temperature distortion due to the energetic electrons and positrons produced by dark matter annihilation ( sunyaev - zel ' dovich effect ), in dwarf spheroidal galaxies ( dsphs ). in the calculation we have included two important effects which were previously ignored. first we show that the electron - positron pairs with energy less than gev, which were neglected in previous calculation, could contribute a significant fraction of the total signal. secondly we also consider the full effects of diffusion loss, which could significantly reduce the density of electron - positron pairs at the center of cuspy halos. for neutralinos, we confirm that detecting such kind of sz effect is beyond the capability of the current or even the next generation experiments. in the case of light dark matter ( ldm ) the signal is much larger, but even in this case it is only marginally detectable with the next generation of experiment such as alma. we conclude that similar to the case of galaxy clusters, in the dwarf galaxies the $ sz _ 2dm } $ effect is not a strong probe of dm annihilations.
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arxiv:1005.2325
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we present a new map - making method for cmb measurements. the method is based on the destriping technique, but it also utilizes information about the noise spectrum. the low - frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum - likelihood analysis, involving the covariance matrix of the amplitudes. we present simulation results with $ 1 / f $ noise and show a reduction in the residual noise with respect to ordinary destriping. this study is related to \ planck lfi activities.
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arxiv:astro-ph/0412517
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we give a simple physical argument to understand the observation that the angular distribution of the top decay lepton depends only on the polarisation of the top and is independent of any anomalous $ tbw $ coupling to linear order.
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arxiv:1809.06285
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we study various non - perturbative approaches to the quantization of the seiberg - witten curve of $ { \ cal n } = 2 $, $ su ( 2 ) $ super yang - mills theory, which is closely related to the modified mathieu operator. the first approach is based on the quantum wkb periods and their resurgent properties. we show that these properties are encoded in the tba equations of gaiotto - moore - neitzke determined by the bps spectrum of the theory, and we relate the borel - resummed quantum periods to instanton calculus. in addition, we use the ts / st correspondence to obtain a closed formula for the fredholm determinant of the modified mathieu operator. finally, by using blowup equations, we explain the connection between this operator and the $ \ tau $ function of painleve $ \ rm iii $.
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arxiv:1908.07065
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we define scattering phases associated to pairs of laplacians on asymptotically hyperbolic manifolds, and prove some spectral asymptotics for them. these result are applications of isozaki - kitada ' s constructions which we adapt to this framework.
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arxiv:math/0312381
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we introduce a new augmented adaptation of the recently developed full coupled - cluster reduction ( fccr ) with a second - order perturbative correction, abbreviated as fccr ( 2 ). fccr is a selected coupled - cluster expansion aimed at optimally reducing the excitation manifold and commutator expansions for high - rank excitations to obtain accurate solutions of the electronic schrodinger equation in a size - extensive manner. the present fccr ( 2 ) enables the estimation of the residual correlation of fccr by the second - order perturbative correction $ e ^ { ( 2 ) } $ from the complementary space of the fccr projection manifold. the linear relationship between $ e ^ { ( 2 ) } $ and the energy of fccr ( 2 ) allows accurate estimates of near - exact energies for a wide variety of molecules with strong electron correlations. the potential of the method is demonstrated using challenging cases, such as the ground state electronic energy of the benzene molecule in equilibrium and stretched geometries, and the isomerization energy of the transition metal complex, [ cu ( nh $ _ 3 $ ) ] $ _ 2 $ o $ _ 2 $ $ ^ { 2 + } $.
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arxiv:2010.01850
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quasi - one - dimensional electron systems display intrinsic instability towards long - range ordered phases at sufficiently low temperatures. the superconducting orders are of particular interest as they can possess either singlet or triplet pairing symmetry and frequently compete with magnetism. here we report on muon spin rotation and relaxation ( $ \ mathrm { \ mu } $ sr ) study of rb $ _ 2 $ mo $ _ 3 $ as $ _ 3 $ characterised by one of the highest critical temperatures $ t _ { \ rm c } = 10. 4 \ \ mathrm { k } $ among quasi - one - dimensional superconductors. the transverse - field $ \ mathrm { \ mu } $ sr signal shows enhanced damping below $ t _ { \ rm c } $ due to the formation of vortex lattice. comparison of vortex lattice broadening against single gap $ s - $, $ p - $ and $ d - $ wave models shows the best agreement for the $ s - $ wave scenario but with the anomalously small superconducting gap, $ \ delta _ 0 $, to $ t _ { \ rm c } $ ratio of $ 2 \ delta _ 0 / k _ { \ rm b } t _ { \ rm c } = 2. 74 ( 1 ) $. the alternative nodal $ p - $ wave or $ d - $ wave scenarios with marginally worse goodness of fit would yield more realistic $ 2 \ delta _ 0 / k _ { \ rm b } t _ { \ rm c } = 3. 50 ( 2 ) $ and $ 2 \ delta _ 0 / k _ { \ rm b } t _ { \ rm c } = 4. 08 ( 1 ) $, respectively, and thus they cannot be ruled out when accounting for the superconducting state in rb $ _ 2 $ mo $ _ 3 $ as $ _ 3 $.
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arxiv:2302.02763
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dark matter particles from the galactic halo can be gravitationally trapped in the solar core or in external orbits. the enhanced density of dark matter particles either in the solar core or in external orbits can result in the annihilation of these particles producing gamma rays via long - lived intermediate states or directly outside the sun, respectively. these processes would yield characteristic features in the energy spectrum of the subsequent gamma rays, i. e., a box - like or line - like shaped feature, respectively. we have performed a dedicated analysis using a 10 - years sample of gamma - ray events from the sun collected by the fermi large area telescope searching for spectral features in the energy spectrum as a signature of dark matter annihilation. in the scenario of gamma - ray production via long - lived mediators we have also evaluated the dark matter - nucleon spin - dependent and spin - independent scattering cross section constraints from the flux limits in a dark matter mass range from 3 gev / c $ ^ 2 $ up to about 1. 8 tev / c $ ^ 2 $. in the mass range up to about 150 gev / c $ ^ 2 $ the limits are in the range $ 10 ^ { - 46 } - 10 ^ { - 45 } $ cm $ ^ { 2 } $ for the spin - dependent scattering and in the range $ 10 ^ { - 48 } - 10 ^ { - 47 } $ cm $ ^ { 2 } $ for the spin - independent case. the range of variation depends on the decay length of the mediator.
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arxiv:2006.04114
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the degree - diameter problem consists of finding the maximum number of vertices $ n $ of a graph with diameter $ d $ and maximum degree $ \ delta $. this problem is well studied, and has been solved for plane graphs of low diameter in which every face is bounded by a 3 - cycle ( triangulations ), and plane graphs in which every face is bounded by a 4 - cycle ( quadrangulations ). in this paper, we solve the degree diameter problem for plane graphs of diameter 3 in which every face is bounded by a 5 - cycle ( pentagulations ). we prove that if $ \ delta \ geq 8 $, then $ n \ leq 3 \ delta - 1 $ for such graphs. this bound is sharp for $ \ delta $ odd.
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arxiv:2401.11187
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weak solutions to parabolic integro - differential operators of order $ \ alpha \ in ( \ alpha _ 0, 2 ) $ are studied. local a priori estimates of h \ " older norms and a weak harnack inequality are proved. these results are robust with respect to $ \ alpha \ nearrow 2 $. in this sense, the presentation is an extension of moser ' s result in 1971.
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arxiv:1203.2126
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multi - person motion prediction is a challenging task, especially for real - world scenarios of highly interacted persons. most previous works have been devoted to studying the case of weak interactions ( e. g., walking together ), in which typically forecasting each human pose in isolation can still achieve good performances. this paper focuses on collaborative motion prediction for multiple persons with extreme motions and attempts to explore the relationships between the highly interactive persons ' pose trajectories. specifically, a novel cross - query attention ( xqa ) module is proposed to bilaterally learn the cross - dependencies between the two pose sequences tailored for this situation. a proxy unit is additionally introduced to bridge the involved persons, which cooperates with our proposed xqa module and subtly controls the bidirectional spatial information flows. these designs are then integrated into a transformer - based architecture and the resulting model is called proxy - bridged game transformer ( pgformer ) for multi - person interactive motion prediction. its effectiveness has been evaluated on the challenging expi dataset, which involves highly interactive actions. our pgformer consistently outperforms the state - of - the - art methods in both short - and long - term predictions by a large margin. besides, our approach can also be compatible with the weakly interacted cmu - mocap and mupots - 3d datasets and extended to the case of more than 2 individuals with encouraging results.
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arxiv:2306.03374
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in this paper, we study the internal stabilizability and internal stabilization problems for multidimensional ( nd ) systems. within the fractional representation approach, a multidimen - sional system can be studied by means of matrices with entries in the integral domain of structurally stable rational fractions, namely the ring of rational functions which have no poles in the closed unit polydisc u n = { z = ( z 1,..., z n ) $ \ in $ c n | | z 1 | 1,..., | z n | 1 }. it is known that the internal stabilizability of a multidimensional system can be investigated by studying a certain polynomial ideal i = p 1,..., p r that can be explicitly described in terms of the transfer matrix of the plant. more precisely the system is stabilizable if and only if v ( i ) = { z $ \ in $ c n | p 1 ( z ) = $ \ times $ $ \ times $ $ \ times $ = p r ( z ) = 0 } $ \ cap $ u n = $ \ emptyset $. in the present article, we consider the specific class of linear nd systems ( which includes the class of 2d systems ) for which the ideal i is zero - dimensional, i. e., the p i ' s have only a finite number of common complex zeros. we propose effective symbolic - numeric algorithms for testing if v ( i ) $ \ cap $ u n = $ \ emptyset $, as well as for computing, if it exists, a stable polynomial p $ \ in $ i which allows the effective computation of a stabilizing controller. we illustrate our algorithms through an example and finally provide running times of prototype implementations for 2d and 3d systems.
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arxiv:1801.04982
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uniaxial compressive strain along the [ 001 ] direction strongly suppresses the spin relaxation in silicon. when the strain level is large enough so that electrons are redistributed only in the two valleys along the strain axis, the dominant scattering mechanisms are quenched and electrons mainly experience intra - axis scattering processes ( intravalley or intervalley scattering within valleys on the same crystal axis ). we first derive the spin - flip matrix elements due to intra - axis electron scattering off impurities, and then provide a comprehensive model of the spin relaxation time due to all possible interactions of conduction - band electrons with impurities and phonons. we predict nearly three orders of magnitude improvement in the spin relaxation time of $ \ sim10 ^ { 19 } \ text { cm } ^ { - 3 } $ antimony - doped silicon ( si : sb ) at low temperatures.
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arxiv:1609.07077
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\ cdot ) } _ l ( \ mathbb { r } ^ n ) $ to the variable hardy space $ h ^ { p ( \ cdot ) } ( \ mathbb { r } ^ n ) $.
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arxiv:1601.06358
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we develop normalisation by evaluation ( nbe ) for dependent types based on presheaf categories. our construction is formulated in the metalanguage of type theory using quotient inductive types. we use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. nbe for simple types uses a logical relation between the syntax and the presheaf interpretation. in our construction, we merge the presheaf interpretation and the logical relation into a proof - relevant logical predicate. we prove normalisation, completeness, stability and decidability of definitional equality. most of the constructions were formalized in agda.
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arxiv:1612.02462
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a multi - quantum wire laser operating in the 1 - d ground state has been achieved in a very high uniformity structure that shows free exciton emission with unprecedented narrow width and low lasing threshold. under optical pumping the spontaneous emission evolves from a sharp free exciton peak to a red - shifted broad band. the lasing photon energy occurs about 5 mev below the free exciton. the observed shift excludes free excitons in lasing and our results show that coulomb interactions in the 1 - d electron - hole system shift the spontaneous emission and play significant roles in laser gain.
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arxiv:cond-mat/0206125
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