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1,802.0646 | Embedding distance graphs in finite field vector spaces | We show that large subsets of vector spaces over finite fields determine
certain point configurations with prescribed distance structure. More
specifically, we consider the complete graph with vertices as the points of $A
\subseteq \mathbf{F}_q^d$ and edges assigned the algebraic distance between
pairs of vertices. We prove nontrivial results on locating specified subgraphs
of maximum vertex degree at most $t$ in dimensions $d \geq 2t$.
| math.CO math.CA math.NT | we show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure more specifically we consider the complete graph with vertices as the points of a subseteq mathbff_qd and edges assigned the algebraic distance between pairs of vertices we prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions d geq 2t | [['we', 'show', 'that', 'large', 'subsets', 'of', 'vector', 'spaces', 'over', 'finite', 'fields', 'determine', 'certain', 'point', 'configurations', 'with', 'prescribed', 'distance', 'structure', 'more', 'specifically', 'we', 'consider', 'the', 'complete', 'graph', 'with', 'vertices', 'as', 'the', 'points', 'of', 'a', 'subseteq', 'mathbff_qd', 'and', 'edges', 'assigned', 'the', 'algebraic', 'distance', 'between', 'pairs', 'of', 'vertices', 'we', 'prove', 'nontrivial', 'results', 'on', 'locating', 'specified', 'subgraphs', 'of', 'maximum', 'vertex', 'degree', 'at', 'most', 't', 'in', 'dimensions', 'd', 'geq', '2t']] | [-0.2157941811656201, 0.14617879346042173, 0.020431963388546137, 0.011503745692607481, -0.0705333607911598, -0.1469767046146444, 0.0847850144491531, 0.3887315859319642, -0.2835949230593542, -0.25904212692694273, -0.0017091198988055112, -0.35067662596702576, -0.10042093296942767, 0.07748619736230467, -0.046864931588061154, -0.004035763491629041, 0.09728040068875998, 0.1430899143233546, -0.06462983088204055, -0.2808627631989111, 0.3723922952776775, -0.09548906539566815, 0.19465445485548116, 0.06436335339094512, 0.13646094471187098, 0.07498958935320843, 0.008018921482289443, 0.09776033471280243, -0.2085419499095451, 0.07160280874813907, 0.26712558806320885, 0.14668574359166087, 0.22434655690813088, -0.38792953034862876, -0.17915009810531046, 0.22921472700545564, 0.0960284714728914, 0.0205656725775043, 0.05162333718612899, -0.22136675505316816, 0.20394721403499716, -0.050862866226680126, -0.15857526428590063, -0.012968869297765195, 0.12037425373273436, 0.02873911127971951, -0.28205093326778297, -0.04431528426357545, 0.05765715061897936, 0.11624438162834849, 0.03395613967040845, -0.18677180643680913, -0.07508990172209451, 0.09641360391833587, -0.05235276798521227, 0.09208457070053555, 0.02236493617965607, -0.11537942120048683, -0.16457517813432787, 0.3364530772669241, -0.014055223859031685, -0.18797270400682464, 0.15861377876717597, -0.2032232248384389, -0.12924945418490097, 0.08687417130568065, 0.19192436051525874, 0.2078176691866247, -0.06603080430159025, 0.14696811988596892, -0.08531343340291642, 0.09858344700705857, 0.16215539870609064, 0.06546221887401771, 0.16650549487530952, 0.08976185475330567, 0.18493362142180558, 0.168929905481491, -0.0406467931206862, -0.01412245726078254, -0.3781990462448448, -0.07858521150046727, -0.2235471655440051, 0.08145418710046215, -0.23335079360526834, -0.17574201701791026, 0.4012693143740762, 0.0944518620162853, 0.29832214607449714, 0.09229820952168666, 0.1677650969941169, 0.05065066430506704, 0.06828782222146401, 0.19869817928702105, 0.073234468800365, 0.1311632297874894, -0.0889278547201684, -0.14861602826567832, 0.0032368442007282283, 0.1503248368971981] |
1,802.06461 | Octupole deformation in neutron-rich actinides and superheavy nuclei and
the role of nodal structure of single-particle wavefunctions in extremely
deformed structures of light nuclei | Octupole deformed shapes in neutron-rich actinides and superheavy nuclei as
well as extremely deformed shapes of the N~Z light nuclei have been
investigated within the framework of covariant density functional theory. We
confirmed the presence of new region of octupole deformation in neutron-rich
actinides with the center around Z~96, N~196 but our calculations do not
predict octupole deformation in the ground states of superheavy Z~108 nuclei.
As exemplified by the study of 36Ar, the nodal structure of the wavefunction of
occupied single-particle orbitals in extremely deformed structures allows to
understand the formation of the alpha-clusters in very light nuclei, the
suppression of the alpha-clusterization with the increase of mass number, the
formation of ellipsoidal mean-field type structures and nuclear molecules.
| nucl-th | octupole deformed shapes in neutronrich actinides and superheavy nuclei as well as extremely deformed shapes of the nz light nuclei have been investigated within the framework of covariant density functional theory we confirmed the presence of new region of octupole deformation in neutronrich actinides with the center around z96 n196 but our calculations do not predict octupole deformation in the ground states of superheavy z108 nuclei as exemplified by the study of 36ar the nodal structure of the wavefunction of occupied singleparticle orbitals in extremely deformed structures allows to understand the formation of the alphaclusters in very light nuclei the suppression of the alphaclusterization with the increase of mass number the formation of ellipsoidal meanfield type structures and nuclear molecules | [['octupole', 'deformed', 'shapes', 'in', 'neutronrich', 'actinides', 'and', 'superheavy', 'nuclei', 'as', 'well', 'as', 'extremely', 'deformed', 'shapes', 'of', 'the', 'nz', 'light', 'nuclei', 'have', 'been', 'investigated', 'within', 'the', 'framework', 'of', 'covariant', 'density', 'functional', 'theory', 'we', 'confirmed', 'the', 'presence', 'of', 'new', 'region', 'of', 'octupole', 'deformation', 'in', 'neutronrich', 'actinides', 'with', 'the', 'center', 'around', 'z96', 'n196', 'but', 'our', 'calculations', 'do', 'not', 'predict', 'octupole', 'deformation', 'in', 'the', 'ground', 'states', 'of', 'superheavy', 'z108', 'nuclei', 'as', 'exemplified', 'by', 'the', 'study', 'of', '36ar', 'the', 'nodal', 'structure', 'of', 'the', 'wavefunction', 'of', 'occupied', 'singleparticle', 'orbitals', 'in', 'extremely', 'deformed', 'structures', 'allows', 'to', 'understand', 'the', 'formation', 'of', 'the', 'alphaclusters', 'in', 'very', 'light', 'nuclei', 'the', 'suppression', 'of', 'the', 'alphaclusterization', 'with', 'the', 'increase', 'of', 'mass', 'number', 'the', 'formation', 'of', 'ellipsoidal', 'meanfield', 'type', 'structures', 'and', 'nuclear', 'molecules']] | [-0.05571123784869721, 0.18579052286144315, -0.07470238452949443, 0.14393254811679865, 0.03630179160532831, -0.04912269309538753, 0.024845469319418136, 0.3472153742400491, -0.1732370498347558, -0.29782822910312784, -0.06958996353596605, -0.2673994924017363, -0.05778543959457834, 0.09171595848498068, 0.025542157494508028, -0.0070789039424550134, 0.0014297166260100213, 0.03149718538067546, -0.1219711558924628, -0.15343068743578525, 0.30683141605959846, 0.11806984325604779, 0.23052258662754246, 0.03756889334230238, -0.020505082226131392, 0.007846814204602181, 0.07064568320633609, -0.021278595254451287, -0.10087803947277554, 0.14385404610691374, 0.2679859251175232, 0.03542110801110936, 0.18611892427223883, -0.4545968169456019, -0.1770346478953813, 0.06869039415311412, 0.2104812641902005, 0.1776564124768146, -0.11569830692889747, -0.32465892898685794, 0.027795047483586965, -0.2366241525482981, -0.2666227633266577, -0.14327401630267375, 0.046105299520642816, 0.10717238275482938, -0.16171275518938288, 0.10801447934995428, -0.0034132534471739617, 0.058251383480996954, -0.1590197242687832, -0.18385657108635367, -0.11076551353355416, 0.02627683800308644, 0.09458379502243855, -0.010396403759451849, 0.20879668478282684, -0.11573010609493035, -0.025260516698667856, 0.43412065804943817, 0.04815532858757412, -0.08366800890844159, 0.0912482078038469, -0.21136052078105697, -0.18994523811412334, 0.19952394686514088, 0.16954214146219881, 0.17410793378479592, -0.06823017419144187, 0.09537424840436105, 0.005932460673067312, 0.16949117663433821, 0.06089628881680928, 0.06860099181908519, 0.2140384762442256, 0.21432009562184767, -0.040316182529131155, 0.06391488886712228, -0.1843687448955822, -0.138269158952846, -0.28519819116517275, -0.0738356695706103, -0.1384074246244771, 0.01670573632432903, -0.035219278706760074, -0.17316242141508253, 0.37442873230501383, -0.04619760267013887, 0.189654405387275, -0.08339259772710189, 0.18725749870621355, 0.016033053975317534, 0.08840902332126499, 0.011967678362368644, 0.34989092134314925, 0.24597176614006153, 0.003546586677925113, -0.3358977873880072, 0.04206303908575733, 0.033546093141096606] |
1,802.06462 | Heuristic Based Induction of Answer Set Programs: From Default theories
to combinatorial problems | Significant research has been conducted in recent years to extend Inductive
Logic Programming (ILP) methods to induce Answer Set Programs (ASP). These
methods perform an exhaustive search for the correct hypothesis by encoding an
ILP problem instance as an ASP program. Exhaustive search, however, results in
loss of scalability. In addition, the language bias employed in these methods
is overly restrictive too. In this paper we extend our previous work on
learning stratified answer set programs that have a single stable model to
learning arbitrary (i.e., non-stratified) ones with multiple stable models. Our
extended algorithm is a greedy FOIL-like algorithm, capable of inducing
non-monotonic logic programs, examples of which includes programs for
combinatorial problems such as graph-coloring and N-queens. To the best of our
knowledge, this is the first heuristic-based ILP algorithm to induce answer set
programs with multiple stable models.
| cs.LO | significant research has been conducted in recent years to extend inductive logic programming ilp methods to induce answer set programs asp these methods perform an exhaustive search for the correct hypothesis by encoding an ilp problem instance as an asp program exhaustive search however results in loss of scalability in addition the language bias employed in these methods is overly restrictive too in this paper we extend our previous work on learning stratified answer set programs that have a single stable model to learning arbitrary ie nonstratified ones with multiple stable models our extended algorithm is a greedy foillike algorithm capable of inducing nonmonotonic logic programs examples of which includes programs for combinatorial problems such as graphcoloring and nqueens to the best of our knowledge this is the first heuristicbased ilp algorithm to induce answer set programs with multiple stable models | [['significant', 'research', 'has', 'been', 'conducted', 'in', 'recent', 'years', 'to', 'extend', 'inductive', 'logic', 'programming', 'ilp', 'methods', 'to', 'induce', 'answer', 'set', 'programs', 'asp', 'these', 'methods', 'perform', 'an', 'exhaustive', 'search', 'for', 'the', 'correct', 'hypothesis', 'by', 'encoding', 'an', 'ilp', 'problem', 'instance', 'as', 'an', 'asp', 'program', 'exhaustive', 'search', 'however', 'results', 'in', 'loss', 'of', 'scalability', 'in', 'addition', 'the', 'language', 'bias', 'employed', 'in', 'these', 'methods', 'is', 'overly', 'restrictive', 'too', 'in', 'this', 'paper', 'we', 'extend', 'our', 'previous', 'work', 'on', 'learning', 'stratified', 'answer', 'set', 'programs', 'that', 'have', 'a', 'single', 'stable', 'model', 'to', 'learning', 'arbitrary', 'ie', 'nonstratified', 'ones', 'with', 'multiple', 'stable', 'models', 'our', 'extended', 'algorithm', 'is', 'a', 'greedy', 'foillike', 'algorithm', 'capable', 'of', 'inducing', 'nonmonotonic', 'logic', 'programs', 'examples', 'of', 'which', 'includes', 'programs', 'for', 'combinatorial', 'problems', 'such', 'as', 'graphcoloring', 'and', 'nqueens', 'to', 'the', 'best', 'of', 'our', 'knowledge', 'this', 'is', 'the', 'first', 'heuristicbased', 'ilp', 'algorithm', 'to', 'induce', 'answer', 'set', 'programs', 'with', 'multiple', 'stable', 'models']] | [-0.08198187161137217, -0.046624752710028715, -0.07190986265860765, 0.10661877286370977, -0.17713375397392417, -0.1816685127992449, 0.08666076719444911, 0.40973113857741866, -0.2883618628972077, -0.39334946469004667, 0.08442092014925688, -0.2216867353667372, -0.15041412571112492, 0.2210120982357434, -0.09355786109725679, 0.11887211783656053, 0.11333369755718326, -0.012572721539930042, -0.037895888779426706, -0.3273732934945396, 0.26868562997385326, 0.047671708524493234, 0.23412813246250153, -0.00590488096599334, 0.07483080901272063, -0.006324970376278673, -0.00969780983203756, 0.06679942090829302, -0.08366989770131893, 0.14186672980680928, 0.38693972627999235, 0.2554949589165127, 0.34273639132401773, -0.4259585803241602, -0.1662160328855472, 0.09826246511324176, 0.11684691460936197, 0.16023562345903233, -0.032491120786705456, -0.26246563929266165, 0.09233926308806986, -0.14603577182362124, -0.008291289885528385, -0.14367000356931905, -0.0023609553197664872, -0.04567228413070552, -0.29083064511069096, -0.04210456048271486, 0.1617889557266608, 0.06287530113809875, -0.041988431718865675, -0.1468649853885706, 0.07057585470444921, 0.04130029983685485, 0.03727705249156575, 0.06820966325966375, 0.08952128351000803, -0.079553399078681, -0.2753001793354217, 0.33451643622081195, -0.04880362192967108, -0.20446252668376214, 0.21549739608474608, -0.002889898914976844, -0.20169109103735536, 0.1471260805447985, 0.2291534561959062, 0.20988679326671575, -0.13360153968845095, 0.11001688264035953, -0.10649466078861483, 0.20144815639526184, 0.05505164693375783, -0.025538633873553148, 0.2022631977884365, 0.23844652293649102, 0.0864158091551092, 0.1518777332418332, 0.03598165976582095, -0.08102437123722796, -0.23177515372517518, -0.11077819174637885, -0.11059731091372668, -0.051514788883546964, -0.05130680538370923, -0.19581351070581668, 0.3526606884518904, 0.242532733338885, 0.13446008586691147, 0.14622175226603368, 0.3467892286467499, 0.07979288125342074, 0.1059255089544292, 0.0713704320144773, 0.16696090633714838, 0.05831738838959219, 0.11383522483852825, -0.1940135718622644, 0.1025624670761837, 0.04203661946480029] |
1,802.06463 | Guaranteed Recovery of One-Hidden-Layer Neural Networks via Cross
Entropy | We study model recovery for data classification, where the training labels
are generated from a one-hidden-layer neural network with sigmoid activations,
also known as a single-layer feedforward network, and the goal is to recover
the weights of the neural network. We consider two network models, the
fully-connected network (FCN) and the non-overlapping convolutional neural
network (CNN). We prove that with Gaussian inputs, the empirical risk based on
cross entropy exhibits strong convexity and smoothness {\em uniformly} in a
local neighborhood of the ground truth, as soon as the sample complexity is
sufficiently large. This implies that if initialized in this neighborhood,
gradient descent converges linearly to a critical point that is provably close
to the ground truth. Furthermore, we show such an initialization can be
obtained via the tensor method. This establishes the global convergence
guarantee for empirical risk minimization using cross entropy via gradient
descent for learning one-hidden-layer neural networks, at the near-optimal
sample and computational complexity with respect to the network input dimension
without unrealistic assumptions such as requiring a fresh set of samples at
each iteration.
| stat.ML cs.LG | we study model recovery for data classification where the training labels are generated from a onehiddenlayer neural network with sigmoid activations also known as a singlelayer feedforward network and the goal is to recover the weights of the neural network we consider two network models the fullyconnected network fcn and the nonoverlapping convolutional neural network cnn we prove that with gaussian inputs the empirical risk based on cross entropy exhibits strong convexity and smoothness em uniformly in a local neighborhood of the ground truth as soon as the sample complexity is sufficiently large this implies that if initialized in this neighborhood gradient descent converges linearly to a critical point that is provably close to the ground truth furthermore we show such an initialization can be obtained via the tensor method this establishes the global convergence guarantee for empirical risk minimization using cross entropy via gradient descent for learning onehiddenlayer neural networks at the nearoptimal sample and computational complexity with respect to the network input dimension without unrealistic assumptions such as requiring a fresh set of samples at each iteration | [['we', 'study', 'model', 'recovery', 'for', 'data', 'classification', 'where', 'the', 'training', 'labels', 'are', 'generated', 'from', 'a', 'onehiddenlayer', 'neural', 'network', 'with', 'sigmoid', 'activations', 'also', 'known', 'as', 'a', 'singlelayer', 'feedforward', 'network', 'and', 'the', 'goal', 'is', 'to', 'recover', 'the', 'weights', 'of', 'the', 'neural', 'network', 'we', 'consider', 'two', 'network', 'models', 'the', 'fullyconnected', 'network', 'fcn', 'and', 'the', 'nonoverlapping', 'convolutional', 'neural', 'network', 'cnn', 'we', 'prove', 'that', 'with', 'gaussian', 'inputs', 'the', 'empirical', 'risk', 'based', 'on', 'cross', 'entropy', 'exhibits', 'strong', 'convexity', 'and', 'smoothness', 'em', 'uniformly', 'in', 'a', 'local', 'neighborhood', 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1,802.06464 | Robust Fitting in Computer Vision: Easy or Hard? | Robust model fitting plays a vital role in computer vision, and research into
algorithms for robust fitting continues to be active. Arguably the most popular
paradigm for robust fitting in computer vision is consensus maximisation, which
strives to find the model parameters that maximise the number of inliers.
Despite the significant developments in algorithms for consensus maximisation,
there has been a lack of fundamental analysis of the problem in the computer
vision literature. In particular, whether consensus maximisation is "tractable"
remains a question that has not been rigorously dealt with, thus making it
difficult to assess and compare the performance of proposed algorithms,
relative to what is theoretically achievable. To shed light on these issues, we
present several computational hardness results for consensus maximisation. Our
results underline the fundamental intractability of the problem, and resolve
several ambiguities existing in the literature.
| cs.CV cs.CC | robust model fitting plays a vital role in computer vision and research into algorithms for robust fitting continues to be active arguably the most popular paradigm for robust fitting in computer vision is consensus maximisation which strives to find the model parameters that maximise the number of inliers despite the significant developments in algorithms for consensus maximisation there has been a lack of fundamental analysis of the problem in the computer vision literature in particular whether consensus maximisation is tractable remains a question that has not been rigorously dealt with thus making it difficult to assess and compare the performance of proposed algorithms relative to what is theoretically achievable to shed light on these issues we present several computational hardness results for consensus maximisation our results underline the fundamental intractability of the problem and resolve several ambiguities existing in the literature | [['robust', 'model', 'fitting', 'plays', 'a', 'vital', 'role', 'in', 'computer', 'vision', 'and', 'research', 'into', 'algorithms', 'for', 'robust', 'fitting', 'continues', 'to', 'be', 'active', 'arguably', 'the', 'most', 'popular', 'paradigm', 'for', 'robust', 'fitting', 'in', 'computer', 'vision', 'is', 'consensus', 'maximisation', 'which', 'strives', 'to', 'find', 'the', 'model', 'parameters', 'that', 'maximise', 'the', 'number', 'of', 'inliers', 'despite', 'the', 'significant', 'developments', 'in', 'algorithms', 'for', 'consensus', 'maximisation', 'there', 'has', 'been', 'a', 'lack', 'of', 'fundamental', 'analysis', 'of', 'the', 'problem', 'in', 'the', 'computer', 'vision', 'literature', 'in', 'particular', 'whether', 'consensus', 'maximisation', 'is', 'tractable', 'remains', 'a', 'question', 'that', 'has', 'not', 'been', 'rigorously', 'dealt', 'with', 'thus', 'making', 'it', 'difficult', 'to', 'assess', 'and', 'compare', 'the', 'performance', 'of', 'proposed', 'algorithms', 'relative', 'to', 'what', 'is', 'theoretically', 'achievable', 'to', 'shed', 'light', 'on', 'these', 'issues', 'we', 'present', 'several', 'computational', 'hardness', 'results', 'for', 'consensus', 'maximisation', 'our', 'results', 'underline', 'the', 'fundamental', 'intractability', 'of', 'the', 'problem', 'and', 'resolve', 'several', 'ambiguities', 'existing', 'in', 'the', 'literature']] | [-0.05893689442544858, -0.023952319892783853, -0.09499492975453852, 0.08913809311632331, -0.12359054637610489, -0.17023188735074396, 0.02561088453760331, 0.4248734563060686, -0.2670536573608043, -0.37401421455309747, 0.13181453806361354, -0.2194742128510583, -0.17907361970250066, 0.22388271415104152, -0.15606823914307863, 0.14137241964687508, 0.09720426745025824, 0.01822345593534674, -0.04428220685597853, -0.2927724585227721, 0.2373559431417297, 0.07541506804182385, 0.32743867678924443, 0.08931060756906761, 0.050322634904440625, -0.02454689209323033, -0.04461566630605582, 0.03617433908045398, -0.12626328375506304, 0.15262393198134575, 0.3359473057038395, 0.21647681805126845, 0.3905597288320039, -0.3919339612892545, -0.2250576208292751, 0.1576589544003182, 0.1691516289910209, 0.11402377425626924, -0.08402231857857621, -0.2252558817201895, 0.09006208685765056, -0.12263805254573888, -0.07452395708293569, -0.08523685465969727, 0.04966354008156357, -0.03784772369297261, -0.22334100401478138, 0.05240472810382538, 0.04389875616362452, 0.04780014572625465, -0.027330332533918745, -0.1419155959911803, 0.07994743240237606, 0.15243969909873203, 0.09652281297595365, 0.04375918355278327, 0.09775251203632736, -0.21001576449959836, -0.1739593967894449, 0.4135483652089082, 0.028666831556284893, -0.18820031911732485, 0.1852618198022775, -0.03688735854217505, -0.21693847037138456, 0.09083029935929052, 0.17479429908215682, 0.08475885901836255, -0.15401088054034304, 0.08122775010914865, -0.05940727016835718, 0.16782486112127806, -0.020828668041326475, 0.005245987722214232, 0.21734942197436402, 0.22363337368955374, 0.08516903318867669, 0.1206341095372757, -0.03692505982083579, -0.17128131863766793, -0.204434369941711, -0.1159206221060966, -0.1776497682790992, -0.03631988340311317, -0.0466583967833253, -0.13316210819381877, 0.3939594569705189, 0.27019628992713723, 0.15107757822735934, 0.03853457048617911, 0.3554731132000262, 0.0778174683829796, 0.04266709586975317, 0.08637383590445769, 0.31418759343940894, 0.13243283438397216, 0.07328451135202396, -0.21550021978782108, 0.14072364317055078, 0.00905589084966597] |
1,802.06465 | The class of a fibre in Noncommutative Geometry | This paper studies the K-homology of a crossed product of a discrete group
acting smoothly on a manifold, with a better understanding of the
noncommutative geometry of the crossed-product as the primary goal, and the
Baum-Connes apparatus as the main tool. Examples suggest that the correct
notion of the `Dirac class' of such a noncommutative space is the image under
the equivalence determined by Baum-Connes of the fibre of the fibration of the
Borel space associated to the action and a smooth model for the classifying
space of the group. We give a systematic study of such fibre, or `Dirac
classes,' with applications to the construction of interesting spectral triples
and computation of their K-theory functionals, and we prove in particular that
both the well-known deformation of the Dolbeault operator on the noncommutative
torus, and the class of the boundary extension of a hyperbolic group, are both
Dirac classes in this sense and therefore can be treated topologically in the
same way.
| math.KT | this paper studies the khomology of a crossed product of a discrete group acting smoothly on a manifold with a better understanding of the noncommutative geometry of the crossedproduct as the primary goal and the baumconnes apparatus as the main tool examples suggest that the correct notion of the dirac class of such a noncommutative space is the image under the equivalence determined by baumconnes of the fibre of the fibration of the borel space associated to the action and a smooth model for the classifying space of the group we give a systematic study of such fibre or dirac classes with applications to the construction of interesting spectral triples and computation of their ktheory functionals and we prove in particular that both the wellknown deformation of the dolbeault operator on the noncommutative torus and the class of the boundary extension of a hyperbolic group are both dirac classes in this sense and therefore can be treated topologically in the same way | [['this', 'paper', 'studies', 'the', 'khomology', 'of', 'a', 'crossed', 'product', 'of', 'a', 'discrete', 'group', 'acting', 'smoothly', 'on', 'a', 'manifold', 'with', 'a', 'better', 'understanding', 'of', 'the', 'noncommutative', 'geometry', 'of', 'the', 'crossedproduct', 'as', 'the', 'primary', 'goal', 'and', 'the', 'baumconnes', 'apparatus', 'as', 'the', 'main', 'tool', 'examples', 'suggest', 'that', 'the', 'correct', 'notion', 'of', 'the', 'dirac', 'class', 'of', 'such', 'a', 'noncommutative', 'space', 'is', 'the', 'image', 'under', 'the', 'equivalence', 'determined', 'by', 'baumconnes', 'of', 'the', 'fibre', 'of', 'the', 'fibration', 'of', 'the', 'borel', 'space', 'associated', 'to', 'the', 'action', 'and', 'a', 'smooth', 'model', 'for', 'the', 'classifying', 'space', 'of', 'the', 'group', 'we', 'give', 'a', 'systematic', 'study', 'of', 'such', 'fibre', 'or', 'dirac', 'classes', 'with', 'applications', 'to', 'the', 'construction', 'of', 'interesting', 'spectral', 'triples', 'and', 'computation', 'of', 'their', 'ktheory', 'functionals', 'and', 'we', 'prove', 'in', 'particular', 'that', 'both', 'the', 'wellknown', 'deformation', 'of', 'the', 'dolbeault', 'operator', 'on', 'the', 'noncommutative', 'torus', 'and', 'the', 'class', 'of', 'the', 'boundary', 'extension', 'of', 'a', 'hyperbolic', 'group', 'are', 'both', 'dirac', 'classes', 'in', 'this', 'sense', 'and', 'therefore', 'can', 'be', 'treated', 'topologically', 'in', 'the', 'same', 'way']] | [-0.1475061169239106, 0.08314151193854617, -0.10451266483725681, 0.06827433122376578, -0.08137687495737164, -0.07918345434936108, -0.0007629751358583662, 0.34247395274355824, -0.30766423432915296, -0.2645674530836397, 0.11572998195073142, -0.2180408245893224, -0.18496681302987086, 0.20982292700949826, -0.13244533041088963, 0.019705463712460097, 0.045174640554497825, 0.07898923853285794, -0.12019614612304226, -0.20839316033424787, 0.4425171463733056, 0.010924008603058295, 0.2396773866487, 0.03612014214776997, 0.10525861704997995, 0.016966257819239005, -0.04990617378131935, 0.010748007597242206, -0.12234119307524655, 0.16660209195860834, 0.25092679508214377, 0.055954269923982614, 0.2216309411465593, -0.34830735105285304, -0.19252580970674493, 0.1481919604221382, 0.08639113544730792, 0.02339763672918909, -0.04152876604923311, -0.32035172678944135, 0.0716524510137754, -0.175381429555228, -0.14392198531681466, -0.06303162823638155, -0.003758170044072616, 0.00045935576853491826, -0.21669084157357799, -0.022119312219459702, 0.11326500480810617, 0.0611718662865, -0.08588699466709829, -0.02807903885094012, -0.07167256504360495, 0.1438501043960935, 0.03174815191614246, 0.024228232574971094, 0.11389014779958, -0.10265551535786348, -0.11454924377167229, 0.43377858083005305, -0.06652329411403632, -0.22474560132131619, 0.16323918478138008, -0.1661443747608796, -0.15857720611053577, 0.09066810807138452, 0.11177584130523933, 0.1509670181268895, -0.052985377667218815, 0.16112531099344868, -0.09842410437650634, 0.07860651401440716, 0.03638295842231148, 0.04345807772313739, 0.1590969181176919, 0.12187421659760775, 0.10433770834617777, 0.13670070551516902, -0.01596433558913787, -0.06707277916297087, -0.37181163983014237, -0.2508257037435765, -0.13621163346594845, 0.10733485793016483, -0.10666565281676019, -0.2072031166818407, 0.4408333518076688, 0.07877766448188067, 0.20576954879338083, 0.06908749556294672, 0.2395549636150216, 0.0656651507615382, 0.05679780805201764, 0.0060795450491117845, 0.1667157130971275, 0.19244974565169096, 0.009213397342619705, -0.19177955925826812, -0.03273203967277099, 0.1685940027696851] |
1,802.06466 | Recurrent Binary Embedding for GPU-Enabled Exhaustive Retrieval from
Billion-Scale Semantic Vectors | Rapid advances in GPU hardware and multiple areas of Deep Learning open up a
new opportunity for billion-scale information retrieval with exhaustive search.
Building on top of the powerful concept of semantic learning, this paper
proposes a Recurrent Binary Embedding (RBE) model that learns compact
representations for real-time retrieval. The model has the unique ability to
refine a base binary vector by progressively adding binary residual vectors to
meet the desired accuracy. The refined vector enables efficient implementation
of exhaustive similarity computation with bit-wise operations, followed by a
near- lossless k-NN selection algorithm, also proposed in this paper. The
proposed algorithms are integrated into an end-to-end multi-GPU system that
retrieves thousands of top items from over a billion candidates in real-time.
The RBE model and the retrieval system were evaluated with data from a major
paid search engine. When measured against the state-of-the-art model for binary
representation and the full precision model for semantic embedding, RBE
significantly outperformed the former, and filled in over 80% of the AUC gap
in-between. Experiments comparing with our production retrieval system also
demonstrated superior performance. While the primary focus of this paper is to
build RBE based on a particular class of semantic models, generalizing to other
types is straightforward, as exemplified by two different models at the end of
the paper.
| cs.IR cs.DC cs.LG | rapid advances in gpu hardware and multiple areas of deep learning open up a new opportunity for billionscale information retrieval with exhaustive search building on top of the powerful concept of semantic learning this paper proposes a recurrent binary embedding rbe model that learns compact representations for realtime retrieval the model has the unique ability to refine a base binary vector by progressively adding binary residual vectors to meet the desired accuracy the refined vector enables efficient implementation of exhaustive similarity computation with bitwise operations followed by a near lossless knn selection algorithm also proposed in this paper the proposed algorithms are integrated into an endtoend multigpu system that retrieves thousands of top items from over a billion candidates in realtime the rbe model and the retrieval system were evaluated with data from a major paid search engine when measured against the stateoftheart model for binary representation and the full precision model for semantic embedding rbe significantly outperformed the former and filled in over 80 of the auc gap inbetween experiments comparing with our production retrieval system also demonstrated superior performance while the primary focus of this paper is to build rbe based on a particular class of semantic models generalizing to other types is straightforward as exemplified by two different models at the end of the paper | [['rapid', 'advances', 'in', 'gpu', 'hardware', 'and', 'multiple', 'areas', 'of', 'deep', 'learning', 'open', 'up', 'a', 'new', 'opportunity', 'for', 'billionscale', 'information', 'retrieval', 'with', 'exhaustive', 'search', 'building', 'on', 'top', 'of', 'the', 'powerful', 'concept', 'of', 'semantic', 'learning', 'this', 'paper', 'proposes', 'a', 'recurrent', 'binary', 'embedding', 'rbe', 'model', 'that', 'learns', 'compact', 'representations', 'for', 'realtime', 'retrieval', 'the', 'model', 'has', 'the', 'unique', 'ability', 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1,802.06467 | Memorize or generalize? Searching for a compositional RNN in a haystack | Neural networks are very powerful learning systems, but they do not readily
generalize from one task to the other. This is partly due to the fact that they
do not learn in a compositional way, that is, by discovering skills that are
shared by different tasks, and recombining them to solve new problems. In this
paper, we explore the compositional generalization capabilities of recurrent
neural networks (RNNs). We first propose the lookup table composition domain as
a simple setup to test compositional behaviour and show that it is
theoretically possible for a standard RNN to learn to behave compositionally in
this domain when trained with standard gradient descent and provided with
additional supervision. We then remove this additional supervision and perform
a search over a large number of model initializations to investigate the
proportion of RNNs that can still converge to a compositional solution. We
discover that a small but non-negligible proportion of RNNs do reach partial
compositional solutions even without special architectural constraints. This
suggests that a combination of gradient descent and evolutionary strategies
directly favouring the minority models that developed more compositional
approaches might suffice to lead standard RNNs towards compositional solutions.
| cs.AI cs.LG cs.NE | neural networks are very powerful learning systems but they do not readily generalize from one task to the other this is partly due to the fact that they do not learn in a compositional way that is by discovering skills that are shared by different tasks and recombining them to solve new problems in this paper we explore the compositional generalization capabilities of recurrent neural networks rnns we first propose the lookup table composition domain as a simple setup to test compositional behaviour and show that it is theoretically possible for a standard rnn to learn to behave compositionally in this domain when trained with standard gradient descent and provided with additional supervision we then remove this additional supervision and perform a search over a large number of model initializations to investigate the proportion of rnns that can still converge to a compositional solution we discover that a small but nonnegligible proportion of rnns do reach partial compositional solutions even without special architectural constraints this suggests that a combination of gradient descent and evolutionary strategies directly favouring the minority models that developed more compositional approaches might suffice to lead standard rnns towards compositional solutions | [['neural', 'networks', 'are', 'very', 'powerful', 'learning', 'systems', 'but', 'they', 'do', 'not', 'readily', 'generalize', 'from', 'one', 'task', 'to', 'the', 'other', 'this', 'is', 'partly', 'due', 'to', 'the', 'fact', 'that', 'they', 'do', 'not', 'learn', 'in', 'a', 'compositional', 'way', 'that', 'is', 'by', 'discovering', 'skills', 'that', 'are', 'shared', 'by', 'different', 'tasks', 'and', 'recombining', 'them', 'to', 'solve', 'new', 'problems', 'in', 'this', 'paper', 'we', 'explore', 'the', 'compositional', 'generalization', 'capabilities', 'of', 'recurrent', 'neural', 'networks', 'rnns', 'we', 'first', 'propose', 'the', 'lookup', 'table', 'composition', 'domain', 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1,802.06468 | Dose evaluation of fast synthetic-CT generation using a generative
adversarial network for general pelvis MR-only radiotherapy | To enable magnetic resonance (MR)-only radiotherapy and facilitate modelling
of radiation attenuation in humans, synthetic-CT (sCT) images need to be
generated. Considering the application of MR-guided radiotherapy and online
adaptive replanning, sCT generation should occur within minutes. This work aims
at assessing whether an existing deep learning network can rapidly generate sCT
images to be used for accurate MR-based dose calculations in the entire pelvis.
A study was conducted on data of 91 patients with prostate, rectal and cervical
cancer who underwent external beam radiotherapy acquiring both CT and MRI for
patients' simulation. Dixon reconstructed water, fat and in-phase images
obtained from a conventional dual gradient-recalled echo sequence were used to
generate sCT images. A conditional generative adversarial network (cGAN) was
trained in a paired fashion on 2D transverse slices of 32 prostate cancer
patients. The trained network was tested on the remaining patients to generate
sCT images. For 30 patients in the test set, dose recalculations of the
clinical plan were performed on sCT images. Dose distributions were evaluated
comparing voxel-based dose differences, gamma and dose-volume histogram (DVH)
analysis. The sCT generation required 5.6 s and 21 s for a single patient
volume on a GPU and CPU, respectively. On average, sCT images resulted in a
higher dose to the target of maximum 0.3%. Results suggest that accurate
MR-based dose calculation using sCT images generated with a cGAN trained on
prostate cancer patients is feasible for the entire pelvis. The sCT generation
was sufficiently fast to be integrated into an MR-guided radiotherapy workflow.
| physics.med-ph | to enable magnetic resonance mronly radiotherapy and facilitate modelling of radiation attenuation in humans syntheticct sct images need to be generated considering the application of mrguided radiotherapy and online adaptive replanning sct generation should occur within minutes this work aims at assessing whether an existing deep learning network can rapidly generate sct images to be used for accurate mrbased dose calculations in the entire pelvis a study was conducted on data of 91 patients with prostate rectal and cervical cancer who underwent external beam radiotherapy acquiring both ct and mri for patients simulation dixon reconstructed water fat and inphase images obtained from a conventional dual gradientrecalled echo sequence were used to generate sct images a conditional generative adversarial network cgan was trained in a paired fashion on 2d transverse slices of 32 prostate cancer patients the trained network was tested on the remaining patients to generate sct images for 30 patients in the test set dose recalculations of the clinical plan were performed on sct images dose distributions were evaluated comparing voxelbased dose differences gamma and dosevolume histogram dvh analysis the sct generation required 56 s and 21 s for a single patient volume on a gpu and cpu respectively on average sct images resulted in a higher dose to the target of maximum 03 results suggest that accurate mrbased dose calculation using sct images generated with a cgan trained on prostate cancer patients is feasible for the entire pelvis the sct generation was sufficiently fast to be integrated into an mrguided radiotherapy workflow | [['to', 'enable', 'magnetic', 'resonance', 'mronly', 'radiotherapy', 'and', 'facilitate', 'modelling', 'of', 'radiation', 'attenuation', 'in', 'humans', 'syntheticct', 'sct', 'images', 'need', 'to', 'be', 'generated', 'considering', 'the', 'application', 'of', 'mrguided', 'radiotherapy', 'and', 'online', 'adaptive', 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1,802.06469 | Active fluids at circular boundaries: Swim pressure and anomalous
droplet ripening | We investigate the swim pressure exerted by non-chiral and chiral active
particles on convex or concave circular boundaries. Active particles are
modeled as non-interacting and non-aligning self-propelled Brownian particles.
The convex and concave circular boundaries are used as models representing a
fixed inclusion immersed in an active bath and a cavity (or container)
enclosing the active particles, respectively. We first present a detailed
analysis of the role of convex versus concave boundary curvature and of the
chirality of active particles on their spatial distribution, chirality-induced
currents, and the swim pressure they exert on the bounding surfaces. The
results will then be used to predict the mechanical equilibria of suspended
fluid enclosures (generically referred to as 'droplets') in a bulk with active
particles being present either inside the bulk fluid or within the suspended
droplets. We show that, while droplets containing active particles and
suspended in a normal bulk behave in accordance with standard capillary
paradigms, those containing a normal fluid exhibit anomalous behaviors when
suspended in an active bulk. In the latter case, the excess swim pressure
results in non-monotonic dependence of the inside droplet pressure on the
droplet radius. As a result, we find a regime of anomalous capillarity for a
single droplet, where the inside droplet pressure increases upon increasing the
droplet size. In the case of two interconnected droplets, we show that
mechanical equilibrium can occur also when they have different sizes. We
further identify a regime of anomalous ripening, where two unequal-sized
droplets can reach a final state of equal sizes upon interconnection, in stark
contrast with the standard Ostwald ripening phenomenon, implying shrinkage of
the smaller droplet in favor of the larger one.
| cond-mat.soft cond-mat.stat-mech physics.bio-ph physics.chem-ph | we investigate the swim pressure exerted by nonchiral and chiral active particles on convex or concave circular boundaries active particles are modeled as noninteracting and nonaligning selfpropelled brownian particles the convex and concave circular boundaries are used as models representing a fixed inclusion immersed in an active bath and a cavity or container enclosing the active particles respectively we first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles on their spatial distribution chiralityinduced currents and the swim pressure they exert on the bounding surfaces the results will then be used to predict the mechanical equilibria of suspended fluid enclosures generically referred to as droplets in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets we show that while droplets containing active particles and suspended in a normal bulk behave in accordance with standard capillary paradigms those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk in the latter case the excess swim pressure results in nonmonotonic dependence of the inside droplet pressure on the droplet radius as a result we find a regime of anomalous capillarity for a single droplet where the inside droplet pressure increases upon increasing the droplet size in the case of two interconnected droplets we show that mechanical equilibrium can occur also when they have different sizes we further identify a regime of anomalous ripening where two unequalsized droplets can reach a final state of equal sizes upon interconnection in stark contrast with the standard ostwald ripening phenomenon implying shrinkage of the smaller droplet in favor of the larger one | [['we', 'investigate', 'the', 'swim', 'pressure', 'exerted', 'by', 'nonchiral', 'and', 'chiral', 'active', 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1,802.0647 | A model for a network of conveyor belts with discontinuous speed and
capacity | We introduce a macroscopic model for a network of conveyor belts with various
speeds and capacities. In a different way from traffic flow models, the product
densities are forced to move with a constant velocity unless they reach a
maximal capacity and start to queue. This kind of dynamics is governed by
scalar conservation laws consisting of a discontinuous flux function. We define
appropriate coupling conditions to get well-posed solutions at intersections
and provide a detailed description of the solution. Some numerical simulations
are presented to illustrate and confirm the theoretical results for different
network configurations.
| math.AP | we introduce a macroscopic model for a network of conveyor belts with various speeds and capacities in a different way from traffic flow models the product densities are forced to move with a constant velocity unless they reach a maximal capacity and start to queue this kind of dynamics is governed by scalar conservation laws consisting of a discontinuous flux function we define appropriate coupling conditions to get wellposed solutions at intersections and provide a detailed description of the solution some numerical simulations are presented to illustrate and confirm the theoretical results for different network configurations | [['we', 'introduce', 'a', 'macroscopic', 'model', 'for', 'a', 'network', 'of', 'conveyor', 'belts', 'with', 'various', 'speeds', 'and', 'capacities', 'in', 'a', 'different', 'way', 'from', 'traffic', 'flow', 'models', 'the', 'product', 'densities', 'are', 'forced', 'to', 'move', 'with', 'a', 'constant', 'velocity', 'unless', 'they', 'reach', 'a', 'maximal', 'capacity', 'and', 'start', 'to', 'queue', 'this', 'kind', 'of', 'dynamics', 'is', 'governed', 'by', 'scalar', 'conservation', 'laws', 'consisting', 'of', 'a', 'discontinuous', 'flux', 'function', 'we', 'define', 'appropriate', 'coupling', 'conditions', 'to', 'get', 'wellposed', 'solutions', 'at', 'intersections', 'and', 'provide', 'a', 'detailed', 'description', 'of', 'the', 'solution', 'some', 'numerical', 'simulations', 'are', 'presented', 'to', 'illustrate', 'and', 'confirm', 'the', 'theoretical', 'results', 'for', 'different', 'network', 'configurations']] | [-0.17242943046827955, 0.12490231345388263, -0.08340104694798356, 0.03392094474596282, -0.0547364203351511, -0.1609598820844743, 0.05185353573566923, 0.3447627716814168, -0.262879128184674, -0.2928848340525292, 0.10420280870918457, -0.26651321704654646, -0.1060143974100356, 0.174780011747013, -0.05210366190294735, 0.07364991518503909, 0.0909928279700883, 0.00630148505812637, -0.04020135847410226, -0.1811669707070299, 0.3217464662059986, 0.02521499162927891, 0.26147492478291195, 0.049533129446596526, 0.12502869721114016, -0.0927926655713236, -0.006506407866254449, 0.05694592205933683, -0.19392868671760274, 0.09111716746701859, 0.21792114039199836, 0.09509584732101455, 0.24394825136793466, -0.4747450259941009, -0.2413963382229364, 0.0726806127349846, 0.11574421273811215, 0.10768458482198184, -0.03210491224156916, -0.2531715202057967, 0.08997656490222046, -0.17827609891052512, -0.1790695960589801, -0.09341263091482688, -0.006593856878074196, 0.08731390427419683, -0.307085884710735, 0.045918592785407476, 0.004161214960428576, 0.046888816432328895, -0.09520890141720884, -0.059719988697906956, -0.03559786922536053, 0.12724479783234224, 0.03872679127016454, -0.024087638206159074, 0.11868399198283441, -0.1329875130953345, -0.09675667132857295, 0.387775174031655, -0.04842370110175883, -0.2675615111850978, 0.20868658935069107, -0.11844461928800835, -0.09676000563194975, 0.12624346269876696, 0.19318933953763917, 0.11576617834604501, -0.15684405198165527, 0.003391336792750129, -0.04482966734212823, 0.1067956589977257, 0.05361510881145174, -0.008044785171174832, 0.21904954900188991, 0.16899798483548997, 0.10783812152900889, 0.14297163891569653, -0.026566650146075215, -0.1601055215433007, -0.34132966798885417, -0.1335034622316016, -0.12086552900533813, 0.07139175544822744, -0.09793667781377735, -0.13600352041733763, 0.387965549651805, 0.14213797243428417, 0.2134940170411331, 0.1246158607682446, 0.2927045041445429, 0.12657220487017184, 0.019105034310390085, 0.1269848925342861, 0.20394639686522473, 0.12782104892782323, 0.13306306545079374, -0.1768973355186366, 0.03214092555208481, 0.08083145137546428] |
1,802.06471 | Solitons and rogue waves in spinor Bose-Einstein condensates | We present a general classification of one-soliton solutions as well as novel
families of rogue-wave solutions for $F=1$ spinor Bose-Einstein condensates
(BECs). These solutions are obtained from the inverse scattering transform for
a focusing matrix nonlinear Schr\"odinger equation which models condensates in
the case of attractive mean field interactions and ferromagnetic spin-exchange
interactions. In particular, we show that, when no background is present, all
one-soliton solutions are reducible via unitary transformations to a
combination of oppositely-polarized solitonic solutions of single-component
BECs. On the other hand, we show that, when a non-zero background is present,
not all matrix one-soliton solutions are reducible to a simple combination of
scalar solutions. We show that some solitons are topological ones and others
are dark-bright solitons. Finally, by taking suitable limits of all the
solutions on a non-zero background we also obtain three families of rogue-wave
(i.e., rational) solutions, two of which are novel to the best of our
knowledge.
| nlin.SI | we present a general classification of onesoliton solutions as well as novel families of roguewave solutions for f1 spinor boseeinstein condensates becs these solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear schrodinger equation which models condensates in the case of attractive mean field interactions and ferromagnetic spinexchange interactions in particular we show that when no background is present all onesoliton solutions are reducible via unitary transformations to a combination of oppositelypolarized solitonic solutions of singlecomponent becs on the other hand we show that when a nonzero background is present not all matrix onesoliton solutions are reducible to a simple combination of scalar solutions we show that some solitons are topological ones and others are darkbright solitons finally by taking suitable limits of all the solutions on a nonzero background we also obtain three families of roguewave ie rational solutions two of which are novel to the best of our knowledge | [['we', 'present', 'a', 'general', 'classification', 'of', 'onesoliton', 'solutions', 'as', 'well', 'as', 'novel', 'families', 'of', 'roguewave', 'solutions', 'for', 'f1', 'spinor', 'boseeinstein', 'condensates', 'becs', 'these', 'solutions', 'are', 'obtained', 'from', 'the', 'inverse', 'scattering', 'transform', 'for', 'a', 'focusing', 'matrix', 'nonlinear', 'schrodinger', 'equation', 'which', 'models', 'condensates', 'in', 'the', 'case', 'of', 'attractive', 'mean', 'field', 'interactions', 'and', 'ferromagnetic', 'spinexchange', 'interactions', 'in', 'particular', 'we', 'show', 'that', 'when', 'no', 'background', 'is', 'present', 'all', 'onesoliton', 'solutions', 'are', 'reducible', 'via', 'unitary', 'transformations', 'to', 'a', 'combination', 'of', 'oppositelypolarized', 'solitonic', 'solutions', 'of', 'singlecomponent', 'becs', 'on', 'the', 'other', 'hand', 'we', 'show', 'that', 'when', 'a', 'nonzero', 'background', 'is', 'present', 'not', 'all', 'matrix', 'onesoliton', 'solutions', 'are', 'reducible', 'to', 'a', 'simple', 'combination', 'of', 'scalar', 'solutions', 'we', 'show', 'that', 'some', 'solitons', 'are', 'topological', 'ones', 'and', 'others', 'are', 'darkbright', 'solitons', 'finally', 'by', 'taking', 'suitable', 'limits', 'of', 'all', 'the', 'solutions', 'on', 'a', 'nonzero', 'background', 'we', 'also', 'obtain', 'three', 'families', 'of', 'roguewave', 'ie', 'rational', 'solutions', 'two', 'of', 'which', 'are', 'novel', 'to', 'the', 'best', 'of', 'our', 'knowledge']] | [-0.17187166330782552, 0.1102252873991217, -0.051339924048977095, 0.08337085894550886, -0.08485581426179738, -0.17112613025472148, -0.042341615223059695, 0.3632092703823242, -0.21627598483865332, -0.2075217499975236, 0.11550146445492887, -0.32853120809735414, -0.1794459352832191, 0.19547194786454467, 0.04127115715679096, 0.06395711321625616, 0.056119211743791385, 0.028866334286119257, -0.08455520074409373, -0.26839324852524254, 0.39850074494886517, -0.10307705770821202, 0.24593457523370524, 0.022573855680613115, 0.1188432310871151, -0.044762225540403225, 0.047691713831109275, 0.001419008748799369, -0.13395288752239046, 0.07177577417815564, 0.22321923662010787, 0.06664879278388697, 0.18003639123212037, -0.42609063020677534, -0.21354718166463948, 0.15320331617198013, 0.2071939752763742, 0.20446533822702462, -0.07211297702848572, -0.327198566456156, 0.046683947053774225, -0.133798260253842, -0.1411510777097292, -0.1706598921869458, 0.01686105623579729, 0.12004755309166072, -0.2689894295158469, 0.08376103410835214, 0.08807860891857826, 0.009315313998150167, -0.1596829054405453, -0.11845507213691636, 0.0067431194580752744, 0.03118268322001526, 0.048602989478665704, -0.0385100807338445, 0.025349390426916734, -0.18667675666934389, -0.1028471016211665, 0.38551298019706043, -0.1323941795101734, -0.2657023984560888, 0.20179261354572298, -0.09746077902881163, -0.09272871080743657, 0.11696529690502816, 0.13694245960599707, 0.15087814959274096, -0.15625466443632288, 0.08995246872314941, -0.07901487405738467, 0.1547578910120775, 0.10306679834793141, 0.03821860895266865, 0.21596413290327682, 0.11509875450192576, 0.056315020670170905, 0.1364871824538946, 0.012991328947487977, -0.11784128522706012, -0.3212196135306852, -0.12107778482090731, -0.13185921120805086, 0.04221923105797032, -0.08504010350485, -0.17483557140766098, 0.40888449075547134, 0.097260940963608, 0.17444022247785484, 0.057207751652912246, 0.24603499318533517, 0.13875449703350154, 0.0036968448042095483, 0.04731336065459174, 0.2733382839301689, 0.1192081430700136, 0.05463642162549031, -0.19124392535410484, -0.07562316786996755, 0.107720667946866] |
1,802.06472 | Online convex optimization for cumulative constraints | We propose the algorithms for online convex optimization which lead to
cumulative squared constraint violations of the form
$\sum\limits_{t=1}^T\big([g(x_t)]_+\big)^2=O(T^{1-\beta})$, where
$\beta\in(0,1)$. Previous literature has focused on long-term constraints of
the form $\sum\limits_{t=1}^Tg(x_t)$. There, strictly feasible solutions can
cancel out the effects of violated constraints. In contrast, the new form
heavily penalizes large constraint violations and cancellation effects cannot
occur.
Furthermore, useful bounds on the single step constraint violation
$[g(x_t)]_+$ are derived.
For convex objectives, our regret bounds generalize existing bounds, and for
strongly convex objectives we give improved regret bounds.
In numerical experiments, we show that our algorithm closely follows the
constraint boundary leading to low cumulative violation.
| cs.LG | we propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form sumlimits_t1tbiggx_t_big2ot1beta where betain01 previous literature has focused on longterm constraints of the form sumlimits_t1tgx_t there strictly feasible solutions can cancel out the effects of violated constraints in contrast the new form heavily penalizes large constraint violations and cancellation effects cannot occur furthermore useful bounds on the single step constraint violation gx_t_ are derived for convex objectives our regret bounds generalize existing bounds and for strongly convex objectives we give improved regret bounds in numerical experiments we show that our algorithm closely follows the constraint boundary leading to low cumulative violation | [['we', 'propose', 'the', 'algorithms', 'for', 'online', 'convex', 'optimization', 'which', 'lead', 'to', 'cumulative', 'squared', 'constraint', 'violations', 'of', 'the', 'form', 'sumlimits_t1tbiggx_t_big2ot1beta', 'where', 'betain01', 'previous', 'literature', 'has', 'focused', 'on', 'longterm', 'constraints', 'of', 'the', 'form', 'sumlimits_t1tgx_t', 'there', 'strictly', 'feasible', 'solutions', 'can', 'cancel', 'out', 'the', 'effects', 'of', 'violated', 'constraints', 'in', 'contrast', 'the', 'new', 'form', 'heavily', 'penalizes', 'large', 'constraint', 'violations', 'and', 'cancellation', 'effects', 'can', 'not', 'occur', 'furthermore', 'useful', 'bounds', 'on', 'the', 'single', 'step', 'constraint', 'violation', 'gx_t_', 'are', 'derived', 'for', 'convex', 'objectives', 'our', 'regret', 'bounds', 'generalize', 'existing', 'bounds', 'and', 'for', 'strongly', 'convex', 'objectives', 'we', 'give', 'improved', 'regret', 'bounds', 'in', 'numerical', 'experiments', 'we', 'show', 'that', 'our', 'algorithm', 'closely', 'follows', 'the', 'constraint', 'boundary', 'leading', 'to', 'low', 'cumulative', 'violation']] | [-0.14125391280274172, 0.057198688752492365, -0.09386386368344077, 0.12783061845649807, -0.15100366106248056, -0.1844764978466731, 0.09834735812004304, 0.3110508619860377, -0.24068370272563594, -0.33209580518656745, 0.12941121543924552, -0.2774922839664626, -0.15160473803154914, 0.19474633822639315, -0.12145994433184278, 0.11727072126319948, 0.05457984058203984, -0.011605168903633108, -0.1273743686912019, -0.30403892855810105, 0.28498249383256685, 0.029218903206780833, 0.29744709566024674, 0.14180770079947938, 0.06532989743051452, -0.01909245047630426, -0.009558049081121836, 0.07769880743416131, -0.18125536655031094, 0.09203145614790045, 0.24542058615962853, 0.22448874892719653, 0.2591656968173272, -0.47060664532319557, -0.15509370132788736, 0.1630442543174931, 0.12059807114935708, 0.04187862114993996, -0.06414758486734738, -0.2536367031236021, 0.02520831275450171, -0.08987456172669553, -0.03369990717356076, -0.09916939151271265, -0.07069464860800302, 0.012389488333730766, -0.39097123665576977, 0.085560907359358, 0.07430331493268791, -0.03243726165086593, -0.03725845558032886, -0.18632881628911732, 0.07230705255642533, 0.06465744938841968, 0.1256422385977546, 0.011868106693310558, 0.13177975196883362, -0.08416354459850996, -0.15462492301814118, 0.36671272900728685, -0.07389356287301711, -0.24650316882245946, 0.13152022393121612, -0.1312241110476261, -0.20632996624511368, 0.1297995948039417, 0.23355858986055092, 0.15658595593028948, -0.1500986315802021, 0.093747753673288, -0.06631419619101644, 0.12687217420349248, 0.04751771570069118, 0.10641488610801972, 0.12337465797120459, 0.10822396205720615, 0.20046635591512862, 0.15338130099347458, -0.020462142490289825, -0.12339299842978846, -0.3521864393128539, -0.03797001076449271, -0.15769719466444035, -0.023629968930865015, -0.11634321425978823, -0.09020665352549052, 0.2820653577954596, 0.11613366706736104, 0.15804380605454152, 0.18730045993974925, 0.29814357626831756, 0.15371981069208387, 0.09036173563415431, 0.12175612709537711, 0.30737835493263843, 0.0547964577563107, 0.030651852307923003, -0.25090043777863513, 0.1472514330075597, 0.04157912926660534] |
1,802.06473 | Examples of tropical-to-Lagrangian correspondence | The paper associates Lagrangian submanifolds in symplectic toric varieties to
certain tropical curves inside the convex polyhedral domains of $\R^n$ that
appear as the images of the moment map of the toric varieties.
We pay a particular attention to the case $n=2$, where we reprove Givental's
theorem on Lagrangian embeddability of non-oriented surfaces to $\C^2$, as well
as to the case $n=3$, where we see appearance of the graph 3-manifolds studied
by Waldhausen as Lagrangian submanifolds. In particular, rational tropical
curves in $\R^3$ produce 3-dimensional rational homology spheres. The order of
their first homology groups is determined by the multiplicity of tropical
curves in the corresponding enumerative problems.
| math.SG | the paper associates lagrangian submanifolds in symplectic toric varieties to certain tropical curves inside the convex polyhedral domains of rn that appear as the images of the moment map of the toric varieties we pay a particular attention to the case n2 where we reprove giventals theorem on lagrangian embeddability of nonoriented surfaces to c2 as well as to the case n3 where we see appearance of the graph 3manifolds studied by waldhausen as lagrangian submanifolds in particular rational tropical curves in r3 produce 3dimensional rational homology spheres the order of their first homology groups is determined by the multiplicity of tropical curves in the corresponding enumerative problems | [['the', 'paper', 'associates', 'lagrangian', 'submanifolds', 'in', 'symplectic', 'toric', 'varieties', 'to', 'certain', 'tropical', 'curves', 'inside', 'the', 'convex', 'polyhedral', 'domains', 'of', 'rn', 'that', 'appear', 'as', 'the', 'images', 'of', 'the', 'moment', 'map', 'of', 'the', 'toric', 'varieties', 'we', 'pay', 'a', 'particular', 'attention', 'to', 'the', 'case', 'n2', 'where', 'we', 'reprove', 'giventals', 'theorem', 'on', 'lagrangian', 'embeddability', 'of', 'nonoriented', 'surfaces', 'to', 'c2', 'as', 'well', 'as', 'to', 'the', 'case', 'n3', 'where', 'we', 'see', 'appearance', 'of', 'the', 'graph', '3manifolds', 'studied', 'by', 'waldhausen', 'as', 'lagrangian', 'submanifolds', 'in', 'particular', 'rational', 'tropical', 'curves', 'in', 'r3', 'produce', '3dimensional', 'rational', 'homology', 'spheres', 'the', 'order', 'of', 'their', 'first', 'homology', 'groups', 'is', 'determined', 'by', 'the', 'multiplicity', 'of', 'tropical', 'curves', 'in', 'the', 'corresponding', 'enumerative', 'problems']] | [-0.18871143368866156, 0.014412529174781715, -0.07026836676047205, 0.1418283142168851, -0.08267040974546776, -0.12264179528466668, -0.04384513832768856, 0.31409656149507675, -0.3156281616452529, -0.23521176554021184, 0.10850630927813688, -0.26412860718038345, -0.19416570878928285, 0.16322152205328974, -0.24637842120568235, 0.02096879207615361, 0.013856533157026948, 0.06993760500982818, -0.11182578188944953, -0.3321706459189752, 0.45048745690534514, -0.07242260014646928, 0.16566154382329573, 0.09712426407538631, 0.07168608510228633, 0.02025503261204533, 0.036855635692417205, 0.0119788659040178, -0.19233680018516208, 0.14849089023967585, 0.369728429036008, 0.053637988120667786, 0.0719467814110599, -0.4339332907822811, -0.16129709109507664, 0.22407913230428542, 0.11793041889797207, -0.0009656823455804477, 0.009813789389294537, -0.24346476311243517, 0.018084248277807125, -0.07531596451169914, -0.22355590822796026, -0.0892138274308915, 0.030131116976176767, 0.06626625197801601, -0.1562321065424907, -0.03966954968766206, 0.12856537746200855, 0.15892938040714297, -0.053589002746674747, -0.09416628338793223, -0.13288752294223136, 0.07584857472856701, 0.03707671391182683, 0.11302748105609445, 0.09749395878882045, -0.09990997461998766, -0.1199516519188398, 0.434519639911337, -0.04677077519617914, -0.2605004414829266, 0.0904848574988406, -0.1679587259552338, -0.19051921869524652, 0.1786516675406515, 0.1438987405401551, 0.2192310079138864, -0.010885268061732253, 0.18317753221425745, -0.13354414799768063, -0.006222955365147855, 0.15178514899754966, -0.06731431929101409, 0.13189624454308715, 0.05448724446533662, 0.09719521795934136, 0.18488674965596552, -0.04470217902929074, -0.10474454469254448, -0.3383928191744619, -0.20397391720433478, -0.12733107957023163, 0.1288035777957972, -0.13109770005879304, -0.18937319428961794, 0.37500801522077787, -0.0078108006596772205, 0.19202418478757696, 0.13944626438293467, 0.24782598992223265, -0.01943819020892045, 0.014914721528637327, 0.022008354538465263, 0.1580288558443836, 0.2208727253773422, 0.019196113696563297, -0.1057092431044482, -0.0682674884107352, 0.2738589672889147] |
1,802.06474 | A Closed-form Solution to Photorealistic Image Stylization | Photorealistic image stylization concerns transferring style of a reference
photo to a content photo with the constraint that the stylized photo should
remain photorealistic. While several photorealistic image stylization methods
exist, they tend to generate spatially inconsistent stylizations with
noticeable artifacts. In this paper, we propose a method to address these
issues. The proposed method consists of a stylization step and a smoothing
step. While the stylization step transfers the style of the reference photo to
the content photo, the smoothing step ensures spatially consistent
stylizations. Each of the steps has a closed-form solution and can be computed
efficiently. We conduct extensive experimental validations. The results show
that the proposed method generates photorealistic stylization outputs that are
more preferred by human subjects as compared to those by the competing methods
while running much faster. Source code and additional results are available at
https://github.com/NVIDIA/FastPhotoStyle .
| cs.CV | photorealistic image stylization concerns transferring style of a reference photo to a content photo with the constraint that the stylized photo should remain photorealistic while several photorealistic image stylization methods exist they tend to generate spatially inconsistent stylizations with noticeable artifacts in this paper we propose a method to address these issues the proposed method consists of a stylization step and a smoothing step while the stylization step transfers the style of the reference photo to the content photo the smoothing step ensures spatially consistent stylizations each of the steps has a closedform solution and can be computed efficiently we conduct extensive experimental validations the results show that the proposed method generates photorealistic stylization outputs that are more preferred by human subjects as compared to those by the competing methods while running much faster source code and additional results are available at httpsgithubcomnvidiafastphotostyle | [['photorealistic', 'image', 'stylization', 'concerns', 'transferring', 'style', 'of', 'a', 'reference', 'photo', 'to', 'a', 'content', 'photo', 'with', 'the', 'constraint', 'that', 'the', 'stylized', 'photo', 'should', 'remain', 'photorealistic', 'while', 'several', 'photorealistic', 'image', 'stylization', 'methods', 'exist', 'they', 'tend', 'to', 'generate', 'spatially', 'inconsistent', 'stylizations', 'with', 'noticeable', 'artifacts', 'in', 'this', 'paper', 'we', 'propose', 'a', 'method', 'to', 'address', 'these', 'issues', 'the', 'proposed', 'method', 'consists', 'of', 'a', 'stylization', 'step', 'and', 'a', 'smoothing', 'step', 'while', 'the', 'stylization', 'step', 'transfers', 'the', 'style', 'of', 'the', 'reference', 'photo', 'to', 'the', 'content', 'photo', 'the', 'smoothing', 'step', 'ensures', 'spatially', 'consistent', 'stylizations', 'each', 'of', 'the', 'steps', 'has', 'a', 'closedform', 'solution', 'and', 'can', 'be', 'computed', 'efficiently', 'we', 'conduct', 'extensive', 'experimental', 'validations', 'the', 'results', 'show', 'that', 'the', 'proposed', 'method', 'generates', 'photorealistic', 'stylization', 'outputs', 'that', 'are', 'more', 'preferred', 'by', 'human', 'subjects', 'as', 'compared', 'to', 'those', 'by', 'the', 'competing', 'methods', 'while', 'running', 'much', 'faster', 'source', 'code', 'and', 'additional', 'results', 'are', 'available', 'at', 'httpsgithubcomnvidiafastphotostyle']] | [-0.012219802055894857, -0.001997813746385591, -0.08268378657603663, 0.07860173508902014, -0.07502493991608351, -0.1787333977998982, 0.0050497541940298825, 0.4901729559814426, -0.254605434392251, -0.351593867180423, 0.08139116219884361, -0.3111762057294623, -0.11381937747552309, 0.19027509916127777, -0.131921462493319, 0.08698998836957862, 0.13590740467566, -0.01938882149004994, -0.04942489501488933, -0.25073109941088106, 0.2909028379994274, 0.06465671054402393, 0.32310734308836325, 0.02130074625913526, 0.13724537765030081, -0.06528305797181813, -0.0912027283781536, 0.004641529421886088, -0.02690583727445288, 0.1447988549463818, 0.28611397275268297, 0.16847215130151263, 0.3088592055817725, -0.45206983969874787, -0.19479601201929256, 0.017826704888827573, 0.15702472099850714, 0.16022908998305688, -0.11309962051407792, -0.3172450137527948, 0.12415726687496817, -0.11993908742114796, -0.02104588970541954, -0.15116238106094615, -0.05227021957111453, -0.0310151957673952, -0.31210452504456043, 0.037087056061095545, 0.07269703669303006, 0.015848348425491383, -0.06971867894425883, -0.1053158521494815, -0.0249259733713009, 0.19258065311185701, 0.031301945342984, 0.06588954804465175, 0.15312195500411407, -0.16889089881647443, -0.10041160261074841, 0.40274752330192376, -0.04047494288861857, -0.2085410595828877, 0.15694143368311647, -0.05551738502674172, -0.0856247458797158, 0.15076947841189905, 0.12616370264834292, 0.1623380430744515, -0.1506938252411127, -0.03559537752470802, -0.05302942883301998, 0.21070494323240882, 0.06660469589938581, -0.007578787282371605, 0.17986314153482377, 0.16776284018636378, 0.04997428068169721, 0.14404912220402685, -0.10839789556864073, -0.05257317932276711, -0.23440697353700518, -0.11423535555483065, -0.15326321167169585, -0.040507021907743225, -0.062370380596278245, -0.12771914568795284, 0.4330172528329135, 0.25071131417357273, 0.22731466843208797, 0.07973654205340262, 0.41021157196119534, 0.03691032984618649, 0.11844815893925097, 0.03707090876898138, 0.12215756823990861, -0.04730777374901612, 0.16406903064868766, -0.1698005975311799, 0.09750153251569456, 0.0629434155670821] |
1,802.06475 | A multivariate Berry--Esseen theorem with explicit constants | We provide a Lyapunov type bound in the multivariate central limit theorem
for sums of independent, but not necessarily identically distributed random
vectors. The error in the normal approximation is estimated for certain classes
of sets, which include the class of measurable convex sets. The error bound is
stated with explicit constants. The result is proved by means of Stein's
method. In addition, we improve the constant in the bound of the Gaussian
perimeter of convex sets.
| math.PR | we provide a lyapunov type bound in the multivariate central limit theorem for sums of independent but not necessarily identically distributed random vectors the error in the normal approximation is estimated for certain classes of sets which include the class of measurable convex sets the error bound is stated with explicit constants the result is proved by means of steins method in addition we improve the constant in the bound of the gaussian perimeter of convex sets | [['we', 'provide', 'a', 'lyapunov', 'type', 'bound', 'in', 'the', 'multivariate', 'central', 'limit', 'theorem', 'for', 'sums', 'of', 'independent', 'but', 'not', 'necessarily', 'identically', 'distributed', 'random', 'vectors', 'the', 'error', 'in', 'the', 'normal', 'approximation', 'is', 'estimated', 'for', 'certain', 'classes', 'of', 'sets', 'which', 'include', 'the', 'class', 'of', 'measurable', 'convex', 'sets', 'the', 'error', 'bound', 'is', 'stated', 'with', 'explicit', 'constants', 'the', 'result', 'is', 'proved', 'by', 'means', 'of', 'steins', 'method', 'in', 'addition', 'we', 'improve', 'the', 'constant', 'in', 'the', 'bound', 'of', 'the', 'gaussian', 'perimeter', 'of', 'convex', 'sets']] | [-0.12968241182260226, 0.09952396606760365, -0.08217613719548884, 0.0858275230275467, -0.006001974214110282, -0.12012769899999287, 0.10272201489318501, 0.30023544044657186, -0.2904854787441043, -0.2243558296921675, 0.11856427253828711, -0.2345519139213705, -0.11883508716709912, 0.2423448479952073, -0.12848226027563214, 0.09760716086398664, 0.03216824278404767, 0.07478016577154555, -0.06200127780147187, -0.31946458013171886, 0.3388708367015465, -0.0468166611072692, 0.2713687994287579, 0.052920226370552916, 0.08104495615879824, 0.032524309756064955, -0.06303813842475994, 0.013860974194748061, -0.1546336817494654, 0.1741295960254048, 0.24798456724587972, 0.1265691452599758, 0.2919687263379569, -0.338342893771924, -0.14335160109807144, 0.17455035904664304, 0.1254912307244036, 0.0660989347697151, 0.004352575447712723, -0.26419268472894253, 0.08767990609509992, -0.10438201395044854, -0.176033914597197, -0.06473125820955286, -0.008965014891287723, 0.08495998703088466, -0.35548820331474984, 0.13173391865929227, 0.15765225301895822, 0.04652540059760213, -0.08250180346129293, -0.16736426577576763, 0.06775203516537492, 0.07195857729968409, 0.0483531518325258, 0.039812665196837155, 0.09602186197600956, -0.019829179148201818, -0.10529642463238402, 0.2949975229702987, -0.07207760777983621, -0.2873769136895607, 0.10508480104436348, -0.1592050477584171, -0.14148720834621942, 0.11732787031728725, 0.17094524072894415, 0.12395091467331369, -0.17013022472912614, 0.16486472246394335, -0.10349543323716173, 0.10342020033435388, 0.10256600638778952, 0.0654618547044017, 0.11042503230636577, 0.08068905721188753, 0.1529602866208592, 0.1528703008850964, -0.03460383935916153, -0.08811650524980255, -0.3660930297397948, -0.13157449002822183, -0.27962646243924444, 0.04822555843868456, -0.17235184768547437, -0.24348863468251444, 0.3098343378779563, 0.0546831499676329, 0.15900809562752966, 0.15838484455341498, 0.23964764240693737, 0.1612811576841133, 0.030565058198672803, 0.12767726708469646, 0.22104829623569527, 0.18586232912025186, -0.027564690079443253, -0.12286392365908855, 0.11896886133479995, 0.14559191709698796] |
1,802.06476 | Simultaneous Modeling of Multiple Complications for Risk Profiling in
Diabetes Care | Type 2 diabetes mellitus (T2DM) is a chronic disease that often results in
multiple complications. Risk prediction and profiling of T2DM complications is
critical for healthcare professionals to design personalized treatment plans
for patients in diabetes care for improved outcomes. In this paper, we study
the risk of developing complications after the initial T2DM diagnosis from
longitudinal patient records. We propose a novel multi-task learning approach
to simultaneously model multiple complications where each task corresponds to
the risk modeling of one complication. Specifically, the proposed method
strategically captures the relationships (1) between the risks of multiple T2DM
complications, (2) between the different risk factors, and (3) between the risk
factor selection patterns. The method uses coefficient shrinkage to identify an
informative subset of risk factors from high-dimensional data, and uses a
hierarchical Bayesian framework to allow domain knowledge to be incorporated as
priors. The proposed method is favorable for healthcare applications because in
additional to improved prediction performance, relationships among the
different risks and risk factors are also identified. Extensive experimental
results on a large electronic medical claims database show that the proposed
method outperforms state-of-the-art models by a significant margin.
Furthermore, we show that the risk associations learned and the risk factors
identified lead to meaningful clinical insights.
| cs.LG cs.AI stat.ML | type 2 diabetes mellitus t2dm is a chronic disease that often results in multiple complications risk prediction and profiling of t2dm complications is critical for healthcare professionals to design personalized treatment plans for patients in diabetes care for improved outcomes in this paper we study the risk of developing complications after the initial t2dm diagnosis from longitudinal patient records we propose a novel multitask learning approach to simultaneously model multiple complications where each task corresponds to the risk modeling of one complication specifically the proposed method strategically captures the relationships 1 between the risks of multiple t2dm complications 2 between the different risk factors and 3 between the risk factor selection patterns the method uses coefficient shrinkage to identify an informative subset of risk factors from highdimensional data and uses a hierarchical bayesian framework to allow domain knowledge to be incorporated as priors the proposed method is favorable for healthcare applications because in additional to improved prediction performance relationships among the different risks and risk factors are also identified extensive experimental results on a large electronic medical claims database show that the proposed method outperforms stateoftheart models by a significant margin furthermore we show that the risk associations learned and the risk factors identified lead to meaningful clinical insights | [['type', '2', 'diabetes', 'mellitus', 't2dm', 'is', 'a', 'chronic', 'disease', 'that', 'often', 'results', 'in', 'multiple', 'complications', 'risk', 'prediction', 'and', 'profiling', 'of', 't2dm', 'complications', 'is', 'critical', 'for', 'healthcare', 'professionals', 'to', 'design', 'personalized', 'treatment', 'plans', 'for', 'patients', 'in', 'diabetes', 'care', 'for', 'improved', 'outcomes', 'in', 'this', 'paper', 'we', 'study', 'the', 'risk', 'of', 'developing', 'complications', 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1,802.06477 | On the sheaf of smooth forms on Lie algebroids over triangulated spaces | Cohomology of a compatible family of Lie algebroids defined on a family of
transverse manifolds is defined. A sheaf of differential forms on a compatible
family of Lie algebroids defined over regular open subsets of a simplicial
complex is constructed. It is proved that sheaf is fine.
| math.AT | cohomology of a compatible family of lie algebroids defined on a family of transverse manifolds is defined a sheaf of differential forms on a compatible family of lie algebroids defined over regular open subsets of a simplicial complex is constructed it is proved that sheaf is fine | [['cohomology', 'of', 'a', 'compatible', 'family', 'of', 'lie', 'algebroids', 'defined', 'on', 'a', 'family', 'of', 'transverse', 'manifolds', 'is', 'defined', 'a', 'sheaf', 'of', 'differential', 'forms', 'on', 'a', 'compatible', 'family', 'of', 'lie', 'algebroids', 'defined', 'over', 'regular', 'open', 'subsets', 'of', 'a', 'simplicial', 'complex', 'is', 'constructed', 'it', 'is', 'proved', 'that', 'sheaf', 'is', 'fine']] | [-0.309283853667055, 0.003969580430458201, -0.05305768569257665, 0.12246958440803785, -0.19881030390078716, -0.12046054618908687, -0.08231728678529567, 0.3782302905270394, -0.35708245222872875, -0.1846508969493369, 0.07747631994611089, -0.18608809579560098, -0.14328790523428866, 0.25874976029104374, -0.20861641735710362, -0.03412759537868043, 0.06519108440013642, 0.14716449906019138, -0.0890507234032563, -0.24565014251052064, 0.545462244210091, -0.03869198676832813, 0.21304584655692763, -0.01889276463895085, 0.22240723132532328, -0.05985620749638753, -0.018216828637300654, 0.0628482216097256, -0.14288187057273388, 0.16064483022436182, 0.3494210221031879, 0.006297866179746516, 0.1718412050382888, -0.25458674156602396, -0.12258926582859551, 0.14712426296256959, 0.1068012557349148, -0.06508123494209127, 0.009829436740937067, -0.29153778376255896, 0.09285725187510252, -0.15837438325298595, -0.1620671458819762, -0.0863036905672956, 0.058256592205230225, 0.013484438326447568, -0.22902839821069798, -0.06611415791384717, 0.05896049666594952, 0.18405898323064632, -0.0841210859015267, -0.060600117354237655, -0.1738232363689136, -0.04384859370939592, -0.15836870410737205, 0.09106455485712975, 0.15810800831210106, 0.005462303242467819, -0.18072805185108742, 0.3688214484198475, -0.051626381741717776, -0.2872377292827723, 0.05105535495788493, -0.12091356626850494, -0.21586530639770182, 0.1582919464228635, 0.04533408471244447, 0.21578060035058794, -0.047140049014953854, 0.2560969547943232, -0.16072156767737358, 0.006147987395029595, 0.13742108440938147, 0.005902405124791759, 0.1633907363730225, 0.24171489968578866, 0.09326847121515806, 0.015459187645861443, 0.09604448948967013, -0.12698246487119097, -0.34445925718767845, -0.19297454765740227, -0.11316757639275586, 0.2271445222357486, -0.05791389827735405, -0.27330087493867317, 0.4278802032324862, -0.015890783214188638, 0.2464655647673545, 0.15254998488470595, 0.13096343511913686, 0.03324510640603431, 0.1446389028743068, 0.020464427571030373, 0.09907461322368459, 0.29061947089243445, -0.0587068559884272, -0.013482374873537411, -0.036283826594181515, 0.1895517397354892] |
1,802.06478 | An Efficient Local Search for the Minimum Independent Dominating Set
Problem | In the present paper, we propose an efficient local search for the minimum
independent dominating set problem. We consider a local search that uses
$k$-swap as the neighborhood operation. Given a feasible solution $S$, it is
the operation of obtaining another feasible solution by dropping exactly $k$
vertices from $S$ and then by adding any number of vertices to it. We show
that, when $k=2$, (resp., $k=3$ and a given solution is minimal with respect to
2-swap), we can find an improved solution in the neighborhood or conclude that
no such solution exists in $O(n\Delta)$ (resp., $O(n\Delta^3)$) time, where $n$
denotes the number of vertices and $\Delta$ denotes the maximum degree. We
develop a metaheuristic algorithm that repeats the proposed local search and
the plateau search iteratively, where the plateau search examines solutions of
the same size as the current solution that are obtainable by exchanging a
solution vertex and a non-solution vertex. The algorithm is so effective that,
among 80 DIMACS graphs, it updates the best-known solution size for five graphs
and performs as well as existing methods for the remaining graphs.
| cs.DS | in the present paper we propose an efficient local search for the minimum independent dominating set problem we consider a local search that uses kswap as the neighborhood operation given a feasible solution s it is the operation of obtaining another feasible solution by dropping exactly k vertices from s and then by adding any number of vertices to it we show that when k2 resp k3 and a given solution is minimal with respect to 2swap we can find an improved solution in the neighborhood or conclude that no such solution exists in ondelta resp ondelta3 time where n denotes the number of vertices and delta denotes the maximum degree we develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively where the plateau search examines solutions of the same size as the current solution that are obtainable by exchanging a solution vertex and a nonsolution vertex the algorithm is so effective that among 80 dimacs graphs it updates the bestknown solution size for five graphs and performs as well as existing methods for the remaining graphs | [['in', 'the', 'present', 'paper', 'we', 'propose', 'an', 'efficient', 'local', 'search', 'for', 'the', 'minimum', 'independent', 'dominating', 'set', 'problem', 'we', 'consider', 'a', 'local', 'search', 'that', 'uses', 'kswap', 'as', 'the', 'neighborhood', 'operation', 'given', 'a', 'feasible', 'solution', 's', 'it', 'is', 'the', 'operation', 'of', 'obtaining', 'another', 'feasible', 'solution', 'by', 'dropping', 'exactly', 'k', 'vertices', 'from', 's', 'and', 'then', 'by', 'adding', 'any', 'number', 'of', 'vertices', 'to', 'it', 'we', 'show', 'that', 'when', 'k2', 'resp', 'k3', 'and', 'a', 'given', 'solution', 'is', 'minimal', 'with', 'respect', 'to', '2swap', 'we', 'can', 'find', 'an', 'improved', 'solution', 'in', 'the', 'neighborhood', 'or', 'conclude', 'that', 'no', 'such', 'solution', 'exists', 'in', 'ondelta', 'resp', 'ondelta3', 'time', 'where', 'n', 'denotes', 'the', 'number', 'of', 'vertices', 'and', 'delta', 'denotes', 'the', 'maximum', 'degree', 'we', 'develop', 'a', 'metaheuristic', 'algorithm', 'that', 'repeats', 'the', 'proposed', 'local', 'search', 'and', 'the', 'plateau', 'search', 'iteratively', 'where', 'the', 'plateau', 'search', 'examines', 'solutions', 'of', 'the', 'same', 'size', 'as', 'the', 'current', 'solution', 'that', 'are', 'obtainable', 'by', 'exchanging', 'a', 'solution', 'vertex', 'and', 'a', 'nonsolution', 'vertex', 'the', 'algorithm', 'is', 'so', 'effective', 'that', 'among', '80', 'dimacs', 'graphs', 'it', 'updates', 'the', 'bestknown', 'solution', 'size', 'for', 'five', 'graphs', 'and', 'performs', 'as', 'well', 'as', 'existing', 'methods', 'for', 'the', 'remaining', 'graphs']] | [-0.15328390303707823, 0.06788453241103255, -0.02995412924727581, 0.021027120945301406, -0.0737929515717499, -0.1734539627373302, 0.10390472977081387, 0.3473043641629603, -0.28421441205470255, -0.34355192786952815, 0.12187858193126824, -0.32825267223339505, -0.1493146853006377, 0.12888531962035005, -0.03448066395556544, 0.025082792745975975, 0.08944662905417841, 0.10515963255854417, -0.02287376645754752, -0.26274664193397, 0.2694109889767107, 0.018068382348709184, 0.19767956361798933, 0.009975215565808658, 0.12146893447244217, 0.0245777292765011, -0.0035681356181645526, 0.07169097595894969, -0.13747702872726283, 0.07151523664757589, 0.23612463055438668, 0.21973819320649265, 0.2663770825289939, -0.3806352299961974, -0.14508945365857812, 0.19454729663306983, 0.15023550967095348, 0.08855321618868818, -0.05305853683902107, -0.19527459760878088, 0.1345488290814943, -0.09968558027124563, -0.1158419959715375, -0.05065618945720122, 0.0714774246004998, 0.012443696185113998, -0.3037900360582095, -0.0073060510277178385, 0.059407816175501484, -0.021692461989736758, -0.01829013995716983, -0.15130082723637783, -0.017068877902048425, 0.07762773605092824, -0.002414475487123696, 0.09421861283650217, 0.04700758546465935, -0.1274540255902408, -0.14258809376497592, 0.36987151339775026, -0.07593794881662759, -0.16787243829441761, 0.1379408635362962, -0.08562195830192812, -0.10152553099431305, 0.11755548592256226, 0.1067737433513075, 0.20276276060437273, -0.1434043861042569, 0.126690042934214, -0.08686693322288092, 0.1527131805352492, 0.07874601724032083, 0.012341372730527801, 0.12947303095218524, 0.19161577820491732, 0.20741948086310533, 0.1571797820552143, -0.06675843240734836, -0.04854825936653261, -0.32339276983168536, -0.13388929067065097, -0.20877214420753318, 0.026942273248091092, -0.13670723728380976, -0.15946442780849737, 0.39864848819743404, 0.1438921777129579, 0.22642858962752133, 0.09778636883080588, 0.2733933527572809, 0.10327293397021393, 0.06117735305207901, 0.192247141399759, 0.16889106872746482, 0.04401580110457648, 0.02775412562235607, -0.21557662257399182, 0.07876313700439544, 0.11962627330742902] |
1,802.06479 | Optimal leader selection and demotion in leader-follower multi-agent
systems | We consider leader-follower multi-agent systems that have many leaders,
defined on any connected weighted undirected graphs, and address the leader
selection and demotion problems. The leader selection problem is formulated as
a minimization problem for the $H^2$ norm of the difference between the
transfer functions of the original and new agent systems, under the assumption
that the leader agents to be demoted are fixed. The leader demotion problem is
that of finding optimal leader agents to be demoted, and is formulated using
the global optimal solution to the leader selection problem. We prove that a
global optimal solution to the leader selection problem is the set of the
original leader agents except for those that are demoted to followers. To this
end, we relax the original problem into a differentiable problem. Then, by
calculating the gradient and Hessian of the objective function of the relaxed
problem, we prove that the function is convex. It is shown that zero points of
the gradient are global optimal solutions to the leader selection problem,
which is a finite combinatorial optimization problem. Furthermore, we prove
that any set of leader agents to be demoted subject to a fixed number of
elements is a solution to the leader demotion problem. By combining the
solutions to the leader selection and demotion problems, we prove that if we
choose new leader agents from the original ones except for those specified by
the set of leader agents to be demoted, then the relative $H^2$ error between
the transfer functions of the original and new agent systems is completely
determined by the numbers of original leader agents and leader agents that are
demoted to follower agents. That is, we reveal that the relative $H^2$ error
does not depend on the number of agents on the graph. Finally, we verify the
solutions using a simple example.
| math.OC | we consider leaderfollower multiagent systems that have many leaders defined on any connected weighted undirected graphs and address the leader selection and demotion problems the leader selection problem is formulated as a minimization problem for the h2 norm of the difference between the transfer functions of the original and new agent systems under the assumption that the leader agents to be demoted are fixed the leader demotion problem is that of finding optimal leader agents to be demoted and is formulated using the global optimal solution to the leader selection problem we prove that a global optimal solution to the leader selection problem is the set of the original leader agents except for those that are demoted to followers to this end we relax the original problem into a differentiable problem then by calculating the gradient and hessian of the objective function of the relaxed problem we prove that the function is convex it is shown that zero points of the gradient are global optimal solutions to the leader selection problem which is a finite combinatorial optimization problem furthermore we prove that any set of leader agents to be demoted subject to a fixed number of elements is a solution to the leader demotion problem by combining the solutions to the leader selection and demotion problems we prove that if we choose new leader agents from the original ones except for those specified by the set of leader agents to be demoted then the relative h2 error between the transfer functions of the original and new agent systems is completely determined by the numbers of original leader agents and leader agents that are demoted to follower agents that is we reveal that the relative h2 error does not depend on the number of agents on the graph finally we verify the solutions using a simple example | [['we', 'consider', 'leaderfollower', 'multiagent', 'systems', 'that', 'have', 'many', 'leaders', 'defined', 'on', 'any', 'connected', 'weighted', 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1,802.0648 | Accelerated Primal-Dual Policy Optimization for Safe Reinforcement
Learning | Constrained Markov Decision Process (CMDP) is a natural framework for
reinforcement learning tasks with safety constraints, where agents learn a
policy that maximizes the long-term reward while satisfying the constraints on
the long-term cost. A canonical approach for solving CMDPs is the primal-dual
method which updates parameters in primal and dual spaces in turn. Existing
methods for CMDPs only use on-policy data for dual updates, which results in
sample inefficiency and slow convergence. In this paper, we propose a policy
search method for CMDPs called Accelerated Primal-Dual Optimization (APDO),
which incorporates an off-policy trained dual variable in the dual update
procedure while updating the policy in primal space with on-policy likelihood
ratio gradient. Experimental results on a simulated robot locomotion task show
that APDO achieves better sample efficiency and faster convergence than
state-of-the-art approaches for CMDPs.
| cs.AI cs.LG stat.ML | constrained markov decision process cmdp is a natural framework for reinforcement learning tasks with safety constraints where agents learn a policy that maximizes the longterm reward while satisfying the constraints on the longterm cost a canonical approach for solving cmdps is the primaldual method which updates parameters in primal and dual spaces in turn existing methods for cmdps only use onpolicy data for dual updates which results in sample inefficiency and slow convergence in this paper we propose a policy search method for cmdps called accelerated primaldual optimization apdo which incorporates an offpolicy trained dual variable in the dual update procedure while updating the policy in primal space with onpolicy likelihood ratio gradient experimental results on a simulated robot locomotion task show that apdo achieves better sample efficiency and faster convergence than stateoftheart approaches for cmdps | [['constrained', 'markov', 'decision', 'process', 'cmdp', 'is', 'a', 'natural', 'framework', 'for', 'reinforcement', 'learning', 'tasks', 'with', 'safety', 'constraints', 'where', 'agents', 'learn', 'a', 'policy', 'that', 'maximizes', 'the', 'longterm', 'reward', 'while', 'satisfying', 'the', 'constraints', 'on', 'the', 'longterm', 'cost', 'a', 'canonical', 'approach', 'for', 'solving', 'cmdps', 'is', 'the', 'primaldual', 'method', 'which', 'updates', 'parameters', 'in', 'primal', 'and', 'dual', 'spaces', 'in', 'turn', 'existing', 'methods', 'for', 'cmdps', 'only', 'use', 'onpolicy', 'data', 'for', 'dual', 'updates', 'which', 'results', 'in', 'sample', 'inefficiency', 'and', 'slow', 'convergence', 'in', 'this', 'paper', 'we', 'propose', 'a', 'policy', 'search', 'method', 'for', 'cmdps', 'called', 'accelerated', 'primaldual', 'optimization', 'apdo', 'which', 'incorporates', 'an', 'offpolicy', 'trained', 'dual', 'variable', 'in', 'the', 'dual', 'update', 'procedure', 'while', 'updating', 'the', 'policy', 'in', 'primal', 'space', 'with', 'onpolicy', 'likelihood', 'ratio', 'gradient', 'experimental', 'results', 'on', 'a', 'simulated', 'robot', 'locomotion', 'task', 'show', 'that', 'apdo', 'achieves', 'better', 'sample', 'efficiency', 'and', 'faster', 'convergence', 'than', 'stateoftheart', 'approaches', 'for', 'cmdps']] | [-0.024518846202322017, -0.006904965413299062, -0.1029198118555012, 0.0791715191527594, -0.15550466108747493, -0.20677084797896, 0.12379732026124317, 0.4768616350492768, -0.2947591884172897, -0.30904465617695404, 0.11222401039793031, -0.19300410506461482, -0.14187166258456435, 0.18527991563575202, -0.15860057615939138, 0.10939937077963086, 0.14513168203359497, 0.022278196070649063, -0.09738606875354021, -0.29499241132845183, 0.23562647197517192, 0.06557213794440031, 0.32018452465756614, -0.05210668018866164, 0.2076662553608098, 0.025485243279931704, 0.02584177883578214, 0.01927326904386525, -0.06614045405800806, 0.12903880197798082, 0.3134138219114115, 0.25626312210850083, 0.3938308253383903, -0.37817540422284807, -0.16030302016870746, 0.1396954559283192, 0.14397201103283397, 0.03296145879917208, -0.05590972333708639, -0.2758771626056353, 0.058518519362590254, -0.12678927707888965, 0.023553795430552103, -0.15037303815644457, -0.08131063185326422, 0.014470303763023842, -0.41781370995093636, 0.010312468619711364, 0.04706056897681373, -0.0014670523224092687, -0.0995060704985578, -0.13628227844201862, 0.03691688593504811, 0.03930218121273193, 0.07946082215331349, 0.0901717037490722, 0.18422550695197684, -0.1370360250080894, -0.2105875441312804, 0.31646243841456834, -0.04924447347860481, -0.2191726394074121, 0.14318413284621131, 0.009599724701091425, -0.1965661023173537, 0.1310545463365183, 0.2652627817674804, 0.22464329823017565, -0.1794457505248598, 0.06725405580789866, -0.05031046674955191, 0.13206862094603591, -0.023659709674208912, -0.022747145632087296, 0.08881411077923823, 0.25085310171594594, 0.1954126481362966, 0.12889836064484247, -0.019866271232908118, -0.2075787046242248, -0.23142308338698167, -0.12135132989557738, -0.15593750699364178, -0.060693635744279, -0.18452208730665387, -0.10917057019778711, 0.32345694355291327, 0.21159737054154332, 0.17669552958695522, 0.20844365280632401, 0.37448917330701403, 0.08677294173403018, 0.04087407901924826, 0.19000387570513202, 0.21142302321985976, 0.01464224609532463, 0.13840462429728706, -0.2901088837846947, 0.14939046380589646, 0.13616741607799682] |
1,802.06481 | Finite-Length Construction of High Performance Spatially-Coupled Codes
via Optimized Partitioning and Lifting | Spatially-coupled (SC) codes are a family of graph-based codes that have
attracted significant attention thanks to their capacity approaching
performance and low decoding latency. An SC code is constructed by partitioning
an underlying block code into a number of components and coupling their copies
together. In this paper, we first introduce a general approach for the
enumeration of detrimental combinatorial objects in the graph of finite-length
SC codes. Our approach is general in the sense that it effectively works for SC
codes with various column weights and memories. Next, we present a two-stage
framework for the construction of high-performance binary SC codes optimized
for additive white Gaussian noise channel; we aim at minimizing the number of
detrimental combinatorial objects in the error floor regime. In the first
stage, we deploy a novel partitioning scheme, called the optimal overlap
partitioning, to produce optimal partitioning corresponding to the smallest
number of detrimental objects. In the second stage, we apply a new circulant
power optimizer to further reduce the number of detrimental objects in the
lifted graph. An SC code constructed by our new framework has nearly 5 orders
of magnitudes error floor performance improvement compared to the uncoupled
setting.
| cs.IT math.IT | spatiallycoupled sc codes are a family of graphbased codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency an sc code is constructed by partitioning an underlying block code into a number of components and coupling their copies together in this paper we first introduce a general approach for the enumeration of detrimental combinatorial objects in the graph of finitelength sc codes our approach is general in the sense that it effectively works for sc codes with various column weights and memories next we present a twostage framework for the construction of highperformance binary sc codes optimized for additive white gaussian noise channel we aim at minimizing the number of detrimental combinatorial objects in the error floor regime in the first stage we deploy a novel partitioning scheme called the optimal overlap partitioning to produce optimal partitioning corresponding to the smallest number of detrimental objects in the second stage we apply a new circulant power optimizer to further reduce the number of detrimental objects in the lifted graph an sc code constructed by our new framework has nearly 5 orders of magnitudes error floor performance improvement compared to the uncoupled setting | [['spatiallycoupled', 'sc', 'codes', 'are', 'a', 'family', 'of', 'graphbased', 'codes', 'that', 'have', 'attracted', 'significant', 'attention', 'thanks', 'to', 'their', 'capacity', 'approaching', 'performance', 'and', 'low', 'decoding', 'latency', 'an', 'sc', 'code', 'is', 'constructed', 'by', 'partitioning', 'an', 'underlying', 'block', 'code', 'into', 'a', 'number', 'of', 'components', 'and', 'coupling', 'their', 'copies', 'together', 'in', 'this', 'paper', 'we', 'first', 'introduce', 'a', 'general', 'approach', 'for', 'the', 'enumeration', 'of', 'detrimental', 'combinatorial', 'objects', 'in', 'the', 'graph', 'of', 'finitelength', 'sc', 'codes', 'our', 'approach', 'is', 'general', 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1,802.06482 | Optimal Graph Laplacian | This paper provides a construction method of the nearest graph Laplacian to a
matrix identified from measurement data of graph Laplacian dynamics that
include biochemical systems, synchronization systems, and multi-agent systems.
We consider the case where the network structure, i.e., the connection
relationship of edges of a given graph, is known. A problem of finding the
nearest graph Laplacian is formulated as a convex optimization problem. Thus,
our problem can be solved using interior point methods. However, the complexity
of each iteration by interior point methods is $O(n^6)$, where $n$ is the
number of nodes of the network. That is, if $n$ is large, interior point
methods cannot solve our problem within a practical time. To resolve this
issue, we propose a simple and efficient algorithm with the calculation
complexity $O(n^2)$. Simulation experiments demonstrate that our method is
useful to perform data-driven modeling of graph Laplacian dynamics.
| math.OC | this paper provides a construction method of the nearest graph laplacian to a matrix identified from measurement data of graph laplacian dynamics that include biochemical systems synchronization systems and multiagent systems we consider the case where the network structure ie the connection relationship of edges of a given graph is known a problem of finding the nearest graph laplacian is formulated as a convex optimization problem thus our problem can be solved using interior point methods however the complexity of each iteration by interior point methods is on6 where n is the number of nodes of the network that is if n is large interior point methods cannot solve our problem within a practical time to resolve this issue we propose a simple and efficient algorithm with the calculation complexity on2 simulation experiments demonstrate that our method is useful to perform datadriven modeling of graph laplacian dynamics | [['this', 'paper', 'provides', 'a', 'construction', 'method', 'of', 'the', 'nearest', 'graph', 'laplacian', 'to', 'a', 'matrix', 'identified', 'from', 'measurement', 'data', 'of', 'graph', 'laplacian', 'dynamics', 'that', 'include', 'biochemical', 'systems', 'synchronization', 'systems', 'and', 'multiagent', 'systems', 'we', 'consider', 'the', 'case', 'where', 'the', 'network', 'structure', 'ie', 'the', 'connection', 'relationship', 'of', 'edges', 'of', 'a', 'given', 'graph', 'is', 'known', 'a', 'problem', 'of', 'finding', 'the', 'nearest', 'graph', 'laplacian', 'is', 'formulated', 'as', 'a', 'convex', 'optimization', 'problem', 'thus', 'our', 'problem', 'can', 'be', 'solved', 'using', 'interior', 'point', 'methods', 'however', 'the', 'complexity', 'of', 'each', 'iteration', 'by', 'interior', 'point', 'methods', 'is', 'on6', 'where', 'n', 'is', 'the', 'number', 'of', 'nodes', 'of', 'the', 'network', 'that', 'is', 'if', 'n', 'is', 'large', 'interior', 'point', 'methods', 'can', 'not', 'solve', 'our', 'problem', 'within', 'a', 'practical', 'time', 'to', 'resolve', 'this', 'issue', 'we', 'propose', 'a', 'simple', 'and', 'efficient', 'algorithm', 'with', 'the', 'calculation', 'complexity', 'on2', 'simulation', 'experiments', 'demonstrate', 'that', 'our', 'method', 'is', 'useful', 'to', 'perform', 'datadriven', 'modeling', 'of', 'graph', 'laplacian', 'dynamics']] | [-0.13524324782947833, -0.0019431205394023375, -0.07056136879868605, 0.03622270637975276, -0.1128218385038545, -0.15156725994500056, 0.05975877470415514, 0.3666377215570695, -0.3197887871238227, -0.3190898975432926, 0.12580509862006717, -0.2687532322204395, -0.23178890289902385, 0.1337774110127341, -0.06767399107637764, 0.07454130733133973, 0.15008977545123245, 0.047812206547933854, -0.03596370353212429, -0.21651261367200325, 0.31024640060747294, 0.030398252608908993, 0.21488272500652317, 0.04099921007464464, 0.1011643073988789, -0.011832172979248335, 0.006765615940723266, 0.06650967006665982, -0.08390044915796425, 0.1296437469647719, 0.3041595889843774, 0.18611929441072247, 0.32855674949934, -0.4279895708392802, -0.23976791042003096, 0.16316705061251777, 0.16703292133752257, 0.1017961419640562, -0.023882883629207877, -0.22968736385794458, 0.11202691927256465, -0.09951148460134612, -0.08587200574362902, -0.0535706096215526, -0.002336248752308657, -0.027389657914141396, -0.30741325298495703, 0.04201019967346125, 0.04828571017581428, -0.0033467105728246876, -0.0029858304659609457, -0.10068781950787918, 0.032700355653965694, 0.12157221700102594, -0.026818601199822198, 0.056205021034976516, 0.09730823878025813, -0.06665617778796602, -0.1699328616739729, 0.4089523835478955, 0.006895157571479275, -0.23796315205510002, 0.13708521177790858, -0.06874049448320088, -0.15822412667644992, 0.09949008995868466, 0.19697670846397994, 0.18104209334312663, -0.1474990011991247, 0.13274930889413036, -0.08032906636268504, 0.17130186871568062, -0.0005279134587711982, -0.03254262146200179, 0.12281635897139691, 0.2461585762684007, 0.15404492973765307, 0.15633095659211757, -0.05866525110920791, -0.09962122563455203, -0.24380851024761796, -0.1085537380267114, -0.2869895046853737, 0.014197652682923945, -0.14765236435148935, -0.17602964230133472, 0.3954952296185798, 0.1622838973401215, 0.2132924793743498, 0.09578733410642205, 0.32568023813183644, 0.1170489329457711, 0.017575265926614125, 0.13831040975826517, 0.14121017542139097, 0.1375563763148101, 0.07374551630818059, -0.22701622293853024, 0.06030632265705011, 0.1340076252078713] |
1,802.06483 | Committee Scoring Rules: Axiomatic Characterization and Hierarchy | Committee scoring voting rules are multiwinner analogues of positional
scoring rules which constitute an important subclass of single-winner voting
rules. We identify several natural subclasses of committee scoring rules,
namely, weakly separable, representation-focused, top-$k$-counting, OWA-based,
and decomposable rules. We characterize SNTV, Bloc, and $k$-Approval
Chamberlin--Courant as the only nontrivial rules in pairwise intersections of
these classes. We provide some axiomatic characterizations for these classes,
where monotonicity properties appear to be especially useful. The class of
decomposable rules is new to the literature. We show that it strictly contains
the class of OWA-based rules and describe some of the applications of
decomposable rules.
| cs.GT | committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of singlewinner voting rules we identify several natural subclasses of committee scoring rules namely weakly separable representationfocused topkcounting owabased and decomposable rules we characterize sntv bloc and kapproval chamberlincourant as the only nontrivial rules in pairwise intersections of these classes we provide some axiomatic characterizations for these classes where monotonicity properties appear to be especially useful the class of decomposable rules is new to the literature we show that it strictly contains the class of owabased rules and describe some of the applications of decomposable rules | [['committee', 'scoring', 'voting', 'rules', 'are', 'multiwinner', 'analogues', 'of', 'positional', 'scoring', 'rules', 'which', 'constitute', 'an', 'important', 'subclass', 'of', 'singlewinner', 'voting', 'rules', 'we', 'identify', 'several', 'natural', 'subclasses', 'of', 'committee', 'scoring', 'rules', 'namely', 'weakly', 'separable', 'representationfocused', 'topkcounting', 'owabased', 'and', 'decomposable', 'rules', 'we', 'characterize', 'sntv', 'bloc', 'and', 'kapproval', 'chamberlincourant', 'as', 'the', 'only', 'nontrivial', 'rules', 'in', 'pairwise', 'intersections', 'of', 'these', 'classes', 'we', 'provide', 'some', 'axiomatic', 'characterizations', 'for', 'these', 'classes', 'where', 'monotonicity', 'properties', 'appear', 'to', 'be', 'especially', 'useful', 'the', 'class', 'of', 'decomposable', 'rules', 'is', 'new', 'to', 'the', 'literature', 'we', 'show', 'that', 'it', 'strictly', 'contains', 'the', 'class', 'of', 'owabased', 'rules', 'and', 'describe', 'some', 'of', 'the', 'applications', 'of', 'decomposable', 'rules']] | [-0.09970384931326479, 0.04887320090604001, -0.06004110303725682, 0.1365923167482548, -0.19075833374917434, -0.1958239907490126, 0.1417553534493873, 0.42880139222332075, -0.27913828258055684, -0.19397586201518482, 0.10763211729913476, -0.2482926743835503, -0.18988648462383187, 0.151838096570881, -0.09770719017650858, 0.027972931979342783, 0.038141524464841564, 0.03793237538918095, -0.027527234148960012, -0.32252946187395093, 0.33300841266891973, -0.07238444807829664, 0.2599789480514386, 0.023031487787032828, 0.07337973614716355, 0.040426746485572235, -0.05579100020786784, 0.10126581096419078, -0.1400181270486535, 0.13294525171502256, 0.3259236671249656, 0.254007612482882, 0.2871494724543071, -0.28778554020705177, -0.08670974585373759, 0.197769591813067, 0.016446493960935258, 0.02092590252298168, 0.0571602518366668, -0.22319271231033638, 0.05889500525332622, -0.1952980967128978, -0.08744594035698694, -0.2235584718211755, 0.011860703604350634, 0.1069064924730828, -0.28812175316453054, 0.011653763958819065, 0.15844264580336326, 0.06476819281484567, -0.05302956218114488, -0.21529156563794424, 0.004678749068475822, 0.08759865931728307, -0.03398498954187494, -0.09586791165387623, 0.07529871678892888, -0.16437854601826984, -0.22549857940597862, 0.4194397080927065, 0.0748698778687885, -0.1854891758982786, 0.14771275902075656, -0.021587576826705653, -0.25646234230211407, 0.05611925624657934, 0.11746490930946653, 0.18493097325257374, -0.19117620667698337, -0.009672855932662702, -0.13833980680461608, 0.08365763651261873, 0.10006344904803544, 0.12508948627567174, 0.19203141742550275, 0.11231304992757299, 0.03163123926987835, 0.17709533640471123, 0.014464280627412247, -0.14286145010698295, -0.3357317792525625, -0.11814504552760399, -0.05296738703127987, 0.04982257126054416, -0.07427383929062475, -0.2304623681394493, 0.3756080386137553, 0.08866073469992033, 0.1019803264076187, 0.12048958865674578, 0.1458280332153663, 0.048209021638339275, 0.12961498987587058, 0.046168720564238874, 0.20727520260113, 0.09168179130510372, -0.023801254706603346, -0.1286358357562373, 0.09604068100395356, 0.1378935741799354] |
1,802.06484 | A positive fraction mutually avoiding sets theorem | Two sets $A$ and $B$ of points in the plane are \emph{mutually avoiding} if
no line generated by any two points in $A$ intersects the convex hull of $B$,
and vice versa. In 1994, Aronov, Erd\H os, Goddard, Kleitman, Klugerman, Pach,
and Schulman showed that every set of $n$ points in the plane in general
position contains a pair of mutually avoiding sets each of size at least
$\sqrt{n/12}$. As a corollary, their result implies that for every set of $n$
points in the plane in general position one can find at least $\sqrt{n/12}$
segments, each joining two of the points, such that these segments are pairwise
crossing. In this note, we prove a fractional version of their theorem: for
every $k > 0$ there is a constant $\varepsilon_k > 0$ such that any
sufficiently large point set $P$ in the plane contains $2k$ subsets
$A_1,\ldots, A_{k},B_1,\ldots, B_k$, each of size at least $\varepsilon_k|P|$,
such that every pair of sets $A = \{a_1,\ldots, a_k\}$ and $B = \{b_1,\ldots,
b_k\}$, with $a_i \in A_i$ and $b_i \in B_i$, are mutually avoiding. Moreover,
we show that $\varepsilon_k = \Omega(1/k^4)$. Similar results are obtained in
higher dimensions
| math.CO | two sets a and b of points in the plane are emphmutually avoiding if no line generated by any two points in a intersects the convex hull of b and vice versa in 1994 aronov erdh os goddard kleitman klugerman pach and schulman showed that every set of n points in the plane in general position contains a pair of mutually avoiding sets each of size at least sqrtn12 as a corollary their result implies that for every set of n points in the plane in general position one can find at least sqrtn12 segments each joining two of the points such that these segments are pairwise crossing in this note we prove a fractional version of their theorem for every k 0 there is a constant varepsilon_k 0 such that any sufficiently large point set p in the plane contains 2k subsets a_1ldots a_kb_1ldots b_k each of size at least varepsilon_kp such that every pair of sets a a_1ldots a_k and b b_1ldots b_k with a_i in a_i and b_i in b_i are mutually avoiding moreover we show that varepsilon_k omega1k4 similar results are obtained in higher dimensions | [['two', 'sets', 'a', 'and', 'b', 'of', 'points', 'in', 'the', 'plane', 'are', 'emphmutually', 'avoiding', 'if', 'no', 'line', 'generated', 'by', 'any', 'two', 'points', 'in', 'a', 'intersects', 'the', 'convex', 'hull', 'of', 'b', 'and', 'vice', 'versa', 'in', '1994', 'aronov', 'erdh', 'os', 'goddard', 'kleitman', 'klugerman', 'pach', 'and', 'schulman', 'showed', 'that', 'every', 'set', 'of', 'n', 'points', 'in', 'the', 'plane', 'in', 'general', 'position', 'contains', 'a', 'pair', 'of', 'mutually', 'avoiding', 'sets', 'each', 'of', 'size', 'at', 'least', 'sqrtn12', 'as', 'a', 'corollary', 'their', 'result', 'implies', 'that', 'for', 'every', 'set', 'of', 'n', 'points', 'in', 'the', 'plane', 'in', 'general', 'position', 'one', 'can', 'find', 'at', 'least', 'sqrtn12', 'segments', 'each', 'joining', 'two', 'of', 'the', 'points', 'such', 'that', 'these', 'segments', 'are', 'pairwise', 'crossing', 'in', 'this', 'note', 'we', 'prove', 'a', 'fractional', 'version', 'of', 'their', 'theorem', 'for', 'every', 'k', '0', 'there', 'is', 'a', 'constant', 'varepsilon_k', '0', 'such', 'that', 'any', 'sufficiently', 'large', 'point', 'set', 'p', 'in', 'the', 'plane', 'contains', '2k', 'subsets', 'a_1ldots', 'a_kb_1ldots', 'b_k', 'each', 'of', 'size', 'at', 'least', 'varepsilon_kp', 'such', 'that', 'every', 'pair', 'of', 'sets', 'a', 'a_1ldots', 'a_k', 'and', 'b', 'b_1ldots', 'b_k', 'with', 'a_i', 'in', 'a_i', 'and', 'b_i', 'in', 'b_i', 'are', 'mutually', 'avoiding', 'moreover', 'we', 'show', 'that', 'varepsilon_k', 'omega1k4', 'similar', 'results', 'are', 'obtained', 'in', 'higher', 'dimensions']] | [-0.21379254334480377, 0.13513641752038352, -0.028311974811996963, -0.011287941784925155, 0.01599525726979246, -0.1593954543784462, 0.07091112716274486, 0.3591176439479396, -0.26652612547213966, -0.1966679152629867, 0.06140233585862694, -0.3795614845245271, -0.09468393660326664, 0.15719970175241296, -0.0683447017032351, -0.019067520391498064, 0.0716022066167883, 0.06929497185943498, -0.024727650941349565, -0.27637157729965306, 0.2884052270897538, -0.1392774346674717, 0.1507508887028372, 0.027923960545779884, 0.07782668004164825, 0.05492396974885786, 0.008819750711523197, 0.054832262268944366, -0.14265148872501732, 0.055802727674410954, 0.2504819877621894, 0.17978535688079492, 0.2833114714380605, -0.3379505875161723, -0.08454077281561252, 0.19966336533276213, 0.14490756375866162, 0.03488495480772611, 0.007655357668881078, -0.19673944466269097, 0.16851409113386998, -0.05984772313889619, -0.15523841510703032, 0.003365860939831347, 0.11151700625699516, 0.026851106722008536, -0.3109169596755827, 0.0016246429166278324, 0.10771772312063321, 0.08244882686617407, 0.008114854393627595, -0.21977668690520363, -0.07774648936339529, 0.09593921631725656, -0.011949390497662731, 0.11482955240392806, 0.02866240213310497, -0.04580309438185666, -0.14888206723876096, 0.3652013397020464, -0.020609574055934728, -0.1978279518920022, 0.14690719790051918, -0.2079844666078586, -0.17349799928079182, 0.11251574054712782, 0.08157747060161184, 0.12225729892961681, -0.06944973594131502, 0.16378887356290392, -0.13903571792903383, 0.13197143968978167, 0.18342966946294983, 0.00022618222125881426, 0.1946520349237363, 0.04939284592731604, 0.11627922230777708, 0.10251465612972105, -0.046271690983023195, 0.014976871247730545, -0.3797728324157966, -0.14592863478370616, -0.20778445051353728, 0.07413157624242878, -0.16398566814628746, -0.1655151746613351, 0.3073081827949028, 0.08482242087405678, 0.28263677481964633, 0.05558245826915309, 0.226548159635953, 0.05974437918134877, 0.031450917119651124, 0.161087550089468, 0.11850586826032078, 0.07669782793728282, -0.02979092152185134, -0.1481788473933734, 0.019355671319204407, 0.13191822704078782] |
1,802.06485 | Robust Estimation via Robust Gradient Estimation | We provide a new computationally-efficient class of estimators for risk
minimization. We show that these estimators are robust for general statistical
models: in the classical Huber epsilon-contamination model and in heavy-tailed
settings. Our workhorse is a novel robust variant of gradient descent, and we
provide conditions under which our gradient descent variant provides accurate
estimators in a general convex risk minimization problem. We provide specific
consequences of our theory for linear regression, logistic regression and for
estimation of the canonical parameters in an exponential family. These results
provide some of the first computationally tractable and provably robust
estimators for these canonical statistical models. Finally, we study the
empirical performance of our proposed methods on synthetic and real datasets,
and find that our methods convincingly outperform a variety of baselines.
| stat.ML cs.AI cs.LG | we provide a new computationallyefficient class of estimators for risk minimization we show that these estimators are robust for general statistical models in the classical huber epsiloncontamination model and in heavytailed settings our workhorse is a novel robust variant of gradient descent and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk minimization problem we provide specific consequences of our theory for linear regression logistic regression and for estimation of the canonical parameters in an exponential family these results provide some of the first computationally tractable and provably robust estimators for these canonical statistical models finally we study the empirical performance of our proposed methods on synthetic and real datasets and find that our methods convincingly outperform a variety of baselines | [['we', 'provide', 'a', 'new', 'computationallyefficient', 'class', 'of', 'estimators', 'for', 'risk', 'minimization', 'we', 'show', 'that', 'these', 'estimators', 'are', 'robust', 'for', 'general', 'statistical', 'models', 'in', 'the', 'classical', 'huber', 'epsiloncontamination', 'model', 'and', 'in', 'heavytailed', 'settings', 'our', 'workhorse', 'is', 'a', 'novel', 'robust', 'variant', 'of', 'gradient', 'descent', 'and', 'we', 'provide', 'conditions', 'under', 'which', 'our', 'gradient', 'descent', 'variant', 'provides', 'accurate', 'estimators', 'in', 'a', 'general', 'convex', 'risk', 'minimization', 'problem', 'we', 'provide', 'specific', 'consequences', 'of', 'our', 'theory', 'for', 'linear', 'regression', 'logistic', 'regression', 'and', 'for', 'estimation', 'of', 'the', 'canonical', 'parameters', 'in', 'an', 'exponential', 'family', 'these', 'results', 'provide', 'some', 'of', 'the', 'first', 'computationally', 'tractable', 'and', 'provably', 'robust', 'estimators', 'for', 'these', 'canonical', 'statistical', 'models', 'finally', 'we', 'study', 'the', 'empirical', 'performance', 'of', 'our', 'proposed', 'methods', 'on', 'synthetic', 'and', 'real', 'datasets', 'and', 'find', 'that', 'our', 'methods', 'convincingly', 'outperform', 'a', 'variety', 'of', 'baselines']] | [-0.00830307941840485, -0.06089185043172676, -0.1294703444090578, 0.15421493288649377, -0.05891425361633012, -0.19238507453814263, 0.03371762004482394, 0.43616248766869997, -0.2648371692111557, -0.251532891519772, 0.12815691514731234, -0.22268159138832905, -0.23724027959875357, 0.2861181550836118, -0.15932826173867193, 0.13215271522139393, 0.10216970792285694, -0.042789887238921985, -0.11535763977882416, -0.3178712624854358, 0.2762747277549013, 0.03723132722946101, 0.3051075301053681, 0.0008918802960515889, 0.13178784558693915, -0.005746156495252205, -0.0024514857213944197, 0.051127091938153256, -0.1501276314788987, 0.18403452459285974, 0.25686390623126526, 0.20055013291480006, 0.3545511810022385, -0.3633586204314763, -0.22932174373345898, 0.15157311154861552, 0.07900080843936912, 0.10891144531032218, -0.09010232493819222, -0.24727903365684573, 0.07025916498969309, -0.156887124722116, -0.049968988468596175, -0.21715857969351518, -0.06673323403495227, 0.04507703512596587, -0.3897561885763046, 0.12653792673332054, 0.0692593957506871, 0.07994864225864064, -0.07132030893911341, -0.19582762345021895, 0.07824165939873215, 0.03981973264409706, 0.0653000799262203, -0.03864001931961943, 0.08078995843367405, -0.0976438791632775, -0.15024379176961244, 0.3169548478380907, -0.0961358680795019, -0.24406516463892866, 0.19689270048293955, -0.024973212755754474, -0.2134854572900939, 0.05640838090185971, 0.2428886476658689, 0.17018883208953595, -0.1471236325410563, 0.044849996192402444, -0.09422961863609709, 0.09201502463556538, -0.057274425882384065, -0.017635984092683698, 0.12274618127181144, 0.19335750947785815, 0.14256009219806323, 0.1485117606050696, -0.11592548560574939, -0.12242495965992295, -0.3054431812141033, -0.12135940201681147, -0.14988145326776792, -0.035658169324805804, -0.18450490300937974, -0.21528503698722798, 0.4121156260226817, 0.21432748701851617, 0.16866907033376222, 0.19418930406808535, 0.32600585986361946, 0.0875061998665405, -0.0006919463432227918, 0.11717871358443743, 0.22023704329026364, 0.1107636251046445, 0.001487609334723201, -0.18920043736421902, 0.09910899506477538, 0.0389562656023619] |
1,802.06486 | Attractor Cosmology from non-minimally Coupled Gravity | By using a bottom-up reconstruction technique for non-minimally coupled
scalar-tensor theories, we realize the Einstein frame attractor cosmologies in
the $\Omega (\phi)$-Jordan frame. For our approach, what is needed for the
reconstruction method to work is the functional form of the non-minimal
coupling $\Omega(\phi)$ and of the scalar-to-tensor ratio, and also the
assumption of the slow-roll inflation in the $\Omega (\phi)$-Jordan frame. By
appropriately choosing the scalar-to-tensor ratio, we demonstrate that the
observational indices of the attractor cosmologies can be realized directly in
the $\Omega (\phi)$-Jordan frame. We investigate the special conditions that
are required to hold true in for this realization to occur, and we provide the
analytic form of the potential in the $\Omega (\phi)$-Jordan frame. Also, by
performing a conformal transformation, we find the corresponding Einstein frame
canonical scalar-tensor theory, and we calculate in detail the corresponding
observational indices. The result indicates that although the spectral index of
the primordial curvature perturbations is the same in the Jordan and Einstein
frames, at leading order in the $e$-foldings number, the scalar-to-tensor ratio
differs. We discuss the possible reasons behind this discrepancy, and we argue
that the difference is due to some approximation we performed to the functional
form of the potential in the Einstein frame, in order to obtain analytical
results, and also due to the difference in the definition of the $e$-foldings
number in the two frames, which is also pointed out in the related literature.
Finally, we find the $F(R)$ gravity corresponding to the Einstein frame
canonical scalar-tensor theory.
| gr-qc astro-ph.CO hep-th | by using a bottomup reconstruction technique for nonminimally coupled scalartensor theories we realize the einstein frame attractor cosmologies in the omega phijordan frame for our approach what is needed for the reconstruction method to work is the functional form of the nonminimal coupling omegaphi and of the scalartotensor ratio and also the assumption of the slowroll inflation in the omega phijordan frame by appropriately choosing the scalartotensor ratio we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the omega phijordan frame we investigate the special conditions that are required to hold true in for this realization to occur and we provide the analytic form of the potential in the omega phijordan frame also by performing a conformal transformation we find the corresponding einstein frame canonical scalartensor theory and we calculate in detail the corresponding observational indices the result indicates that although the spectral index of the primordial curvature perturbations is the same in the jordan and einstein frames at leading order in the efoldings number the scalartotensor ratio differs we discuss the possible reasons behind this discrepancy and we argue that the difference is due to some approximation we performed to the functional form of the potential in the einstein frame in order to obtain analytical results and also due to the difference in the definition of the efoldings number in the two frames which is also pointed out in the related literature finally we find the fr gravity corresponding to the einstein frame canonical scalartensor theory | [['by', 'using', 'a', 'bottomup', 'reconstruction', 'technique', 'for', 'nonminimally', 'coupled', 'scalartensor', 'theories', 'we', 'realize', 'the', 'einstein', 'frame', 'attractor', 'cosmologies', 'in', 'the', 'omega', 'phijordan', 'frame', 'for', 'our', 'approach', 'what', 'is', 'needed', 'for', 'the', 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1,802.06487 | Poisson geometry and representations of PI 4-dimensional Sklyanin
algebras | Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is
module-finite over its center Z; thus, S is PI. Our first result is the
construction of a Poisson Z-order structure on S such that the induced Poisson
bracket on Z is non-vanishing. We also provide the explicit Jacobian structure
of this bracket, leading to a description of the symplectic core decomposition
of the maximal spectrum Y of Z. We then classify the irreducible
representations of S by combining (1) the geometry of the Poisson order
structures, with (2) algebro-geometric methods for the elliptic curve attached
to S, along with (3) representation-theoretic methods using line and fat point
modules of S. Along the way, we improve results of Smith and Tate obtaining a
description the singular locus of Y for such S. The classification results for
irreducible representations are in turn used to determine the zero sets of the
discriminants ideals of these algebras S.
| math.RT math.QA math.RA math.SG | take s to be a 4dimensional sklyanin elliptic algebra that is modulefinite over its center z thus s is pi our first result is the construction of a poisson zorder structure on s such that the induced poisson bracket on z is nonvanishing we also provide the explicit jacobian structure of this bracket leading to a description of the symplectic core decomposition of the maximal spectrum y of z we then classify the irreducible representations of s by combining 1 the geometry of the poisson order structures with 2 algebrogeometric methods for the elliptic curve attached to s along with 3 representationtheoretic methods using line and fat point modules of s along the way we improve results of smith and tate obtaining a description the singular locus of y for such s the classification results for irreducible representations are in turn used to determine the zero sets of the discriminants ideals of these algebras s | [['take', 's', 'to', 'be', 'a', '4dimensional', 'sklyanin', 'elliptic', 'algebra', 'that', 'is', 'modulefinite', 'over', 'its', 'center', 'z', 'thus', 's', 'is', 'pi', 'our', 'first', 'result', 'is', 'the', 'construction', 'of', 'a', 'poisson', 'zorder', 'structure', 'on', 's', 'such', 'that', 'the', 'induced', 'poisson', 'bracket', 'on', 'z', 'is', 'nonvanishing', 'we', 'also', 'provide', 'the', 'explicit', 'jacobian', 'structure', 'of', 'this', 'bracket', 'leading', 'to', 'a', 'description', 'of', 'the', 'symplectic', 'core', 'decomposition', 'of', 'the', 'maximal', 'spectrum', 'y', 'of', 'z', 'we', 'then', 'classify', 'the', 'irreducible', 'representations', 'of', 's', 'by', 'combining', '1', 'the', 'geometry', 'of', 'the', 'poisson', 'order', 'structures', 'with', '2', 'algebrogeometric', 'methods', 'for', 'the', 'elliptic', 'curve', 'attached', 'to', 's', 'along', 'with', '3', 'representationtheoretic', 'methods', 'using', 'line', 'and', 'fat', 'point', 'modules', 'of', 's', 'along', 'the', 'way', 'we', 'improve', 'results', 'of', 'smith', 'and', 'tate', 'obtaining', 'a', 'description', 'the', 'singular', 'locus', 'of', 'y', 'for', 'such', 's', 'the', 'classification', 'results', 'for', 'irreducible', 'representations', 'are', 'in', 'turn', 'used', 'to', 'determine', 'the', 'zero', 'sets', 'of', 'the', 'discriminants', 'ideals', 'of', 'these', 'algebras', 's']] | [-0.1613980922787901, 0.039138011111607474, -0.12313427471315429, 0.038555398795964015, -0.08589244033059766, -0.13241026610917142, 0.0007884366437792778, 0.33725777838018633, -0.33883893963910877, -0.20862830765845794, 0.07475714018313034, -0.26325249851591165, -0.10982486182643521, 0.19849233432642877, -0.07529875134989139, -0.023325875030845523, 0.058653162143403485, 0.0891974366437118, -0.1346811999206341, -0.2915377570376281, 0.39849596287935013, 0.004786248644813895, 0.2086154760146934, 0.0037507794977676484, 0.11293965931080523, 0.016969214277642388, -0.05809510664173192, -0.03985726246309857, -0.15458432234750474, 0.17835797885838414, 0.2807772802985123, 0.0616261736610003, 0.13825474042866018, -0.32873500340407896, -0.1316826682385703, 0.16556323866750444, 0.13573629735037684, 0.02568087227221939, 0.03322441777845304, -0.24314270358712922, 0.15458866806941168, -0.1674286414523639, -0.17769788745189866, -0.07289808632565602, 0.0685866901981494, 0.0274505986141101, -0.25387348251252045, 0.01010400328255679, 0.11801531064894892, 0.09842406674138, -0.05279878568460023, -0.1531962189462877, -0.08894935350774998, 0.07056884448975324, -0.02397198880301608, 0.07037550108507276, 0.08180288444423388, -0.10542766030637488, -0.1280580117817848, 0.3460694232264594, -0.0430643102371945, -0.2096657031606282, 0.12906816617976274, -0.14994832536716374, -0.1439906521940664, 0.162542585544889, 0.10109000141401925, 0.11501202895118284, -0.04770060450274257, 0.18175702101115376, -0.08607777666841303, 0.03726340522632874, 0.08374613537096358, -0.04236383844888018, 0.15805642877615267, 0.10224238012676999, 0.0670559948445448, 0.0767112051850305, -0.0624800137063909, -0.006953985566994355, -0.37684237440266916, -0.19607431781196577, -0.11354705881808073, 0.14220428005641989, -0.12314598094953615, -0.15584929561723143, 0.41755193500749527, 0.08325665712116226, 0.26952601339547866, 0.05619073751712999, 0.21646988196598907, 0.08754504061409182, 0.05273042878947191, 0.05603212107934298, 0.10593523052671264, 0.22354910716925178, 0.008312441612924298, -0.15482453480362893, -0.017132180484552537, 0.1851022024008055] |
1,802.06488 | Tiny SSD: A Tiny Single-shot Detection Deep Convolutional Neural Network
for Real-time Embedded Object Detection | Object detection is a major challenge in computer vision, involving both
object classification and object localization within a scene. While deep neural
networks have been shown in recent years to yield very powerful techniques for
tackling the challenge of object detection, one of the biggest challenges with
enabling such object detection networks for widespread deployment on embedded
devices is high computational and memory requirements. Recently, there has been
an increasing focus in exploring small deep neural network architectures for
object detection that are more suitable for embedded devices, such as Tiny YOLO
and SqueezeDet. Inspired by the efficiency of the Fire microarchitecture
introduced in SqueezeNet and the object detection performance of the
single-shot detection macroarchitecture introduced in SSD, this paper
introduces Tiny SSD, a single-shot detection deep convolutional neural network
for real-time embedded object detection that is composed of a highly optimized,
non-uniform Fire sub-network stack and a non-uniform sub-network stack of
highly optimized SSD-based auxiliary convolutional feature layers designed
specifically to minimize model size while maintaining object detection
performance. The resulting Tiny SSD possess a model size of 2.3MB (~26X smaller
than Tiny YOLO) while still achieving an mAP of 61.3% on VOC 2007 (~4.2% higher
than Tiny YOLO). These experimental results show that very small deep neural
network architectures can be designed for real-time object detection that are
well-suited for embedded scenarios.
| cs.CV cs.AI cs.NE | object detection is a major challenge in computer vision involving both object classification and object localization within a scene while deep neural networks have been shown in recent years to yield very powerful techniques for tackling the challenge of object detection one of the biggest challenges with enabling such object detection networks for widespread deployment on embedded devices is high computational and memory requirements recently there has been an increasing focus in exploring small deep neural network architectures for object detection that are more suitable for embedded devices such as tiny yolo and squeezedet inspired by the efficiency of the fire microarchitecture introduced in squeezenet and the object detection performance of the singleshot detection macroarchitecture introduced in ssd this paper introduces tiny ssd a singleshot detection deep convolutional neural network for realtime embedded object detection that is composed of a highly optimized nonuniform fire subnetwork stack and a nonuniform subnetwork stack of highly optimized ssdbased auxiliary convolutional feature layers designed specifically to minimize model size while maintaining object detection performance the resulting tiny ssd possess a model size of 23mb 26x smaller than tiny yolo while still achieving an map of 613 on voc 2007 42 higher than tiny yolo these experimental results show that very small deep neural network architectures can be designed for realtime object detection that are wellsuited for embedded scenarios | [['object', 'detection', 'is', 'a', 'major', 'challenge', 'in', 'computer', 'vision', 'involving', 'both', 'object', 'classification', 'and', 'object', 'localization', 'within', 'a', 'scene', 'while', 'deep', 'neural', 'networks', 'have', 'been', 'shown', 'in', 'recent', 'years', 'to', 'yield', 'very', 'powerful', 'techniques', 'for', 'tackling', 'the', 'challenge', 'of', 'object', 'detection', 'one', 'of', 'the', 'biggest', 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1,802.06489 | Local field theory construction of Very Special Conformal Symmetry | Cohen and Glashow argued that very special conformal field theories of a
particular kind (i.e. with HOM(2) or SIM(2) invariance) cannot be constructed
within the framework of local field theories. We, however, show examples of
local construction by using non-linear realization. We further construct linear
realization from the topological twist at the cost of unitarity. To demonstrate
the ubiquity of our idea, we also present corresponding holographic models.
| hep-th hep-ph | cohen and glashow argued that very special conformal field theories of a particular kind ie with hom2 or sim2 invariance cannot be constructed within the framework of local field theories we however show examples of local construction by using nonlinear realization we further construct linear realization from the topological twist at the cost of unitarity to demonstrate the ubiquity of our idea we also present corresponding holographic models | [['cohen', 'and', 'glashow', 'argued', 'that', 'very', 'special', 'conformal', 'field', 'theories', 'of', 'a', 'particular', 'kind', 'ie', 'with', 'hom2', 'or', 'sim2', 'invariance', 'can', 'not', 'be', 'constructed', 'within', 'the', 'framework', 'of', 'local', 'field', 'theories', 'we', 'however', 'show', 'examples', 'of', 'local', 'construction', 'by', 'using', 'nonlinear', 'realization', 'we', 'further', 'construct', 'linear', 'realization', 'from', 'the', 'topological', 'twist', 'at', 'the', 'cost', 'of', 'unitarity', 'to', 'demonstrate', 'the', 'ubiquity', 'of', 'our', 'idea', 'we', 'also', 'present', 'corresponding', 'holographic', 'models']] | [-0.08831842689086562, 0.12107366422508452, -0.08243856844289796, 0.05646516217013308, -0.10759476045200574, -0.13343449194065254, -0.003075945855833698, 0.3301345352353393, -0.25015168117723713, -0.2904110438041929, 0.06989489515325513, -0.18908367317129413, -0.23796233706567707, 0.1769014565051412, -0.07275204198916638, 0.044842969167275704, -5.1653694253468856e-05, 0.03356648734568254, -0.11870138292568669, -0.25480505076331506, 0.34094222560288734, 0.05383437095830838, 0.2756725579932116, 0.05444424652049075, 0.10559457361671155, 0.009429099888581297, -0.00449181435143818, 0.07053731901628518, -0.12090205232854477, 0.12511904632159765, 0.21891606970171595, 0.11005323733189616, 0.20348704055093392, -0.4437327127417792, -0.23897004439588299, 0.08523823758182318, 0.09843733599004538, 0.15882445553290672, -0.06670940019176815, -0.30279949110379256, 0.10512749497623493, -0.1939566083846317, -0.17526884434366788, -0.14149211016753555, -0.03442167953345115, -0.04420925517046851, -0.23508078898505672, 0.041374649882461687, 0.06337488831385323, 0.07402260653148203, -0.022116489931131186, -0.03527735010383354, -0.030741277667086408, 0.01582231839268428, 0.06348553881643043, 0.01483456864008221, 0.09840712800244059, -0.17269645490940067, -0.15918545595005804, 0.3792088477993789, -0.07856737991012093, -0.17863865015164448, 0.17890874390908773, -0.14204915280224403, -0.18964180600343514, 0.06178015627243651, 0.10955778032581767, 0.11178073435481908, -0.1035471763799264, 0.16562872197043718, -0.06323418542877704, 0.13190051126361324, 0.08322806892903063, 0.05615212480821039, 0.22319203277752883, 0.09565569975825054, 0.0357971850755638, 0.1451976657760721, -0.034616319428913404, -0.08989097591003646, -0.41308389107386273, -0.14072625037068434, -0.17077826313080563, 0.0908012474936423, -0.06893950879579727, -0.12811127777440826, 0.38782917011691176, 0.1646919186398694, 0.19973854185419454, 0.0945503217694552, 0.2021509511531263, 0.12290241755038986, 0.12696549811980862, 0.07353428733008711, 0.25120928017017635, 0.1267489753022412, 0.02904109842231686, -0.19027534598042595, -0.04388819949067049, 0.1268580417432215] |
1,802.0649 | On the exact solvability of the anisotropic central spin model: An
operator approach | Using an operator approach based on a commutator scheme that has been
previously applied to Richardson's reduced BCS model and the inhomogeneous
Dicke model, we obtain general exact solvability requirements for an
anisotropic central spin model with $XXZ$-type hyperfine coupling between the
central spin and the spin bath, without any prior knowledge of integrability of
the model. We outline the basic steps of the usage of the operator approach,
and pedagogically summarize them into two \emph{Lemmas} and two
\emph{Constraints}. Through a step-by-step construction of the eigen-problem,
we show that the condition $g'^2_j-g_j^2=c$ naturally arises for the model to
be exactly solvable, where $c$ is a constant independent of the bath-spin index
$j$, and $\{g_j\}$ and $\{g'_j\}$ are the longitudinal and transverse hyperfine
interactions, respectively. The obtained conditions and the resulting Bethe
ansatz equations are consistent with that in previous literature.
| cond-mat.stat-mech quant-ph | using an operator approach based on a commutator scheme that has been previously applied to richardsons reduced bcs model and the inhomogeneous dicke model we obtain general exact solvability requirements for an anisotropic central spin model with xxztype hyperfine coupling between the central spin and the spin bath without any prior knowledge of integrability of the model we outline the basic steps of the usage of the operator approach and pedagogically summarize them into two emphlemmas and two emphconstraints through a stepbystep construction of the eigenproblem we show that the condition g2_jg_j2c naturally arises for the model to be exactly solvable where c is a constant independent of the bathspin index j and g_j and g_j are the longitudinal and transverse hyperfine interactions respectively the obtained conditions and the resulting bethe ansatz equations are consistent with that in previous literature | [['using', 'an', 'operator', 'approach', 'based', 'on', 'a', 'commutator', 'scheme', 'that', 'has', 'been', 'previously', 'applied', 'to', 'richardsons', 'reduced', 'bcs', 'model', 'and', 'the', 'inhomogeneous', 'dicke', 'model', 'we', 'obtain', 'general', 'exact', 'solvability', 'requirements', 'for', 'an', 'anisotropic', 'central', 'spin', 'model', 'with', 'xxztype', 'hyperfine', 'coupling', 'between', 'the', 'central', 'spin', 'and', 'the', 'spin', 'bath', 'without', 'any', 'prior', 'knowledge', 'of', 'integrability', 'of', 'the', 'model', 'we', 'outline', 'the', 'basic', 'steps', 'of', 'the', 'usage', 'of', 'the', 'operator', 'approach', 'and', 'pedagogically', 'summarize', 'them', 'into', 'two', 'emphlemmas', 'and', 'two', 'emphconstraints', 'through', 'a', 'stepbystep', 'construction', 'of', 'the', 'eigenproblem', 'we', 'show', 'that', 'the', 'condition', 'g2_jg_j2c', 'naturally', 'arises', 'for', 'the', 'model', 'to', 'be', 'exactly', 'solvable', 'where', 'c', 'is', 'a', 'constant', 'independent', 'of', 'the', 'bathspin', 'index', 'j', 'and', 'g_j', 'and', 'g_j', 'are', 'the', 'longitudinal', 'and', 'transverse', 'hyperfine', 'interactions', 'respectively', 'the', 'obtained', 'conditions', 'and', 'the', 'resulting', 'bethe', 'ansatz', 'equations', 'are', 'consistent', 'with', 'that', 'in', 'previous', 'literature']] | [-0.11007568918113761, 0.12202991158483201, -0.053624866724182055, 0.040754839076886554, -0.08208482078899738, -0.1653295694165589, 0.00503728336736779, 0.37965515151325446, -0.25143140186007845, -0.2692839701194316, 0.06926647109674591, -0.24386417807545513, -0.10489070273401654, 0.178010971242603, 0.02716713396469405, 0.025103990026229227, 0.050212423628716564, 0.051201649044421225, -0.09391050984541995, -0.21803584847743074, 0.34296798966961967, 0.011029307853759211, 0.2744224955978793, 0.06442827294043074, 0.11988511583459673, 0.02135342376662747, 0.009867376065813005, 0.0021129105212714743, -0.13803235223932622, 0.10958216032389935, 0.20744615311987752, 0.07267719525059553, 0.21060165171237552, -0.424428080304471, -0.1759553171798282, 0.07231248524348143, 0.12773973083890536, 0.16519010198531117, 0.0016213375313193811, -0.2923974132315968, 0.040250058844000756, -0.19782835176652847, -0.144045700380743, -0.0814036999055294, 0.006052105198785498, 0.002641354687511921, -0.3068493705256568, 0.09961391614941771, 0.11180685338673785, 0.03161945040320086, -0.09586093433694366, -0.13806375780961175, -0.014248660060248393, 0.09919322810053606, 0.04493780576825991, 0.029094556834024843, 0.0700462914092521, -0.09072283885496504, -0.12370551800738801, 0.35338866703130084, -0.08069932625135955, -0.22597558841602328, 0.13517733028001042, -0.09978819829891161, -0.12557284834945356, 0.06069854365812395, 0.0967077698544873, 0.09876342869007632, -0.17195046340930276, 0.1447191825718619, -0.05441284075940905, 0.14009300839354502, 0.006948923046686961, 0.0033750551609794937, 0.1358250063049662, 0.10925072860503432, 0.03936411128790282, 0.12845628607507986, -0.028060704600006026, -0.1336273474204491, -0.311697629513219, -0.13547453235407694, -0.1827421076458824, 0.05731402037610464, -0.1154087451620452, -0.13308803874122746, 0.41220360920303445, 0.1734393323686163, 0.18485376769539846, 0.034098692608120686, 0.26758858907337796, 0.16317607746596502, 0.0411109387239455, 0.07527421038556735, 0.21654656311661444, 0.18803753978435828, 0.0543826026003123, -0.2633008485974963, 0.009537817821290125, 0.10089210501995266] |
1,802.06491 | Trace Ideals and the Gorenstein Property | Let R be a local Noetherian commutative ring. We prove that R is an Artinian
Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss
when the trace ideal of a module coincides with its double annihilator.
| math.AC | let r be a local noetherian commutative ring we prove that r is an artinian gorenstein ring if and only if every ideal in r is a trace ideal we discuss when the trace ideal of a module coincides with its double annihilator | [['let', 'r', 'be', 'a', 'local', 'noetherian', 'commutative', 'ring', 'we', 'prove', 'that', 'r', 'is', 'an', 'artinian', 'gorenstein', 'ring', 'if', 'and', 'only', 'if', 'every', 'ideal', 'in', 'r', 'is', 'a', 'trace', 'ideal', 'we', 'discuss', 'when', 'the', 'trace', 'ideal', 'of', 'a', 'module', 'coincides', 'with', 'its', 'double', 'annihilator']] | [-0.2458913477440906, -0.04508709843334103, -0.10639461420129898, 0.00421014062648769, -0.0468996386585194, -0.3056892585659096, -0.16040923704154963, 0.3572593182325363, -0.4705908886308587, 8.711816613064256e-05, 0.15303930894439216, -0.23159744397758744, -0.032243925948129144, 0.15182988085719043, -0.14131641821112745, -0.1880384766358644, 0.06114744323544031, 0.19064315982422855, -0.08244569794014962, -0.3086528746887695, 0.3652444720961327, 0.07575847080713788, 0.11455831085981498, 0.02826795627384685, 0.09880238643652478, 0.037971381238813315, -0.0063239053368221885, 0.10422501957238933, -0.2184693178787711, 0.029791162674163662, 0.3228068053289208, 0.0838612852737221, 0.27148146442202636, -0.36734461214942965, 0.00401270400386217, 0.2857073623427125, 0.14746767639853928, -0.08651601490672937, -0.009050895687365947, -0.15776058793241202, 0.2563925123188731, -0.2944985604736694, -0.19638430463626635, -0.03824602433501981, 0.202680392320766, 0.034625651964614555, -0.39697902528352513, -0.03481180021582648, 0.10612442110513531, 0.19628624873625677, -0.0029302142522579363, 0.011619856212894583, -0.08404745137708824, -0.030633043543148657, -0.17959700272483534, 0.037578272741547854, 0.15665724751035964, -0.09801459710958392, -0.0900629946832047, 0.36693100444972515, -0.13204967927358244, -0.18172182814694596, 0.1181391371240796, -0.28624940576941466, -0.025146404432869234, 0.0837523357639479, -0.14564549290510112, 0.14455793376708792, -0.005655814391671853, 0.32600074529858997, -0.2779889402607846, 0.10896819899248522, 0.037305515367797644, 0.04579038832466616, 0.2532405681301688, 0.08203881469468564, 0.11996702681062743, 0.15981516807047694, -0.02076982949362245, 0.15582212470038687, -0.38338268704192585, -0.28894650531109684, -0.2011862492925206, 0.20340277479831562, -0.10403586932164238, -0.12499530600427194, 0.4071025966211807, 0.10839312965440195, 0.1397943971462028, 0.0737522985179757, 0.26364495869466037, -0.0047200288796840715, 0.06177616093394368, 0.1694279340346077, 0.07147621853428698, 0.23883582166461056, -0.0750469877059723, -0.11106172876519173, 0.001506696422692648, 0.20325809476767168] |
1,802.06492 | Attributed Hierarchical Port Graphs and Applications | We present attributed hierarchical port graphs (AHP) as an extension of port
graphs that aims at facilitating the design of modular port graph models for
complex systems. AHP consist of a number of interconnected layers, where each
layer defines a port graph whose nodes may link to layers further down the
hierarchy; attributes are used to store user-defined data as well as
visualisation and run-time system parameters. We also generalise the notion of
strategic port graph rewriting (a particular kind of graph transformation
system, where port graph rewriting rules are controlled by user-defined
strategies) to deal with AHP following the Single Push-out approach. We outline
examples of application in two areas: functional programming and financial
modelling.
| cs.LO cs.SE cs.SI | we present attributed hierarchical port graphs ahp as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems ahp consist of a number of interconnected layers where each layer defines a port graph whose nodes may link to layers further down the hierarchy attributes are used to store userdefined data as well as visualisation and runtime system parameters we also generalise the notion of strategic port graph rewriting a particular kind of graph transformation system where port graph rewriting rules are controlled by userdefined strategies to deal with ahp following the single pushout approach we outline examples of application in two areas functional programming and financial modelling | [['we', 'present', 'attributed', 'hierarchical', 'port', 'graphs', 'ahp', 'as', 'an', 'extension', 'of', 'port', 'graphs', 'that', 'aims', 'at', 'facilitating', 'the', 'design', 'of', 'modular', 'port', 'graph', 'models', 'for', 'complex', 'systems', 'ahp', 'consist', 'of', 'a', 'number', 'of', 'interconnected', 'layers', 'where', 'each', 'layer', 'defines', 'a', 'port', 'graph', 'whose', 'nodes', 'may', 'link', 'to', 'layers', 'further', 'down', 'the', 'hierarchy', 'attributes', 'are', 'used', 'to', 'store', 'userdefined', 'data', 'as', 'well', 'as', 'visualisation', 'and', 'runtime', 'system', 'parameters', 'we', 'also', 'generalise', 'the', 'notion', 'of', 'strategic', 'port', 'graph', 'rewriting', 'a', 'particular', 'kind', 'of', 'graph', 'transformation', 'system', 'where', 'port', 'graph', 'rewriting', 'rules', 'are', 'controlled', 'by', 'userdefined', 'strategies', 'to', 'deal', 'with', 'ahp', 'following', 'the', 'single', 'pushout', 'approach', 'we', 'outline', 'examples', 'of', 'application', 'in', 'two', 'areas', 'functional', 'programming', 'and', 'financial', 'modelling']] | [-0.1408515788135948, 0.027986261842231436, -0.019798437382319366, 0.04114910165763235, -0.1677736283263898, -0.187100216605829, 0.07519705585055535, 0.3709494425947296, -0.33620388788203226, -0.3660598278350743, 0.09028704759789277, -0.2589894740537194, -0.1736510360436835, 0.13466133725636736, -0.09667546208747181, 0.06263608096873965, 0.10593075571774409, 0.03214509892759138, 0.030710782279694003, -0.20636437486296175, 0.3553669203779307, 0.01947087205239925, 0.2245272469690776, 0.00959935345173139, 0.10643320727856541, 0.045501915693829026, -0.028042204152182514, 0.02679149307920758, -0.10957805781680659, 0.10068049645533078, 0.3529290365840066, 0.1926119579162834, 0.26888930015587087, -0.48674951012824375, -0.1406497906347544, 0.06620395571748115, 0.11909077200910141, 0.04845418235094383, 0.04683957522702885, -0.26380351895530674, 0.07160565761572296, -0.2155083831144268, -0.06458908985449194, -0.09674426767140112, -0.03630085739082303, 0.04928538320859059, -0.266015952750077, -0.09403194883725519, 0.06338472686535358, 0.061066829234136845, 0.021898197991661084, -0.10025298598439208, -0.04992827040079082, 0.1257661379681065, -0.06964784365243695, -0.014226038964336803, 0.1541920287839683, -0.12297250391465836, -0.19543623676170305, 0.3413263827498103, -0.005063529556882086, -0.19697852726576143, 0.1677710729699325, 0.02339779687965096, -0.19093923475834187, 0.0509617182843644, 0.19593800194681912, 0.07660166490501885, -0.16471264164108013, 0.06845805453887241, -0.014045008072822258, 0.20886034727225017, 0.13029234564726658, 0.0021420681873207978, 0.180050008250842, 0.2373627318884246, 0.0924904002639433, 0.21321869264999083, -0.007159477320563947, -0.09510053540098257, -0.2904816504471518, -0.13943560794999438, -0.15716602139030422, -0.0493682652695811, -0.13881995566244487, -0.2100717025409565, 0.43718073057845747, 0.14179122356541357, 0.16971030644294685, 0.08933363606398605, 0.29791018089825483, 0.08673417832850928, 0.11163914565334161, 0.06932471010930322, 0.07936894730263358, 0.10908022434209827, 0.12569284240378004, -0.10257444732244415, 0.08810880514672668, 0.08111964530664785] |
1,802.06493 | A Method to Translate Order-Sorted Algebras to Many-Sorted Algebras | Order-sorted algebras and many sorted algebras exist in a long history with
many different implementations and applications. A lot of language
specifications have been defined in order-sorted algebra frameworks such as the
language specifications in K (an order-sorted algebra framework). The biggest
problem in a lot of the order-sorted algebra frameworks is that even if they
might allow developers to write programs and language specifications easily,
but they do not have a large set of tools to provide reasoning infrastructures
to reason about the specifications built on the frameworks, which are very
common in some many-sorted algebra framework such as Isabelle/HOL, Coq and FDR.
This fact brings us the necessity to marry the worlds of order-sorted algebras
and many sorted algebras. In this paper, we propose an algorithm to translate a
strictly sensible order-sorted algebra to a many-sorted one in a restricted
domain by requiring the order-sorted algebra to be strictly sensible. The key
idea of the translation is to add an equivalence relation called core equality
to the translated many-sorted algebras. By defining this relation, we reduce
the complexity of translating a strictly sensible order-sorted algebra to a
many-sorted one, make the translated many-sorted algebra equations only
increasing by a very small amount of new equations, and keep the number of
rewrite rules in the algebra in the same amount. We then prove the order-sorted
algebra and its translated many-sorted algebra are bisimilar. To the best of
our knowledge, our translation and bisimilar proof is the first attempt in
translating and relating an order-sorted algebra with a many-sorted one in a
way that keeps the size of the translated many-sorted algebra relatively small.
| cs.PL cs.LO | ordersorted algebras and many sorted algebras exist in a long history with many different implementations and applications a lot of language specifications have been defined in ordersorted algebra frameworks such as the language specifications in k an ordersorted algebra framework the biggest problem in a lot of the ordersorted algebra frameworks is that even if they might allow developers to write programs and language specifications easily but they do not have a large set of tools to provide reasoning infrastructures to reason about the specifications built on the frameworks which are very common in some manysorted algebra framework such as isabellehol coq and fdr this fact brings us the necessity to marry the worlds of ordersorted algebras and many sorted algebras in this paper we propose an algorithm to translate a strictly sensible ordersorted algebra to a manysorted one in a restricted domain by requiring the ordersorted algebra to be strictly sensible the key idea of the translation is to add an equivalence relation called core equality to the translated manysorted algebras by defining this relation we reduce the complexity of translating a strictly sensible ordersorted algebra to a manysorted one make the translated manysorted algebra equations only increasing by a very small amount of new equations and keep the number of rewrite rules in the algebra in the same amount we then prove the ordersorted algebra and its translated manysorted algebra are bisimilar to the best of our knowledge our translation and bisimilar proof is the first attempt in translating and relating an ordersorted algebra with a manysorted one in a way that keeps the size of the translated manysorted algebra relatively small | [['ordersorted', 'algebras', 'and', 'many', 'sorted', 'algebras', 'exist', 'in', 'a', 'long', 'history', 'with', 'many', 'different', 'implementations', 'and', 'applications', 'a', 'lot', 'of', 'language', 'specifications', 'have', 'been', 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1,802.06494 | Transforming Proof Tableaux of Hoare Logic into Inference Sequences of
Rewriting Induction | A proof tableau of Hoare logic is an annotated program with pre- and
post-conditions, which corresponds to an inference tree of Hoare logic. In this
paper, we show that a proof tableau for partial correctness can be transformed
into an inference sequence of rewriting induction for constrained rewriting. We
also show that the resulting sequence is a valid proof for an inductive theorem
corresponding to the Hoare triple if the constrained rewriting system obtained
from the program is terminating. Such a valid proof with termination of the
constrained rewriting system implies total correctness of the program w.r.t.
the Hoare triple. The transformation enables us to apply techniques for proving
termination of constrained rewriting to proving total correctness of programs
together with proof tableaux for partial correctness.
| cs.LO | a proof tableau of hoare logic is an annotated program with pre and postconditions which corresponds to an inference tree of hoare logic in this paper we show that a proof tableau for partial correctness can be transformed into an inference sequence of rewriting induction for constrained rewriting we also show that the resulting sequence is a valid proof for an inductive theorem corresponding to the hoare triple if the constrained rewriting system obtained from the program is terminating such a valid proof with termination of the constrained rewriting system implies total correctness of the program wrt the hoare triple the transformation enables us to apply techniques for proving termination of constrained rewriting to proving total correctness of programs together with proof tableaux for partial correctness | [['a', 'proof', 'tableau', 'of', 'hoare', 'logic', 'is', 'an', 'annotated', 'program', 'with', 'pre', 'and', 'postconditions', 'which', 'corresponds', 'to', 'an', 'inference', 'tree', 'of', 'hoare', 'logic', 'in', 'this', 'paper', 'we', 'show', 'that', 'a', 'proof', 'tableau', 'for', 'partial', 'correctness', 'can', 'be', 'transformed', 'into', 'an', 'inference', 'sequence', 'of', 'rewriting', 'induction', 'for', 'constrained', 'rewriting', 'we', 'also', 'show', 'that', 'the', 'resulting', 'sequence', 'is', 'a', 'valid', 'proof', 'for', 'an', 'inductive', 'theorem', 'corresponding', 'to', 'the', 'hoare', 'triple', 'if', 'the', 'constrained', 'rewriting', 'system', 'obtained', 'from', 'the', 'program', 'is', 'terminating', 'such', 'a', 'valid', 'proof', 'with', 'termination', 'of', 'the', 'constrained', 'rewriting', 'system', 'implies', 'total', 'correctness', 'of', 'the', 'program', 'wrt', 'the', 'hoare', 'triple', 'the', 'transformation', 'enables', 'us', 'to', 'apply', 'techniques', 'for', 'proving', 'termination', 'of', 'constrained', 'rewriting', 'to', 'proving', 'total', 'correctness', 'of', 'programs', 'together', 'with', 'proof', 'tableaux', 'for', 'partial', 'correctness']] | [-0.11368768150726008, -0.01579083805388239, -0.11905051339122039, 0.08377767191083717, -0.1639562370292547, -0.1503128317805628, 0.0976256361214577, 0.2965508899429724, -0.3465298612616838, -0.3447305661559637, 0.09632307833101275, -0.19196467748325732, -0.055913876158200086, 0.18195108438117635, -0.14122065942039683, 0.06150775990589329, 0.11650064845924221, 0.03576195786618406, -0.08209032599725538, -0.2474289147020687, 0.29058511011184207, -0.0077635301277041435, 0.1704781745146546, 0.028813237967413096, 0.10917622367629692, 0.11231091521340349, -0.023446923432250816, 0.038043329222423455, -0.07433029834519692, 0.12985712064370986, 0.30288677594609675, 0.2930351411923766, 0.2617322587600303, -0.4077299879863858, -0.015267287240555835, 0.022295064699377806, 0.1304159963518263, 0.10905065810024213, 0.0005010007751277752, -0.29751565857302575, 0.11994113539168168, -0.17906926776881196, -0.10201885573388565, -0.10477036475721332, 0.02500447318963115, 0.003331066190545994, -0.29713833434063763, -0.07136496180490733, 0.24363723193990097, 0.08976145104564254, -0.028479593118564003, -0.05659837110359813, -0.05631352724537017, 0.037856916379597455, -0.03385938316147538, 0.037118473042187, 0.07858457321870244, -0.057475443650406625, -0.2088726718340897, 0.30541991875580854, -0.04043362221850585, -0.17436011914821667, 0.1562193834171113, -0.003856913415744664, -0.2603147773789094, 0.12895822507284938, 0.06982683268789616, 0.16541126676435983, -0.17077219123686, 0.11130522266871089, -0.06415769107831967, 0.262557349411682, 0.12218645477430924, 0.015375765240085977, 0.19840874677405707, 0.1944840688919944, 0.06301534033217837, 0.21300590602174727, 0.06364329851099423, -0.09908355739972895, -0.37737839731077355, -0.23216754784955393, -0.10414404334825655, 0.0017448987974415695, -0.07616993037478846, -0.22211712925502705, 0.3260693030047511, 0.1719267793084746, 0.0664180997714755, 0.25317148191000644, 0.26983947168281747, 0.2096253548053995, 0.11028261092077526, 0.0358766683452164, 0.14916296413866803, 0.18433116717561562, 0.09083190191138003, -0.18695997663991645, 0.11680260098480161, 0.18365859324186448] |
1,802.06495 | Efficient Implementation of Evaluation Strategies via Token-Guided Graph
Rewriting | In implementing evaluation strategies of the lambda-calculus, both
correctness and efficiency of implementation are valid concerns. While the
notion of correctness is determined by the evaluation strategy, regarding
efficiency there is a larger design space that can be explored, in particular
the trade-off between space versus time efficiency. We contributed to the study
of this trade-off by the introduction of an abstract machine for call-by-need,
inspired by Girard's Geometry of Interaction, a machine combining token passing
and graph rewriting. This work presents an extension of the machine, to
additionally accommodate left-to-right and right-to-left call-by-value
strategies. We show soundness and completeness of the extended machine with
respect to each of the call-by-need and two call-by-value strategies. Analysing
time cost of its execution classifies the machine as "efficient" in Accattoli's
taxonomy of abstract machines.
| cs.PL cs.LO | in implementing evaluation strategies of the lambdacalculus both correctness and efficiency of implementation are valid concerns while the notion of correctness is determined by the evaluation strategy regarding efficiency there is a larger design space that can be explored in particular the tradeoff between space versus time efficiency we contributed to the study of this tradeoff by the introduction of an abstract machine for callbyneed inspired by girards geometry of interaction a machine combining token passing and graph rewriting this work presents an extension of the machine to additionally accommodate lefttoright and righttoleft callbyvalue strategies we show soundness and completeness of the extended machine with respect to each of the callbyneed and two callbyvalue strategies analysing time cost of its execution classifies the machine as efficient in accattolis taxonomy of abstract machines | [['in', 'implementing', 'evaluation', 'strategies', 'of', 'the', 'lambdacalculus', 'both', 'correctness', 'and', 'efficiency', 'of', 'implementation', 'are', 'valid', 'concerns', 'while', 'the', 'notion', 'of', 'correctness', 'is', 'determined', 'by', 'the', 'evaluation', 'strategy', 'regarding', 'efficiency', 'there', 'is', 'a', 'larger', 'design', 'space', 'that', 'can', 'be', 'explored', 'in', 'particular', 'the', 'tradeoff', 'between', 'space', 'versus', 'time', 'efficiency', 'we', 'contributed', 'to', 'the', 'study', 'of', 'this', 'tradeoff', 'by', 'the', 'introduction', 'of', 'an', 'abstract', 'machine', 'for', 'callbyneed', 'inspired', 'by', 'girards', 'geometry', 'of', 'interaction', 'a', 'machine', 'combining', 'token', 'passing', 'and', 'graph', 'rewriting', 'this', 'work', 'presents', 'an', 'extension', 'of', 'the', 'machine', 'to', 'additionally', 'accommodate', 'lefttoright', 'and', 'righttoleft', 'callbyvalue', 'strategies', 'we', 'show', 'soundness', 'and', 'completeness', 'of', 'the', 'extended', 'machine', 'with', 'respect', 'to', 'each', 'of', 'the', 'callbyneed', 'and', 'two', 'callbyvalue', 'strategies', 'analysing', 'time', 'cost', 'of', 'its', 'execution', 'classifies', 'the', 'machine', 'as', 'efficient', 'in', 'accattolis', 'taxonomy', 'of', 'abstract', 'machines']] | [-0.12760645238626184, 0.032363745795120136, -0.08548634842913033, 0.06916235002449178, -0.11638801910378264, -0.15997543627974775, 0.11437341892407417, 0.38269664117163327, -0.31303125278050586, -0.32929465042958106, 0.06884172938809956, -0.20806544868162635, -0.09881030975675183, 0.1881986701028478, -0.14840096582228204, 0.06421049901197848, 0.057188041151896345, 0.007078486716967414, -0.05070158730924242, -0.2723314598016176, 0.32835641018358397, 0.0577152562045464, 0.2883545056101866, 0.037761649300316065, 0.09696838088028457, 0.05928334390222462, -0.06000787734537329, 0.02737370071267695, -0.08867106061618622, 0.17488879709024774, 0.2937362204613623, 0.2554412839024074, 0.32820653425755375, -0.38822613808213535, -0.11798196530788008, 0.09425226071228583, 0.1286475887754932, 0.06331310298286774, -0.011345332714192795, -0.28357510199544556, 0.10206155487597271, -0.19049298147861424, -0.05694630037583975, -0.11449742099891107, 0.019802224621261386, 0.02583199493705196, -0.21000577541152862, -0.024897606690611803, 0.1386527428077181, 0.11942228487213001, -0.03001900519633306, -0.07907585934453616, 0.005441681724429752, 0.08777563152552555, 0.025807042052320234, 0.03043006718067001, 0.10972983763856588, -0.12058319724041433, -0.23907703003197006, 0.3646561747494464, -0.052478064500698536, -0.1920836153085199, 0.17122333694009506, 0.018792542874121642, -0.14132944195510141, 0.07090220293453471, 0.16761782417906393, 0.08729177472096952, -0.14145196572821023, 0.12138397999903343, 0.024334220049874573, 0.18850907120698443, 0.09222825452029197, 0.03537747625501431, 0.12103745869050424, 0.2576928509409878, 0.025444623061709783, 0.19151937777342304, 0.008583476012008208, -0.13999320707763685, -0.3137215262730465, -0.20839758722418497, -0.12190613076271609, -0.06521207732360133, -0.09202214106015603, -0.1277853531099743, 0.3836666844559438, 0.19125151408793914, 0.13751673488172167, 0.14957063109613955, 0.33147633622160577, 0.09638330459711142, 0.057643087926077315, 0.09042797016621934, 0.18001063088322003, 0.074139724286259, 0.11039258370521676, -0.2343221929287679, 0.10919908640040155, 0.06794848924530952] |
1,802.06496 | Reduced Dependency Spaces for Existential Parameterised Boolean Equation
Systems | A parameterised Boolean equation system (PBES) is a set of equations that
defines sets satisfying the equations as the least and/or greatest
fixed-points. Thus this system is regarded as a declarative program defining
predicates, where a program execution returns whether a given ground atomic
formula holds or not. The program execution corresponds to the membership
problem of PBESs, which is however undecidable in general.
This paper proposes a subclass of PBESs which expresses universal-quantifiers
free formulas, and studies a technique to solve the problem on it. We use the
fact that the membership problem is reduced to the problem whether a proof
graph exists. To check the latter problem, we introduce a so-called dependency
space which is a graph containing all of the minimal proof graphs. Dependency
spaces are, however, infinite in general. Thus, we propose some conditions for
equivalence relations to preserve the result of the membership problem, then we
identify two vertices as the same under the relation. In this sense, dependency
spaces possibly result in a finite graph. We show some examples having infinite
dependency spaces which are reducible to finite graphs by equivalence
relations. We provide a procedure to construct finite dependency spaces and
show the soundness of the procedure. We also implement the procedure using an
SMT solver and experiment on some examples including a downsized McCarthy 91
function.
| cs.LO | a parameterised boolean equation system pbes is a set of equations that defines sets satisfying the equations as the least andor greatest fixedpoints thus this system is regarded as a declarative program defining predicates where a program execution returns whether a given ground atomic formula holds or not the program execution corresponds to the membership problem of pbess which is however undecidable in general this paper proposes a subclass of pbess which expresses universalquantifiers free formulas and studies a technique to solve the problem on it we use the fact that the membership problem is reduced to the problem whether a proof graph exists to check the latter problem we introduce a socalled dependency space which is a graph containing all of the minimal proof graphs dependency spaces are however infinite in general thus we propose some conditions for equivalence relations to preserve the result of the membership problem then we identify two vertices as the same under the relation in this sense dependency spaces possibly result in a finite graph we show some examples having infinite dependency spaces which are reducible to finite graphs by equivalence relations we provide a procedure to construct finite dependency spaces and show the soundness of the procedure we also implement the procedure using an smt solver and experiment on some examples including a downsized mccarthy 91 function | [['a', 'parameterised', 'boolean', 'equation', 'system', 'pbes', 'is', 'a', 'set', 'of', 'equations', 'that', 'defines', 'sets', 'satisfying', 'the', 'equations', 'as', 'the', 'least', 'andor', 'greatest', 'fixedpoints', 'thus', 'this', 'system', 'is', 'regarded', 'as', 'a', 'declarative', 'program', 'defining', 'predicates', 'where', 'a', 'program', 'execution', 'returns', 'whether', 'a', 'given', 'ground', 'atomic', 'formula', 'holds', 'or', 'not', 'the', 'program', 'execution', 'corresponds', 'to', 'the', 'membership', 'problem', 'of', 'pbess', 'which', 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1,802.06497 | Transforming Dependency Chains of Constrained TRSs into Bounded Monotone
Sequences of Integers | In the dependency pair framework for proving termination of rewriting
systems, polynomial interpretations are used to transform dependency chains
into bounded decreasing sequences of integers, and they play an important role
for the success of proving termination, especially for constrained rewriting
systems. In this paper, we show sufficient conditions of linear polynomial
interpretations for transforming dependency chains into bounded monotone (i.e.,
decreasing or increasing) sequences of integers. Such polynomial
interpretations transform rewrite sequences of the original system into
decreasing or increasing sequences independently of the transformation of
dependency chains. When we transform rewrite sequences into increasing
sequences, polynomial interpretations have non-positive coefficients for
reducible positions of marked function symbols. We propose four DP processors
parameterized by transforming dependency chains and rewrite sequences into
either decreasing or increasing sequences of integers, respectively. We show
that such polynomial interpretations make us succeed in proving termination of
the McCarthy 91 function over the integers.
| cs.LO | in the dependency pair framework for proving termination of rewriting systems polynomial interpretations are used to transform dependency chains into bounded decreasing sequences of integers and they play an important role for the success of proving termination especially for constrained rewriting systems in this paper we show sufficient conditions of linear polynomial interpretations for transforming dependency chains into bounded monotone ie decreasing or increasing sequences of integers such polynomial interpretations transform rewrite sequences of the original system into decreasing or increasing sequences independently of the transformation of dependency chains when we transform rewrite sequences into increasing sequences polynomial interpretations have nonpositive coefficients for reducible positions of marked function symbols we propose four dp processors parameterized by transforming dependency chains and rewrite sequences into either decreasing or increasing sequences of integers respectively we show that such polynomial interpretations make us succeed in proving termination of the mccarthy 91 function over the integers | [['in', 'the', 'dependency', 'pair', 'framework', 'for', 'proving', 'termination', 'of', 'rewriting', 'systems', 'polynomial', 'interpretations', 'are', 'used', 'to', 'transform', 'dependency', 'chains', 'into', 'bounded', 'decreasing', 'sequences', 'of', 'integers', 'and', 'they', 'play', 'an', 'important', 'role', 'for', 'the', 'success', 'of', 'proving', 'termination', 'especially', 'for', 'constrained', 'rewriting', 'systems', 'in', 'this', 'paper', 'we', 'show', 'sufficient', 'conditions', 'of', 'linear', 'polynomial', 'interpretations', 'for', 'transforming', 'dependency', 'chains', 'into', 'bounded', 'monotone', 'ie', 'decreasing', 'or', 'increasing', 'sequences', 'of', 'integers', 'such', 'polynomial', 'interpretations', 'transform', 'rewrite', 'sequences', 'of', 'the', 'original', 'system', 'into', 'decreasing', 'or', 'increasing', 'sequences', 'independently', 'of', 'the', 'transformation', 'of', 'dependency', 'chains', 'when', 'we', 'transform', 'rewrite', 'sequences', 'into', 'increasing', 'sequences', 'polynomial', 'interpretations', 'have', 'nonpositive', 'coefficients', 'for', 'reducible', 'positions', 'of', 'marked', 'function', 'symbols', 'we', 'propose', 'four', 'dp', 'processors', 'parameterized', 'by', 'transforming', 'dependency', 'chains', 'and', 'rewrite', 'sequences', 'into', 'either', 'decreasing', 'or', 'increasing', 'sequences', 'of', 'integers', 'respectively', 'we', 'show', 'that', 'such', 'polynomial', 'interpretations', 'make', 'us', 'succeed', 'in', 'proving', 'termination', 'of', 'the', 'mccarthy', '91', 'function', 'over', 'the', 'integers']] | [-0.17996419867691862, 0.12554227311361893, -0.05263292292342676, 0.08993897072289336, -0.062331699918869214, -0.18290729892273613, 0.02239158174519532, 0.3455899142573853, -0.38992137283037437, -0.27118017151643403, 0.06889026186317945, -0.27608133389287637, -0.13103043604549638, 0.1727755843856008, -0.04283937766750201, 0.07041445555202416, 0.07591527685004947, 0.009054258195930068, -0.10488329547078083, -0.31368782744428375, 0.3059546955458709, -0.03244582310763021, 0.20213889763598017, 0.006289878890954501, 0.0987031338798092, 0.09434199014754538, -0.05813891385891629, 0.0016773202956117542, -0.11965449625150715, 0.0824012098392928, 0.2727897948314072, 0.20150391193760547, 0.2726702715566271, -0.4529562073432847, -0.14497469046109954, 0.1759553114260664, 0.22664322182135224, 0.041097723858393206, -0.020032293055305222, -0.2475025560213438, 0.10437267060878853, -0.1156446899114707, -0.07274250803065845, -0.06931286718733362, 0.09008056190580327, 0.09434154025272817, -0.2796012456498004, -0.027540308767117272, 0.18252859686482822, 0.11619254682731155, -0.07562732785964842, -0.15209617815674314, 0.008094717156364034, 0.11061641212575143, 0.011650380715481098, 0.02935610506806942, 0.0412487592363101, -0.0828538702551078, -0.12552556144428248, 0.2947394264097147, -0.0665329728839882, -0.2226720535048339, 0.1591993554353418, -0.07880396705386013, -0.22406487602475314, 0.12448164129888775, 0.12671735883375865, 0.11288829111734665, -0.06844553850263138, 0.0985629691099378, -0.004449045267079445, 0.19979903389027479, 0.18632519118401486, 0.07606032507383073, 0.21766685511275435, 0.0804930048256909, 0.0645618940740577, 0.21693620939325814, 0.06920682133132258, -0.09398990670305411, -0.256672186215735, -0.17838314593467391, -0.1327571953887379, 0.015061918060358503, -0.11011990135985068, -0.19665965622303305, 0.3569913030669883, 0.10255983380588475, 0.17778238824365156, 0.18135590622176892, 0.22974255045919081, 0.1910729438651643, 0.07101220943593414, -0.0034361550343895196, 0.04852178698985387, 0.1360061363246144, 0.033805693755703456, -0.16922300711076782, 0.12604714604094625, 0.13870191819320543] |
1,802.06498 | Space Improvements and Equivalences in a Functional Core Language | We explore space improvements in LRP, a polymorphically typed call-by-need
functional core language. A relaxed space measure is chosen for the maximal
size usage during an evaluation. It abstracts from the details of the
implementation via abstract machines, but it takes garbage collection into
account and thus can be seen as a realistic approximation of space usage. The
results are: a context lemma for space improving translations and for space
equivalences, all but one reduction rule of the calculus are shown to be space
improvements, and for the exceptional one we show bounds on the space increase.
Several further program transformations are shown to be space improvements or
space equivalences in particular the translation into machine expressions is a
space equivalence. We also classify certain space-worsening transformations as
space-leaks or as space-safe. These results are a step forward in making
predictions about the change in runtime space behavior of optimizing
transformations in call-by-need functional languages.
| cs.PL | we explore space improvements in lrp a polymorphically typed callbyneed functional core language a relaxed space measure is chosen for the maximal size usage during an evaluation it abstracts from the details of the implementation via abstract machines but it takes garbage collection into account and thus can be seen as a realistic approximation of space usage the results are a context lemma for space improving translations and for space equivalences all but one reduction rule of the calculus are shown to be space improvements and for the exceptional one we show bounds on the space increase several further program transformations are shown to be space improvements or space equivalences in particular the translation into machine expressions is a space equivalence we also classify certain spaceworsening transformations as spaceleaks or as spacesafe these results are a step forward in making predictions about the change in runtime space behavior of optimizing transformations in callbyneed functional languages | [['we', 'explore', 'space', 'improvements', 'in', 'lrp', 'a', 'polymorphically', 'typed', 'callbyneed', 'functional', 'core', 'language', 'a', 'relaxed', 'space', 'measure', 'is', 'chosen', 'for', 'the', 'maximal', 'size', 'usage', 'during', 'an', 'evaluation', 'it', 'abstracts', 'from', 'the', 'details', 'of', 'the', 'implementation', 'via', 'abstract', 'machines', 'but', 'it', 'takes', 'garbage', 'collection', 'into', 'account', 'and', 'thus', 'can', 'be', 'seen', 'as', 'a', 'realistic', 'approximation', 'of', 'space', 'usage', 'the', 'results', 'are', 'a', 'context', 'lemma', 'for', 'space', 'improving', 'translations', 'and', 'for', 'space', 'equivalences', 'all', 'but', 'one', 'reduction', 'rule', 'of', 'the', 'calculus', 'are', 'shown', 'to', 'be', 'space', 'improvements', 'and', 'for', 'the', 'exceptional', 'one', 'we', 'show', 'bounds', 'on', 'the', 'space', 'increase', 'several', 'further', 'program', 'transformations', 'are', 'shown', 'to', 'be', 'space', 'improvements', 'or', 'space', 'equivalences', 'in', 'particular', 'the', 'translation', 'into', 'machine', 'expressions', 'is', 'a', 'space', 'equivalence', 'we', 'also', 'classify', 'certain', 'spaceworsening', 'transformations', 'as', 'spaceleaks', 'or', 'as', 'spacesafe', 'these', 'results', 'are', 'a', 'step', 'forward', 'in', 'making', 'predictions', 'about', 'the', 'change', 'in', 'runtime', 'space', 'behavior', 'of', 'optimizing', 'transformations', 'in', 'callbyneed', 'functional', 'languages']] | [-0.08445289515350994, 0.07555479823244432, -0.09201513636722475, 0.13671897659782858, -0.13272146904522455, -0.09586563842535006, 0.06727577397281206, 0.408070651887867, -0.31132363628498033, -0.3127038865350187, 0.14019211835004267, -0.24150275924138873, -0.12133753528101615, 0.23945321541549147, -0.09094738512986193, 0.03287328716281703, 0.08946882566057243, 0.0276607274243265, -0.12106679709579207, -0.28985211056485577, 0.30824389587321904, 0.010277107259944865, 0.2761953164774336, 0.007401774018561761, 0.09638551524595211, 0.01258041306803199, -0.033224946696703374, 0.03733319850844533, -0.0833423182944228, 0.13234068767939644, 0.28936910938692134, 0.2002829305649931, 0.2706276589275436, -0.3858658729464208, -0.19465744377751099, 0.09781608930605121, 0.12901212165046386, 0.10656823752766573, 0.01673119741577753, -0.318127210915248, 0.05920144180172907, -0.15121712586934385, -0.05100532412210381, -0.1672759017237695, 0.03625257075672332, -0.006110750610769412, -0.24787560822273677, -0.07056113168781801, 0.10850307764485478, 0.05719295009897139, -0.08656925695494895, -0.07516155401428573, -0.014236457305837814, 0.12637393984416695, 0.02269591050112228, 0.06481236857545905, 0.14461324581919288, -0.07532849440069281, -0.1367794072598611, 0.397164034994172, -0.05649491173435787, -0.2535816486434717, 0.1566316486538486, -0.08842288653709386, -0.19295671072139062, 0.1063286355163559, 0.16788391456449112, 0.06505877071513648, -0.11205195027593474, 0.1270816897361472, -0.016192924170019597, 0.15147516951210013, 0.09919037362851668, 0.06603739862743839, 0.13481469436756974, 0.20033093616458295, 0.06145933203056062, 0.15470939153257, 0.0010748967439499929, -0.09726866655584768, -0.34305138148728903, -0.22954005259701885, -0.10660787121818621, -0.04180517043661032, -0.09635786535986163, -0.13850399103983746, 0.34160280921557723, 0.11529267822563845, 0.19927269475240456, 0.1153517946628486, 0.26251713774093477, 0.10794392400528427, 0.11967713505682216, 0.07245268116362001, 0.16006404817361677, 0.0631031752257657, 0.07117358026842244, -0.136314474432239, 0.08361141084031642, 0.09059033838811477] |
1,802.06499 | Higher order Hamiltonians for the trigonometric Gaudin model | We consider the trigonometric classical $r$-matrix for $\mathfrak{gl}_N$ and
the associated quantum Gaudin model. We produce higher Hamiltonians in an
explicit form by applying the limit $q\to 1$ to elements of the Bethe
subalgebra for the $XXZ$ model.
| math.QA math-ph math.MP | we consider the trigonometric classical rmatrix for mathfrakgl_n and the associated quantum gaudin model we produce higher hamiltonians in an explicit form by applying the limit qto 1 to elements of the bethe subalgebra for the xxz model | [['we', 'consider', 'the', 'trigonometric', 'classical', 'rmatrix', 'for', 'mathfrakgl_n', 'and', 'the', 'associated', 'quantum', 'gaudin', 'model', 'we', 'produce', 'higher', 'hamiltonians', 'in', 'an', 'explicit', 'form', 'by', 'applying', 'the', 'limit', 'qto', '1', 'to', 'elements', 'of', 'the', 'bethe', 'subalgebra', 'for', 'the', 'xxz', 'model']] | [-0.11756595538922977, 0.06363744371131026, 0.006029114421260984, 0.08800315979476038, -0.052719788527802416, -0.176907834449881, -0.02286232716869563, 0.32491198721292774, -0.3006055501142615, -0.16943913906518565, 0.06829451345593522, -0.28392950098618475, -0.09889341486421854, 0.23251061689255662, 0.0001462763052825865, 0.05026217589252874, 0.06619802298097822, 0.0895957731592812, -0.16796130591415262, -0.17784331418500332, 0.3611391643062234, 0.040542615390701316, 0.20473193661554864, -0.07265741927059073, 0.09657140247719853, 0.053364357727236654, 0.12895351226784682, -0.13799840591749862, -0.16943047005119488, 0.15020335254896627, 0.2194194170327759, 0.014008385827764869, 0.10586241412123568, -0.4215255003226431, -0.10597335848663199, 0.1347492049497209, 0.2042236605806178, 0.17272580890475134, 0.03330457021825408, -0.2922703152350885, 0.005075349258013854, -0.33001470258214366, -0.2276676948991065, -0.1090153619941128, 0.005825722295986979, -0.01791319143223135, -0.30661891530709046, 0.10002157275908087, 0.10033954439782783, 0.1145183363635289, -0.07286275820316453, -0.1777496603930271, 0.012216270803228804, 0.08230152804600566, -0.066071229738698, 0.0153338163478398, 0.03980570644336311, -0.15624574816932804, -0.18676072898271837, 0.38002314065632065, -0.04262135294266045, -0.2543383895566589, 0.09063298409608633, -0.13737201310792252, -0.17889221958619983, 0.06336883759420169, 0.05315667498660715, 0.06676114649560891, -0.14077741194418386, 0.22803294083783648, -0.04019224445188516, 0.06011678927921151, 0.006981440501189546, -0.030361181002502378, 0.12749320946290696, 0.012427745509500565, -0.019808988699591475, 0.1947684864219474, 0.02379502337517854, -0.16045688210349335, -0.34016270494382633, -0.17588414594923196, -0.17327961370373438, 0.13305824181359066, -0.13480552196415374, -0.16831869681022668, 0.3926151882256626, 0.1895498392512213, 0.19744784470745608, 0.09554501603308477, 0.13949730894283244, 0.23530336430198268, 0.05293502491947852, 0.06410127010588583, 0.16636630579044945, 0.2549648246249968, -0.018039866546659095, -0.2568151153697583, -0.08504368064581956, 0.24386092888093308] |
1,802.065 | The Initial Approximations for Achromatic Doublets of the XVIII Century | Analysis of the both type (flint-forward and crown-forward) achromatic
doublets was carried out. The investigation revealed possible initial
approximations which could be used by opticians at producing of the achromatic
doublets in last half of XVIII century. The comparative analysis of approximate
versions of achromatic doublets has provided additional explanation to some
historical events. One more confirmation that the earliest achromatic doublets
were really flint-forward type was found.
| physics.hist-ph | analysis of the both type flintforward and crownforward achromatic doublets was carried out the investigation revealed possible initial approximations which could be used by opticians at producing of the achromatic doublets in last half of xviii century the comparative analysis of approximate versions of achromatic doublets has provided additional explanation to some historical events one more confirmation that the earliest achromatic doublets were really flintforward type was found | [['analysis', 'of', 'the', 'both', 'type', 'flintforward', 'and', 'crownforward', 'achromatic', 'doublets', 'was', 'carried', 'out', 'the', 'investigation', 'revealed', 'possible', 'initial', 'approximations', 'which', 'could', 'be', 'used', 'by', 'opticians', 'at', 'producing', 'of', 'the', 'achromatic', 'doublets', 'in', 'last', 'half', 'of', 'xviii', 'century', 'the', 'comparative', 'analysis', 'of', 'approximate', 'versions', 'of', 'achromatic', 'doublets', 'has', 'provided', 'additional', 'explanation', 'to', 'some', 'historical', 'events', 'one', 'more', 'confirmation', 'that', 'the', 'earliest', 'achromatic', 'doublets', 'were', 'really', 'flintforward', 'type', 'was', 'found']] | [-0.11249932690272824, 0.07913379576057196, -0.12406268912869003, 0.13955856328024172, -0.11877583293244243, -0.23136903092068117, 0.03657178758428647, 0.3738679809639087, -0.11067214501448548, -0.36037977372224517, 0.14410066940427685, -0.2866246695128771, -0.07402520516457466, 0.1433171251645455, -0.00858728617716294, -0.02041588591841551, 0.056108349359307724, -0.03271375693953954, -0.023373578844341235, -0.2672879097195199, 0.19073501779482915, 0.05014486857331716, 0.2519936481920572, -0.036652939981566025, 0.06502459439663932, -0.024185855679500563, -0.09902857523053311, -0.024682417812828834, -0.08326471440478389, 0.0467840326591753, 0.1775890352634283, 0.10889584130535905, 0.2561061921601112, -0.3974369264565981, -0.17143649618284634, 0.13965373712753018, 0.17383253277333166, 0.05845886755985423, -0.028565304788375774, -0.2783784646254319, 0.047625979821000676, -0.07375224830331997, -0.18551044655390658, -0.02550075054168701, 0.03087445256801752, -0.05228070616722107, -0.22306710216574943, 0.04602346839741445, 0.0449208705757673, 0.11524258250227341, -0.024597431432742338, -0.1848313295783905, -0.07097235343490656, 0.030135983092567094, 0.12227738292601247, -0.04936170454065387, 0.018588336694161767, -0.06867269167246727, -0.14130709496541666, 0.3749080400627393, -0.06042039821354243, 4.808937127773578e-05, 0.14750460845131713, -0.14037451355073313, -0.16166874096513942, 0.19335900261425054, 0.07868075855971815, 0.08340004005899224, -0.16315700373110864, -0.03480880325033258, -0.05858744132117583, 0.19240117681821664, 0.11400711183937697, 0.021777911419765306, 0.28771685032317273, 0.14367760197760968, -0.04291395811507335, 0.11088575872485168, -0.1254978223918722, -0.08012920325854793, -0.3248142284556077, -0.15799408943320697, -0.09018067718268587, 0.04727424351283564, -0.020700847307139506, -0.11309901026005928, 0.4632204647677449, 0.09613447023483997, 0.11547670252621174, -0.10200898564743022, 0.2816259799381861, 0.07677942775906278, 0.10611060419334815, -0.005143519677221775, 0.3442010306847246, 0.13297414834826038, 0.13890356985995403, -0.13114819967975982, 0.10459099512260694, 0.0673822964183413] |
1,802.06501 | Recommendations with Negative Feedback via Pairwise Deep Reinforcement
Learning | Recommender systems play a crucial role in mitigating the problem of
information overload by suggesting users' personalized items or services. The
vast majority of traditional recommender systems consider the recommendation
procedure as a static process and make recommendations following a fixed
strategy. In this paper, we propose a novel recommender system with the
capability of continuously improving its strategies during the interactions
with users. We model the sequential interactions between users and a
recommender system as a Markov Decision Process (MDP) and leverage
Reinforcement Learning (RL) to automatically learn the optimal strategies via
recommending trial-and-error items and receiving reinforcements of these items
from users' feedback. Users' feedback can be positive and negative and both
types of feedback have great potentials to boost recommendations. However, the
number of negative feedback is much larger than that of positive one; thus
incorporating them simultaneously is challenging since positive feedback could
be buried by negative one. In this paper, we develop a novel approach to
incorporate them into the proposed deep recommender system (DEERS) framework.
The experimental results based on real-world e-commerce data demonstrate the
effectiveness of the proposed framework. Further experiments have been
conducted to understand the importance of both positive and negative feedback
in recommendations.
| cs.IR cs.LG stat.ML | recommender systems play a crucial role in mitigating the problem of information overload by suggesting users personalized items or services the vast majority of traditional recommender systems consider the recommendation procedure as a static process and make recommendations following a fixed strategy in this paper we propose a novel recommender system with the capability of continuously improving its strategies during the interactions with users we model the sequential interactions between users and a recommender system as a markov decision process mdp and leverage reinforcement learning rl to automatically learn the optimal strategies via recommending trialanderror items and receiving reinforcements of these items from users feedback users feedback can be positive and negative and both types of feedback have great potentials to boost recommendations however the number of negative feedback is much larger than that of positive one thus incorporating them simultaneously is challenging since positive feedback could be buried by negative one in this paper we develop a novel approach to incorporate them into the proposed deep recommender system deers framework the experimental results based on realworld ecommerce data demonstrate the effectiveness of the proposed framework further experiments have been conducted to understand the importance of both positive and negative feedback in recommendations | [['recommender', 'systems', 'play', 'a', 'crucial', 'role', 'in', 'mitigating', 'the', 'problem', 'of', 'information', 'overload', 'by', 'suggesting', 'users', 'personalized', 'items', 'or', 'services', 'the', 'vast', 'majority', 'of', 'traditional', 'recommender', 'systems', 'consider', 'the', 'recommendation', 'procedure', 'as', 'a', 'static', 'process', 'and', 'make', 'recommendations', 'following', 'a', 'fixed', 'strategy', 'in', 'this', 'paper', 'we', 'propose', 'a', 'novel', 'recommender', 'system', 'with', 'the', 'capability', 'of', 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1,802.06502 | EA-CG: An Approximate Second-Order Method for Training Fully-Connected
Neural Networks | For training fully-connected neural networks (FCNNs), we propose a practical
approximate second-order method including: 1) an approximation of the Hessian
matrix and 2) a conjugate gradient (CG) based method. Our proposed approximate
Hessian matrix is memory-efficient and can be applied to any FCNNs where the
activation and criterion functions are twice differentiable. We devise a
CG-based method incorporating one-rank approximation to derive Newton
directions for training FCNNs, which significantly reduces both space and time
complexity. This CG-based method can be employed to solve any linear equation
where the coefficient matrix is Kronecker-factored, symmetric and positive
definite. Empirical studies show the efficacy and efficiency of our proposed
method.
| cs.LG | for training fullyconnected neural networks fcnns we propose a practical approximate secondorder method including 1 an approximation of the hessian matrix and 2 a conjugate gradient cg based method our proposed approximate hessian matrix is memoryefficient and can be applied to any fcnns where the activation and criterion functions are twice differentiable we devise a cgbased method incorporating onerank approximation to derive newton directions for training fcnns which significantly reduces both space and time complexity this cgbased method can be employed to solve any linear equation where the coefficient matrix is kroneckerfactored symmetric and positive definite empirical studies show the efficacy and efficiency of our proposed method | [['for', 'training', 'fullyconnected', 'neural', 'networks', 'fcnns', 'we', 'propose', 'a', 'practical', 'approximate', 'secondorder', 'method', 'including', '1', 'an', 'approximation', 'of', 'the', 'hessian', 'matrix', 'and', '2', 'a', 'conjugate', 'gradient', 'cg', 'based', 'method', 'our', 'proposed', 'approximate', 'hessian', 'matrix', 'is', 'memoryefficient', 'and', 'can', 'be', 'applied', 'to', 'any', 'fcnns', 'where', 'the', 'activation', 'and', 'criterion', 'functions', 'are', 'twice', 'differentiable', 'we', 'devise', 'a', 'cgbased', 'method', 'incorporating', 'onerank', 'approximation', 'to', 'derive', 'newton', 'directions', 'for', 'training', 'fcnns', 'which', 'significantly', 'reduces', 'both', 'space', 'and', 'time', 'complexity', 'this', 'cgbased', 'method', 'can', 'be', 'employed', 'to', 'solve', 'any', 'linear', 'equation', 'where', 'the', 'coefficient', 'matrix', 'is', 'kroneckerfactored', 'symmetric', 'and', 'positive', 'definite', 'empirical', 'studies', 'show', 'the', 'efficacy', 'and', 'efficiency', 'of', 'our', 'proposed', 'method']] | [-0.022767895006767985, -0.011962648642437207, -0.08148860064212163, 0.04958033657584445, -0.11088073418150603, -0.19820407248664437, 0.03067485049788682, 0.41948832655852697, -0.290490675609963, -0.2648451487656753, 0.08698884261561171, -0.20858813225805653, -0.2506050355380999, 0.1610116641254621, -0.033118438678530024, 0.11521958469914026, 0.07749057266826057, 0.00921876311855707, -0.16012044652488153, -0.3036233878898751, 0.27076551000113197, 0.014461862709689534, 0.2930548126668722, 0.053492241126116155, 0.18916018471940813, -0.023557900503840087, 0.009888430420344449, 0.02136372984359524, -0.04886603751659112, 0.1407064898315716, 0.2672585934281947, 0.18272492859099623, 0.3310699361499469, -0.3991907214710735, -0.22132880893702847, 0.16034941883968576, 0.15828628615335613, 0.10944933330372222, -0.0359936219481927, -0.2640127180680141, 0.14411470254241787, -0.15139674528870942, -0.06130699161879437, -0.17890681236551828, -0.06066381137923531, 0.024073160713635175, -0.3883939827078479, 0.08385634748484799, 0.04472301710168568, -0.01753384354612175, -0.04250217024851942, -0.17762434009884326, 0.054087898808197594, 0.05778077422676362, -0.019717294175863126, 0.0718173556730485, 0.10493191440572154, -0.05233361481311116, -0.08943859890832584, 0.3125996678136289, -0.06597593834377685, -0.29743441136307874, 0.12069102162539186, -0.02069637240877129, -0.09247452727703483, 0.11223868017067325, 0.2364365434370724, 0.18979447817798914, -0.12205740679077418, 0.09072385290044553, -0.0015542648934741628, 0.16768384036357636, 0.02255730458781264, -0.08123613061506371, 0.04172671432519015, 0.14486972087080469, 0.1100467277804987, 0.12912801535852816, -0.09916884874714152, -0.1032993588113349, -0.2521973981978899, -0.1597758941440228, -0.24235508670889824, -0.0016015686165049392, -0.16622678135913788, -0.15579007716107024, 0.4035113515323555, 0.1601787328737665, 0.196485274532845, 0.16266880381329618, 0.3345939708557331, 0.17026226814036732, 0.07737902873294551, 0.15210377125350652, 0.18184888792522955, 0.12884206200932274, 0.06946575220779709, -0.225937731994562, 0.07778594217192873, 0.15123108093503793] |
1,802.06503 | Multicolor Gallai-Ramsey numbers of $C_9$ and $C_{11}$ | A Gallai coloring is a coloring of the edges of a complete graph without
rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$
colors. We study Ramsey-type problems in Gallai colorings. Given an integer
$k\ge1$ and a graph $H$, the Gallai-Ramsey number $GR_k(H)$ is the least
positive integer $n$ such that every Gallai $k$-coloring of the complete graph
on $n$ vertices contains a monochromatic copy of $H$. It turns out that
$GR_k(H)$ is more well-behaved than the classical Ramsey number $R_k(H)$.
However, finding exact values of $GR_k (H)$ is far from trivial. In this paper,
we study Gallai-Ramsey numbers of odd cycles. We prove that for $n\in\{4,5\}$
and all $k\ge1$, $GR_k(C_{2n+1})= n\cdot 2^k+1$. This new result provides
partial evidence for the first two open cases of the Triple Odd Cycle
Conjecture of Bondy and Erd\H{o}s from 1973. Our technique relies heavily on
the structural result of Gallai on Gallai colorings of complete graphs. We
believe the method we developed can be used to determine the exact values of
$GR_k(C_{2n+1})$ for all $n\ge6$.
| math.CO | a gallai coloring is a coloring of the edges of a complete graph without rainbow triangles and a gallai kcoloring is a gallai coloring that uses k colors we study ramseytype problems in gallai colorings given an integer kge1 and a graph h the gallairamsey number gr_kh is the least positive integer n such that every gallai kcoloring of the complete graph on n vertices contains a monochromatic copy of h it turns out that gr_kh is more wellbehaved than the classical ramsey number r_kh however finding exact values of gr_k h is far from trivial in this paper we study gallairamsey numbers of odd cycles we prove that for nin45 and all kge1 gr_kc_2n1 ncdot 2k1 this new result provides partial evidence for the first two open cases of the triple odd cycle conjecture of bondy and erdhos from 1973 our technique relies heavily on the structural result of gallai on gallai colorings of complete graphs we believe the method we developed can be used to determine the exact values of gr_kc_2n1 for all nge6 | [['a', 'gallai', 'coloring', 'is', 'a', 'coloring', 'of', 'the', 'edges', 'of', 'a', 'complete', 'graph', 'without', 'rainbow', 'triangles', 'and', 'a', 'gallai', 'kcoloring', 'is', 'a', 'gallai', 'coloring', 'that', 'uses', 'k', 'colors', 'we', 'study', 'ramseytype', 'problems', 'in', 'gallai', 'colorings', 'given', 'an', 'integer', 'kge1', 'and', 'a', 'graph', 'h', 'the', 'gallairamsey', 'number', 'gr_kh', 'is', 'the', 'least', 'positive', 'integer', 'n', 'such', 'that', 'every', 'gallai', 'kcoloring', 'of', 'the', 'complete', 'graph', 'on', 'n', 'vertices', 'contains', 'a', 'monochromatic', 'copy', 'of', 'h', 'it', 'turns', 'out', 'that', 'gr_kh', 'is', 'more', 'wellbehaved', 'than', 'the', 'classical', 'ramsey', 'number', 'r_kh', 'however', 'finding', 'exact', 'values', 'of', 'gr_k', 'h', 'is', 'far', 'from', 'trivial', 'in', 'this', 'paper', 'we', 'study', 'gallairamsey', 'numbers', 'of', 'odd', 'cycles', 'we', 'prove', 'that', 'for', 'nin45', 'and', 'all', 'kge1', 'gr_kc_2n1', 'ncdot', '2k1', 'this', 'new', 'result', 'provides', 'partial', 'evidence', 'for', 'the', 'first', 'two', 'open', 'cases', 'of', 'the', 'triple', 'odd', 'cycle', 'conjecture', 'of', 'bondy', 'and', 'erdhos', 'from', '1973', 'our', 'technique', 'relies', 'heavily', 'on', 'the', 'structural', 'result', 'of', 'gallai', 'on', 'gallai', 'colorings', 'of', 'complete', 'graphs', 'we', 'believe', 'the', 'method', 'we', 'developed', 'can', 'be', 'used', 'to', 'determine', 'the', 'exact', 'values', 'of', 'gr_kc_2n1', 'for', 'all', 'nge6']] | [-0.2221778994925054, 0.11654566757821677, -0.07218758157853569, 0.04760139822893377, -0.12658928659345423, -0.14451320406847767, 0.0835138047865725, 0.34425190793616434, -0.23004777641434754, -0.33219975518328804, 0.0643301970338715, -0.3343802188376763, -0.16217986749884272, 0.12400309752273772, -0.13670222252873437, 0.020011754817096515, 0.14325348223692605, 0.07432377129190303, 0.08137707276402839, -0.2915942300388789, 0.2570201183083866, -0.1043530086427927, 0.12135737490441117, 0.1135268188720303, 0.04744292186040963, 0.08198154848468091, -0.0075649465061724186, 0.09369803317630222, -0.21872386400804056, 0.049234713611326045, 0.2614918608378087, 0.18865575195556242, 0.25555291019380094, -0.36799390225721124, -0.12353969484700689, 0.21963808262986798, 0.10173730612333332, 0.07954294871804969, 0.003722976161682579, -0.17924705882589997, 0.14888017637488832, -0.06591218284464308, -0.09102571111172438, 0.0018308087278689658, 0.13775737966809953, -0.042782599311987204, -0.27550475075308767, -0.027360540222642678, 0.1492283435684762, 0.07188370180050177, 0.08562121927206005, -0.20972700173434403, -0.035584362653483234, 0.08067165635260089, -0.07896698507812938, 0.07946994188141876, -0.03415266356331163, -0.09710168010006393, -0.19062371062380926, 0.3649897177730288, -0.024346993311857138, -0.10999808672017285, 0.09931753617445273, -0.12216453075408935, -0.2280302350276283, 0.13943918554361776, 0.03315746980054038, 0.22921240083873273, -0.0673555594496429, 0.1413124516672854, -0.21310412117945296, 0.13332623435117835, 0.19087699595838786, 0.010866594607276577, 0.1114944178477994, 0.09105264818561928, 0.16795433143619448, 0.1869304533828316, 0.03884196898101696, 0.03627185747293489, -0.290549337563238, -0.15074548165047807, -0.2463559266765203, 0.13983145119356258, -0.16044709833787887, -0.21492483390761274, 0.4021651748993567, 0.11834291036340541, 0.15574558308081968, 0.1168812933670623, 0.2389297199189397, 0.061397588458577436, 0.01176697518210858, 0.16561637554118144, 0.10146541202174766, 0.2004528896404164, -0.04779695537207382, -0.1671309378423861, 0.026695795547483223, 0.19795301065114992] |
1,802.06504 | Compiling Diderot: From Tensor Calculus to C | Diderot is a parallel domain-specific language for analysis and visualization
of multidimensional scientific images, such as those produced by CT and MRI
scanners. In particular, it supports algorithms where tensor fields (i.e.,
functions from 3D points to tensor values) are used to represent the underlying
physical objects that were scanned by the imaging device. Diderot supports
higher-order programming where tensor fields are first-class values and where
differential operators and lifted linear-algebra operators can be used to
express mathematical reasoning directly in the language. While such lifted
field operations are central to the definition and computation of many
scientific visualization algorithms, to date they have required extensive
manual derivations and laborious implementation.
The challenge for the Diderot compiler is to effectively translate the
high-level mathematical concepts that are expressible in the surface language
to a low-level and efficient implementation in C. This paper describes our
approach to this challenge, which is based around the careful design of an
intermediate representation (IR), called EIN, and a number of compiler
transformations that lower the program from tensor calculus to C while avoiding
combinatorial explosion in the size of the IR. We describe the challenges in
compiling a language like Diderot, the design of EIN, and the transformation
used by the compiler. We also present an evaluation of EIN with respect to both
compiler efficiency and quality of generated code.
| cs.PL cs.MS | diderot is a parallel domainspecific language for analysis and visualization of multidimensional scientific images such as those produced by ct and mri scanners in particular it supports algorithms where tensor fields ie functions from 3d points to tensor values are used to represent the underlying physical objects that were scanned by the imaging device diderot supports higherorder programming where tensor fields are firstclass values and where differential operators and lifted linearalgebra operators can be used to express mathematical reasoning directly in the language while such lifted field operations are central to the definition and computation of many scientific visualization algorithms to date they have required extensive manual derivations and laborious implementation the challenge for the diderot compiler is to effectively translate the highlevel mathematical concepts that are expressible in the surface language to a lowlevel and efficient implementation in c this paper describes our approach to this challenge which is based around the careful design of an intermediate representation ir called ein and a number of compiler transformations that lower the program from tensor calculus to c while avoiding combinatorial explosion in the size of the ir we describe the challenges in compiling a language like diderot the design of ein and the transformation used by the compiler we also present an evaluation of ein with respect to both compiler efficiency and quality of generated code | [['diderot', 'is', 'a', 'parallel', 'domainspecific', 'language', 'for', 'analysis', 'and', 'visualization', 'of', 'multidimensional', 'scientific', 'images', 'such', 'as', 'those', 'produced', 'by', 'ct', 'and', 'mri', 'scanners', 'in', 'particular', 'it', 'supports', 'algorithms', 'where', 'tensor', 'fields', 'ie', 'functions', 'from', '3d', 'points', 'to', 'tensor', 'values', 'are', 'used', 'to', 'represent', 'the', 'underlying', 'physical', 'objects', 'that', 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1,802.06505 | What Do Your Friends Think? Efficient Polling Methods for Networks Using
Friendship Paradox | This paper deals with randomized polling of a social network. In the case of
forecasting the outcome of an election between two candidates A and B,
classical intent polling asks randomly sampled individuals: who will you vote
for? Expectation polling asks: who do you think will win? In this paper, we
propose a novel neighborhood expectation polling (NEP) strategy that asks
randomly sampled individuals: what is your estimate of the fraction of votes
for A? Therefore, in NEP, sampled individuals will naturally look at their
neighbors (defined by the underlying social network graph) when answering this
question. Hence, the mean squared error (MSE) of NEP methods rely on selecting
the optimal set of samples from the network. To this end, we propose three NEP
algorithms for the following cases: (i) the social network graph is not known
but, random walks (sequential exploration) can be performed on the graph (ii)
the social network graph is unknown. For case (i) and (ii), two algorithms
based on a graph theoretic consequence called friendship paradox are proposed.
Theoretical results on the dependence of the MSE of the algorithms on the
properties of the network are established. Numerical results on real and
synthetic data sets are provided to illustrate the performance of the
algorithms.
| cs.SI physics.soc-ph | this paper deals with randomized polling of a social network in the case of forecasting the outcome of an election between two candidates a and b classical intent polling asks randomly sampled individuals who will you vote for expectation polling asks who do you think will win in this paper we propose a novel neighborhood expectation polling nep strategy that asks randomly sampled individuals what is your estimate of the fraction of votes for a therefore in nep sampled individuals will naturally look at their neighbors defined by the underlying social network graph when answering this question hence the mean squared error mse of nep methods rely on selecting the optimal set of samples from the network to this end we propose three nep algorithms for the following cases i the social network graph is not known but random walks sequential exploration can be performed on the graph ii the social network graph is unknown for case i and ii two algorithms based on a graph theoretic consequence called friendship paradox are proposed theoretical results on the dependence of the mse of the algorithms on the properties of the network are established numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms | [['this', 'paper', 'deals', 'with', 'randomized', 'polling', 'of', 'a', 'social', 'network', 'in', 'the', 'case', 'of', 'forecasting', 'the', 'outcome', 'of', 'an', 'election', 'between', 'two', 'candidates', 'a', 'and', 'b', 'classical', 'intent', 'polling', 'asks', 'randomly', 'sampled', 'individuals', 'who', 'will', 'you', 'vote', 'for', 'expectation', 'polling', 'asks', 'who', 'do', 'you', 'think', 'will', 'win', 'in', 'this', 'paper', 'we', 'propose', 'a', 'novel', 'neighborhood', 'expectation', 'polling', 'nep', 'strategy', 'that', 'asks', 'randomly', 'sampled', 'individuals', 'what', 'is', 'your', 'estimate', 'of', 'the', 'fraction', 'of', 'votes', 'for', 'a', 'therefore', 'in', 'nep', 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1,802.06506 | Equidistribution of zeros of polynomials | A classical result of Erdos and Turan states that if a monic polynomial has
small size on the unit circle and its constant coefficient is not too small,
then its zeros cluster near the unit circle and become equidistributed in
angle. Using Fourier analysis we give a short and self-contained proof of this
result.
| math.CA | a classical result of erdos and turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small then its zeros cluster near the unit circle and become equidistributed in angle using fourier analysis we give a short and selfcontained proof of this result | [['a', 'classical', 'result', 'of', 'erdos', 'and', 'turan', 'states', 'that', 'if', 'a', 'monic', 'polynomial', 'has', 'small', 'size', 'on', 'the', 'unit', 'circle', 'and', 'its', 'constant', 'coefficient', 'is', 'not', 'too', 'small', 'then', 'its', 'zeros', 'cluster', 'near', 'the', 'unit', 'circle', 'and', 'become', 'equidistributed', 'in', 'angle', 'using', 'fourier', 'analysis', 'we', 'give', 'a', 'short', 'and', 'selfcontained', 'proof', 'of', 'this', 'result']] | [-0.16393777013204439, 0.11394956499269163, -0.11132420206235515, 0.043467641411418165, -0.09070137905439844, -0.15410427834528187, 0.08612954021534985, 0.3067055058803547, -0.2972763685026654, -0.20738219374066424, 0.16342969651816897, -0.2987612354120723, -0.15506475993121663, 0.2044838311633578, -0.11916425667220244, 0.030990272663378466, 0.1039223063012792, 0.08244677474377332, -0.037141332898668396, -0.3059177707397827, 0.2594203184039711, 0.02829553186893463, 0.16076114828077456, 0.12245941815759849, 0.09206133027112594, 0.05217487340862, -0.005908920024349181, -0.013640279191787596, -0.16370125714739617, 0.08506552888300373, 0.20229313167726137, 0.10609592997503502, 0.2926511012569622, -0.390043577765701, -0.08952575519301549, 0.1714469012114461, 0.18085679296335136, 0.01879673830612942, -0.03643176294820107, -0.20928511894911667, 0.09818496946590366, -0.10363532031489606, -0.20027296895299246, -0.047372471541166306, 0.11273201620551171, 0.042152210078374656, -0.2206964332834576, 0.07936871677844061, 0.13148926698637228, 0.11092891801079666, 0.002420376042007572, -0.12756049995207125, 0.03227044968796825, 0.08324811079849799, 0.044503897889862185, 0.10597799834795296, 0.0899713372518481, -0.03441669822549792, -0.027458782385413844, 0.33763768973208413, -0.0581554425664729, -0.2277181523817557, 0.11796626372745743, -0.22701522911450378, -0.16704207190519405, 0.10748225605736177, 0.11834334682121321, 0.15536923775518383, -0.029954427594525948, 0.15585867861820454, -0.1519355132692942, 0.19229272042435627, 0.143680308221115, 0.028148213004762376, 0.1669219417359542, 0.05410137060270817, 0.12739827122573774, 0.15506338665296357, -0.061158219158339, -0.05985995839108472, -0.2813415623235482, -0.14344116940197568, -0.2990757253245209, 0.11078495086258044, -0.14989662027154635, -0.24103939815864173, 0.3824796800122217, 0.01717911676516653, 0.2216985836383645, 0.1552504120843002, 0.2523037488054898, 0.13404404251249852, 0.07697760582366889, 0.07769290786408992, 0.1474691884316228, 0.20463541243225336, 0.06204223059359248, -0.1365304039446292, 0.03147410249544515, 0.16410938018708732] |
1,802.06507 | Modeling communication processes in the human connectome through
cooperative learning | Communication processes within the human brain at different cognitive states
are neither well understood nor completely characterized. We assess
communication processes in the human connectome using ant colony-inspired
cooperative learning algorithm, starting from a source with no a priori
information about the network topology, and cooperatively searching for the
target through a pheromone-inspired model. This framework relies on two
parameters, namely pheromone perception and edge perception, to define the
cognizance and subsequent behaviour of the ants on the network and, overall,
the communication processes happening between source and target nodes.
Simulations obtained through different configurations allow the identification
of path-ensembles that are involved in the communication between node pairs.
These path-ensembles may contain different number of paths depending on the
perception parameters and the node pair. In order to assess the different
communication regimes displayed on the simulations and their associations with
functional connectivity, we introduce two network measurements, effective
path-length and arrival rate. These communication features are tested as
individual as well as combined predictors of functional connectivity during
different tasks. Finally, different communication regimes are found in
different specialized functional networks. Overall, this framework may be used
as a test-bed for different communication regimes on top of an underlaying
topology.
| q-bio.NC | communication processes within the human brain at different cognitive states are neither well understood nor completely characterized we assess communication processes in the human connectome using ant colonyinspired cooperative learning algorithm starting from a source with no a priori information about the network topology and cooperatively searching for the target through a pheromoneinspired model this framework relies on two parameters namely pheromone perception and edge perception to define the cognizance and subsequent behaviour of the ants on the network and overall the communication processes happening between source and target nodes simulations obtained through different configurations allow the identification of pathensembles that are involved in the communication between node pairs these pathensembles may contain different number of paths depending on the perception parameters and the node pair in order to assess the different communication regimes displayed on the simulations and their associations with functional connectivity we introduce two network measurements effective pathlength and arrival rate these communication features are tested as individual as well as combined predictors of functional connectivity during different tasks finally different communication regimes are found in different specialized functional networks overall this framework may be used as a testbed for different communication regimes on top of an underlaying topology | [['communication', 'processes', 'within', 'the', 'human', 'brain', 'at', 'different', 'cognitive', 'states', 'are', 'neither', 'well', 'understood', 'nor', 'completely', 'characterized', 'we', 'assess', 'communication', 'processes', 'in', 'the', 'human', 'connectome', 'using', 'ant', 'colonyinspired', 'cooperative', 'learning', 'algorithm', 'starting', 'from', 'a', 'source', 'with', 'no', 'a', 'priori', 'information', 'about', 'the', 'network', 'topology', 'and', 'cooperatively', 'searching', 'for', 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1,802.06508 | Exactly Solvable Pairing Models | Some results for two distinct but complementary exactly solvable algebraic
models for pairing in atomic nuclei are presented: 1) binding energy
predictions for isotopic chains of nuclei based on an extended pairing model
that includes multi-pair excitations; and 2) fine structure effects among
excited $0^+$ states in $N \approx Z$ nuclei that track with the proton-neutron
($pn$) and like-particle isovector pairing interactions as realized within an
algebraic $sp(4)$ shell model. The results show that these models can be used
to reproduce significant ranges of known experimental data, and in so doing,
confirm their power to predict pairing-dominated phenomena in domains where
data is unavailable.
| nucl-th | some results for two distinct but complementary exactly solvable algebraic models for pairing in atomic nuclei are presented 1 binding energy predictions for isotopic chains of nuclei based on an extended pairing model that includes multipair excitations and 2 fine structure effects among excited 0 states in n approx z nuclei that track with the protonneutron pn and likeparticle isovector pairing interactions as realized within an algebraic sp4 shell model the results show that these models can be used to reproduce significant ranges of known experimental data and in so doing confirm their power to predict pairingdominated phenomena in domains where data is unavailable | [['some', 'results', 'for', 'two', 'distinct', 'but', 'complementary', 'exactly', 'solvable', 'algebraic', 'models', 'for', 'pairing', 'in', 'atomic', 'nuclei', 'are', 'presented', '1', 'binding', 'energy', 'predictions', 'for', 'isotopic', 'chains', 'of', 'nuclei', 'based', 'on', 'an', 'extended', 'pairing', 'model', 'that', 'includes', 'multipair', 'excitations', 'and', '2', 'fine', 'structure', 'effects', 'among', 'excited', '0', 'states', 'in', 'n', 'approx', 'z', 'nuclei', 'that', 'track', 'with', 'the', 'protonneutron', 'pn', 'and', 'likeparticle', 'isovector', 'pairing', 'interactions', 'as', 'realized', 'within', 'an', 'algebraic', 'sp4', 'shell', 'model', 'the', 'results', 'show', 'that', 'these', 'models', 'can', 'be', 'used', 'to', 'reproduce', 'significant', 'ranges', 'of', 'known', 'experimental', 'data', 'and', 'in', 'so', 'doing', 'confirm', 'their', 'power', 'to', 'predict', 'pairingdominated', 'phenomena', 'in', 'domains', 'where', 'data', 'is', 'unavailable']] | [-0.09938841737417993, 0.16036476347017897, -0.05356259840072666, 0.16643255732578308, -0.008979769337705328, -0.19145361948035006, 0.027426924350789014, 0.3967009990937212, -0.21769681457176948, -0.29183844572783096, -0.026737637704835067, -0.29969350783407545, -0.07643899167256342, 0.1773274937074957, 0.05466533393273582, -0.017981048745727077, 0.019575814164957954, 0.0267590985597265, -0.05560038881421595, -0.19917516079188768, 0.3150952155204508, 0.023061322012138598, 0.23479378859973649, 0.07607922046835244, 0.023927421998503864, -0.011402108152713445, 0.035737310717045105, -0.024719731475326044, -0.14417067852691529, 0.07209806816225184, 0.3209392263866126, 0.03510436289536866, 0.13318209057375427, -0.45951235455289047, -0.20867608468617918, 0.1062464496150197, 0.22002069469884905, 0.12985350857307973, -0.03741707263663592, -0.279136998054472, 0.06269900734509223, -0.23006105303619673, -0.14488593744819314, -0.1442735660369101, 0.03710196906411387, 0.06572017941660094, -0.26172657752945316, 0.05022874047292523, 0.046786554768066674, 0.05913591733296573, -0.11115250640404094, -0.1935806694447325, -0.04160511549743055, 0.10818866706787816, 0.06316012092097437, 0.004196763723564235, 0.10884975850609249, -0.11112377426397164, -0.12436579652944381, 0.38028373985180575, -0.006450186311764625, -0.16215647207301798, 0.15961632346372726, -0.11101100809908318, -0.1772076165059455, 0.1466574812741968, 0.13624709347902697, 0.0784820043888775, -0.10451469213749255, 0.0864832246324581, -0.03510073704862045, 0.21066693805194306, -0.007937841282397943, 0.05546139834846542, 0.1456545290076038, 0.1411937531988019, -0.016761013008292438, 0.033467986118003216, -0.0831392967318483, -0.10521587761553022, -0.29961015735255575, -0.07712140479418947, -0.1729857942216026, 0.011224553224097178, -0.034569140640793826, -0.10458919823676058, 0.35256972070783377, 0.09396961948481723, 0.23442012882899962, 0.009948063519720024, 0.23372512509666601, 0.036258831275491385, 0.08536990132924278, 0.06510651607554659, 0.25287435973177264, 0.15854945304595586, -0.008143289842037032, -0.23634421466894953, 0.03260690611289832, 0.019554261407516534] |
1,802.06509 | On the Optimization of Deep Networks: Implicit Acceleration by
Overparameterization | Conventional wisdom in deep learning states that increasing depth improves
expressiveness but complicates optimization. This paper suggests that,
sometimes, increasing depth can speed up optimization. The effect of depth on
optimization is decoupled from expressiveness by focusing on settings where
additional layers amount to overparameterization - linear neural networks, a
well-studied model. Theoretical analysis, as well as experiments, show that
here depth acts as a preconditioner which may accelerate convergence. Even on
simple convex problems such as linear regression with $\ell_p$ loss, $p>2$,
gradient descent can benefit from transitioning to a non-convex
overparameterized objective, more than it would from some common acceleration
schemes. We also prove that it is mathematically impossible to obtain the
acceleration effect of overparametrization via gradients of any regularizer.
| cs.LG | conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization this paper suggests that sometimes increasing depth can speed up optimization the effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization linear neural networks a wellstudied model theoretical analysis as well as experiments show that here depth acts as a preconditioner which may accelerate convergence even on simple convex problems such as linear regression with ell_p loss p2 gradient descent can benefit from transitioning to a nonconvex overparameterized objective more than it would from some common acceleration schemes we also prove that it is mathematically impossible to obtain the acceleration effect of overparametrization via gradients of any regularizer | [['conventional', 'wisdom', 'in', 'deep', 'learning', 'states', 'that', 'increasing', 'depth', 'improves', 'expressiveness', 'but', 'complicates', 'optimization', 'this', 'paper', 'suggests', 'that', 'sometimes', 'increasing', 'depth', 'can', 'speed', 'up', 'optimization', 'the', 'effect', 'of', 'depth', 'on', 'optimization', 'is', 'decoupled', 'from', 'expressiveness', 'by', 'focusing', 'on', 'settings', 'where', 'additional', 'layers', 'amount', 'to', 'overparameterization', 'linear', 'neural', 'networks', 'a', 'wellstudied', 'model', 'theoretical', 'analysis', 'as', 'well', 'as', 'experiments', 'show', 'that', 'here', 'depth', 'acts', 'as', 'a', 'preconditioner', 'which', 'may', 'accelerate', 'convergence', 'even', 'on', 'simple', 'convex', 'problems', 'such', 'as', 'linear', 'regression', 'with', 'ell_p', 'loss', 'p2', 'gradient', 'descent', 'can', 'benefit', 'from', 'transitioning', 'to', 'a', 'nonconvex', 'overparameterized', 'objective', 'more', 'than', 'it', 'would', 'from', 'some', 'common', 'acceleration', 'schemes', 'we', 'also', 'prove', 'that', 'it', 'is', 'mathematically', 'impossible', 'to', 'obtain', 'the', 'acceleration', 'effect', 'of', 'overparametrization', 'via', 'gradients', 'of', 'any', 'regularizer']] | [-0.04155057735672434, 0.04901989441952805, -0.08191536028571732, 0.07409734617571392, -0.14396473282535913, -0.20285145639533514, 0.03254957276789593, 0.4393720817981196, -0.37906479829594064, -0.2947523058964642, 0.10495528309189973, -0.24971082184051516, -0.19928641635619226, 0.2167306449550555, -0.13652621485964686, 0.0786862732903635, 0.10040008430951275, -0.010159331923503368, -0.09909267334427807, -0.2878215856483725, 0.2577562107490834, 0.06763695516851616, 0.28760374221782825, 0.04482946859397849, 0.10329882385587076, -0.008487821297078837, 0.06415290497319742, 0.06301939892239075, -0.03985637039844076, 0.11685707366435605, 0.2773680887490389, 0.18554306785827962, 0.36259942997979827, -0.4303656058905066, -0.27718555024962444, 0.11943720097913117, 0.20299569945629747, 0.09139405701168217, -0.04761304132142734, -0.21396409895759624, 0.047398411241344744, -0.12547614604814863, -0.035724302564869775, -0.12474691590721734, -0.04144119893078555, 0.019827000548696665, -0.32061564562876604, 0.07277781969355228, 0.11443498706708463, 0.0484588993846851, -0.03250400829090752, -0.1475664469199713, 0.0042983247177125735, 0.027272733069620417, 0.07849606056029709, 0.07720897552083994, 0.14725661908131338, -0.16079057958625928, -0.10296593369442786, 0.3505851402344396, -0.07265702889696408, -0.21435741368742262, 0.22049279512119951, -0.028924227718905102, -0.11844276086442539, 0.10756602411570608, 0.23574352102567914, 0.12040890378450028, -0.08276415689415145, 0.06424867173992709, -0.046241228327491, 0.18862718300222128, 0.058755523294256234, 0.00873102999977447, 0.11050983035715571, 0.19767704530481678, 0.17996228304662987, 0.15728130002628218, -0.053045988997032285, -0.09109014165816737, -0.24106701443613063, -0.0883228112485443, -0.18097112943097704, 0.04294217556245533, -0.1089747657571904, -0.13922155114104512, 0.3172016457547663, 0.19517348284287317, 0.21768447963070492, 0.1286829843607609, 0.3694948989699488, 0.10260143370337052, 0.12142314235908819, 0.09314253674171193, 0.24008719706511866, 0.08923407920567533, 0.08812140870732485, -0.1949258730641841, 0.11704039225950226, 0.05275274695233121] |
1,802.0651 | Thermodynamics and structural transition of binary atomic Bose-Fermi
mixtures in box or harmonic potentials: A path-integral study | Experimental realizations of a variety of atomic binary Bose-Fermi mixtures
have brought opportunities for studying composite quantum systems with
different spin-statistics. The binary atomic mixtures can exhibit a structural
transition from a mixture into phase separation as the boson-fermion
interaction increases. By using a path-integral formalism to evaluate the grand
partition function and thermodynamic grand potential, we obtain the effective
potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad
range of temperatures and interactions are also derived. The structural
transition can be identified as a loop of the effective potential curve, and
the volume fraction of phase separation can be determined by the lever rule.
For $^6$Li-$^7$Li and $^6$Li-$^{41}$K mixtures, we present the phase diagrams
of the mixtures in a box potential at zero and finite temperatures. Due to the
flexible densities of atomic gases, the construction of phase separation is
more complicated when compared to conventional liquid or solid mixtures where
the individual densities are fixed. For harmonically trapped mixtures, we use
the local density approximation to map out the finite-temperature density
profiles and present typical trap structures, including the mixture, partially
separated phases, and fully separated phases.
| cond-mat.quant-gas cond-mat.stat-mech quant-ph | experimental realizations of a variety of atomic binary bosefermi mixtures have brought opportunities for studying composite quantum systems with different spinstatistics the binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the bosonfermion interaction increases by using a pathintegral formalism to evaluate the grand partition function and thermodynamic grand potential we obtain the effective potential of binary bosefermi mixtures thermodynamic quantities in a broad range of temperatures and interactions are also derived the structural transition can be identified as a loop of the effective potential curve and the volume fraction of phase separation can be determined by the lever rule for 6li7li and 6li41k mixtures we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures due to the flexible densities of atomic gases the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed for harmonically trapped mixtures we use the local density approximation to map out the finitetemperature density profiles and present typical trap structures including the mixture partially separated phases and fully separated phases | [['experimental', 'realizations', 'of', 'a', 'variety', 'of', 'atomic', 'binary', 'bosefermi', 'mixtures', 'have', 'brought', 'opportunities', 'for', 'studying', 'composite', 'quantum', 'systems', 'with', 'different', 'spinstatistics', 'the', 'binary', 'atomic', 'mixtures', 'can', 'exhibit', 'a', 'structural', 'transition', 'from', 'a', 'mixture', 'into', 'phase', 'separation', 'as', 'the', 'bosonfermion', 'interaction', 'increases', 'by', 'using', 'a', 'pathintegral', 'formalism', 'to', 'evaluate', 'the', 'grand', 'partition', 'function', 'and', 'thermodynamic', 'grand', 'potential', 'we', 'obtain', 'the', 'effective', 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1,802.06511 | Reconfiguration of Colorable Sets in Classes of Perfect Graphs | A set of vertices in a graph is c-colorable if the subgraph induced by the
set has a proper c-coloring. In this paper, we study the problem of finding a
step-by-step transformation (reconfiguration) between two c-colorable sets in
the same graph. This problem generalizes the well-studied Independent Set
Reconfiguration problem. As the first step toward a systematic understanding of
the complexity of this general problem, we study the problem on classes of
perfect graphs. We first focus on interval graphs and give a combinatorial
characterization of the distance between two c-colorable sets. This gives a
linear-time algorithm for finding an actual shortest reconfiguration sequence
for interval graphs. Since interval graphs are exactly the graphs that are
simultaneously chordal and co-comparability, we then complement the positive
result by showing that even deciding reachability is PSPACE-complete for
chordal graphs and for co-comparability graphs. The hardness for chordal graphs
holds even for split graphs. We also consider the case where c is a fixed
constant and show that in such a case the reachability problem is
polynomial-time solvable for split graphs but still PSPACE-complete for
co-comparability graphs. The complexity of this case for chordal graphs remains
unsettled. As by-products, our positive results give the first polynomial-time
solvable cases (split graphs and interval graphs) for Feedback Vertex Set
Reconfiguration.
| cs.DS cs.DM math.CO | a set of vertices in a graph is ccolorable if the subgraph induced by the set has a proper ccoloring in this paper we study the problem of finding a stepbystep transformation reconfiguration between two ccolorable sets in the same graph this problem generalizes the wellstudied independent set reconfiguration problem as the first step toward a systematic understanding of the complexity of this general problem we study the problem on classes of perfect graphs we first focus on interval graphs and give a combinatorial characterization of the distance between two ccolorable sets this gives a lineartime algorithm for finding an actual shortest reconfiguration sequence for interval graphs since interval graphs are exactly the graphs that are simultaneously chordal and cocomparability we then complement the positive result by showing that even deciding reachability is pspacecomplete for chordal graphs and for cocomparability graphs the hardness for chordal graphs holds even for split graphs we also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomialtime solvable for split graphs but still pspacecomplete for cocomparability graphs the complexity of this case for chordal graphs remains unsettled as byproducts our positive results give the first polynomialtime solvable cases split graphs and interval graphs for feedback vertex set reconfiguration | [['a', 'set', 'of', 'vertices', 'in', 'a', 'graph', 'is', 'ccolorable', 'if', 'the', 'subgraph', 'induced', 'by', 'the', 'set', 'has', 'a', 'proper', 'ccoloring', 'in', 'this', 'paper', 'we', 'study', 'the', 'problem', 'of', 'finding', 'a', 'stepbystep', 'transformation', 'reconfiguration', 'between', 'two', 'ccolorable', 'sets', 'in', 'the', 'same', 'graph', 'this', 'problem', 'generalizes', 'the', 'wellstudied', 'independent', 'set', 'reconfiguration', 'problem', 'as', 'the', 'first', 'step', 'toward', 'a', 'systematic', 'understanding', 'of', 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1,802.06512 | Asymmetric Modulation Design for Wireless Information and Power Transfer
with Nonlinear Energy Harvesting | Far-field wireless power transfer (WPT) and simultaneous wireless information
and power transfer (SWIPT) have become increasingly important in radio
frequency (RF) and communication communities recently. The problem of
modulation design for SWIPT has however been scarcely addressed. In this paper,
a modulation scheme based on asymmetric phase-shift keying (PSK) is considered,
which improves the SWIPT rate-energy tradeoff region significantly. The
nonlinear rectifier model, which accurately models the energy harvester, is
adopted for evaluating the output direct current (DC) power at the receiver.
The harvested DC power is maximized under an average power constraint at the
transmitter and a constraint on the rate of information transmitted via a
multi-carrier signal over a flat fading channel. As a consequence of the
rectifier nonlinearity, this work highlights that asymmetric PSK modulation
provides benefits over conventional symmetric PSK modulation in SWIPT and opens
the door to systematic modulation design tailored for SWIPT.
| cs.IT math.IT | farfield wireless power transfer wpt and simultaneous wireless information and power transfer swipt have become increasingly important in radio frequency rf and communication communities recently the problem of modulation design for swipt has however been scarcely addressed in this paper a modulation scheme based on asymmetric phaseshift keying psk is considered which improves the swipt rateenergy tradeoff region significantly the nonlinear rectifier model which accurately models the energy harvester is adopted for evaluating the output direct current dc power at the receiver the harvested dc power is maximized under an average power constraint at the transmitter and a constraint on the rate of information transmitted via a multicarrier signal over a flat fading channel as a consequence of the rectifier nonlinearity this work highlights that asymmetric psk modulation provides benefits over conventional symmetric psk modulation in swipt and opens the door to systematic modulation design tailored for swipt | [['farfield', 'wireless', 'power', 'transfer', 'wpt', 'and', 'simultaneous', 'wireless', 'information', 'and', 'power', 'transfer', 'swipt', 'have', 'become', 'increasingly', 'important', 'in', 'radio', 'frequency', 'rf', 'and', 'communication', 'communities', 'recently', 'the', 'problem', 'of', 'modulation', 'design', 'for', 'swipt', 'has', 'however', 'been', 'scarcely', 'addressed', 'in', 'this', 'paper', 'a', 'modulation', 'scheme', 'based', 'on', 'asymmetric', 'phaseshift', 'keying', 'psk', 'is', 'considered', 'which', 'improves', 'the', 'swipt', 'rateenergy', 'tradeoff', 'region', 'significantly', 'the', 'nonlinear', 'rectifier', 'model', 'which', 'accurately', 'models', 'the', 'energy', 'harvester', 'is', 'adopted', 'for', 'evaluating', 'the', 'output', 'direct', 'current', 'dc', 'power', 'at', 'the', 'receiver', 'the', 'harvested', 'dc', 'power', 'is', 'maximized', 'under', 'an', 'average', 'power', 'constraint', 'at', 'the', 'transmitter', 'and', 'a', 'constraint', 'on', 'the', 'rate', 'of', 'information', 'transmitted', 'via', 'a', 'multicarrier', 'signal', 'over', 'a', 'flat', 'fading', 'channel', 'as', 'a', 'consequence', 'of', 'the', 'rectifier', 'nonlinearity', 'this', 'work', 'highlights', 'that', 'asymmetric', 'psk', 'modulation', 'provides', 'benefits', 'over', 'conventional', 'symmetric', 'psk', 'modulation', 'in', 'swipt', 'and', 'opens', 'the', 'door', 'to', 'systematic', 'modulation', 'design', 'tailored', 'for', 'swipt']] | [-0.2747200428070878, 0.017257804486714146, -0.02247861504391138, -0.026384758464897656, -0.10424366236563672, -0.27674197161841957, 0.07463097248802188, 0.4009731670808538, -0.2825510619503975, -0.2406528276868001, 0.06874314175267401, -0.22970464423132078, -0.1852293740682669, 0.2550180268873511, -0.09589024035223112, 0.10174997067204802, -0.006575077787872303, 0.0056566084118408935, -0.032149397059362636, -0.16721852191698713, 0.2720289987675544, 0.19738719875710337, 0.42971795144163677, 0.04514649070483141, 0.11526816083445542, 0.02054131238538822, -0.007541206791191487, -0.110566085273702, -0.09070054468773722, 0.07518086570859384, 0.3715675236114564, 0.1287381376054868, 0.25511290447635426, -0.37652628714017367, -0.3682630254094162, 0.11845401960316529, 0.1556585124572676, 0.06708615776812155, -0.09969177142861677, -0.2173693881219102, 0.08797756160571668, -0.2962086492633397, 0.05844527254403393, 0.0268842860917888, -0.038417160745813965, 0.06080497800281297, -0.3649167931305144, 0.03542821433369976, 0.05405907596542494, 0.05736176064080634, -0.04732439796931136, -0.1310340218699059, 0.02729137215725574, 0.11089018328945983, -0.03249189311975135, -0.010735739977413637, 0.08015244273229728, -0.08742563099273153, -0.09166927596969479, 0.3313776919275296, -0.015175785633382967, -0.2125141208777456, 0.03935445576939241, -0.06510270986630506, -0.013502019375713693, 0.15874531140041262, 0.2534615480580141, 0.0367485499953398, -0.1639884216545741, 0.03452099088030376, 0.052436561383483175, 0.23268362642438906, 0.12147007452173007, 0.15305910025396058, 0.21012189278278398, 0.18398927460342795, 0.15418027548278318, 0.16510652061599004, -0.14850978279384827, -0.12055086312938255, -0.15604665187011296, -0.054837064704278835, -0.22452695068991366, 0.05467811557527229, -0.0672858584688141, -0.03802601996230314, 0.4453316427432927, 0.10214904405812204, 0.09505127320015752, 0.041970097955404406, 0.48444909954795967, 0.17328782583865324, 0.04122316606053327, 0.08755275685453436, 0.2627637914721728, 0.1616229155868594, 0.21699179503028407, -0.2378697512825523, 0.049237872933264114, -0.06920172096657995] |
1,802.06513 | Constrained Least Squares, SDP, and QCQP Perspectives on Joint Biconvex
Radar Receiver and Waveform design | Joint radar receive filter and waveform design is non-convex, but is
individually convex for a fixed receiver filter while optimizing the waveform,
and vice versa. Such classes of problems are fre- quently encountered in
optimization, and are referred to biconvex programs. Alternating minimization
(AM) is perhaps the most popu- lar, effective, and simplest algorithm that can
deal with bi-convexity. In this paper we consider new perspectives on this
problem via older, well established problems in the optimization literature. It
is shown here specifically that the radar waveform optimization may be cast as
constrained least squares, semi-definite programs (SDP), and quadratically
constrained quadratic programs (QCQP). The bi-convex constraint introduces sets
which vary for each iteration in the alternat- ing minimization. We prove
convergence of alternating minimization for biconvex problems with biconvex
constraints by showing the equivalence of this to a biconvex problem with
constrained Cartesian product convex sets but for convex hulls of small
diameter.
| eess.SP | joint radar receive filter and waveform design is nonconvex but is individually convex for a fixed receiver filter while optimizing the waveform and vice versa such classes of problems are fre quently encountered in optimization and are referred to biconvex programs alternating minimization am is perhaps the most popu lar effective and simplest algorithm that can deal with biconvexity in this paper we consider new perspectives on this problem via older well established problems in the optimization literature it is shown here specifically that the radar waveform optimization may be cast as constrained least squares semidefinite programs sdp and quadratically constrained quadratic programs qcqp the biconvex constraint introduces sets which vary for each iteration in the alternat ing minimization we prove convergence of alternating minimization for biconvex problems with biconvex constraints by showing the equivalence of this to a biconvex problem with constrained cartesian product convex sets but for convex hulls of small diameter | [['joint', 'radar', 'receive', 'filter', 'and', 'waveform', 'design', 'is', 'nonconvex', 'but', 'is', 'individually', 'convex', 'for', 'a', 'fixed', 'receiver', 'filter', 'while', 'optimizing', 'the', 'waveform', 'and', 'vice', 'versa', 'such', 'classes', 'of', 'problems', 'are', 'fre', 'quently', 'encountered', 'in', 'optimization', 'and', 'are', 'referred', 'to', 'biconvex', 'programs', 'alternating', 'minimization', 'am', 'is', 'perhaps', 'the', 'most', 'popu', 'lar', 'effective', 'and', 'simplest', 'algorithm', 'that', 'can', 'deal', 'with', 'biconvexity', 'in', 'this', 'paper', 'we', 'consider', 'new', 'perspectives', 'on', 'this', 'problem', 'via', 'older', 'well', 'established', 'problems', 'in', 'the', 'optimization', 'literature', 'it', 'is', 'shown', 'here', 'specifically', 'that', 'the', 'radar', 'waveform', 'optimization', 'may', 'be', 'cast', 'as', 'constrained', 'least', 'squares', 'semidefinite', 'programs', 'sdp', 'and', 'quadratically', 'constrained', 'quadratic', 'programs', 'qcqp', 'the', 'biconvex', 'constraint', 'introduces', 'sets', 'which', 'vary', 'for', 'each', 'iteration', 'in', 'the', 'alternat', 'ing', 'minimization', 'we', 'prove', 'convergence', 'of', 'alternating', 'minimization', 'for', 'biconvex', 'problems', 'with', 'biconvex', 'constraints', 'by', 'showing', 'the', 'equivalence', 'of', 'this', 'to', 'a', 'biconvex', 'problem', 'with', 'constrained', 'cartesian', 'product', 'convex', 'sets', 'but', 'for', 'convex', 'hulls', 'of', 'small', 'diameter']] | [-0.12335274628670947, 0.02478563328413597, -0.038912057050266395, 0.07970666508966436, -0.1376848957559179, -0.22528168472637927, -0.0041550411074270125, 0.3919410766269768, -0.37990025755739315, -0.3000526644009488, 0.18880104616716553, -0.2403082352442046, -0.1863114429589093, 0.17341536937244967, -0.14970653863879396, 0.10775550999267794, 0.07400240368925771, -0.054355538675403284, -0.1472179057210489, -0.2746877316461596, 0.23558768173040567, 0.005627482870800627, 0.19599282989594963, 0.009872513750166284, 0.1437646990224987, 0.06680597299466433, 0.025919871103456792, 0.07749685087527325, -0.06269015156516723, 0.13021785700183933, 0.35659224834609654, 0.2661142240938871, 0.3219653828635666, -0.4073432270267041, -0.16109345431798716, 0.13079253876630484, 0.14151628293078758, 0.039348987743008906, -0.03858847594652568, -0.20430447650598546, 0.056803067387507775, -0.10397099299064162, -0.013005115880076986, -0.036542388756631634, -0.05139924380076087, 0.038185240009577424, -0.33302605444918465, 0.04012622543077252, 0.036262676565682675, -0.0013139343021012953, -0.08789212681167437, -0.2039039724269042, 0.05518666073357309, -0.012735648092880747, 0.06476326068495004, 0.05492007910742674, 0.1064873334587996, -0.033886656601870666, -0.13412389655603596, 0.38059277156538335, 0.011604018602786537, -0.26439170993474964, 0.15562332604457838, -0.04387451756166924, -0.14887967899447807, 0.13389119180223716, 0.23147492279512413, 0.20416275949180857, -0.16703807482848954, 0.1087029835805023, -0.08468939807704266, 0.14460712040658869, 0.07446346549907687, -0.00048705362075684115, 0.15366681430068815, 0.1566020923490131, 0.2419397286565524, 0.22032544587120972, -0.010455335141920478, -0.09068126462588659, -0.23177722291229597, -0.07929606114824612, -0.212124849757137, -0.03717470984507255, -0.07330871607415497, -0.15169222171785876, 0.35388845964974047, 0.05730285115153498, 0.11855762081945108, 0.17153063975046298, 0.34349224075455875, 0.13971538178461415, 0.05125018283785655, 0.08904142399148078, 0.23294988786649518, 0.1144097799486998, 0.050756876962563764, -0.23182272531238257, 0.0364951164213624, 0.08404447847758145] |
1,802.06514 | Anti-adiabatic evolution in quantum-classical hybrid system | The adiabatic theorem is an important concept in quantum mechanics, it tells
that a quantum system subjected to gradually changing external conditions
remains to the same instantaneous eigenstate of its Hamiltonian as it initially
in. In this paper, we study the another extreme circumstance where the external
conditions vary rapidly such that the quantum system can not follow the change
and remains in its initial state (or wavefunction). We call this type of
evolution anit-adiabatic evolution. We examine the matter-wave pressure in this
situation and derive the condition for such an evolution. The study is
conducted by considering a quantum particle in an infinitely deep potential,
the potential width $Q$ is assumed to be change rapidly. We show that the total
energy of the quantum subsystem decreases as $Q$ increases, and this rapidly
change exerts a force on the wall which plays the role of boundary of the
potential. For $Q<Q_{0}$ ($Q_0$ is the initial width of the potential), the
force is repulsive, and for $Q>Q_{0}$, the force is positive. The condition for
the anti-adiabatic evolution is given via a spin-$\frac 1 2$ in a rotating
magnetic field.
| quant-ph | the adiabatic theorem is an important concept in quantum mechanics it tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its hamiltonian as it initially in in this paper we study the another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state or wavefunction we call this type of evolution anitadiabatic evolution we examine the matterwave pressure in this situation and derive the condition for such an evolution the study is conducted by considering a quantum particle in an infinitely deep potential the potential width q is assumed to be change rapidly we show that the total energy of the quantum subsystem decreases as q increases and this rapidly change exerts a force on the wall which plays the role of boundary of the potential for qq_0 q_0 is the initial width of the potential the force is repulsive and for qq_0 the force is positive the condition for the antiadiabatic evolution is given via a spinfrac 1 2 in a rotating magnetic field | [['the', 'adiabatic', 'theorem', 'is', 'an', 'important', 'concept', 'in', 'quantum', 'mechanics', 'it', 'tells', 'that', 'a', 'quantum', 'system', 'subjected', 'to', 'gradually', 'changing', 'external', 'conditions', 'remains', 'to', 'the', 'same', 'instantaneous', 'eigenstate', 'of', 'its', 'hamiltonian', 'as', 'it', 'initially', 'in', 'in', 'this', 'paper', 'we', 'study', 'the', 'another', 'extreme', 'circumstance', 'where', 'the', 'external', 'conditions', 'vary', 'rapidly', 'such', 'that', 'the', 'quantum', 'system', 'can', 'not', 'follow', 'the', 'change', 'and', 'remains', 'in', 'its', 'initial', 'state', 'or', 'wavefunction', 'we', 'call', 'this', 'type', 'of', 'evolution', 'anitadiabatic', 'evolution', 'we', 'examine', 'the', 'matterwave', 'pressure', 'in', 'this', 'situation', 'and', 'derive', 'the', 'condition', 'for', 'such', 'an', 'evolution', 'the', 'study', 'is', 'conducted', 'by', 'considering', 'a', 'quantum', 'particle', 'in', 'an', 'infinitely', 'deep', 'potential', 'the', 'potential', 'width', 'q', 'is', 'assumed', 'to', 'be', 'change', 'rapidly', 'we', 'show', 'that', 'the', 'total', 'energy', 'of', 'the', 'quantum', 'subsystem', 'decreases', 'as', 'q', 'increases', 'and', 'this', 'rapidly', 'change', 'exerts', 'a', 'force', 'on', 'the', 'wall', 'which', 'plays', 'the', 'role', 'of', 'boundary', 'of', 'the', 'potential', 'for', 'qq_0', 'q_0', 'is', 'the', 'initial', 'width', 'of', 'the', 'potential', 'the', 'force', 'is', 'repulsive', 'and', 'for', 'qq_0', 'the', 'force', 'is', 'positive', 'the', 'condition', 'for', 'the', 'antiadiabatic', 'evolution', 'is', 'given', 'via', 'a', 'spinfrac', '1', '2', 'in', 'a', 'rotating', 'magnetic', 'field']] | [-0.17089784223048446, 0.19420605338821972, -0.10482263726675335, 0.046954728941243876, -0.020000405057383912, -0.11360336210389427, 0.01438181932435376, 0.3388600130391153, -0.2902359331143711, -0.2736568316931831, 0.07563276809607856, -0.2410368207981561, -0.12545362808791433, 0.16513744957638, -0.03286686473536021, 0.021259030022777934, 0.03660563367697844, 0.09620805463957835, -0.050817996079231646, -0.19968096129496626, 0.3634510598279894, 0.05188989167940245, 0.25606067413414385, 0.08926452956047845, 0.07908755481581796, 0.03193479778997122, 0.05460059868649923, 0.006583955872276011, -0.13277062699929432, 0.01775224448211571, 0.1508476875615331, 0.09244085170009876, 0.3126114771556966, -0.41430954642115747, -0.20656088749921064, 0.11244744274087927, 0.13592211491762, 0.1416417624406706, -0.043864093155644955, -0.2384411085989665, 0.050535859241284786, -0.168156889969493, -0.1994195298371428, -0.025270490222959158, 0.07393386403041428, 0.002491022039324364, -0.27036790744237166, 0.0828442752665098, 0.08667114226740193, 0.038687112391303805, -0.10126127601840239, -0.0344902557547498, -0.006457676109982366, 0.13803202491427927, 0.03719243357321596, 0.09114923164494992, 0.17978388949342192, -0.17080954031490866, -0.03551767828107318, 0.37987208857828564, -0.0697804664393618, -0.20678217273783236, 0.1703887034063153, -0.1216663896843273, -0.0832697291253695, 0.078210014400426, 0.1250615962258077, 0.09390021619551323, -0.10950051128047514, 0.10900202959920355, -0.006400569505805279, 0.16146820241318927, 0.049517702704723825, 0.004483624229476573, 0.2179129168261739, 0.1415236247703433, 0.08396127329451993, 0.17303901075766506, -0.07930423549431212, -0.12986565981667866, -0.30886952688339797, -0.18924318431791934, -0.1941129542805658, 0.09151248455199819, -0.0585443887154243, -0.18016363210717146, 0.37630553196936367, 0.148958784250423, 0.19056855502319248, -0.01940808381155671, 0.270726042239364, 0.17680484637304303, 0.04369219493638864, 0.05393349771502423, 0.27425680231840854, 0.12749653271733122, 0.1260742766329431, -0.27214247621546056, 0.057359690260002635, 0.0028847817662744756] |
1,802.06515 | Image Forensics: Detecting duplication of scientific images with
manipulation-invariant image similarity | Manipulation and re-use of images in scientific publications is a concerning
problem that currently lacks a scalable solution. Current tools for detecting
image duplication are mostly manual or semi-automated, despite the availability
of an overwhelming target dataset for a learning-based approach. This paper
addresses the problem of determining if, given two images, one is a manipulated
version of the other by means of copy, rotation, translation, scale,
perspective transform, histogram adjustment, or partial erasing. We propose a
data-driven solution based on a 3-branch Siamese Convolutional Neural Network.
The ConvNet model is trained to map images into a 128-dimensional space, where
the Euclidean distance between duplicate images is smaller than or equal to 1,
and the distance between unique images is greater than 1. Our results suggest
that such an approach has the potential to improve surveillance of the
published and in-peer-review literature for image manipulation.
| cs.CV | manipulation and reuse of images in scientific publications is a concerning problem that currently lacks a scalable solution current tools for detecting image duplication are mostly manual or semiautomated despite the availability of an overwhelming target dataset for a learningbased approach this paper addresses the problem of determining if given two images one is a manipulated version of the other by means of copy rotation translation scale perspective transform histogram adjustment or partial erasing we propose a datadriven solution based on a 3branch siamese convolutional neural network the convnet model is trained to map images into a 128dimensional space where the euclidean distance between duplicate images is smaller than or equal to 1 and the distance between unique images is greater than 1 our results suggest that such an approach has the potential to improve surveillance of the published and inpeerreview literature for image manipulation | [['manipulation', 'and', 'reuse', 'of', 'images', 'in', 'scientific', 'publications', 'is', 'a', 'concerning', 'problem', 'that', 'currently', 'lacks', 'a', 'scalable', 'solution', 'current', 'tools', 'for', 'detecting', 'image', 'duplication', 'are', 'mostly', 'manual', 'or', 'semiautomated', 'despite', 'the', 'availability', 'of', 'an', 'overwhelming', 'target', 'dataset', 'for', 'a', 'learningbased', 'approach', 'this', 'paper', 'addresses', 'the', 'problem', 'of', 'determining', 'if', 'given', 'two', 'images', 'one', 'is', 'a', 'manipulated', 'version', 'of', 'the', 'other', 'by', 'means', 'of', 'copy', 'rotation', 'translation', 'scale', 'perspective', 'transform', 'histogram', 'adjustment', 'or', 'partial', 'erasing', 'we', 'propose', 'a', 'datadriven', 'solution', 'based', 'on', 'a', '3branch', 'siamese', 'convolutional', 'neural', 'network', 'the', 'convnet', 'model', 'is', 'trained', 'to', 'map', 'images', 'into', 'a', '128dimensional', 'space', 'where', 'the', 'euclidean', 'distance', 'between', 'duplicate', 'images', 'is', 'smaller', 'than', 'or', 'equal', 'to', '1', 'and', 'the', 'distance', 'between', 'unique', 'images', 'is', 'greater', 'than', '1', 'our', 'results', 'suggest', 'that', 'such', 'an', 'approach', 'has', 'the', 'potential', 'to', 'improve', 'surveillance', 'of', 'the', 'published', 'and', 'inpeerreview', 'literature', 'for', 'image', 'manipulation']] | [-0.066941010899326, 0.004246239943515522, -0.05285760334582948, 0.05400849891399654, -0.10964927230573569, -0.16712434094289266, 0.03047898013755912, 0.42082429653964937, -0.27243251802994767, -0.3294785998425343, 0.10490232527606874, -0.32264567577254233, -0.14719915527894045, 0.19502082659164444, -0.15251787940441217, 0.05161838893804492, 0.1291261336617582, 0.03409929963527247, -0.05711852602945555, -0.23413579636770818, 0.3195222934979635, 0.017144065822422918, 0.32583583280211315, 0.011691527568877468, 0.13298180696438067, -0.004863615642534569, -0.07788002772657718, -0.012236088905006505, -0.06574811817669494, 0.19012827265477325, 0.24268461452609497, 0.238197640823071, 0.33210593791187015, -0.39780959826748585, -0.21295340405696253, 0.10562777210078719, 0.16515899198000422, 0.11972070131580242, -0.07507086029848627, -0.31304955236595966, 0.11496092968081939, -0.13894042830603817, -0.024462698386438813, -0.07854595783606379, 0.035059552629213106, -0.06640341162306464, -0.27307221594188985, 0.04273941813153215, 0.05755099805780143, 0.109478829624196, -0.06899435545912841, -0.08343302255768019, 0.021833486788738, 0.15915411170539706, 0.022127497211234488, 0.12641524607250984, 0.11873079194144036, -0.19330777082844483, -0.13107472999642292, 0.3770595456072543, -0.03324765258427457, -0.23296434942716993, 0.15500782845224925, -0.05395155316930161, -0.1074013113183254, 0.11829803963579859, 0.16804444805812738, 0.12716561041048002, -0.17230304767144844, 0.010456339558408622, -0.04776575922894861, 0.2161293707192979, 0.07648823144457613, -0.0055267676329498906, 0.1828924617835178, 0.2401722701356953, 0.08400958739932524, 0.13947092583758705, -0.1417662220175973, -0.029585207825423114, -0.2132844679355104, -0.14297605143211614, -0.22276725649296875, 0.011834674070996698, -0.07077527367790834, -0.16124060720742112, 0.389992183840756, 0.19251373186448795, 0.19626012861651057, 0.07719969456472124, 0.3678503349656239, 0.027707737014376715, 0.12583467595848358, 0.054271467207905114, 0.15833751322417003, 0.008269814947400138, 0.07590598074602894, -0.1382422180678178, 0.08398139431546446, 0.07568170255075933] |
1,802.06516 | Subspace Network: Deep Multi-Task Censored Regression for Modeling
Neurodegenerative Diseases | Over the past decade a wide spectrum of machine learning models have been
developed to model the neurodegenerative diseases, associating biomarkers,
especially non-intrusive neuroimaging markers, with key clinical scores
measuring the cognitive status of patients. Multi-task learning (MTL) has been
commonly utilized by these studies to address high dimensionality and small
cohort size challenges. However, most existing MTL approaches are based on
linear models and suffer from two major limitations: 1) they cannot explicitly
consider upper/lower bounds in these clinical scores; 2) they lack the
capability to capture complicated non-linear interactions among the variables.
In this paper, we propose Subspace Network, an efficient deep modeling approach
for non-linear multi-task censored regression. Each layer of the subspace
network performs a multi-task censored regression to improve upon the
predictions from the last layer via sketching a low-dimensional subspace to
perform knowledge transfer among learning tasks. Under mild assumptions, for
each layer the parametric subspace can be recovered using only one pass of
training data. Empirical results demonstrate that the proposed subspace network
quickly picks up the correct parameter subspaces, and outperforms
state-of-the-arts in predicting neurodegenerative clinical scores using
information in brain imaging.
| cs.LG cs.AI stat.ML | over the past decade a wide spectrum of machine learning models have been developed to model the neurodegenerative diseases associating biomarkers especially nonintrusive neuroimaging markers with key clinical scores measuring the cognitive status of patients multitask learning mtl has been commonly utilized by these studies to address high dimensionality and small cohort size challenges however most existing mtl approaches are based on linear models and suffer from two major limitations 1 they cannot explicitly consider upperlower bounds in these clinical scores 2 they lack the capability to capture complicated nonlinear interactions among the variables in this paper we propose subspace network an efficient deep modeling approach for nonlinear multitask censored regression each layer of the subspace network performs a multitask censored regression to improve upon the predictions from the last layer via sketching a lowdimensional subspace to perform knowledge transfer among learning tasks under mild assumptions for each layer the parametric subspace can be recovered using only one pass of training data empirical results demonstrate that the proposed subspace network quickly picks up the correct parameter subspaces and outperforms stateofthearts in predicting neurodegenerative clinical scores using information in brain imaging | [['over', 'the', 'past', 'decade', 'a', 'wide', 'spectrum', 'of', 'machine', 'learning', 'models', 'have', 'been', 'developed', 'to', 'model', 'the', 'neurodegenerative', 'diseases', 'associating', 'biomarkers', 'especially', 'nonintrusive', 'neuroimaging', 'markers', 'with', 'key', 'clinical', 'scores', 'measuring', 'the', 'cognitive', 'status', 'of', 'patients', 'multitask', 'learning', 'mtl', 'has', 'been', 'commonly', 'utilized', 'by', 'these', 'studies', 'to', 'address', 'high', 'dimensionality', 'and', 'small', 'cohort', 'size', 'challenges', 'however', 'most', 'existing', 'mtl', 'approaches', 'are', 'based', 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1,802.06517 | Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian
Linear Inverse Problems | We develop a framework for goal-oriented optimal design of experiments
(GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This
framework differs from classical Bayesian optimal design of experiments (ODE)
in the following sense: we seek experimental designs that minimize the
posterior uncertainty in the experiment end-goal, e.g., a quantity of interest
(QoI), rather than the estimated parameter itself. This is suitable for
scenarios in which the solution of an inverse problem is an intermediate step
and the estimated parameter is then used to compute a QoI. In such problems, a
GOODE approach has two benefits: the designs can avoid wastage of experimental
resources by a targeted collection of data, and the resulting design criteria
are computationally easier to evaluate due to the often low-dimensionality of
the QoIs. We present two modified design criteria, A-GOODE and D-GOODE, which
are natural analogues of classical Bayesian A- and D-optimal criteria. We
analyze the connections to other ODE criteria, and provide interpretations for
the GOODE criteria by using tools from information theory. Then, we develop an
efficient gradient-based optimization framework for solving the GOODE
optimization problems. Additionally, we present comprehensive numerical
experiments testing the various aspects of the presented approach. The driving
application is the optimal placement of sensors to identify the source of
contaminants in a diffusion and transport problem. We enforce sparsity of the
sensor placements using an $\ell_1$-norm penalty approach, and propose a
practical strategy for specifying the associated penalty parameter.
| cs.CE math.NA math.OC stat.AP | we develop a framework for goaloriented optimal design of experiments goode for largescale bayesian linear inverse problems governed by pdes this framework differs from classical bayesian optimal design of experiments ode in the following sense we seek experimental designs that minimize the posterior uncertainty in the experiment endgoal eg a quantity of interest qoi rather than the estimated parameter itself this is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a qoi in such problems a goode approach has two benefits the designs can avoid wastage of experimental resources by a targeted collection of data and the resulting design criteria are computationally easier to evaluate due to the often lowdimensionality of the qois we present two modified design criteria agoode and dgoode which are natural analogues of classical bayesian a and doptimal criteria we analyze the connections to other ode criteria and provide interpretations for the goode criteria by using tools from information theory then we develop an efficient gradientbased optimization framework for solving the goode optimization problems additionally we present comprehensive numerical experiments testing the various aspects of the presented approach the driving application is the optimal placement of sensors to identify the source of contaminants in a diffusion and transport problem we enforce sparsity of the sensor placements using an ell_1norm penalty approach and propose a practical strategy for specifying the associated penalty parameter | [['we', 'develop', 'a', 'framework', 'for', 'goaloriented', 'optimal', 'design', 'of', 'experiments', 'goode', 'for', 'largescale', 'bayesian', 'linear', 'inverse', 'problems', 'governed', 'by', 'pdes', 'this', 'framework', 'differs', 'from', 'classical', 'bayesian', 'optimal', 'design', 'of', 'experiments', 'ode', 'in', 'the', 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1,802.06518 | Frequency-domain gravitational waveform models for inspiraling binary
neutron stars | We develop a model for frequency-domain gravitational waveforms from
inspiraling binary neutron stars. Our waveform model is calibrated by
comparison with hybrid waveforms constructed from our latest high-precision
numerical-relativity waveforms and the SEOBNRv2T waveforms in the frequency
range of $10$--$1000\,{\rm Hz}$. We show that the phase difference between our
waveform model and the hybrid waveforms is always smaller than $0.1\, {\rm
rad}$ for the binary tidal deformability, ${\tilde \Lambda}$, in the range
$300\lesssim{\tilde \Lambda}\lesssim1900$ and for the mass ratio between 0.73
and 1. We show that, for $10$--$1000\,{\rm Hz}$, the distinguishability for the
signal-to-noise ratio $\lesssim50$ and the mismatch between our waveform model
and the hybrid waveforms are always smaller than 0.25 and $1.1\times10^{-5}$,
respectively. The systematic error of our waveform model in the measurement of
${\tilde \Lambda}$ is always smaller than $20$ with respect to the hybrid
waveforms for $300\lesssim{\tilde \Lambda}\lesssim1900$. The statistical error
in the measurement of binary parameters is computed employing our waveform
model, and we obtain results consistent with the previous studies. We show that
the systematic error of our waveform model is always smaller than $20\%$
(typically smaller than $10\%$) of the statistical error for events with the
signal-to-noise ratio of $50$.
| gr-qc astro-ph.HE | we develop a model for frequencydomain gravitational waveforms from inspiraling binary neutron stars our waveform model is calibrated by comparison with hybrid waveforms constructed from our latest highprecision numericalrelativity waveforms and the seobnrv2t waveforms in the frequency range of 101000rm hz we show that the phase difference between our waveform model and the hybrid waveforms is always smaller than 01 rm rad for the binary tidal deformability tilde lambda in the range 300lesssimtilde lambdalesssim1900 and for the mass ratio between 073 and 1 we show that for 101000rm hz the distinguishability for the signaltonoise ratio lesssim50 and the mismatch between our waveform model and the hybrid waveforms are always smaller than 025 and 11times105 respectively the systematic error of our waveform model in the measurement of tilde lambda is always smaller than 20 with respect to the hybrid waveforms for 300lesssimtilde lambdalesssim1900 the statistical error in the measurement of binary parameters is computed employing our waveform model and we obtain results consistent with the previous studies we show that the systematic error of our waveform model is always smaller than 20 typically smaller than 10 of the statistical error for events with the signaltonoise ratio of 50 | [['we', 'develop', 'a', 'model', 'for', 'frequencydomain', 'gravitational', 'waveforms', 'from', 'inspiraling', 'binary', 'neutron', 'stars', 'our', 'waveform', 'model', 'is', 'calibrated', 'by', 'comparison', 'with', 'hybrid', 'waveforms', 'constructed', 'from', 'our', 'latest', 'highprecision', 'numericalrelativity', 'waveforms', 'and', 'the', 'seobnrv2t', 'waveforms', 'in', 'the', 'frequency', 'range', 'of', '101000rm', 'hz', 'we', 'show', 'that', 'the', 'phase', 'difference', 'between', 'our', 'waveform', 'model', 'and', 'the', 'hybrid', 'waveforms', 'is', 'always', 'smaller', 'than', '01', 'rm', 'rad', 'for', 'the', 'binary', 'tidal', 'deformability', 'tilde', 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1,802.06519 | Quantum key distribution with an efficient countermeasure against
correlated intensity fluctuations in optical pulses | Quantum key distribution (QKD) allows two distant parties to share secret
keys with the proven security even in the presence of an eavesdropper with
unbounded computational power. Recently, GHz-clock decoy QKD systems have been
realized by employing ultrafast optical communication devices. However,
security loopholes of high-speed systems have not been fully explored yet. Here
we point out a security loophole at the transmitter of the GHz-clock QKD, which
is a common problem in high-speed QKD systems using practical band-width
limited devices. We experimentally observe the inter-pulse intensity
correlation and modulation-pattern dependent intensity deviation in a practical
high-speed QKD system. Such correlation violates the assumption of most
security theories. We also provide its countermeasure which does not require
significant changes of hardware and can generate keys secure over 100 km fiber
transmission. Our countermeasure is simple, effective and applicable to wide
range of high-speed QKD systems, and thus paves the way to realize ultrafast
and security-certified commercial QKD systems.
| quant-ph | quantum key distribution qkd allows two distant parties to share secret keys with the proven security even in the presence of an eavesdropper with unbounded computational power recently ghzclock decoy qkd systems have been realized by employing ultrafast optical communication devices however security loopholes of highspeed systems have not been fully explored yet here we point out a security loophole at the transmitter of the ghzclock qkd which is a common problem in highspeed qkd systems using practical bandwidth limited devices we experimentally observe the interpulse intensity correlation and modulationpattern dependent intensity deviation in a practical highspeed qkd system such correlation violates the assumption of most security theories we also provide its countermeasure which does not require significant changes of hardware and can generate keys secure over 100 km fiber transmission our countermeasure is simple effective and applicable to wide range of highspeed qkd systems and thus paves the way to realize ultrafast and securitycertified commercial qkd systems | [['quantum', 'key', 'distribution', 'qkd', 'allows', 'two', 'distant', 'parties', 'to', 'share', 'secret', 'keys', 'with', 'the', 'proven', 'security', 'even', 'in', 'the', 'presence', 'of', 'an', 'eavesdropper', 'with', 'unbounded', 'computational', 'power', 'recently', 'ghzclock', 'decoy', 'qkd', 'systems', 'have', 'been', 'realized', 'by', 'employing', 'ultrafast', 'optical', 'communication', 'devices', 'however', 'security', 'loopholes', 'of', 'highspeed', 'systems', 'have', 'not', 'been', 'fully', 'explored', 'yet', 'here', 'we', 'point', 'out', 'a', 'security', 'loophole', 'at', 'the', 'transmitter', 'of', 'the', 'ghzclock', 'qkd', 'which', 'is', 'a', 'common', 'problem', 'in', 'highspeed', 'qkd', 'systems', 'using', 'practical', 'bandwidth', 'limited', 'devices', 'we', 'experimentally', 'observe', 'the', 'interpulse', 'intensity', 'correlation', 'and', 'modulationpattern', 'dependent', 'intensity', 'deviation', 'in', 'a', 'practical', 'highspeed', 'qkd', 'system', 'such', 'correlation', 'violates', 'the', 'assumption', 'of', 'most', 'security', 'theories', 'we', 'also', 'provide', 'its', 'countermeasure', 'which', 'does', 'not', 'require', 'significant', 'changes', 'of', 'hardware', 'and', 'can', 'generate', 'keys', 'secure', 'over', '100', 'km', 'fiber', 'transmission', 'our', 'countermeasure', 'is', 'simple', 'effective', 'and', 'applicable', 'to', 'wide', 'range', 'of', 'highspeed', 'qkd', 'systems', 'and', 'thus', 'paves', 'the', 'way', 'to', 'realize', 'ultrafast', 'and', 'securitycertified', 'commercial', 'qkd', 'systems']] | [-0.25265592716138374, 0.06335193828716285, -0.11176383610385433, 0.03072281410258457, -0.017946820349323673, -0.33364825256701025, 0.08284776468229081, 0.43270504674209015, -0.2528183687237914, -0.2892962798427839, 0.08120268422508516, -0.23332404399257797, -0.0952128895691463, 0.2935844800955096, -0.162706380988193, 0.1826758929259936, 0.005654758828172049, -0.062016414330823215, -0.0071006024864127305, -0.24892664759407762, 0.2714111521710073, 0.056663362947731076, 0.36994546867586525, 0.07277087923804564, 0.11659803606460911, 0.004775178286113909, 0.026825300203152484, -0.10365225507139966, -0.05987501031697982, 0.0965873818325696, 0.3322496191196313, 0.11790167469857865, 0.31453682182284143, -0.40661094535456654, -0.26000224023621965, 0.1241157686854894, 0.17949892350021968, 0.149343056539255, -0.08535746477133074, -0.30427398002863704, 0.07934518990880966, -0.2869455140528523, -0.12609060120586663, -0.07917302204658846, -0.023769515063069374, 0.03672942663913339, -0.2218813068572093, -0.011039251048501895, -0.00297792391494739, 0.12084255032483246, 0.0916375175109753, 0.0015414210630568688, 0.0450010151169928, 0.15120242017452823, -0.05049564400324961, -0.03645621746092091, 0.16447693476296188, -0.09878430326881987, -0.138950930738235, 0.35252265427896584, 0.021597568830172834, -0.13773700650539492, 0.1745552193757461, -0.09643359403972598, -0.12648454453651006, 0.11539375231383586, 0.177989966181249, 0.05060376313986716, -0.1688657562662666, 0.008411310986213555, -0.011481739356871936, 0.2673964158190768, 0.07927017829489785, 0.21973839482631197, 0.2138286778422121, 0.15815454440844523, 0.09519692749244632, 0.07108392118016718, -0.12437843539836732, -0.13514022524816335, -0.22823371412837273, -0.1707081055123504, -0.2580053662705876, 0.08105713065109645, -0.04395940581398227, -0.05512232352471487, 0.34436308746468036, 0.2404912558109076, 0.0623692713841167, 0.027446428023568996, 0.42536180335786433, 0.05701882541315727, 0.12580350734287413, 0.12714914636468733, 0.2820734567940235, 0.09610551672038174, 0.15204294395932397, -0.11471895971290114, 0.16396033236085644, -0.10773399940921695] |
1,802.0652 | Pricing Options with Exponential Levy Neural Network | In this paper, we propose the exponential Levy neural network (ELNN) for
option pricing, which is a new non-parametric exponential Levy model using
artificial neural networks (ANN). The ELNN fully integrates the ANNs with the
exponential Levy model, a conventional pricing model. So, the ELNN can improve
ANN-based models to avoid several essential issues such as unacceptable
outcomes and inconsistent pricing of over-the-counter products. Moreover, the
ELNN is the first applicable non-parametric exponential Levy model by virtue of
outstanding researches on optimization in the field of ANN. The existing
non-parametric models are too vulnerable to be employed in practice. The
empirical tests with S\&P 500 option prices show that the ELNN outperforms two
parametric models, the Merton and Kou models, in terms of fitting performance
and stability of estimates.
| q-fin.PR q-fin.CP q-fin.ST | in this paper we propose the exponential levy neural network elnn for option pricing which is a new nonparametric exponential levy model using artificial neural networks ann the elnn fully integrates the anns with the exponential levy model a conventional pricing model so the elnn can improve annbased models to avoid several essential issues such as unacceptable outcomes and inconsistent pricing of overthecounter products moreover the elnn is the first applicable nonparametric exponential levy model by virtue of outstanding researches on optimization in the field of ann the existing nonparametric models are too vulnerable to be employed in practice the empirical tests with sp 500 option prices show that the elnn outperforms two parametric models the merton and kou models in terms of fitting performance and stability of estimates | [['in', 'this', 'paper', 'we', 'propose', 'the', 'exponential', 'levy', 'neural', 'network', 'elnn', 'for', 'option', 'pricing', 'which', 'is', 'a', 'new', 'nonparametric', 'exponential', 'levy', 'model', 'using', 'artificial', 'neural', 'networks', 'ann', 'the', 'elnn', 'fully', 'integrates', 'the', 'anns', 'with', 'the', 'exponential', 'levy', 'model', 'a', 'conventional', 'pricing', 'model', 'so', 'the', 'elnn', 'can', 'improve', 'annbased', 'models', 'to', 'avoid', 'several', 'essential', 'issues', 'such', 'as', 'unacceptable', 'outcomes', 'and', 'inconsistent', 'pricing', 'of', 'overthecounter', 'products', 'moreover', 'the', 'elnn', 'is', 'the', 'first', 'applicable', 'nonparametric', 'exponential', 'levy', 'model', 'by', 'virtue', 'of', 'outstanding', 'researches', 'on', 'optimization', 'in', 'the', 'field', 'of', 'ann', 'the', 'existing', 'nonparametric', 'models', 'are', 'too', 'vulnerable', 'to', 'be', 'employed', 'in', 'practice', 'the', 'empirical', 'tests', 'with', 'sp', '500', 'option', 'prices', 'show', 'that', 'the', 'elnn', 'outperforms', 'two', 'parametric', 'models', 'the', 'merton', 'and', 'kou', 'models', 'in', 'terms', 'of', 'fitting', 'performance', 'and', 'stability', 'of', 'estimates']] | [-0.0038981220148893636, -0.0027788461207650427, -0.09059839240860107, 0.14524031989727632, -0.09784070027147442, -0.21394143680240527, 0.056287661912244595, 0.4182106279876343, -0.2579958580881935, -0.2602982817419855, 0.14659487363853485, -0.24191335777124, -0.20137928353348214, 0.2007196563360996, -0.15741815125703262, 0.13172302644450737, 0.03395488330112525, -0.047658930664391135, 0.014572137159966799, -0.28862685195798443, 0.26108454408975995, 0.0756136823243411, 0.31962655819663705, -0.022292485411907006, 0.11592160724825407, -0.04364255880517343, -0.05779365480556189, -0.03729104950695566, -0.10274734041075333, 0.1790044354924629, 0.26276020607119155, 0.10334199499844234, 0.36030944748673327, -0.4332817241318466, -0.2492958577719784, 0.17762817048951407, 0.10853408356810841, 0.04096168681777032, 0.0030655940992815435, -0.2706243016201165, 0.0317405819849566, -0.2484768675062661, -0.08022752063269474, -0.11774121694151284, -0.02533743510387347, 0.06637562053907994, -0.35115336215253484, 0.07943380149367311, 0.08728689206186538, 0.01268746779307492, -0.04751576569523345, -0.17022243882132362, 0.01850233014037674, 0.03469514257686083, 0.08748783737911965, -0.03475660690315818, 0.10264280734063927, -0.1390440190200109, -0.20302722961894532, 0.31256313507161787, -0.12271158216573486, -0.22128740455522095, 0.15973313894548566, -0.03245994858236175, -0.13202153103761807, 0.07721324711893648, 0.19435819976262805, 0.07372104231351193, -0.2038911121514763, 0.11576416936762587, -0.009400434597113799, 0.11032970912768975, 0.031347063842929845, -0.05957069034081732, 0.1415861927752578, 0.23292746169622555, 0.057273442997748766, 0.09863558449410624, -0.08634117016633756, -0.1686230018056294, -0.2528742997105731, -0.0848581434133672, -0.15392211015343435, 0.01561955752955793, -0.1250207034918135, -0.17938801969758905, 0.4105562016425669, 0.21257132193968856, 0.13524270280130757, 0.13424025119784064, 0.3005033053977545, 0.14035807723132532, 0.03483688290584688, 0.10660134001103476, 0.18365282326388035, 0.048937366937843056, 0.12167705594410383, -0.13781160779131302, 0.1713700062999603, 0.024271073863054663] |
1,802.06521 | Human and Smart Machine Co-Learning with Brain Computer Interface | Machine learning has become a very popular approach for cybernetics systems,
and it has always been considered important research in the Computational
Intelligence area. Nevertheless, when it comes to smart machines, it is not
just about the methodologies. We need to consider systems and cybernetics as
well as include human in the loop. The purpose of this article is as follows:
(1) To integrate the open source Facebook AI Research (FAIR) DarkForest program
of Facebook with Item Response Theory (IRT), to the new open learning system,
namely, DDF learning system; (2) To integrate DDF Go with Robot namely Robotic
DDF Go system; (3) To invite the professional Go players to attend the activity
to play Go games on site with a smart machine. The research team will apply
this technology to education, such as, playing games to enhance the children
concentration on learning mathematics, languages, and other topics. With the
detected brainwaves, the robot will be able to speak some words that are very
much to the point for the students and to assist the teachers in classroom in
the future.
| cs.AI cs.HC | machine learning has become a very popular approach for cybernetics systems and it has always been considered important research in the computational intelligence area nevertheless when it comes to smart machines it is not just about the methodologies we need to consider systems and cybernetics as well as include human in the loop the purpose of this article is as follows 1 to integrate the open source facebook ai research fair darkforest program of facebook with item response theory irt to the new open learning system namely ddf learning system 2 to integrate ddf go with robot namely robotic ddf go system 3 to invite the professional go players to attend the activity to play go games on site with a smart machine the research team will apply this technology to education such as playing games to enhance the children concentration on learning mathematics languages and other topics with the detected brainwaves the robot will be able to speak some words that are very much to the point for the students and to assist the teachers in classroom in the future | [['machine', 'learning', 'has', 'become', 'a', 'very', 'popular', 'approach', 'for', 'cybernetics', 'systems', 'and', 'it', 'has', 'always', 'been', 'considered', 'important', 'research', 'in', 'the', 'computational', 'intelligence', 'area', 'nevertheless', 'when', 'it', 'comes', 'to', 'smart', 'machines', 'it', 'is', 'not', 'just', 'about', 'the', 'methodologies', 'we', 'need', 'to', 'consider', 'systems', 'and', 'cybernetics', 'as', 'well', 'as', 'include', 'human', 'in', 'the', 'loop', 'the', 'purpose', 'of', 'this', 'article', 'is', 'as', 'follows', '1', 'to', 'integrate', 'the', 'open', 'source', 'facebook', 'ai', 'research', 'fair', 'darkforest', 'program', 'of', 'facebook', 'with', 'item', 'response', 'theory', 'irt', 'to', 'the', 'new', 'open', 'learning', 'system', 'namely', 'ddf', 'learning', 'system', '2', 'to', 'integrate', 'ddf', 'go', 'with', 'robot', 'namely', 'robotic', 'ddf', 'go', 'system', '3', 'to', 'invite', 'the', 'professional', 'go', 'players', 'to', 'attend', 'the', 'activity', 'to', 'play', 'go', 'games', 'on', 'site', 'with', 'a', 'smart', 'machine', 'the', 'research', 'team', 'will', 'apply', 'this', 'technology', 'to', 'education', 'such', 'as', 'playing', 'games', 'to', 'enhance', 'the', 'children', 'concentration', 'on', 'learning', 'mathematics', 'languages', 'and', 'other', 'topics', 'with', 'the', 'detected', 'brainwaves', 'the', 'robot', 'will', 'be', 'able', 'to', 'speak', 'some', 'words', 'that', 'are', 'very', 'much', 'to', 'the', 'point', 'for', 'the', 'students', 'and', 'to', 'assist', 'the', 'teachers', 'in', 'classroom', 'in', 'the', 'future']] | [-0.012315006846901627, 0.06042163892525624, -0.09088877411121862, 0.0950498160628283, -0.16434524050857152, -0.25144822495727087, 0.043995710894419136, 0.4068507869877127, -0.26164491772548765, -0.33881473477713725, 0.10876034160260158, -0.31759291509608867, -0.1629100531810452, 0.1909859058738542, -0.1385651631152144, 0.01853736150927471, 0.06942847380041561, 0.10192557694827778, 0.04062333858561656, -0.3109352118271346, 0.27935623338713583, 0.07093878792989897, 0.2742054521708199, 0.05435831951831586, 0.06434898982236152, 0.002712372923269868, 0.00497423318724112, -0.008753117019547283, -0.07022420101538102, 0.15388701123813198, 0.4142582997659129, 0.24114623389628753, 0.40830497855824827, -0.41402295324436866, -0.19402829986142808, 0.06911689269829809, 0.13064500799875975, 0.09075562068317806, -0.011933113016748997, -0.31322010964906427, 0.07909999426308947, -0.20189608863004335, -0.09863163437051133, -0.08154004091880598, 0.019537787833019515, -0.005898259442495131, -0.20927787586166754, -0.08547133695879612, 0.05901799095313461, 0.11763886844183612, -0.02213240879875973, -0.13918264603141942, 0.05594594364095665, 0.241407676774382, 0.085208636036436, 0.06971877009880559, 0.18978734712440581, -0.17756484992395655, -0.16367585202730492, 0.39786433866916443, 0.0075231503697822276, -0.15391133303718013, 0.2300346728860663, -0.07606880479358466, -0.16982783757417735, 0.021149408391249774, 0.2482310740395516, 0.05987494579871386, -0.16487100690473655, 0.03481476686512846, 0.0048377782837050395, 0.1733948535773741, 0.03650893471319516, -0.02717382177062209, 0.19679932006588463, 0.2189879460602443, 0.08965782471289292, 0.0764270823829015, -0.020507214094373238, -0.1400114844079793, -0.20959400287340524, -0.1791123536245599, -0.12078811365915514, 0.013494963399041316, 0.018889080220125923, -0.13226811123049678, 0.33822857259222155, 0.21856899674755434, 0.07385177580505939, 0.052784663993281244, 0.27976400058366646, 0.043324388034940174, 0.1258874420283712, 0.08861401170564208, 0.19863675917882745, 0.04221940279464901, 0.2527077533793507, -0.15156440992417708, 0.06477195356113229, -0.004255434856762935] |
1,802.06522 | Spin-Orbit Coupling Induced Resonance in an Ultracold Bose Gas | We study a two-component Bose gas with artificial spin-orbit coupling (SOC)
which couples the center-of-mass momentum of atom to its internal states. We
show that in this system resonance can be induced by tuning SOC strength. With
a two-dimensional SOC, resonances in two scattering channels can be induced by
tuning the aspect ratio of SOC strengths. With a three-dimensional SOC,
resonance in all scattering channels can be induced by tuning the appropriate
SOC strength. Similarly, we also find that in a Fermi gas with two- or
three-dimensional SOC resonance can be induced by tuning SOC strength.
| cond-mat.quant-gas | we study a twocomponent bose gas with artificial spinorbit coupling soc which couples the centerofmass momentum of atom to its internal states we show that in this system resonance can be induced by tuning soc strength with a twodimensional soc resonances in two scattering channels can be induced by tuning the aspect ratio of soc strengths with a threedimensional soc resonance in all scattering channels can be induced by tuning the appropriate soc strength similarly we also find that in a fermi gas with two or threedimensional soc resonance can be induced by tuning soc strength | [['we', 'study', 'a', 'twocomponent', 'bose', 'gas', 'with', 'artificial', 'spinorbit', 'coupling', 'soc', 'which', 'couples', 'the', 'centerofmass', 'momentum', 'of', 'atom', 'to', 'its', 'internal', 'states', 'we', 'show', 'that', 'in', 'this', 'system', 'resonance', 'can', 'be', 'induced', 'by', 'tuning', 'soc', 'strength', 'with', 'a', 'twodimensional', 'soc', 'resonances', 'in', 'two', 'scattering', 'channels', 'can', 'be', 'induced', 'by', 'tuning', 'the', 'aspect', 'ratio', 'of', 'soc', 'strengths', 'with', 'a', 'threedimensional', 'soc', 'resonance', 'in', 'all', 'scattering', 'channels', 'can', 'be', 'induced', 'by', 'tuning', 'the', 'appropriate', 'soc', 'strength', 'similarly', 'we', 'also', 'find', 'that', 'in', 'a', 'fermi', 'gas', 'with', 'two', 'or', 'threedimensional', 'soc', 'resonance', 'can', 'be', 'induced', 'by', 'tuning', 'soc', 'strength']] | [-0.22004337043351066, 0.24251871163141914, 0.027001734483443823, -0.011441401726187905, -0.016463910767924972, -0.19744220350306327, 0.04593308925783882, 0.3979149913260092, -0.2647031358986472, -0.35096874557590735, -0.061011278344570506, -0.21170499528913447, -0.157319326698295, 0.16022095959973134, 0.06858318327188802, -0.009059964194724065, 0.050695274908017986, -0.1097406469367949, -0.05378380121449785, -0.20484165670738244, 0.34356265293899924, 0.047652021292985104, 0.24713692813869179, 0.1294885761308251, -0.00892899720929563, 0.0213290296002621, 0.1513017916076933, 0.05109781911596656, -0.09530878981922797, 0.07232397836863431, 0.2150250031845644, -0.10322248666003968, 0.20681747517179852, -0.3794933033641428, -0.16717483650427312, 0.056570322461387455, 0.14322635275311768, 0.17670966831186283, 0.015584169086650945, -0.3790338493611974, -0.0266276994952932, -0.20856861786645217, -0.11077710776589811, -0.11734709202088804, 0.05321762647751408, 0.021411029593461233, -0.3558852015072868, 0.038616212130667314, 0.11651874733312677, 0.1367353433452081, -0.06974691623205824, -0.07124969667953944, -0.06583607835151876, -0.015501094135591606, 0.012193679014065614, 0.02743980683104989, 0.2017362648572695, -0.14210534460289637, -0.10213607738357193, 0.3589662356728998, -0.1689369957675808, -0.2267975105496589, 0.2126081675135841, -0.1195867599065726, -0.00467079159958909, 0.13326448336980926, 0.1889401608677872, -0.02042440028162673, -0.13468946213833988, 0.14418891239135215, -0.021137292196120445, 0.18871402053628117, 0.03719229317114999, 0.048364285757998005, 0.27222394834583, 0.13168053821815798, 0.027801994447751593, 0.1385884555396236, -0.14824653286389852, -0.06277551693589582, -0.22207353679308048, -0.13214451539776442, -0.2403944083804769, 0.08329929533647373, -0.010558901728169682, -0.06992620367964264, 0.39509162721030106, 0.14143456084123804, 0.24121370756377777, -0.13063551468925047, 0.2009295591075594, 0.1964875186968129, 0.12417977012713284, 0.0796407814923441, 0.3780533249761599, 0.10920358555934702, 0.029867312967932474, -0.34158251467548933, -0.012889800020881617, 0.01171842087933328] |
1,802.06523 | Casimir interaction of two dielectric half spaces with Chern-Simons
boundary layers | A diffraction problem for a flat Chern-Simons layer at plane boundary of a
dielectric half space is solved. The Casimir energy of two dielectric half
spaces with Chern-Simons layers at plane-parallel boundaries separated by a
vacuum slit is derived. Crossing from the repulsive to the attractive Casimir
force is analyzed for two Au and two Si half spaces with boundary Chern-Simons
layers. Boundary quantum Hall layers in external magnetic field lead to Casimir
repulsion at nanoscales. We discuss features that make systems with boundary
quantum Hall layers unique for force measurements and search of long-range
interactions beyond electromagnetism.
| cond-mat.mes-hall cond-mat.mtrl-sci hep-th quant-ph | a diffraction problem for a flat chernsimons layer at plane boundary of a dielectric half space is solved the casimir energy of two dielectric half spaces with chernsimons layers at planeparallel boundaries separated by a vacuum slit is derived crossing from the repulsive to the attractive casimir force is analyzed for two au and two si half spaces with boundary chernsimons layers boundary quantum hall layers in external magnetic field lead to casimir repulsion at nanoscales we discuss features that make systems with boundary quantum hall layers unique for force measurements and search of longrange interactions beyond electromagnetism | [['a', 'diffraction', 'problem', 'for', 'a', 'flat', 'chernsimons', 'layer', 'at', 'plane', 'boundary', 'of', 'a', 'dielectric', 'half', 'space', 'is', 'solved', 'the', 'casimir', 'energy', 'of', 'two', 'dielectric', 'half', 'spaces', 'with', 'chernsimons', 'layers', 'at', 'planeparallel', 'boundaries', 'separated', 'by', 'a', 'vacuum', 'slit', 'is', 'derived', 'crossing', 'from', 'the', 'repulsive', 'to', 'the', 'attractive', 'casimir', 'force', 'is', 'analyzed', 'for', 'two', 'au', 'and', 'two', 'si', 'half', 'spaces', 'with', 'boundary', 'chernsimons', 'layers', 'boundary', 'quantum', 'hall', 'layers', 'in', 'external', 'magnetic', 'field', 'lead', 'to', 'casimir', 'repulsion', 'at', 'nanoscales', 'we', 'discuss', 'features', 'that', 'make', 'systems', 'with', 'boundary', 'quantum', 'hall', 'layers', 'unique', 'for', 'force', 'measurements', 'and', 'search', 'of', 'longrange', 'interactions', 'beyond', 'electromagnetism']] | [-0.2094900712028754, 0.20064485385747893, -0.03482662114535687, 0.03861613103963093, -0.06239390243985215, -0.21616045919684124, -0.024852542216148302, 0.38862526428182514, -0.2657500056939542, -0.2854163459708857, 0.01330239341739204, -0.31699821221813257, -0.11759882705400185, 0.14506269475131542, 0.036768516905757845, 0.04466145705165608, 0.01130625652386902, -0.0107177671862348, -0.1044019648249318, -0.2020289786017443, 0.39409417058436236, -0.025861387647099186, 0.21664536406038976, 0.09232031139640176, 0.08948329181353352, 0.013210763515695473, 0.10917600300353096, 0.07458950413779442, -0.15554142010682417, 0.06564961758570517, 0.23359848948300113, -0.16159460421803654, 0.19778356410334913, -0.49574338840510773, -0.22270812506654433, -0.02162414793951475, 0.09123959049240363, 0.10148869416372357, -0.017051319449151656, -0.3031419980890897, -0.011136532029403108, -0.10566964956019453, -0.12255259220754462, 0.00016271583355811177, -0.0025828718956160757, -0.09359584828097449, -0.24936335036835197, 0.07271167260300064, 0.009245162719280973, 0.103149806054271, -0.13601241228930958, -0.09871991022432945, -0.04130080638320318, 0.09427340540616792, 0.029032893941561902, 0.05377806120133978, 0.19026799874418243, -0.16955883323918192, -0.10397510959681276, 0.36641195424053136, -0.05468624235339919, -0.19532278379216333, 0.21815554300746026, -0.17356187106604326, -0.002682557358045359, 0.17065774047823282, 0.11133750014919408, 0.060094624400205375, -0.1292392430750995, 0.12148632396045807, 0.009867980539304565, 0.1630154423681753, 0.1630102302974128, 0.00358116684234416, 0.304481074812689, 0.12935270462185144, 0.09078253491553573, 0.1729532826919945, -0.10120398389328181, -0.0846541880532548, -0.31913375306152264, -0.20378617757969364, -0.21835712998587525, 0.035663779435337196, -0.11793748823877148, -0.23176853280818585, 0.2970347098283926, 0.12081937018392265, 0.1418956216728809, 0.0006940581821551433, 0.29150957570468283, 0.0886808715235651, 0.10995403225818763, 0.047216067869900444, 0.3089621225401655, 0.19604575745903943, 0.153257791542125, -0.2251406584947123, -0.07225505157364343, 0.13618665215160167] |
1,802.06524 | Non-self-averaging behaviors and ergodicity in quenched trap model with
finite system size | Tracking tracer particles in heterogeneous environments plays an important
role in unraveling the material properties. These heterogeneous structures are
often static and depend on the sample realizations. Sample-to-sample
fluctuations of such disorder realizations sometimes become considerably large.
When we investigate the sample-to-sample fluctuations, fundamental averaging
procedures are a thermal average for a single disorder realization and the
disorder average for different disorder realizations. Here, we report on
non-self-averaging phenomena in quenched trap models with finite system sizes,
where we consider the periodic and the reflecting boundary conditions.
Sample-to-sample fluctuations of diffusivity greatly exceeds
trajectory-to-trajectory fluctuations of diffusivity in the corresponding
annealed model. For a single disorder realization, the time-averaged mean
square displacement and position-dependent observables converge to constants
with the aid of the existence of the equilibrium distribution. This is a
manifestation of ergodicity. As a result, the time-averaged quantities do not
depend on the initial condition nor on the thermal histories but depend
crucially on the disorder realization.
| cond-mat.stat-mech | tracking tracer particles in heterogeneous environments plays an important role in unraveling the material properties these heterogeneous structures are often static and depend on the sample realizations sampletosample fluctuations of such disorder realizations sometimes become considerably large when we investigate the sampletosample fluctuations fundamental averaging procedures are a thermal average for a single disorder realization and the disorder average for different disorder realizations here we report on nonselfaveraging phenomena in quenched trap models with finite system sizes where we consider the periodic and the reflecting boundary conditions sampletosample fluctuations of diffusivity greatly exceeds trajectorytotrajectory fluctuations of diffusivity in the corresponding annealed model for a single disorder realization the timeaveraged mean square displacement and positiondependent observables converge to constants with the aid of the existence of the equilibrium distribution this is a manifestation of ergodicity as a result the timeaveraged quantities do not depend on the initial condition nor on the thermal histories but depend crucially on the disorder realization | [['tracking', 'tracer', 'particles', 'in', 'heterogeneous', 'environments', 'plays', 'an', 'important', 'role', 'in', 'unraveling', 'the', 'material', 'properties', 'these', 'heterogeneous', 'structures', 'are', 'often', 'static', 'and', 'depend', 'on', 'the', 'sample', 'realizations', 'sampletosample', 'fluctuations', 'of', 'such', 'disorder', 'realizations', 'sometimes', 'become', 'considerably', 'large', 'when', 'we', 'investigate', 'the', 'sampletosample', 'fluctuations', 'fundamental', 'averaging', 'procedures', 'are', 'a', 'thermal', 'average', 'for', 'a', 'single', 'disorder', 'realization', 'and', 'the', 'disorder', 'average', 'for', 'different', 'disorder', 'realizations', 'here', 'we', 'report', 'on', 'nonselfaveraging', 'phenomena', 'in', 'quenched', 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1,802.06525 | Efficiency and power of minimally nonlinear irreversible heat engines
with broken time-reversal symmetry | We study the minimally nonlinear irreversible heat engines in which the
time-reversal symmetry for the systems may b e broken. The expressions for the
power and the efficiency are derived, in which the effects of the nonlinear
terms due to dissipations are included. We show that, as within the linear
responses, the minimally nonlinear irreversible heat engines enable attainment
of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn
limit imposed on the efficiency at maximum power can be overcomed if the
time-reversal symmetry is broken.
| cond-mat.stat-mech | we study the minimally nonlinear irreversible heat engines in which the timereversal symmetry for the systems may b e broken the expressions for the power and the efficiency are derived in which the effects of the nonlinear terms due to dissipations are included we show that as within the linear responses the minimally nonlinear irreversible heat engines enable attainment of carnot efficiency at positive power we also find that the curzonahlborn limit imposed on the efficiency at maximum power can be overcomed if the timereversal symmetry is broken | [['we', 'study', 'the', 'minimally', 'nonlinear', 'irreversible', 'heat', 'engines', 'in', 'which', 'the', 'timereversal', 'symmetry', 'for', 'the', 'systems', 'may', 'b', 'e', 'broken', 'the', 'expressions', 'for', 'the', 'power', 'and', 'the', 'efficiency', 'are', 'derived', 'in', 'which', 'the', 'effects', 'of', 'the', 'nonlinear', 'terms', 'due', 'to', 'dissipations', 'are', 'included', 'we', 'show', 'that', 'as', 'within', 'the', 'linear', 'responses', 'the', 'minimally', 'nonlinear', 'irreversible', 'heat', 'engines', 'enable', 'attainment', 'of', 'carnot', 'efficiency', 'at', 'positive', 'power', 'we', 'also', 'find', 'that', 'the', 'curzonahlborn', 'limit', 'imposed', 'on', 'the', 'efficiency', 'at', 'maximum', 'power', 'can', 'be', 'overcomed', 'if', 'the', 'timereversal', 'symmetry', 'is', 'broken']] | [-0.1416679578939114, 0.14766440909906206, -0.0016753882889381864, 0.035763326681758786, -0.07680607959628105, -0.12433952518569474, 0.05919564591551369, 0.30443859405138274, -0.2755211165852167, -0.2776726963718168, 0.09367249553906731, -0.31435820242305373, -0.1086920881326395, 0.24016333661380818, -0.0366129551786633, 0.04940752358710266, -0.02144483555986715, 0.0536572869697755, -0.04664657790933482, -0.20247163689716466, 0.26712718758393417, 0.09019074038687078, 0.32434197717388585, 0.08804688964102586, 0.06925266331580299, -0.04934902511939237, 0.04849757521878928, 0.05431236117146909, -0.09857919476268183, 0.04693280911305919, 0.244315286770209, 0.042706053111363544, 0.21205101046838204, -0.4465062681225721, -0.2363124791934917, 0.14523338379380715, 0.07546101550079501, 0.06722022909194823, -0.04370315297406209, -0.21051468698053874, 0.10022060136014427, -0.16015723358247091, -0.08618128175889565, -0.12140724260825664, -0.010105127214708111, 0.030680694154315544, -0.2793299129380929, 0.14534728880409437, 0.15392453969583253, 0.03248051158152521, -0.03671018024165691, -0.02889807626012374, -0.09388842460678214, 0.08235783609349957, 0.03705278735089285, -0.08683654864249878, 0.15748924418320795, -0.16435493765906853, -0.10905754095239734, 0.4259861640801484, -0.06548886383163997, -0.22555601243353027, 0.15609994011835873, -0.15160069137346, -0.1171810722047336, 0.10252493009267544, 0.1895223390734331, 0.11377634296976877, -0.143673114466682, 0.09768688325196061, 0.026035208564942215, 0.14594967394474556, 0.03674539895357818, 0.035933854487004945, 0.2265704778573391, 0.09460608869134872, 0.08203709447248415, 0.17795136786695698, -0.0303106984118296, -0.08667018042813818, -0.3550055935153399, -0.1425856558225033, -0.1687978073234924, 0.08324259776749056, -0.08179826743947739, -0.06327875121496618, 0.3764788407239724, 0.1271405881918988, 0.12732037775938146, 0.07134151634950699, 0.26068538131022995, 0.25414702829518565, 0.07199815320266433, 0.13280728027034042, 0.29542359831446613, 0.11721245458995161, 0.12652799392394212, -0.34963805484585464, 0.017175724465315314, 0.03204328371000222] |
1,802.06526 | Heron Inference for Bayesian Graphical Models | Bayesian graphical models have been shown to be a powerful tool for
discovering uncertainty and causal structure from real-world data in many
application fields. Current inference methods primarily follow different kinds
of trade-offs between computational complexity and predictive accuracy. At one
end of the spectrum, variational inference approaches perform well in
computational efficiency, while at the other end, Gibbs sampling approaches are
known to be relatively accurate for prediction in practice. In this paper, we
extend an existing Gibbs sampling method, and propose a new deterministic Heron
inference (Heron) for a family of Bayesian graphical models. In addition to the
support for nontrivial distributability, one more benefit of Heron is that it
is able to not only allow us to easily assess the convergence status but also
largely improve the running efficiency. We evaluate Heron against the standard
collapsed Gibbs sampler and state-of-the-art state augmentation method in
inference for well-known graphical models. Experimental results using publicly
available real-life data have demonstrated that Heron significantly outperforms
the baseline methods for inferring Bayesian graphical models.
| cs.LG stat.ML | bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from realworld data in many application fields current inference methods primarily follow different kinds of tradeoffs between computational complexity and predictive accuracy at one end of the spectrum variational inference approaches perform well in computational efficiency while at the other end gibbs sampling approaches are known to be relatively accurate for prediction in practice in this paper we extend an existing gibbs sampling method and propose a new deterministic heron inference heron for a family of bayesian graphical models in addition to the support for nontrivial distributability one more benefit of heron is that it is able to not only allow us to easily assess the convergence status but also largely improve the running efficiency we evaluate heron against the standard collapsed gibbs sampler and stateoftheart state augmentation method in inference for wellknown graphical models experimental results using publicly available reallife data have demonstrated that heron significantly outperforms the baseline methods for inferring bayesian graphical models | [['bayesian', 'graphical', 'models', 'have', 'been', 'shown', 'to', 'be', 'a', 'powerful', 'tool', 'for', 'discovering', 'uncertainty', 'and', 'causal', 'structure', 'from', 'realworld', 'data', 'in', 'many', 'application', 'fields', 'current', 'inference', 'methods', 'primarily', 'follow', 'different', 'kinds', 'of', 'tradeoffs', 'between', 'computational', 'complexity', 'and', 'predictive', 'accuracy', 'at', 'one', 'end', 'of', 'the', 'spectrum', 'variational', 'inference', 'approaches', 'perform', 'well', 'in', 'computational', 'efficiency', 'while', 'at', 'the', 'other', 'end', 'gibbs', 'sampling', 'approaches', 'are', 'known', 'to', 'be', 'relatively', 'accurate', 'for', 'prediction', 'in', 'practice', 'in', 'this', 'paper', 'we', 'extend', 'an', 'existing', 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1,802.06527 | Salient Object Detection by Lossless Feature Reflection | Salient object detection, which aims to identify and locate the most salient
pixels or regions in images, has been attracting more and more interest due to
its various real-world applications. However, this vision task is quite
challenging, especially under complex image scenes. Inspired by the intrinsic
reflection of natural images, in this paper we propose a novel feature learning
framework for large-scale salient object detection. Specifically, we design a
symmetrical fully convolutional network (SFCN) to learn complementary saliency
features under the guidance of lossless feature reflection. The location
information, together with contextual and semantic information, of salient
objects are jointly utilized to supervise the proposed network for more
accurate saliency predictions. In addition, to overcome the blurry boundary
problem, we propose a new structural loss function to learn clear object
boundaries and spatially consistent saliency. The coarse prediction results are
effectively refined by these structural information for performance
improvements. Extensive experiments on seven saliency detection datasets
demonstrate that our approach achieves consistently superior performance and
outperforms the very recent state-of-the-art methods.
| cs.CV | salient object detection which aims to identify and locate the most salient pixels or regions in images has been attracting more and more interest due to its various realworld applications however this vision task is quite challenging especially under complex image scenes inspired by the intrinsic reflection of natural images in this paper we propose a novel feature learning framework for largescale salient object detection specifically we design a symmetrical fully convolutional network sfcn to learn complementary saliency features under the guidance of lossless feature reflection the location information together with contextual and semantic information of salient objects are jointly utilized to supervise the proposed network for more accurate saliency predictions in addition to overcome the blurry boundary problem we propose a new structural loss function to learn clear object boundaries and spatially consistent saliency the coarse prediction results are effectively refined by these structural information for performance improvements extensive experiments on seven saliency detection datasets demonstrate that our approach achieves consistently superior performance and outperforms the very recent stateoftheart methods | [['salient', 'object', 'detection', 'which', 'aims', 'to', 'identify', 'and', 'locate', 'the', 'most', 'salient', 'pixels', 'or', 'regions', 'in', 'images', 'has', 'been', 'attracting', 'more', 'and', 'more', 'interest', 'due', 'to', 'its', 'various', 'realworld', 'applications', 'however', 'this', 'vision', 'task', 'is', 'quite', 'challenging', 'especially', 'under', 'complex', 'image', 'scenes', 'inspired', 'by', 'the', 'intrinsic', 'reflection', 'of', 'natural', 'images', 'in', 'this', 'paper', 'we', 'propose', 'a', 'novel', 'feature', 'learning', 'framework', 'for', 'largescale', 'salient', 'object', 'detection', 'specifically', 'we', 'design', 'a', 'symmetrical', 'fully', 'convolutional', 'network', 'sfcn', 'to', 'learn', 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1,802.06528 | Scaling theory for Mott-Hubbard transitions | We present a $T=0K$ renormalization group (RG) phase diagram for the
electronic Hubbard model in two dimensions on the square lattice at, and away
from, half filling. The RG procedure treats quantum fluctuations in the single
particle occupation number nonperturbatively via the unitarily decoupling of
one electronic state at every RG step. The resulting phase diagram thus possess
the quantum fluctuation energy scale ($\omega$) as one of its axes. A relation
is derived between $\omega$ and the effective temperature scale upto which
gapless, as well as emergent gapped, phases can be obtained. We find that the
transition in the half-filled Hubbard model involves, for any on-site
repulsion, passage from a marginal Fermi liquid to a topologically-ordered
gapped Mott liquid through a pseudogapped phase bookended by Fermi surface
topology-changing Lifshitz transitions. Using effective Hamiltonians and
wavefunctions for the low-energy many-body eigenstates for the doped Mott
liquid obtained from the stable fixed point of the RG flow, we demonstrate the
collapse of the pseudogap for charge excitations (Mottness) at a quantum
critical point possessing a nodal non-Fermi liquid with superconducting
fluctuations, and spin-pseudogapping near the antinodes. d-wave Superconducting
order is shown to arise from this quantum critical state of matter.
Benchmarking of the ground state energy per particle and the double-occupancy
fraction against existing numerical results also yields excellent agreement. We
present detailed insight into the $T=0$ origin of several experimentally
observed findings in the cuprates, including Homes law and Planckian
dissipation. Our results offer insight on the ubiquitous origin of
superconductivity in doped Mott insulating states, and pave the way towards a
systematic search for higher superconducting transition temperatures in such
systems.
| cond-mat.str-el cond-mat.supr-con | we present a t0k renormalization group rg phase diagram for the electronic hubbard model in two dimensions on the square lattice at and away from half filling the rg procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every rg step the resulting phase diagram thus possess the quantum fluctuation energy scale omega as one of its axes a relation is derived between omega and the effective temperature scale upto which gapless as well as emergent gapped phases can be obtained we find that the transition in the halffilled hubbard model involves for any onsite repulsion passage from a marginal fermi liquid to a topologicallyordered gapped mott liquid through a pseudogapped phase bookended by fermi surface topologychanging lifshitz transitions using effective hamiltonians and wavefunctions for the lowenergy manybody eigenstates for the doped mott liquid obtained from the stable fixed point of the rg flow we demonstrate the collapse of the pseudogap for charge excitations mottness at a quantum critical point possessing a nodal nonfermi liquid with superconducting fluctuations and spinpseudogapping near the antinodes dwave superconducting order is shown to arise from this quantum critical state of matter benchmarking of the ground state energy per particle and the doubleoccupancy fraction against existing numerical results also yields excellent agreement we present detailed insight into the t0 origin of several experimentally observed findings in the cuprates including homes law and planckian dissipation our results offer insight on the ubiquitous origin of superconductivity in doped mott insulating states and pave the way towards a systematic search for higher superconducting transition temperatures in such systems | [['we', 'present', 'a', 't0k', 'renormalization', 'group', 'rg', 'phase', 'diagram', 'for', 'the', 'electronic', 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1,802.06529 | Automatic supermartingales acting on sequences | This paper describes a construction of supermartingales realized as automatic
functions. A capital of supermartingales is represented using automatic capital
groups~(ACG). Properties of these automatic supermartingales are then studied.
Automatic supermartingales induce a notion of random infinite binary sequence.
We show that the class of random sequences coincide with that of disjunctive
sequences.
| cs.FL | this paper describes a construction of supermartingales realized as automatic functions a capital of supermartingales is represented using automatic capital groupsacg properties of these automatic supermartingales are then studied automatic supermartingales induce a notion of random infinite binary sequence we show that the class of random sequences coincide with that of disjunctive sequences | [['this', 'paper', 'describes', 'a', 'construction', 'of', 'supermartingales', 'realized', 'as', 'automatic', 'functions', 'a', 'capital', 'of', 'supermartingales', 'is', 'represented', 'using', 'automatic', 'capital', 'groupsacg', 'properties', 'of', 'these', 'automatic', 'supermartingales', 'are', 'then', 'studied', 'automatic', 'supermartingales', 'induce', 'a', 'notion', 'of', 'random', 'infinite', 'binary', 'sequence', 'we', 'show', 'that', 'the', 'class', 'of', 'random', 'sequences', 'coincide', 'with', 'that', 'of', 'disjunctive', 'sequences']] | [-0.12868270629013961, 0.12481803124627242, -0.07419233142326657, 0.12640937929973006, -0.04695369759932733, -0.10867237296994202, 0.06794960765490451, 0.43118456049034226, -0.2887086831391431, -0.19100249064369842, 0.1366792292952036, -0.20977908895852473, -0.17988686686238417, 0.19828620180487633, -0.1734888021601364, 0.07208906947142588, 0.11336732668300661, 0.0325199430450224, -0.04341998172458261, -0.2523480176751036, 0.34112382664058644, -0.02701578654635411, 0.2567997699818359, -0.03569569641079467, 0.15705777301739615, 0.03158251140624858, -0.10822693951642857, 0.07325373160151336, -0.09958583750687047, 0.15532339124295574, 0.2875253888912714, 0.21576099169368929, 0.36602723153415495, -0.34265211292614156, -0.13614274018226963, 0.20033105634726012, 0.06916883119489424, 0.050740632228553295, -0.06545629282481968, -0.2731224726281093, 0.1377347832581458, -0.2266811689142532, -0.08101635340314645, -0.08246941085403356, -0.027236198854202833, 0.13605892988674056, -0.3468847737038651, 0.01434246339620306, 0.17370876705703828, 0.08148136407208557, -0.06390326793413036, -0.10635826554006109, -0.04971499575857216, 0.14759027871052519, 0.018446327272193648, 0.004327354809412589, 0.12480430250378469, -0.0657732977057234, -0.2441842079234238, 0.3129833515267819, -0.08219226071825968, -0.22763744573323771, 0.15485370511977145, -0.07634988588352616, -0.22106724752722165, 0.07093342238714775, 0.1772656933261225, 0.134026955275868, -0.14954794685427958, 0.07327394780273047, -0.11783417450407377, 0.15065700589464262, 0.1261944480580636, 0.07762265218815838, 0.16351751764663136, 0.1711787084887664, 0.04339188530754585, 0.20063533211270204, 0.058836208298229255, -0.06319857711115709, -0.2803964569018437, -0.1532636924088225, -0.17567866467512572, 0.04683455169763944, -0.10111352840725046, -0.3499655465667064, 0.38103309757291126, 0.12967914896300778, 0.12679943150410858, 0.215072934784425, 0.21043856649731213, 0.1321356728328213, 0.0244990319524032, -0.009545186758399583, 0.11370108792415032, 0.0707438698110099, 0.04204089706763625, -0.12481407067165352, 0.15825524757831141, 0.22563814665549076] |
1,802.0653 | Alternative renormalizable minimal SO(10) GUT and the Seesaw Scale | Alternative renormalizable minimal non-SUSY SO(10) GUT model is proposed.
Instead of a ${\bf 126}$-dimensional Higgs field, a ${\bf 120}$-dimensional
Higgs filed is ntroducedin addition to a ${\bf 10}$-dimensional Higgs field and
plays a crucial role to reproduce the realistic charged fermion mass matrices.
With contributions of ${\bf 120}$ Higgs field, the original Witten's scenario
of inducing the right-handed Majorana neutrino mass through 2-loop diagrams
becomes phenomenologically viable. This model inherits the nice features of the
conventional renormalizable minimal SO(10) GUT model with ${\bf 10}+{\bf
\overline{126}}$ Higgs fields, while supplemented with a low scale seesaw
mechanism due to the 2-loop induced right-handed Majorana neutrino mass.
%
| hep-ph | alternative renormalizable minimal nonsusy so10 gut model is proposed instead of a bf 126dimensional higgs field a bf 120dimensional higgs filed is ntroducedin addition to a bf 10dimensional higgs field and plays a crucial role to reproduce the realistic charged fermion mass matrices with contributions of bf 120 higgs field the original wittens scenario of inducing the righthanded majorana neutrino mass through 2loop diagrams becomes phenomenologically viable this model inherits the nice features of the conventional renormalizable minimal so10 gut model with bf 10bf overline126 higgs fields while supplemented with a low scale seesaw mechanism due to the 2loop induced righthanded majorana neutrino mass | [['alternative', 'renormalizable', 'minimal', 'nonsusy', 'so10', 'gut', 'model', 'is', 'proposed', 'instead', 'of', 'a', 'bf', '126dimensional', 'higgs', 'field', 'a', 'bf', '120dimensional', 'higgs', 'filed', 'is', 'ntroducedin', 'addition', 'to', 'a', 'bf', '10dimensional', 'higgs', 'field', 'and', 'plays', 'a', 'crucial', 'role', 'to', 'reproduce', 'the', 'realistic', 'charged', 'fermion', 'mass', 'matrices', 'with', 'contributions', 'of', 'bf', '120', 'higgs', 'field', 'the', 'original', 'wittens', 'scenario', 'of', 'inducing', 'the', 'righthanded', 'majorana', 'neutrino', 'mass', 'through', '2loop', 'diagrams', 'becomes', 'phenomenologically', 'viable', 'this', 'model', 'inherits', 'the', 'nice', 'features', 'of', 'the', 'conventional', 'renormalizable', 'minimal', 'so10', 'gut', 'model', 'with', 'bf', '10bf', 'overline126', 'higgs', 'fields', 'while', 'supplemented', 'with', 'a', 'low', 'scale', 'seesaw', 'mechanism', 'due', 'to', 'the', '2loop', 'induced', 'righthanded', 'majorana', 'neutrino', 'mass']] | [-0.15729653613992256, 0.2936896565554682, 0.02620601691167322, 0.2277925820101403, -0.16220100101609114, -0.25374120970182856, 0.005918468929605909, 0.2682929903840517, -0.12864195072267315, -0.29270187207027387, -0.03659663039563906, -0.18990181659412855, -0.08171045993626784, 0.06372694340119563, -0.015601018960080525, 0.009770091752162074, -0.017808396406102888, -0.01791043778521811, -0.08108830862300526, -0.2851527740597946, 0.2874600935086497, 0.05006375589804484, 0.22156860660946015, 0.049424383936837166, 0.1443713394150433, -0.04077340104607957, 0.007164015937227719, -0.17558515774510283, -0.07872807212395243, 0.06451734593962227, 0.15561752601775644, 0.013824636079739817, 0.07496410036588659, -0.34249142682096817, -0.19304919196869072, 0.18926297135346817, 0.15609421490663938, 0.09874090712545162, -0.08267010478210626, -0.30804893687957585, 0.11722799154957479, -0.25256491692201927, -0.10864639015969738, -0.0885295321695774, -0.07254311006336409, -0.2648390314944024, -0.41978366691031316, 0.11462947725327594, -0.0693111621986096, 0.03486192351815724, 0.040672001083114064, -0.15326398375010727, -0.1295867371050143, -0.05046483893224066, 0.24084412862689666, 0.061789829302394746, 0.17933120765944593, -0.24650683795046616, -0.13129206751196618, 0.4510629392577114, -0.12187004022848894, -0.1600211783528955, 0.1205343856282606, -0.0869600347584427, -0.09279748056047034, 0.1270925361515567, 0.11698128133412856, 0.052627932294421725, -0.16475831172290709, 0.3408634353283272, -0.11451960197364044, 0.12065199087373912, 0.030207934189993558, 0.0018906406182242503, 0.3450199245558222, 0.19358914707139557, 0.027850142965960032, -0.03269188045662376, -0.030759898189565923, -0.10731061765610582, -0.4692360400821608, -0.10313411367743618, -0.0776749976523368, 0.08413302017338943, -0.09884490836212886, -0.1717875743616778, 0.49147711662889115, 0.14411345642004716, 0.22845001112396535, 0.021664511587581422, 0.23161171710736458, 0.042415807798209755, 0.14757881811900656, 0.015092173286962628, 0.2513950326765823, 0.21223448081135676, 0.10636123004000597, -0.2466617155506617, -0.15857804334943765, 0.16030659429074293] |
1,802.06531 | Hardy-type and Heisenberg's inequality in Morrey spaces | We use the Morrey norm estimate for the imaginary power of the Laplacian to
prove an interpolation inequality for the fractional power of the Laplacian on
Morrey spaces. We then prove a Hardy-type inequality and use it together with
the interpolation inequality to obtain a Heisenberg-type inequality in Morrey
spaces.
| math.AP | we use the morrey norm estimate for the imaginary power of the laplacian to prove an interpolation inequality for the fractional power of the laplacian on morrey spaces we then prove a hardytype inequality and use it together with the interpolation inequality to obtain a heisenbergtype inequality in morrey spaces | [['we', 'use', 'the', 'morrey', 'norm', 'estimate', 'for', 'the', 'imaginary', 'power', 'of', 'the', 'laplacian', 'to', 'prove', 'an', 'interpolation', 'inequality', 'for', 'the', 'fractional', 'power', 'of', 'the', 'laplacian', 'on', 'morrey', 'spaces', 'we', 'then', 'prove', 'a', 'hardytype', 'inequality', 'and', 'use', 'it', 'together', 'with', 'the', 'interpolation', 'inequality', 'to', 'obtain', 'a', 'heisenbergtype', 'inequality', 'in', 'morrey', 'spaces']] | [-0.07910859335213899, 0.007868998882186133, -0.1122603929467732, 0.19499315666034817, -0.11965174052864314, -0.12899833051487802, -0.004672475568950177, 0.3208318960666656, -0.36242182940244677, -0.18419433751725592, 0.17538314672885463, -0.33578632444143297, -0.10991531034582294, 0.19862419679760934, -0.152755520157516, 0.06996514902450145, 0.021214667595922946, 0.03429096173495054, -0.10792890187352895, -0.24278724569827317, 0.4143689930438995, -0.08675208732485772, 0.20129035003483295, 0.11411657621152699, 0.06073293939232826, -0.008188702864572406, 0.01320346126332879, -0.07833274230360984, -0.25098048940300943, 0.2687990633584559, 0.2039931258559227, 0.049533601570874455, 0.3770342270284891, -0.391676584854722, -0.16476433968171478, 0.26277095448225735, 0.07043184965848923, -0.10079070430248976, -0.012651452308055013, -0.3468250246345997, -0.0007139471918344497, -0.11128884594887495, -0.18053047522669657, -0.16010853270068764, -0.018155719228088854, 0.10045671053230762, -0.44199057929217817, 0.15322579897940158, 0.07723179995315149, 0.0150617391243577, -0.1906179224140942, -0.09100516945123673, 0.04171312822028995, -0.009626545924693346, -0.011669433610513806, 0.02546262544579804, 0.023143290411680936, -0.01670324683189392, -0.12547450159676374, 0.29482093967497347, -0.01875830575823784, -0.31268653690814974, -0.037746752575039864, -0.1905313693359494, -0.15396359557285905, -0.11051309831440449, 0.1439291723817587, 0.10277103312022519, -0.05496277313679457, 0.1686941841605585, -0.04805405791848898, 0.11360972052440048, 0.11463214121758938, 0.10561811238527298, -0.06281257286667824, 0.025753262899816037, 0.3050371325016022, 0.19562169425189496, -0.03576003939379006, -0.08217654668493196, -0.3549890960380435, -0.254924627407454, -0.2836799740046263, 0.11447860013693571, -0.25553220615693134, -0.18128443593159319, 0.30836102813482286, 0.056679063122719524, 0.15259866954758763, 0.19176768559962512, 0.22033908717334272, 0.15797510689124464, 0.062270428836345676, 0.05135817316360772, 0.23718559369444847, 0.2713853728398681, 0.18186181927099823, -0.12983599015453365, -0.04255924394354224, 0.31025619177147745] |
1,802.06532 | Discrepancy Analysis of a New Randomized Diffusion Algorithm | For an arbitrary initial configuration of discrete loads over vertices of a
distributed graph, we consider the problem of minimizing the {\em discrepancy}
between the maximum and minimum loads among all vertices. For this problem,
this paper is concerned with the ability of natural diffusion-based iterative
algorithms: at each discrete and synchronous time step on an algorithm, each
vertex is allowed to distribute its loads to each neighbor (including itself)
without occurring negative loads or using the information of previous time
steps.
In this setting, this paper presents a new {\em randomized} diffusion
algorithm like multiple random walks. Our algorithm archives $O(\sqrt{d \log
N})$ discrepancy for any $d$-regular graph with $N$ vertices with high
probability, while {\em deterministic} diffusion algorithms have $\Omega(d)$
lower bound. Furthermore, we succeed in generalizing our algorithm to any
symmetric round matrix. This yields that $O(\sqrt{ d_{\max} \log N})$
discrepancy for arbitrary graphs without using the information of maximum
degree $d_{\max}$.
| cs.DS cs.DC | for an arbitrary initial configuration of discrete loads over vertices of a distributed graph we consider the problem of minimizing the em discrepancy between the maximum and minimum loads among all vertices for this problem this paper is concerned with the ability of natural diffusionbased iterative algorithms at each discrete and synchronous time step on an algorithm each vertex is allowed to distribute its loads to each neighbor including itself without occurring negative loads or using the information of previous time steps in this setting this paper presents a new em randomized diffusion algorithm like multiple random walks our algorithm archives osqrtd log n discrepancy for any dregular graph with n vertices with high probability while em deterministic diffusion algorithms have omegad lower bound furthermore we succeed in generalizing our algorithm to any symmetric round matrix this yields that osqrt d_max log n discrepancy for arbitrary graphs without using the information of maximum degree d_max | [['for', 'an', 'arbitrary', 'initial', 'configuration', 'of', 'discrete', 'loads', 'over', 'vertices', 'of', 'a', 'distributed', 'graph', 'we', 'consider', 'the', 'problem', 'of', 'minimizing', 'the', 'em', 'discrepancy', 'between', 'the', 'maximum', 'and', 'minimum', 'loads', 'among', 'all', 'vertices', 'for', 'this', 'problem', 'this', 'paper', 'is', 'concerned', 'with', 'the', 'ability', 'of', 'natural', 'diffusionbased', 'iterative', 'algorithms', 'at', 'each', 'discrete', 'and', 'synchronous', 'time', 'step', 'on', 'an', 'algorithm', 'each', 'vertex', 'is', 'allowed', 'to', 'distribute', 'its', 'loads', 'to', 'each', 'neighbor', 'including', 'itself', 'without', 'occurring', 'negative', 'loads', 'or', 'using', 'the', 'information', 'of', 'previous', 'time', 'steps', 'in', 'this', 'setting', 'this', 'paper', 'presents', 'a', 'new', 'em', 'randomized', 'diffusion', 'algorithm', 'like', 'multiple', 'random', 'walks', 'our', 'algorithm', 'archives', 'osqrtd', 'log', 'n', 'discrepancy', 'for', 'any', 'dregular', 'graph', 'with', 'n', 'vertices', 'with', 'high', 'probability', 'while', 'em', 'deterministic', 'diffusion', 'algorithms', 'have', 'omegad', 'lower', 'bound', 'furthermore', 'we', 'succeed', 'in', 'generalizing', 'our', 'algorithm', 'to', 'any', 'symmetric', 'round', 'matrix', 'this', 'yields', 'that', 'osqrt', 'd_max', 'log', 'n', 'discrepancy', 'for', 'arbitrary', 'graphs', 'without', 'using', 'the', 'information', 'of', 'maximum', 'degree', 'd_max']] | [-0.15499816432054486, 0.10645342217626862, -0.02514452292854267, 0.009121746279209132, -0.08194166453435056, -0.20357337201374673, 0.1186356023855267, 0.4029487004007904, -0.2768274439228398, -0.345868094175333, 0.06618939838447277, -0.28407110568556576, -0.130007929624539, 0.10751417709304201, -0.0886289054678092, 0.09002359266986229, 0.08277659987309767, 0.08639513496609945, -0.002598022330071657, -0.30417285804193644, 0.2696360688874378, 0.04156607749661611, 0.22179497245308613, 0.0026306855161824533, 0.13097522342878004, 0.05714127791805133, -0.011599829216157237, 0.0396256746228544, -0.1233335305542794, 0.10772290506490297, 0.24819436025234962, 0.1696908570435499, 0.3058842034349518, -0.43291148930307355, -0.17131232994218026, 0.2293705180918257, 0.131015491703405, 0.10620052846779506, 0.0007295469727156864, -0.19231432127135414, 0.11566750012608545, -0.10116974032388235, -0.07262019958692573, 0.029997130986603518, 0.0436385182603713, 0.019415749284634066, -0.3308932618868928, 0.030551854875539578, 0.07800052647418793, 0.018268645985893183, 0.02386568941461343, -0.15581528767342528, 0.05436851258179353, 0.12419567696089226, -0.02974960702516499, 0.0734895135200913, 0.05125499069540491, -0.06066855532117188, -0.18379366296313462, 0.34623018812027667, -0.03968975160331015, -0.1835680082132439, 0.1126349066579414, -0.07473552523841781, -0.17457967690762974, 0.12904503037852624, 0.19436532056199446, 0.1749301973835475, -0.12276339936971424, 0.10674924597429532, -0.05544414230652394, 0.14237790432938885, 0.09598877300778705, 0.008061468962865371, 0.07861730378391521, 0.13399456479857044, 0.19354163602805666, 0.15315672073873782, -0.03323940279623193, -0.08157260600898054, -0.27254429748469605, -0.14107248814844137, -0.25269032818370407, 0.02243777002628532, -0.21407797993179561, -0.1718178085862629, 0.35791820008307695, 0.1387862689432598, 0.24753369083027205, 0.1710915689266497, 0.33139210788593176, 0.0839314226166255, -0.0024317566575782915, 0.21059882277622818, 0.10023575046460234, 0.08404737350440794, 0.0680416084773418, -0.21361386982663985, 0.12226266874330899, 0.10464328035652157] |
1,802.06533 | Arc spaces and chiral symplectic cores | We introduce the notion of chiral symplectic cores in a vertex Poisson
variety, which can be viewed as analogs of symplectic leaves in Poisson
varieties. As an application we show that any quasi-lisse vertex algebra is a
quantization of the arc space of its associated variety, in the sense that its
reduced singular support coincides with the reduced arc space of its associated
variety. We also show that the coordinate ring of the arc space of Slodowy
slices is free over its vertex Poisson center, and the latter coincides with
the vertex Poisson center of the coordinate ring of the arc space of the dual
of the corresponding simple Lie algebra.
| math.RT math.AG | we introduce the notion of chiral symplectic cores in a vertex poisson variety which can be viewed as analogs of symplectic leaves in poisson varieties as an application we show that any quasilisse vertex algebra is a quantization of the arc space of its associated variety in the sense that its reduced singular support coincides with the reduced arc space of its associated variety we also show that the coordinate ring of the arc space of slodowy slices is free over its vertex poisson center and the latter coincides with the vertex poisson center of the coordinate ring of the arc space of the dual of the corresponding simple lie algebra | [['we', 'introduce', 'the', 'notion', 'of', 'chiral', 'symplectic', 'cores', 'in', 'a', 'vertex', 'poisson', 'variety', 'which', 'can', 'be', 'viewed', 'as', 'analogs', 'of', 'symplectic', 'leaves', 'in', 'poisson', 'varieties', 'as', 'an', 'application', 'we', 'show', 'that', 'any', 'quasilisse', 'vertex', 'algebra', 'is', 'a', 'quantization', 'of', 'the', 'arc', 'space', 'of', 'its', 'associated', 'variety', 'in', 'the', 'sense', 'that', 'its', 'reduced', 'singular', 'support', 'coincides', 'with', 'the', 'reduced', 'arc', 'space', 'of', 'its', 'associated', 'variety', 'we', 'also', 'show', 'that', 'the', 'coordinate', 'ring', 'of', 'the', 'arc', 'space', 'of', 'slodowy', 'slices', 'is', 'free', 'over', 'its', 'vertex', 'poisson', 'center', 'and', 'the', 'latter', 'coincides', 'with', 'the', 'vertex', 'poisson', 'center', 'of', 'the', 'coordinate', 'ring', 'of', 'the', 'arc', 'space', 'of', 'the', 'dual', 'of', 'the', 'corresponding', 'simple', 'lie', 'algebra']] | [-0.1723530662774637, 0.057150544229656805, -0.07667651467511917, 0.008753630334746328, -0.12131589555038928, -0.07548497753167474, -0.017685911853101338, 0.3633817470556981, -0.3592771318749533, -0.1652592579657967, 0.10431758403727734, -0.21046099924222306, -0.16073304432368762, 0.17179153012195686, -0.13044549287338783, -0.05119857743072013, 0.0774411996784578, 0.16091763669926976, -0.14183980032071672, -0.2501278616601249, 0.41616342488575625, 0.04952385715368363, 0.22702894697536355, -0.013858037488954561, 0.1784929873354666, 0.04236746576052528, -0.01805795083107712, 0.06310341567082146, -0.097065286395108, 0.11713981210581355, 0.23352352166883983, 0.08302607249703493, 0.19182131362256702, -0.36990391527646566, -0.14468938541841936, 0.141723924777932, 0.13456893142581255, 0.029894974201221253, 0.005580333850203871, -0.25568272096213995, 0.12798253487929837, -0.21926748161078305, -0.2244496279005968, -0.005080109772582849, 0.02490529797232903, 0.023989666035180695, -0.17854708828334068, -0.006055177258891851, 0.09056412679487252, 0.059520118836279924, -0.07332967957985159, -0.08497801895446337, -0.11240279835833421, 0.06502928335622356, -0.0730217238846193, 0.08823190172211276, 0.15270838654088276, -0.11306628092351528, -0.1663653770438605, 0.4150746862198486, -0.029910457493561145, -0.2148165680249935, 0.15736421977111079, -0.18628669398845182, -0.13406066417794776, 0.15249172318726778, 0.0755000380161512, 0.09375888134378034, -0.04216235474188317, 0.21102528314280264, -0.12090224398065123, -0.009168546601735593, 0.09002613075715196, 0.021402167794000997, 0.1752375792019774, 0.11297212927476377, 0.15552842291543964, 0.1495602677884587, -0.08678465394559107, -0.09554713667026377, -0.38484802323200545, -0.20524481178244558, -0.16181627730629197, 0.08714107247824604, -0.1516653578769078, -0.1994232164007855, 0.41049744133409616, 0.05716311332123639, 0.2631906967710804, 0.047843458954253244, 0.19188860205509742, 0.13904379334862907, 0.1096727611111091, 0.05911034054483648, 0.0980087217816093, 0.18637076410808945, -0.0026109743378804743, -0.21425915982884666, -0.03228219099728777, 0.13379582473253077] |
1,802.06534 | A Simple and Effective Solution to the Constrained QM/MM Simulations | It is a promising extension of the quantum mechanical/molecular mechanical
(QM/MM) approach to incorporate the solvent molecules surrounding the QM solute
into the QM region to ensure the adequate description of the electronic
polarization of the solute. However, the solvent molecules in the QM region
inevitably diffuse into the MM bulk during the QM/MM simulation. In this
article we developed a simple and efficient method, referred to as boundary
constraint with correction (BCC), to prevent the diffusion of the solvent water
molecules by means of a constraint po- tential. The point of the BCC method is
to compensate the error in a statistical property due to the bias potential by
adding a correction term obtained through a set of QM/MM simulations. The BCC
method is designed so that the effect of the bias potential completely vanishes
when the QM solvent is identical with the MM solvent. Furthermore, the
desirable conditions, that is, the continuities of energy and force and the
conservations of energy and momentum, are fulfilled in principle. We applied
the QM/MM-BCC method to a hydronium ion in aqueous solution to construct the
radial distribution function(RDF) of the solvent around the solute. It was
demonstrated that the correction term fairly compensated the error and led the
RDF in good agreement with the result given by an ab initio molecular dynamics
simulation.
| cond-mat.soft physics.chem-ph | it is a promising extension of the quantum mechanicalmolecular mechanical qmmm approach to incorporate the solvent molecules surrounding the qm solute into the qm region to ensure the adequate description of the electronic polarization of the solute however the solvent molecules in the qm region inevitably diffuse into the mm bulk during the qmmm simulation in this article we developed a simple and efficient method referred to as boundary constraint with correction bcc to prevent the diffusion of the solvent water molecules by means of a constraint po tential the point of the bcc method is to compensate the error in a statistical property due to the bias potential by adding a correction term obtained through a set of qmmm simulations the bcc method is designed so that the effect of the bias potential completely vanishes when the qm solvent is identical with the mm solvent furthermore the desirable conditions that is the continuities of energy and force and the conservations of energy and momentum are fulfilled in principle we applied the qmmmbcc method to a hydronium ion in aqueous solution to construct the radial distribution functionrdf of the solvent around the solute it was demonstrated that the correction term fairly compensated the error and led the rdf in good agreement with the result given by an ab initio molecular dynamics simulation | [['it', 'is', 'a', 'promising', 'extension', 'of', 'the', 'quantum', 'mechanicalmolecular', 'mechanical', 'qmmm', 'approach', 'to', 'incorporate', 'the', 'solvent', 'molecules', 'surrounding', 'the', 'qm', 'solute', 'into', 'the', 'qm', 'region', 'to', 'ensure', 'the', 'adequate', 'description', 'of', 'the', 'electronic', 'polarization', 'of', 'the', 'solute', 'however', 'the', 'solvent', 'molecules', 'in', 'the', 'qm', 'region', 'inevitably', 'diffuse', 'into', 'the', 'mm', 'bulk', 'during', 'the', 'qmmm', 'simulation', 'in', 'this', 'article', 'we', 'developed', 'a', 'simple', 'and', 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1,802.06535 | The long-period massive binary HD~54662 revisited | HD54662 is an O-type binary star belonging to the CMa OB1 association. Due to
its long-period orbit, this system is an interesting target to test the
adiabatic wind shock model. The goal is to improve our knowledge of the orbital
and stellar parameters of HD54662 and to analyze its X-ray emission to test the
theoretical scaling of the X-ray emission with orbital separation for adiabatic
wind shocks. We applied a spectral disentangling code to optical spectra to
determine the radial velocities and the individual spectra of each star. The
individual spectra were analyzed using the CMFGEN model atmosphere code. We
fitted two X-ray spectra using a Markov Chain Monte Carlo algorithm and
compared them to the emission expected from adiabatic shocks. We determine an
orbital period of 2103.4days, a low orbital eccentricity of 0.11, and a mass
ratio m2/m1=0.84. Combined with the orbital inclination inferred in a previous
astrometric study, we obtain surprisingly low masses of 9.7 and 8.2Msun. From
the individual spectra, we infer O6.5 spectral types for both stars and a
brightness ratio of l1/l2~2. The softness of the X-ray spectra, the very small
variation of spectral parameters, and the comparison of the X-ray-to-bolometric
luminosity ratio with the canonical value for O-type stars allow us to conclude
that X-ray emission from the wind interaction region is quite low. We cannot
confirm the runaway status previously attributed to HD54662 and we find no
X-ray emission associated with the bow shock detected in the infrared. The lack
of hard X-ray emission from the wind-shock region suggests that the mass-loss
rates are lower than expected and/or that the pre-shock wind velocities are
much lower than the terminal wind velocities. The bow shock associated with
HD54662 possibly corresponds to a wind-blown arc created by the interaction of
the stellar winds with the ionized gas of CMa OB1. (abridged)
| astro-ph.SR | hd54662 is an otype binary star belonging to the cma ob1 association due to its longperiod orbit this system is an interesting target to test the adiabatic wind shock model the goal is to improve our knowledge of the orbital and stellar parameters of hd54662 and to analyze its xray emission to test the theoretical scaling of the xray emission with orbital separation for adiabatic wind shocks we applied a spectral disentangling code to optical spectra to determine the radial velocities and the individual spectra of each star the individual spectra were analyzed using the cmfgen model atmosphere code we fitted two xray spectra using a markov chain monte carlo algorithm and compared them to the emission expected from adiabatic shocks we determine an orbital period of 21034days a low orbital eccentricity of 011 and a mass ratio m2m1084 combined with the orbital inclination inferred in a previous astrometric study we obtain surprisingly low masses of 97 and 82msun from the individual spectra we infer o65 spectral types for both stars and a brightness ratio of l1l22 the softness of the xray spectra the very small variation of spectral parameters and the comparison of the xraytobolometric luminosity ratio with the canonical value for otype stars allow us to conclude that xray emission from the wind interaction region is quite low we cannot confirm the runaway status previously attributed to hd54662 and we find no xray emission associated with the bow shock detected in the infrared the lack of hard xray emission from the windshock region suggests that the massloss rates are lower than expected andor that the preshock wind velocities are much lower than the terminal wind velocities the bow shock associated with hd54662 possibly corresponds to a windblown arc created by the interaction of the stellar winds with the ionized gas of cma ob1 abridged | [['hd54662', 'is', 'an', 'otype', 'binary', 'star', 'belonging', 'to', 'the', 'cma', 'ob1', 'association', 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1,802.06536 | Ferromagnetic Peierls insulator state in
$\mathit{A}$Mg$_4$Mn$_6$O$_{15}$ ($\mathit{A}$ = K, Rb, Cs) | Using the density-functional-theory based electronic structure calculations,
we study the electronic state of recently discovered mixed-valent manganese
oxides $A$Mg$_4$Mn$_6$O$_{15}$ ($A=$ K, Rb, Cs), which are fully spin-polarized
ferromagnetic insulators with a cubic crystal structure. We show that the
system may be described as a three-dimensional arrangement of the
one-dimensional chains of a $2p$ orbital of O and a $3d$ orbital of Mn running
along the three axes of the cubic lattice. We thereby argue that in the ground
state the chains are fully spin polarized due to the double-exchange mechanism
and are distorted by the Peierls mechanism to make the system insulating.
| cond-mat.str-el cond-mat.mtrl-sci | using the densityfunctionaltheory based electronic structure calculations we study the electronic state of recently discovered mixedvalent manganese oxides amg_4mn_6o_15 a k rb cs which are fully spinpolarized ferromagnetic insulators with a cubic crystal structure we show that the system may be described as a threedimensional arrangement of the onedimensional chains of a 2p orbital of o and a 3d orbital of mn running along the three axes of the cubic lattice we thereby argue that in the ground state the chains are fully spin polarized due to the doubleexchange mechanism and are distorted by the peierls mechanism to make the system insulating | [['using', 'the', 'densityfunctionaltheory', 'based', 'electronic', 'structure', 'calculations', 'we', 'study', 'the', 'electronic', 'state', 'of', 'recently', 'discovered', 'mixedvalent', 'manganese', 'oxides', 'amg_4mn_6o_15', 'a', 'k', 'rb', 'cs', 'which', 'are', 'fully', 'spinpolarized', 'ferromagnetic', 'insulators', 'with', 'a', 'cubic', 'crystal', 'structure', 'we', 'show', 'that', 'the', 'system', 'may', 'be', 'described', 'as', 'a', 'threedimensional', 'arrangement', 'of', 'the', 'onedimensional', 'chains', 'of', 'a', '2p', 'orbital', 'of', 'o', 'and', 'a', '3d', 'orbital', 'of', 'mn', 'running', 'along', 'the', 'three', 'axes', 'of', 'the', 'cubic', 'lattice', 'we', 'thereby', 'argue', 'that', 'in', 'the', 'ground', 'state', 'the', 'chains', 'are', 'fully', 'spin', 'polarized', 'due', 'to', 'the', 'doubleexchange', 'mechanism', 'and', 'are', 'distorted', 'by', 'the', 'peierls', 'mechanism', 'to', 'make', 'the', 'system', 'insulating']] | [-0.1961436604500038, 0.1763544498048354, -0.008518354487743709, 0.0012937221620785127, -0.02746721654484915, -0.13727270088407514, 0.08206106643054155, 0.43656143542416026, -0.28203028857265366, -0.2576938535796829, 0.02769289015317428, -0.306329482548529, -0.13743614883042207, 0.1081819914461178, 0.10433713035049415, 0.0027811471649473256, 0.01642500179460143, -0.05608591831538199, -0.1439105389538304, -0.2252259159571316, 0.2967064483736706, 0.004520265141151624, 0.25731932497260596, 0.028539190686649025, 0.022028211126159325, 0.009701628486930144, 0.1619592228129801, 0.018915026494772127, -0.12478134725868154, 0.15145475213821646, 0.21107509906293068, -0.07049245042449767, 0.1564320132256218, -0.48281635959992314, -0.20682677263301788, -0.025870723262576775, 0.10035325232247758, 0.2063786081524824, -0.0658603239975095, -0.3020459562908895, 0.07949521643395471, -0.1834454041868817, -0.13329675277731945, -0.12474264552134394, -0.043330718325174385, 0.019793562920727203, -0.22031331308172222, 0.044424611536813624, 0.1006367177089289, 0.08066141984526629, -0.12592016940586048, -0.13381696111144553, -0.14649966095417444, 0.025483715560029048, -0.008982411087813353, 0.05568452625268019, 0.08062321750797552, -0.061844387302626994, -0.14903572484813998, 0.4187179617768172, -0.04331001251622444, -0.11321455890792284, 0.16355994102397547, -0.17666342215944486, -0.09271448579072805, 0.17657069312316356, 0.10434536277120564, 0.11963673796744483, -0.13765149819549394, 0.1157244038895622, -0.04739547371956529, 0.20097752450475478, -0.030459258811419258, 0.062165646887577995, 0.2509553631546326, 0.17042949485896838, 0.006209086682094206, 0.14474303804517788, -0.13417841761492857, -0.0848262325888223, -0.1665684686475756, -0.22298748349531158, -0.23500484442061717, 0.048597712498527054, -0.024354289604828112, -0.19835207662037987, 0.40469527837479174, 0.09002073600745326, 0.19266800281803798, -0.1076627808178102, 0.21210154308245913, 0.06308839967045564, 0.04201244119333454, 0.0184936617918331, 0.22925528111212914, 0.17460519049344309, 0.07279921893150278, -0.3033975608241145, 0.07850512414986249, 0.07338485875083964] |
1,802.06537 | Average Behavior of Minimal Free Resolutions of Monomial Ideals | We describe the typical homological properties of monomial ideals defined by
random generating sets. We show that, under mild assumptions, random monomial
ideals (RMI's) will almost always have resolutions of maximal length; that is,
the projective dimension will almost always be $n$, where $n$ is the number of
variables in the polynomial ring. We give a rigorous proof that
Cohen-Macaulayness is a "rare" property. We characterize when an RMI is
generic/strongly generic, and when it "is Scarf"---in other words, when the
algebraic Scarf complex of $M\subset S=k[x_1,\ldots,x_n]$ gives a minimal free
resolution of $S/M$. As a result we see that, outside of a very specific ratio
of model parameters, RMI's are Scarf only when they are generic. We end with a
discussion of the average magnitude of Betti numbers.
| math.AC math.CO math.PR | we describe the typical homological properties of monomial ideals defined by random generating sets we show that under mild assumptions random monomial ideals rmis will almost always have resolutions of maximal length that is the projective dimension will almost always be n where n is the number of variables in the polynomial ring we give a rigorous proof that cohenmacaulayness is a rare property we characterize when an rmi is genericstrongly generic and when it is scarfin other words when the algebraic scarf complex of msubset skx_1ldotsx_n gives a minimal free resolution of sm as a result we see that outside of a very specific ratio of model parameters rmis are scarf only when they are generic we end with a discussion of the average magnitude of betti numbers | [['we', 'describe', 'the', 'typical', 'homological', 'properties', 'of', 'monomial', 'ideals', 'defined', 'by', 'random', 'generating', 'sets', 'we', 'show', 'that', 'under', 'mild', 'assumptions', 'random', 'monomial', 'ideals', 'rmis', 'will', 'almost', 'always', 'have', 'resolutions', 'of', 'maximal', 'length', 'that', 'is', 'the', 'projective', 'dimension', 'will', 'almost', 'always', 'be', 'n', 'where', 'n', 'is', 'the', 'number', 'of', 'variables', 'in', 'the', 'polynomial', 'ring', 'we', 'give', 'a', 'rigorous', 'proof', 'that', 'cohenmacaulayness', 'is', 'a', 'rare', 'property', 'we', 'characterize', 'when', 'an', 'rmi', 'is', 'genericstrongly', 'generic', 'and', 'when', 'it', 'is', 'scarfin', 'other', 'words', 'when', 'the', 'algebraic', 'scarf', 'complex', 'of', 'msubset', 'skx_1ldotsx_n', 'gives', 'a', 'minimal', 'free', 'resolution', 'of', 'sm', 'as', 'a', 'result', 'we', 'see', 'that', 'outside', 'of', 'a', 'very', 'specific', 'ratio', 'of', 'model', 'parameters', 'rmis', 'are', 'scarf', 'only', 'when', 'they', 'are', 'generic', 'we', 'end', 'with', 'a', 'discussion', 'of', 'the', 'average', 'magnitude', 'of', 'betti', 'numbers']] | [-0.18651196060658204, 0.13996206344699755, -0.06810738031539744, 0.06837536064691578, -0.0749086365910379, -0.19325153439445056, -0.03442827070967888, 0.35520571362095205, -0.3030641985338504, -0.20190028688232378, 0.11040178986585251, -0.25911674533391327, -0.13663923464656816, 0.2023882956567631, -0.12203589923621162, -0.01626717714284818, 0.0725028936798853, 0.09597262865533744, -0.06818376483916357, -0.3394877631510571, 0.347967345084203, 0.024112664075113657, 0.20030663048071184, 0.03189480604602053, 0.08812394024488905, -0.014623635111185978, -0.0019115237555811255, 0.05121205939258647, -0.16759139296940645, 0.07789565807604414, 0.25441857647356086, 0.15044684744968012, 0.2293138515321523, -0.3693473481419166, -0.1117636468518144, 0.2045035890090888, 0.13755031383603694, 0.06390858697590389, 0.002451089219974838, -0.17426067214517846, 0.16648100189292642, -0.14777686914766397, -0.2048785604030539, -0.09450913070404066, 0.06541490912672103, 0.05565537127673509, -0.30110946407460965, -0.005621096174283994, 0.11466991402370137, 0.14729690732889053, 0.01589005536905776, -0.08786202538446854, -0.03175302301936849, 0.03422426254539861, -0.0013125886669470453, -0.015554721635861659, 0.08244936532656273, -0.12782640101967424, -0.0916615128452985, 0.370206811747653, -0.045133678259980665, -0.24257344318788468, 0.15858218825502893, -0.1793029142734338, -0.13030216511323825, 0.11087552297449722, 0.06356789081496751, 0.13086002333617702, -0.07766958024200624, 0.16607973692429023, -0.15669123316550349, 0.140457818266756, 0.09728830639734923, 0.0563987177122003, 0.13044263583087312, 0.11866446984675164, 0.10861153442868193, 0.14213096951711995, -0.01566098595962046, -0.03755318647888526, -0.34775720589508224, -0.17316756539750755, -0.1651795638228334, 0.12872911474161494, -0.13208526769260176, -0.19148703248012722, 0.40383673472491305, 0.1181253721245691, 0.20643332253730906, 0.11492506083555695, 0.2620870022792516, 0.07997086675613972, 0.03413129736867359, 0.05911324576357394, 0.15357061142219217, 0.12662337971282903, -0.006588421959987306, -0.10858144664652938, 0.04847892964860116, 0.13947276059743458] |
1,802.06538 | Link Selection for Secure Cooperative Networks with Buffer-Aided
Relaying | This paper investigates the secure communication in a two-hop cooperative
wireless network, where a buffer-aided relay is utilized to forward data from
the source to destination, and a passive eavesdropper attempts to intercept
data transmission from both the source and relay. Depending on the availability
of instantaneous channel state information of the source, two cases of
transmission mechanisms, i.e., adaptive-rate transmission and fixed-rate
transmission are considered. To enhance the security of the system, novel link
selection policies are proposed for both cases to select source-to-relay,
relay-to-destination, or no link transmission based on the channels qualities.
Closed-form expressions are derived for the end-to-end secrecy outage
probability (SOP), secrecy outage capacity (SOC), and exact secrecy throughput
(EST), respectively. Furthermore, we prove the condition that EST reaches its
maximum, and explore how to minimize the SOP and maximize the SOC by optimizing
the link selection parameters. Finally, simulations are conducted to
demonstrate the validity of our theoretical performance evaluation, and
extensive numerical results are provided to illustrate the efficiency of the
proposed link selection polices for the secure communication in two-hop
cooperative networks.
| cs.IT math.IT | this paper investigates the secure communication in a twohop cooperative wireless network where a bufferaided relay is utilized to forward data from the source to destination and a passive eavesdropper attempts to intercept data transmission from both the source and relay depending on the availability of instantaneous channel state information of the source two cases of transmission mechanisms ie adaptiverate transmission and fixedrate transmission are considered to enhance the security of the system novel link selection policies are proposed for both cases to select sourcetorelay relaytodestination or no link transmission based on the channels qualities closedform expressions are derived for the endtoend secrecy outage probability sop secrecy outage capacity soc and exact secrecy throughput est respectively furthermore we prove the condition that est reaches its maximum and explore how to minimize the sop and maximize the soc by optimizing the link selection parameters finally simulations are conducted to demonstrate the validity of our theoretical performance evaluation and extensive numerical results are provided to illustrate the efficiency of the proposed link selection polices for the secure communication in twohop cooperative networks | [['this', 'paper', 'investigates', 'the', 'secure', 'communication', 'in', 'a', 'twohop', 'cooperative', 'wireless', 'network', 'where', 'a', 'bufferaided', 'relay', 'is', 'utilized', 'to', 'forward', 'data', 'from', 'the', 'source', 'to', 'destination', 'and', 'a', 'passive', 'eavesdropper', 'attempts', 'to', 'intercept', 'data', 'transmission', 'from', 'both', 'the', 'source', 'and', 'relay', 'depending', 'on', 'the', 'availability', 'of', 'instantaneous', 'channel', 'state', 'information', 'of', 'the', 'source', 'two', 'cases', 'of', 'transmission', 'mechanisms', 'ie', 'adaptiverate', 'transmission', 'and', 'fixedrate', 'transmission', 'are', 'considered', 'to', 'enhance', 'the', 'security', 'of', 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1,802.06539 | Existence of cocompact lattices in Lie groups with a bi-invariant metric
of index 2 | We study the existence of cocompact lattices in Lie groups with bi-invariant
metric of signature $(2,n-2)$. We assume in addition that the Lie groups under
consideration are simply-connected, indecomposable and solvable. Then their
centre is one- or two-dimensional. In both cases, a parametrisation of the set
of such Lie groups is known. We give a necessary and sufficient condition for
the existence of a lattice in terms of these parameters. For groups with
one-dimensional centre this problem is related to Salem numbers.
| math.DG | we study the existence of cocompact lattices in lie groups with biinvariant metric of signature 2n2 we assume in addition that the lie groups under consideration are simplyconnected indecomposable and solvable then their centre is one or twodimensional in both cases a parametrisation of the set of such lie groups is known we give a necessary and sufficient condition for the existence of a lattice in terms of these parameters for groups with onedimensional centre this problem is related to salem numbers | [['we', 'study', 'the', 'existence', 'of', 'cocompact', 'lattices', 'in', 'lie', 'groups', 'with', 'biinvariant', 'metric', 'of', 'signature', '2n2', 'we', 'assume', 'in', 'addition', 'that', 'the', 'lie', 'groups', 'under', 'consideration', 'are', 'simplyconnected', 'indecomposable', 'and', 'solvable', 'then', 'their', 'centre', 'is', 'one', 'or', 'twodimensional', 'in', 'both', 'cases', 'a', 'parametrisation', 'of', 'the', 'set', 'of', 'such', 'lie', 'groups', 'is', 'known', 'we', 'give', 'a', 'necessary', 'and', 'sufficient', 'condition', 'for', 'the', 'existence', 'of', 'a', 'lattice', 'in', 'terms', 'of', 'these', 'parameters', 'for', 'groups', 'with', 'onedimensional', 'centre', 'this', 'problem', 'is', 'related', 'to', 'salem', 'numbers']] | [-0.1987193492014052, 0.10551796697659373, -0.05396841853720749, 0.0649919286852975, -0.11771070993528134, -0.11219023456001972, 0.020632539537917004, 0.41957837602169046, -0.2613108304226998, -0.24420782286537493, 0.16391470282702003, -0.2257410717482832, -0.1528100998647704, 0.19770259516052446, -0.07934701158210816, -0.03790688281310949, 0.04052076464314468, 0.1283562211774108, -0.0745179327857885, -0.2972542007976189, 0.4051130398108465, -0.04677622710218335, 0.21917669235433385, 0.05267314934498267, 0.09378301091605752, -0.01342442930426176, 0.013383480842316114, 0.0024945874140651476, -0.1663633733765093, 0.1037873655725157, 0.2728932634359453, 0.04456872741759914, 0.207416031839008, -0.34950754373822723, -0.16862455040511742, 0.2251799759673659, 0.11550157369546048, 0.06375405701195322, -0.059978811689311774, -0.2584865795584714, 0.10616979253955366, -0.14234040199392817, -0.18524206666525725, -0.04970659266748443, 0.05524444661284911, 0.016533839104628963, -0.21403274560210908, 0.08507566013168998, 0.09295555509672296, 0.10951772574476419, -0.11895919929076804, -0.08326190656687064, -0.013181223230232008, 0.13233022942355402, -0.030782816008800958, -0.029993667832303155, 0.06812767565772845, -0.075506201158732, -0.12880183431524328, 0.4845492846627788, -0.023269309327233492, -0.26186187965113944, 0.210540269955811, -0.18963586240325395, -0.20555118224356414, 0.09018442561145781, 0.13125780208899482, 0.12874119354003086, -0.07627650466179703, 0.1491780357716446, -0.14423125475735926, 0.0520711082524319, 0.06868433667823853, 0.007823972536886974, 0.14952779244404377, 0.12124209836829544, 0.12427096992160375, 0.15229167382619002, 0.03367362174818792, -0.0029004630916638343, -0.3729347497133947, -0.16252598101443544, -0.12193504644262536, 0.10340934838509051, -0.08573828414955642, -0.16896456311933877, 0.38991557540962607, 0.06840515999327891, 0.17334096996885975, 0.09612556891061547, 0.16379523917850924, 0.06208854506630593, 0.0607963094413962, 0.07855876199844317, 0.13659118553169253, 0.21636493115191824, -0.08249265787748211, -0.14230221370235085, -0.0600865762623981, 0.14158264172218013] |
1,802.0654 | Generalized perspective on chiral measurements without magnetic
interactions | We present a unified description of several methods of chiral discrimination
based exclusively on electric-dipole interactions. It includes photoelectron
circular dichroism (PECD), enantio-sensitive microwave spectroscopy (EMWS),
photoexcitation circular dichroism (PXCD), and photoelectron-photoexcitation
circular dichroism (PXECD). We show that, in spite of the fact that the physics
underlying the appearance of a chiral response is very different in all these
methods, the enantio-sensitive and dichroic observable in all cases has a
unique form. It is a polar vector given by the product of (i) a molecular
pseudoscalar and (ii) a field pseudovector specified by the configuration of
the electric fields interacting with the isotropic ensemble of chiral
molecules. The molecular pseudoscalar is a rotationally invariant property,
which is composed from different molecule-specific vectors and in the simplest
case is a triple product of such vectors. The key property that enables the
chiral response is the non-coplanarity of the vectors forming such triple
product. The key property that enables chiral detection without relying on the
chirality of the electromagnetic fields is the vectorial nature of the
enantio-sensitive observable. Our compact and general expression for this
observable shows what ultimately determines the efficiency of the chiral signal
and if, or when, it can reach 100%. We also discuss the differences between the
two phenomena, which rely on the bound states, PXCD and EMWS, and the two
phenomena using the continuum states, PECD and PXECD. Finally, we extend these
methods to arbitrary polarizations of the electric fields used to induce and
probe the chiral response.
| physics.atom-ph physics.atm-clus physics.chem-ph physics.optics quant-ph | we present a unified description of several methods of chiral discrimination based exclusively on electricdipole interactions it includes photoelectron circular dichroism pecd enantiosensitive microwave spectroscopy emws photoexcitation circular dichroism pxcd and photoelectronphotoexcitation circular dichroism pxecd we show that in spite of the fact that the physics underlying the appearance of a chiral response is very different in all these methods the enantiosensitive and dichroic observable in all cases has a unique form it is a polar vector given by the product of i a molecular pseudoscalar and ii a field pseudovector specified by the configuration of the electric fields interacting with the isotropic ensemble of chiral molecules the molecular pseudoscalar is a rotationally invariant property which is composed from different moleculespecific vectors and in the simplest case is a triple product of such vectors the key property that enables the chiral response is the noncoplanarity of the vectors forming such triple product the key property that enables chiral detection without relying on the chirality of the electromagnetic fields is the vectorial nature of the enantiosensitive observable our compact and general expression for this observable shows what ultimately determines the efficiency of the chiral signal and if or when it can reach 100 we also discuss the differences between the two phenomena which rely on the bound states pxcd and emws and the two phenomena using the continuum states pecd and pxecd finally we extend these methods to arbitrary polarizations of the electric fields used to induce and probe the chiral response | [['we', 'present', 'a', 'unified', 'description', 'of', 'several', 'methods', 'of', 'chiral', 'discrimination', 'based', 'exclusively', 'on', 'electricdipole', 'interactions', 'it', 'includes', 'photoelectron', 'circular', 'dichroism', 'pecd', 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1,802.06541 | Electroweak probes with ATLAS | Measuring electroweak bosons in relativistic heavy ion collisions at high
energy provide an opportunity to understand temporal evolution of the
quark-gluon plasma created in such collisions by constraining the initial state
of the interaction. Due to lack of color charges the bosons and or particles
produced in their leptonic decays are unaffected by the quark-gluon plasma and
therefore preserve the information about the very early stage of the collision
when they were born. This singles electroweak bosons as a unique and very
interesting class of observables in heavy ion collisions. The ATLAS experiment
at LHC measures production of electroweak bosons in pp, p+Pb, and Pb + Pb
collisions systems. A review of the existing results is given in this
proceeding that includes studies made with isolated photons to constraint
kinematic properties and flavour composition of associated jets, measurements
of W and Z bosons used to estimate nuclear modification of parton distribution
function and the production rates of the bosons used to verify geometric models
implied to estimate event centrality. A novel analysis on measuring
two-particle correlations in pp collisions where the Z boson is registered is
also discussed in the proceeding. This is the first attempt to break into the
initial geometry of the pp collisions by constraining the impact parameter with
a hard scattering process. It shows that the strength of the two particle
correlations in such collision is 1.08+/-0.06 above the inclusive. To make the
measurement ATLAS solves the technical problem of measuring the underlying
event in high pileup condition.
| nucl-ex | measuring electroweak bosons in relativistic heavy ion collisions at high energy provide an opportunity to understand temporal evolution of the quarkgluon plasma created in such collisions by constraining the initial state of the interaction due to lack of color charges the bosons and or particles produced in their leptonic decays are unaffected by the quarkgluon plasma and therefore preserve the information about the very early stage of the collision when they were born this singles electroweak bosons as a unique and very interesting class of observables in heavy ion collisions the atlas experiment at lhc measures production of electroweak bosons in pp ppb and pb pb collisions systems a review of the existing results is given in this proceeding that includes studies made with isolated photons to constraint kinematic properties and flavour composition of associated jets measurements of w and z bosons used to estimate nuclear modification of parton distribution function and the production rates of the bosons used to verify geometric models implied to estimate event centrality a novel analysis on measuring twoparticle correlations in pp collisions where the z boson is registered is also discussed in the proceeding this is the first attempt to break into the initial geometry of the pp collisions by constraining the impact parameter with a hard scattering process it shows that the strength of the two particle correlations in such collision is 108006 above the inclusive to make the measurement atlas solves the technical problem of measuring the underlying event in high pileup condition | [['measuring', 'electroweak', 'bosons', 'in', 'relativistic', 'heavy', 'ion', 'collisions', 'at', 'high', 'energy', 'provide', 'an', 'opportunity', 'to', 'understand', 'temporal', 'evolution', 'of', 'the', 'quarkgluon', 'plasma', 'created', 'in', 'such', 'collisions', 'by', 'constraining', 'the', 'initial', 'state', 'of', 'the', 'interaction', 'due', 'to', 'lack', 'of', 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1,802.06542 | Seismic Cross-coupling Noise in Torsion Pendulums | Detection of low frequency gravitational waves around 0.1 Hz is one of the
important targets for future gravitational wave observation. One of the main
sources of the expected signals is gravi- tational waves from binary
intermediate-mass black hole coalescences which is proposed as one of the
formation scenarios of supermassive black holes. By using a torsion pendulum,
which can have a resonance frequency of a few millihertz, such signals can be
measured on the ground since its rotational motion can act as a free mass down
to 0.01 Hz. However, sensitivity of a realistic tor- sion pendulum will suffer
from torsional displacement noise introduced from translational ground motion
in the main frequency band of interest. Such noise is called seismic
cross-coupling noise and there have been little research on it. In this paper,
systematic investigation is performed to identify routes of cross-coupling
transfer for standard torsion pendulums. Based on the results this paper also
proposes reduction schemes of cross-coupling noise, and they were demonstrated
experimen- tally in agreement with theory. This result establishes a basic way
to reduce seismic noise in torsion pendulums for the most significant coupling
routes.
| physics.ins-det | detection of low frequency gravitational waves around 01 hz is one of the important targets for future gravitational wave observation one of the main sources of the expected signals is gravi tational waves from binary intermediatemass black hole coalescences which is proposed as one of the formation scenarios of supermassive black holes by using a torsion pendulum which can have a resonance frequency of a few millihertz such signals can be measured on the ground since its rotational motion can act as a free mass down to 001 hz however sensitivity of a realistic tor sion pendulum will suffer from torsional displacement noise introduced from translational ground motion in the main frequency band of interest such noise is called seismic crosscoupling noise and there have been little research on it in this paper systematic investigation is performed to identify routes of crosscoupling transfer for standard torsion pendulums based on the results this paper also proposes reduction schemes of crosscoupling noise and they were demonstrated experimen tally in agreement with theory this result establishes a basic way to reduce seismic noise in torsion pendulums for the most significant coupling routes | [['detection', 'of', 'low', 'frequency', 'gravitational', 'waves', 'around', '01', 'hz', 'is', 'one', 'of', 'the', 'important', 'targets', 'for', 'future', 'gravitational', 'wave', 'observation', 'one', 'of', 'the', 'main', 'sources', 'of', 'the', 'expected', 'signals', 'is', 'gravi', 'tational', 'waves', 'from', 'binary', 'intermediatemass', 'black', 'hole', 'coalescences', 'which', 'is', 'proposed', 'as', 'one', 'of', 'the', 'formation', 'scenarios', 'of', 'supermassive', 'black', 'holes', 'by', 'using', 'a', 'torsion', 'pendulum', 'which', 'can', 'have', 'a', 'resonance', 'frequency', 'of', 'a', 'few', 'millihertz', 'such', 'signals', 'can', 'be', 'measured', 'on', 'the', 'ground', 'since', 'its', 'rotational', 'motion', 'can', 'act', 'as', 'a', 'free', 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1,802.06543 | Optimal Beamforming for Physical Layer Security in MISO Wireless
Networks | A wireless network of multiple transmitter-user pairs overheard by an
eavesdropper, where the transmitters are equipped with multiple antennas while
the users and eavesdropper are equipped with a single antenna, is considered.
At different levels of wireless channel knowledge, the problem of interest is
beamforming to optimize the users' quality-of-service (QoS) in terms of their
secrecy throughputs or maximize the network's energy efficiency under users'
QoS. All these problems are seen as very difficult optimization problems with
many nonconvex constraints and nonlinear equality constraints in beamforming
vectors. The paper develops path-following computational procedures of
low-complexity and rapid convergence for the optimal beamforming solution.
Their practicability is demonstrated through numerical examples.
| cs.IT math.IT | a wireless network of multiple transmitteruser pairs overheard by an eavesdropper where the transmitters are equipped with multiple antennas while the users and eavesdropper are equipped with a single antenna is considered at different levels of wireless channel knowledge the problem of interest is beamforming to optimize the users qualityofservice qos in terms of their secrecy throughputs or maximize the networks energy efficiency under users qos all these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors the paper develops pathfollowing computational procedures of lowcomplexity and rapid convergence for the optimal beamforming solution their practicability is demonstrated through numerical examples | [['a', 'wireless', 'network', 'of', 'multiple', 'transmitteruser', 'pairs', 'overheard', 'by', 'an', 'eavesdropper', 'where', 'the', 'transmitters', 'are', 'equipped', 'with', 'multiple', 'antennas', 'while', 'the', 'users', 'and', 'eavesdropper', 'are', 'equipped', 'with', 'a', 'single', 'antenna', 'is', 'considered', 'at', 'different', 'levels', 'of', 'wireless', 'channel', 'knowledge', 'the', 'problem', 'of', 'interest', 'is', 'beamforming', 'to', 'optimize', 'the', 'users', 'qualityofservice', 'qos', 'in', 'terms', 'of', 'their', 'secrecy', 'throughputs', 'or', 'maximize', 'the', 'networks', 'energy', 'efficiency', 'under', 'users', 'qos', 'all', 'these', 'problems', 'are', 'seen', 'as', 'very', 'difficult', 'optimization', 'problems', 'with', 'many', 'nonconvex', 'constraints', 'and', 'nonlinear', 'equality', 'constraints', 'in', 'beamforming', 'vectors', 'the', 'paper', 'develops', 'pathfollowing', 'computational', 'procedures', 'of', 'lowcomplexity', 'and', 'rapid', 'convergence', 'for', 'the', 'optimal', 'beamforming', 'solution', 'their', 'practicability', 'is', 'demonstrated', 'through', 'numerical', 'examples']] | [-0.29213796032233796, -0.014959456064656094, 0.045860493166901925, 0.014552744291913017, -0.12507481406946933, -0.29130905466378504, 0.07310228714604067, 0.42800462433914527, -0.2794353058647125, -0.30251856320836673, 0.09404950859580496, -0.2879169427687217, -0.1608915884974797, 0.12924742865923006, -0.15396056308863906, 0.13538596533033825, 0.06610286945408773, 0.04622282299700133, -0.046618631827311775, -0.3213759241711109, 0.3003187607802929, 0.12941024519092992, 0.370738249024325, 0.01877929218307804, 0.11004527070380132, -0.007160523237763058, 0.020849241554702913, -0.0464378918057581, -0.06983954729213285, 0.09866008842513478, 0.4346736072468648, 0.23757982803850408, 0.33928654705165723, -0.4490416890198211, -0.23785190372257878, 0.07931045228999895, 0.1629294291557317, 0.004453376471705803, -0.049821935431741245, -0.27883175074404803, 0.15252350060346134, -0.203191891201524, 0.012038895847498003, -0.003991170042971952, -0.15421457783481396, 0.10369700554773263, -0.39253509061735703, -0.023250251256544657, -0.04992483317031773, 0.03495712091274764, -0.0779933007134962, -0.10984209321712682, 0.02617054246793236, 0.16207003107490958, 0.1070653110499058, -0.05638838490607952, 0.09935588455425763, -0.12371300120726911, -0.13613575423315782, 0.396940405668537, 0.08260894264308137, -0.29218657412181753, 0.15025073112244397, -0.031896212292031954, -0.09204926058530398, 0.19475584943701915, 0.2716075459990753, 0.09432985526808632, -0.19533737388294226, 0.03222050043858947, 0.0065997383693967935, 0.12859634144889584, 0.10097714523793361, 0.15162070245917783, 0.16314831662521517, 0.1870850579719136, 0.21379095869546824, 0.12396705132234123, -0.049790327223615906, -0.0978481133955471, -0.20158995828834797, -0.08856161153413902, -0.2522636563655997, -0.014139252958323705, -0.13239101705810485, -0.036571506316850494, 0.34930027233235916, 0.08867637144076988, 0.09527226610092121, 0.16311345606563835, 0.4295957603175706, 0.10333672686642327, 0.020576825109096843, 0.1353002968116091, 0.20268767287339504, 0.10733408609099704, 0.17102490460987144, -0.1932969917073299, 0.0709296686130516, -0.05649852938950062] |
1,802.06544 | Cooperative ligation breaks sequence symmetry and stabilizes early
molecular replication | Each living species carries a complex DNA sequence that determines their
unique features and functionalities. It is generally assumed that life started
from a random pool of oligonucleotides sequences, generated by a prebiotic
polymerization of nucleotides. The mechanism that initially facilitated the
emergence of sequences that code for the function of the first species from
such a random pool of sequences remains unknown. It is a central problem of the
origin of life. An interesting option would be a self-selection mechanism by
spontaneous symmetry breaking. Initial concentration fluctuations of specific
sequence motifs would have been amplified and outcompeted less abundant
sequences, enhancing the signal to noise to replicate and select functional
sequences. Here, we demonstrate with experimental and theoretical findings that
templated ligation would provide such a self-selection. In templated ligation,
two adjacent single sequences strands are chemically joined when a third
complementary strand sequence brought them in close proximity. This simple
mechanism was a likely side-product of a prebiotic polymerization chemistry
once the strands reach the length to form double stranded species. As shown
here, the ligation gave rise to a nonlinear replication process by the
cooperative ligation of matching sequences which self-promoted their own
elongation. This led to a cascade of enhanced template binding and faster
ligation reactions. A requirement was the reshuffling of the strands by thermal
cycling, enabled for example by microscale convection. Assuming that templated
ligation was driven by the same chemical mechanism that generated prebiotic
polymerization of oligonucleotides, the mechanism could function as a missing
link between polymerization and the self-stabilized replication, offering a
pathway to the autonomous emergence of Darwinian evolution for the origin of
life.
| physics.bio-ph q-bio.BM | each living species carries a complex dna sequence that determines their unique features and functionalities it is generally assumed that life started from a random pool of oligonucleotides sequences generated by a prebiotic polymerization of nucleotides the mechanism that initially facilitated the emergence of sequences that code for the function of the first species from such a random pool of sequences remains unknown it is a central problem of the origin of life an interesting option would be a selfselection mechanism by spontaneous symmetry breaking initial concentration fluctuations of specific sequence motifs would have been amplified and outcompeted less abundant sequences enhancing the signal to noise to replicate and select functional sequences here we demonstrate with experimental and theoretical findings that templated ligation would provide such a selfselection in templated ligation two adjacent single sequences strands are chemically joined when a third complementary strand sequence brought them in close proximity this simple mechanism was a likely sideproduct of a prebiotic polymerization chemistry once the strands reach the length to form double stranded species as shown here the ligation gave rise to a nonlinear replication process by the cooperative ligation of matching sequences which selfpromoted their own elongation this led to a cascade of enhanced template binding and faster ligation reactions a requirement was the reshuffling of the strands by thermal cycling enabled for example by microscale convection assuming that templated ligation was driven by the same chemical mechanism that generated prebiotic polymerization of oligonucleotides the mechanism could function as a missing link between polymerization and the selfstabilized replication offering a pathway to the autonomous emergence of darwinian evolution for the origin of life | [['each', 'living', 'species', 'carries', 'a', 'complex', 'dna', 'sequence', 'that', 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1,802.06545 | Upper and lower bounds for dynamic data structures on strings | We consider a range of simply stated dynamic data structure problems on
strings. An update changes one symbol in the input and a query asks us to
compute some function of the pattern of length $m$ and a substring of a longer
text. We give both conditional and unconditional lower bounds for variants of
exact matching with wildcards, inner product, and Hamming distance computation
via a sequence of reductions. As an example, we show that there does not exist
an $O(m^{1/2-\varepsilon})$ time algorithm for a large range of these problems
unless the online Boolean matrix-vector multiplication conjecture is false. We
also provide nearly matching upper bounds for most of the problems we consider.
| cs.DS cs.CC | we consider a range of simply stated dynamic data structure problems on strings an update changes one symbol in the input and a query asks us to compute some function of the pattern of length m and a substring of a longer text we give both conditional and unconditional lower bounds for variants of exact matching with wildcards inner product and hamming distance computation via a sequence of reductions as an example we show that there does not exist an om12varepsilon time algorithm for a large range of these problems unless the online boolean matrixvector multiplication conjecture is false we also provide nearly matching upper bounds for most of the problems we consider | [['we', 'consider', 'a', 'range', 'of', 'simply', 'stated', 'dynamic', 'data', 'structure', 'problems', 'on', 'strings', 'an', 'update', 'changes', 'one', 'symbol', 'in', 'the', 'input', 'and', 'a', 'query', 'asks', 'us', 'to', 'compute', 'some', 'function', 'of', 'the', 'pattern', 'of', 'length', 'm', 'and', 'a', 'substring', 'of', 'a', 'longer', 'text', 'we', 'give', 'both', 'conditional', 'and', 'unconditional', 'lower', 'bounds', 'for', 'variants', 'of', 'exact', 'matching', 'with', 'wildcards', 'inner', 'product', 'and', 'hamming', 'distance', 'computation', 'via', 'a', 'sequence', 'of', 'reductions', 'as', 'an', 'example', 'we', 'show', 'that', 'there', 'does', 'not', 'exist', 'an', 'om12varepsilon', 'time', 'algorithm', 'for', 'a', 'large', 'range', 'of', 'these', 'problems', 'unless', 'the', 'online', 'boolean', 'matrixvector', 'multiplication', 'conjecture', 'is', 'false', 'we', 'also', 'provide', 'nearly', 'matching', 'upper', 'bounds', 'for', 'most', 'of', 'the', 'problems', 'we', 'consider']] | [-0.1593277447557609, 0.06329205164404682, -0.043581318555100425, 0.11372922328155255, -0.0844556385730227, -0.1309945586295466, 0.10429191977371895, 0.38222224309408503, -0.30968643382844413, -0.33031411740064087, 0.1462335399607712, -0.2400446777754561, -0.1317526245256886, 0.21863565567348683, -0.08740106834089342, 0.058954494350473396, 0.08275261335074902, 0.0865604461476843, -0.10548928773122108, -0.29457452470212175, 0.29071747574822177, 0.005701496326115115, 0.1981915300046759, 0.0684825309810029, 0.10777408969858827, 0.03611018629245726, -0.02186942666802289, -0.007983404053707741, -0.16627107955023998, 0.12255467445727065, 0.26034161240594195, 0.23561887214808458, 0.258378284378393, -0.4111925660067105, -0.131545666902509, 0.17591854438485047, 0.15149599180274112, 0.11315157801644611, -0.03950397984902208, -0.2015406742741886, 0.12529361683742277, -0.13771165288198972, -0.03427352002056848, -0.026772644890505553, 0.07584188705576318, -0.011157391522179491, -0.33076200457383365, 0.02113134506855983, 0.09097841560807345, 0.021687757784872832, -0.05957108660991902, -0.12374939946624051, 0.1005777697261822, 0.1244974283285306, 0.01998978908938755, 0.042117583802402284, 0.05699349275008509, -0.12424498629739641, -0.18146119486274465, 0.36156580224633217, -0.06815124652348459, -0.20633500405321165, 0.1293186989496462, -0.08974016114578783, -0.15299306589544617, 0.09840958686878107, 0.1808163995821295, 0.1491611240531451, -0.07414691524432523, 0.11296144889950353, -0.11409090293039169, 0.2146839605245207, 0.13229214791707428, 0.05875054088703889, 0.13395588274579495, 0.11988815765861156, 0.15847137138812936, 0.15278830597942164, -0.0336741053719639, -0.050643391732592136, -0.2886128228357328, -0.15868548874589447, -0.18341790900532423, 0.010259853017097547, -0.16559210091976898, -0.23987263723704796, 0.3554308416247035, 0.1154829155213, 0.24497797669521656, 0.15700264693753394, 0.26441340517651823, 0.11856504969494251, 0.0391312312401299, 0.14881026532384567, 0.11670784216221364, 0.10047654100656343, 0.029113392819583948, -0.15629744557632616, 0.08182729805204352, 0.10669341797308464] |
1,802.06546 | A spectral interpolation scheme on the unit sphere based on the nodes of
spherical Lissajous curves | For sampling values along spherical Lissajous curves we establish a spectral
interpolation and quadrature scheme on the sphere. We provide a mathematical
analysis of spherical Lissajous curves and study the characteristic properties
of their intersection points. Based on a discrete orthogonality structure we
are able to prove the unisolvence of the interpolation problem. As basis
functions for the interpolation space we use a parity-modified double Fourier
basis on the sphere which allows us to implement the interpolation scheme in an
efficient way. We further show that the numerical condition number of the
interpolation scheme displays a logarithmic growth.
As an application, we use the developed interpolation algorithm to estimate
the rotation of an object based on measurements at the spherical Lissajous
nodes.
| math.NA | for sampling values along spherical lissajous curves we establish a spectral interpolation and quadrature scheme on the sphere we provide a mathematical analysis of spherical lissajous curves and study the characteristic properties of their intersection points based on a discrete orthogonality structure we are able to prove the unisolvence of the interpolation problem as basis functions for the interpolation space we use a paritymodified double fourier basis on the sphere which allows us to implement the interpolation scheme in an efficient way we further show that the numerical condition number of the interpolation scheme displays a logarithmic growth as an application we use the developed interpolation algorithm to estimate the rotation of an object based on measurements at the spherical lissajous nodes | [['for', 'sampling', 'values', 'along', 'spherical', 'lissajous', 'curves', 'we', 'establish', 'a', 'spectral', 'interpolation', 'and', 'quadrature', 'scheme', 'on', 'the', 'sphere', 'we', 'provide', 'a', 'mathematical', 'analysis', 'of', 'spherical', 'lissajous', 'curves', 'and', 'study', 'the', 'characteristic', 'properties', 'of', 'their', 'intersection', 'points', 'based', 'on', 'a', 'discrete', 'orthogonality', 'structure', 'we', 'are', 'able', 'to', 'prove', 'the', 'unisolvence', 'of', 'the', 'interpolation', 'problem', 'as', 'basis', 'functions', 'for', 'the', 'interpolation', 'space', 'we', 'use', 'a', 'paritymodified', 'double', 'fourier', 'basis', 'on', 'the', 'sphere', 'which', 'allows', 'us', 'to', 'implement', 'the', 'interpolation', 'scheme', 'in', 'an', 'efficient', 'way', 'we', 'further', 'show', 'that', 'the', 'numerical', 'condition', 'number', 'of', 'the', 'interpolation', 'scheme', 'displays', 'a', 'logarithmic', 'growth', 'as', 'an', 'application', 'we', 'use', 'the', 'developed', 'interpolation', 'algorithm', 'to', 'estimate', 'the', 'rotation', 'of', 'an', 'object', 'based', 'on', 'measurements', 'at', 'the', 'spherical', 'lissajous', 'nodes']] | [-0.12148279947621271, -0.0102531997212026, -0.17702296185730534, 0.08788345379404693, -0.0941577307217993, -0.09577934914614913, 0.0914176128631985, 0.39941562056803137, -0.27620190033335085, -0.2298707434395713, 0.12575284715968932, -0.21123444151014478, -0.18784431005445162, 0.2626782459291545, -0.07546591124264523, 0.08951482399521214, 0.03500016460345273, 0.0007863169892456321, -0.13178209012782216, -0.2274981778680755, 0.3199462852583167, 0.030112666370393323, 0.2762827555502742, -0.0020310442109615348, 0.10962443670242532, 0.06357470272524544, -0.03639880666693996, -0.023390958105138894, -0.18248658879759408, 0.18004100708279389, 0.15683735773152063, 0.10216499695531285, 0.2416668005984215, -0.41047586996323804, -0.14889886267560204, 0.1070284580827252, 0.14034135439933454, 0.0753584065318708, -0.05597882967034339, -0.20695288250730795, 0.051884438780959975, -0.12723223646440782, -0.19601445742074616, -0.13388279465812236, -0.02032573102426923, 0.07620806688460144, -0.3017553957857476, 0.012758558604496815, 0.03967817668506706, 0.09554521600746603, -0.06688661107549074, -0.06464883239462602, 0.015061907824282805, 0.08728242861414867, -0.03249077748291749, 0.012256895828884373, 0.07155432346881144, -0.03081450261722111, -0.10946961127467884, 0.37136795906704073, -0.0310604058683288, -0.2554280993428605, 0.15942179578287172, -0.12808578231656723, -0.10862446625424503, 0.1078132784363529, 0.20493151307537044, 0.13038607749511671, -0.059224649352187, 0.08275048938783824, -0.0642448538252391, 0.15914305407276824, 0.08873293083161116, -0.0011893080490687478, 0.14028611810192898, 0.09563361998062489, 0.12054866704751145, 0.15887865473993493, -0.15990493375873424, -0.08518659197994746, -0.3393162516646149, -0.18926982996862166, -0.21964503001144603, -0.014032240902181437, -0.13356850088803937, -0.2103563719852404, 0.40442944475195747, 0.10083889152300506, 0.23498728657372234, 0.07606644920469839, 0.30980733409523964, 0.13424615640951368, 0.04338049438150892, 0.07085720201846489, 0.1802223140435401, 0.1530052339273297, 0.052067389069048085, -0.1851985387750401, -0.0050468403145609315, 0.17552221919797661] |
1,802.06547 | Weighted Linear Discriminant Analysis based on Class Saliency
Information | In this paper, we propose a new variant of Linear Discriminant Analysis to
overcome underlying drawbacks of traditional LDA and other LDA variants
targeting problems involving imbalanced classes. Traditional LDA sets
assumptions related to Gaussian class distribution and neglects influence of
outlier classes, that might hurt in performance. We exploit intuitions coming
from a probabilistic interpretation of visual saliency estimation in order to
define saliency of a class in multi-class setting. Such information is then
used to redefine the between-class and within-class scatters in a more robust
manner. Compared to traditional LDA and other weight-based LDA variants, the
proposed method has shown certain improvements on facial image classification
problems in publicly available datasets.
| cs.CV | in this paper we propose a new variant of linear discriminant analysis to overcome underlying drawbacks of traditional lda and other lda variants targeting problems involving imbalanced classes traditional lda sets assumptions related to gaussian class distribution and neglects influence of outlier classes that might hurt in performance we exploit intuitions coming from a probabilistic interpretation of visual saliency estimation in order to define saliency of a class in multiclass setting such information is then used to redefine the betweenclass and withinclass scatters in a more robust manner compared to traditional lda and other weightbased lda variants the proposed method has shown certain improvements on facial image classification problems in publicly available datasets | [['in', 'this', 'paper', 'we', 'propose', 'a', 'new', 'variant', 'of', 'linear', 'discriminant', 'analysis', 'to', 'overcome', 'underlying', 'drawbacks', 'of', 'traditional', 'lda', 'and', 'other', 'lda', 'variants', 'targeting', 'problems', 'involving', 'imbalanced', 'classes', 'traditional', 'lda', 'sets', 'assumptions', 'related', 'to', 'gaussian', 'class', 'distribution', 'and', 'neglects', 'influence', 'of', 'outlier', 'classes', 'that', 'might', 'hurt', 'in', 'performance', 'we', 'exploit', 'intuitions', 'coming', 'from', 'a', 'probabilistic', 'interpretation', 'of', 'visual', 'saliency', 'estimation', 'in', 'order', 'to', 'define', 'saliency', 'of', 'a', 'class', 'in', 'multiclass', 'setting', 'such', 'information', 'is', 'then', 'used', 'to', 'redefine', 'the', 'betweenclass', 'and', 'withinclass', 'scatters', 'in', 'a', 'more', 'robust', 'manner', 'compared', 'to', 'traditional', 'lda', 'and', 'other', 'weightbased', 'lda', 'variants', 'the', 'proposed', 'method', 'has', 'shown', 'certain', 'improvements', 'on', 'facial', 'image', 'classification', 'problems', 'in', 'publicly', 'available', 'datasets']] | [-0.004003483968976457, -0.08260734592753965, -0.107441885166068, 0.14410183302938642, -0.14493244976645944, -0.17988336948364708, 0.05641022170543572, 0.43163389283998876, -0.33144453176157135, -0.2921755438035898, 0.06542656400686014, -0.30826300809539, -0.17982830168201333, 0.1652685722358838, -0.19386692939787709, 0.10214594178379768, 0.1070277397984441, 0.04938141808770927, -0.12497391243052125, -0.3026169000885787, 0.3279717344197288, 0.02119367015836513, 0.35911281855232946, 0.001288418765221022, 0.06933494054803015, -0.004034235869509588, -0.07985516332540109, 0.05984399721553895, -0.07359477353677106, 0.20472268615560854, 0.35552813275923245, 0.1772242294814009, 0.35674625172370433, -0.373985405335516, -0.2622996920048037, 0.13945194590935664, 0.1169640335575801, 0.08885073224692996, -0.008251687297128775, -0.30763989355645877, 0.08112828228705093, -0.1737609385075954, 0.0035523476730207953, -0.1661468658728146, -0.06094230485016859, -0.017313134765862364, -0.29607226902338785, 0.1263025504767697, 0.07571571299278762, 0.04777159172613009, -0.06560345128615412, -0.19121473240954553, 0.08215200858998352, 0.06731748589998589, 0.07661623161067709, 0.0172106008659904, 0.11845626612399927, -0.15264884377335222, -0.16031095866872147, 0.39396057490556113, -0.08058966033107115, -0.2504874076611832, 0.23224345721980244, 0.007206007562149151, -0.20146348336670317, 0.0681946199980721, 0.24540700953849384, 0.08601458818833055, -0.1401374140523572, 0.025753284501637108, -0.04170328815492381, 0.1799092642072819, 0.07202764044194358, 0.02152584303186926, 0.13048185054387948, 0.18922186243158262, 0.0717843506996215, 0.1597862211189983, -0.14399800907647387, -0.08405712482610107, -0.1732866601251989, -0.06770864974262308, -0.16127425147245217, -0.05478739225721827, -0.09368033280989682, -0.18809305453766756, 0.41427911546048335, 0.2455818106510998, 0.18674885780360978, 0.08670816655513888, 0.3260027620244969, 0.03050254848249982, 0.0778847894079126, 0.09758875484009628, 0.1349745234994803, 0.07924176898447022, 0.059970393310202104, -0.1349466211694103, 0.09563336403117376, 0.07069249543262464] |
1,802.06548 | Level Zero Trigger Processor for the NA62 experiment | The NA62 experiment is designed to measure the ultra-rare decay $K^+
\rightarrow \pi^+ \nu \bar{\nu}$ branching ratio with a precision of $\sim
10\%$ at the CERN Super Proton Synchrotron (SPS). The trigger system of NA62
consists in three different levels designed to select events of physics
interest in a high beam rate environment. The L0 Trigger Processor (L0TP) is
the lowest level system of the trigger chain. It is hardware implemented using
programmable logic. The architecture of the NA62 L0TP system is a new approach
compared to existing systems used in high-energy physics experiments. It is
fully digital, based on a standard gigabit Ethernet communication between
detectors and the L0TP Board. The L0TP Board is a commercial development board,
mounting a programmable logic device (FPGA). The primitives generated by
sub-detectors are sent asynchronously using the UDP protocol to the L0TP during
the entire beam spill period. The L0TP realigns in time the primitives coming
from seven different sources and performs a data selection based on the
characteristics of the event such as energy, multiplicity and topology of hits
in the sub-detectors. It guarantees a maximum latency of 1 ms. The maximum
input rate is about 10 MHz for each sub-detector, while the design maximum
output trigger rate is 1 MHz. A description of the trigger algorithm is
presented here.
| physics.ins-det hep-ex | the na62 experiment is designed to measure the ultrarare decay k rightarrow pi nu barnu branching ratio with a precision of sim 10 at the cern super proton synchrotron sps the trigger system of na62 consists in three different levels designed to select events of physics interest in a high beam rate environment the l0 trigger processor l0tp is the lowest level system of the trigger chain it is hardware implemented using programmable logic the architecture of the na62 l0tp system is a new approach compared to existing systems used in highenergy physics experiments it is fully digital based on a standard gigabit ethernet communication between detectors and the l0tp board the l0tp board is a commercial development board mounting a programmable logic device fpga the primitives generated by subdetectors are sent asynchronously using the udp protocol to the l0tp during the entire beam spill period the l0tp realigns in time the primitives coming from seven different sources and performs a data selection based on the characteristics of the event such as energy multiplicity and topology of hits in the subdetectors it guarantees a maximum latency of 1 ms the maximum input rate is about 10 mhz for each subdetector while the design maximum output trigger rate is 1 mhz a description of the trigger algorithm is presented here | [['the', 'na62', 'experiment', 'is', 'designed', 'to', 'measure', 'the', 'ultrarare', 'decay', 'k', 'rightarrow', 'pi', 'nu', 'barnu', 'branching', 'ratio', 'with', 'a', 'precision', 'of', 'sim', '10', 'at', 'the', 'cern', 'super', 'proton', 'synchrotron', 'sps', 'the', 'trigger', 'system', 'of', 'na62', 'consists', 'in', 'three', 'different', 'levels', 'designed', 'to', 'select', 'events', 'of', 'physics', 'interest', 'in', 'a', 'high', 'beam', 'rate', 'environment', 'the', 'l0', 'trigger', 'processor', 'l0tp', 'is', 'the', 'lowest', 'level', 'system', 'of', 'the', 'trigger', 'chain', 'it', 'is', 'hardware', 'implemented', 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1,802.06549 | Thermodynamics of energy, charge and spin currents in thermoelectric
quantum-dot spin valve | We provide a thermodynamically consistent description of energy, charge and
spin transfers in a thermoelectric quantum-dot spin valve in the collinear
configuration based on nonequilibrium Green's function and full counting
statistics. We use the fluctuation theorem symmetry and the concept of entropy
production to characterize the efficiency with which thermal gradients can
transduce charges or spins against their chemical potentials, arbitrary far
from equilibrium. Close to equilibrium, we recover the Onsager reciprocal
relations and the connection to linear response notions of performance such as
the figure of merit. We also identify regimes where work extraction is more
efficient far then close from equilibrium.
| cond-mat.mes-hall cond-mat.stat-mech | we provide a thermodynamically consistent description of energy charge and spin transfers in a thermoelectric quantumdot spin valve in the collinear configuration based on nonequilibrium greens function and full counting statistics we use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials arbitrary far from equilibrium close to equilibrium we recover the onsager reciprocal relations and the connection to linear response notions of performance such as the figure of merit we also identify regimes where work extraction is more efficient far then close from equilibrium | [['we', 'provide', 'a', 'thermodynamically', 'consistent', 'description', 'of', 'energy', 'charge', 'and', 'spin', 'transfers', 'in', 'a', 'thermoelectric', 'quantumdot', 'spin', 'valve', 'in', 'the', 'collinear', 'configuration', 'based', 'on', 'nonequilibrium', 'greens', 'function', 'and', 'full', 'counting', 'statistics', 'we', 'use', 'the', 'fluctuation', 'theorem', 'symmetry', 'and', 'the', 'concept', 'of', 'entropy', 'production', 'to', 'characterize', 'the', 'efficiency', 'with', 'which', 'thermal', 'gradients', 'can', 'transduce', 'charges', 'or', 'spins', 'against', 'their', 'chemical', 'potentials', 'arbitrary', 'far', 'from', 'equilibrium', 'close', 'to', 'equilibrium', 'we', 'recover', 'the', 'onsager', 'reciprocal', 'relations', 'and', 'the', 'connection', 'to', 'linear', 'response', 'notions', 'of', 'performance', 'such', 'as', 'the', 'figure', 'of', 'merit', 'we', 'also', 'identify', 'regimes', 'where', 'work', 'extraction', 'is', 'more', 'efficient', 'far', 'then', 'close', 'from', 'equilibrium']] | [-0.10138749741402102, 0.13333098131042082, -0.10741770854762313, 0.06458338422958458, -0.054910712563477966, -0.1199411753818248, 0.08179085422533303, 0.3448913618198876, -0.27830209666682243, -0.2662252659448287, 0.017200415816103803, -0.31478103255690304, -0.10926450807736843, 0.17684858254138922, 0.007116192757396154, 0.05790121408938927, -0.027866484543073524, 0.02539874688587694, -0.10300588795408896, -0.14461010101011693, 0.2824378759752523, 0.0642662978667802, 0.32079464139290226, 0.08536775743823896, 0.09627107617479763, 0.03874371090261899, 0.05389228708944871, 0.05052703574386841, -0.1896779603162075, 0.08137287309809217, 0.26276579638943076, 0.02630997066684429, 0.18756959988262042, -0.43173198696696063, -0.15955602702259727, 0.09017562962959981, 0.09074204218646204, 0.14004644731543417, -0.027167533067291267, -0.20013613298702623, 0.06255355400476352, -0.20824818054521546, -0.13843388459871261, -0.15416978970644724, -0.005682756091260071, 0.03751977914673032, -0.2514142618668311, 0.10936494915518973, 0.08068045586781594, 0.04858788072348581, -0.07078464395927211, -0.1016533945470108, -0.08261758113478862, 0.11317202776842253, 0.003557730599496405, -0.015217532340473341, 0.2236867933590598, -0.13823167569438014, -0.13232428943105404, 0.329690729597927, -0.033559353253578096, -0.21933742906012146, 0.1955797422283953, -0.15018775950647095, -0.09124077395174326, 0.09038339241959371, 0.1270667480901607, 0.12891237986572449, -0.1862567061540282, 0.0368900890055212, 0.013268982883072595, 0.1373916809058305, 0.08941811654101876, 0.09595185297188684, 0.2634650770850588, 0.1268469514325261, 0.07796192745162735, 0.1954850058423952, -0.07603371852457307, -0.15476582102586053, -0.2682289185581132, -0.15626268372735352, -0.20628797666404794, 0.11990962478612523, -0.0730001891876155, -0.15353712100463296, 0.3959305117141853, 0.1925804841522019, 0.16415864526682977, 0.05118163001556311, 0.31851832713316947, 0.14149147397680298, 0.03970198366944723, 0.05599249955560578, 0.26353171460773545, 0.18140718931766245, 0.08952828513648252, -0.26521572347242134, 0.037278658384909326, 0.054626565354252324] |
1,802.0655 | Non-perturbative results for the luminosity and area distances | The notion of luminosity distance is most often defined in purely FLRW
(Friedmann-Lemaitre-Robertson-Walker) cosmological spacetimes, or small
perturbations thereof. However, the abstract notion of luminosity distance is
actually much more robust than this, and can be defined non-perturbatively in
almost arbitrary spacetimes. Some quite general results are already known, in
terms of $dA_\mathrm{observer}/d\Omega_\mathrm{source}$, the cross-sectional
area per unit solid angle of a null geodesic spray emitted from some source and
subsequently detected by some observer. We shall reformulate these results in
terms of a suitably normalized null geodesic affine parameter and the van Vleck
determinant, $\Delta_{vV}$. The contribution due to the null geodesic affine
parameter is effectively the inverse square law for luminosity, and the van
Vleck determinant can be viewed as providing a measure of deviations from the
inverse square law. This formulation is closely related to the so-called Jacobi
determinant, but the van Vleck determinant has somewhat nicer analytic
properties and wider and deeper theoretical base in the general relativity,
quantum physics, and quantum field theory communities. In the current article
we shall concentrate on non-perturbative results, leaving near-FLRW
perturbative investigation for future work.
| gr-qc astro-ph.CO | the notion of luminosity distance is most often defined in purely flrw friedmannlemaitrerobertsonwalker cosmological spacetimes or small perturbations thereof however the abstract notion of luminosity distance is actually much more robust than this and can be defined nonperturbatively in almost arbitrary spacetimes some quite general results are already known in terms of da_mathrmobserverdomega_mathrmsource the crosssectional area per unit solid angle of a null geodesic spray emitted from some source and subsequently detected by some observer we shall reformulate these results in terms of a suitably normalized null geodesic affine parameter and the van vleck determinant delta_vv the contribution due to the null geodesic affine parameter is effectively the inverse square law for luminosity and the van vleck determinant can be viewed as providing a measure of deviations from the inverse square law this formulation is closely related to the socalled jacobi determinant but the van vleck determinant has somewhat nicer analytic properties and wider and deeper theoretical base in the general relativity quantum physics and quantum field theory communities in the current article we shall concentrate on nonperturbative results leaving nearflrw perturbative investigation for future work | [['the', 'notion', 'of', 'luminosity', 'distance', 'is', 'most', 'often', 'defined', 'in', 'purely', 'flrw', 'friedmannlemaitrerobertsonwalker', 'cosmological', 'spacetimes', 'or', 'small', 'perturbations', 'thereof', 'however', 'the', 'abstract', 'notion', 'of', 'luminosity', 'distance', 'is', 'actually', 'much', 'more', 'robust', 'than', 'this', 'and', 'can', 'be', 'defined', 'nonperturbatively', 'in', 'almost', 'arbitrary', 'spacetimes', 'some', 'quite', 'general', 'results', 'are', 'already', 'known', 'in', 'terms', 'of', 'da_mathrmobserverdomega_mathrmsource', 'the', 'crosssectional', 'area', 'per', 'unit', 'solid', 'angle', 'of', 'a', 'null', 'geodesic', 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1,802.06551 | Verifying Semantic Conflict-Freedom in Three-Way Program Merges | Even though many programmers rely on 3-way merge tools to integrate changes
from different branches, such tools can introduce subtle bugs in the
integration process. This paper aims to mitigate this problem by defining a
semantic notion of confict-freedom, which ensures that the merged program does
not introduce new unwanted behaviors. We also show how to verify this property
using a novel, compositional algorithm that combines lightweight dependence
analysis for shared program fragments and precise relational reasoning for the
modifications. We evaluate our tool called SafeMerge on 52 real-world merge
scenarios obtained from Github and compare the results against a textual merge
tool. The experimental results demonstrate the benefits of our approach over
syntactic confict-freedom and indicate that SafeMerge is both precise and
practical.
| cs.PL | even though many programmers rely on 3way merge tools to integrate changes from different branches such tools can introduce subtle bugs in the integration process this paper aims to mitigate this problem by defining a semantic notion of confictfreedom which ensures that the merged program does not introduce new unwanted behaviors we also show how to verify this property using a novel compositional algorithm that combines lightweight dependence analysis for shared program fragments and precise relational reasoning for the modifications we evaluate our tool called safemerge on 52 realworld merge scenarios obtained from github and compare the results against a textual merge tool the experimental results demonstrate the benefits of our approach over syntactic confictfreedom and indicate that safemerge is both precise and practical | [['even', 'though', 'many', 'programmers', 'rely', 'on', '3way', 'merge', 'tools', 'to', 'integrate', 'changes', 'from', 'different', 'branches', 'such', 'tools', 'can', 'introduce', 'subtle', 'bugs', 'in', 'the', 'integration', 'process', 'this', 'paper', 'aims', 'to', 'mitigate', 'this', 'problem', 'by', 'defining', 'a', 'semantic', 'notion', 'of', 'confictfreedom', 'which', 'ensures', 'that', 'the', 'merged', 'program', 'does', 'not', 'introduce', 'new', 'unwanted', 'behaviors', 'we', 'also', 'show', 'how', 'to', 'verify', 'this', 'property', 'using', 'a', 'novel', 'compositional', 'algorithm', 'that', 'combines', 'lightweight', 'dependence', 'analysis', 'for', 'shared', 'program', 'fragments', 'and', 'precise', 'relational', 'reasoning', 'for', 'the', 'modifications', 'we', 'evaluate', 'our', 'tool', 'called', 'safemerge', 'on', '52', 'realworld', 'merge', 'scenarios', 'obtained', 'from', 'github', 'and', 'compare', 'the', 'results', 'against', 'a', 'textual', 'merge', 'tool', 'the', 'experimental', 'results', 'demonstrate', 'the', 'benefits', 'of', 'our', 'approach', 'over', 'syntactic', 'confictfreedom', 'and', 'indicate', 'that', 'safemerge', 'is', 'both', 'precise', 'and', 'practical']] | [-0.06544557113496315, 0.01178949031746015, -0.13802236180054023, 0.11708358015998784, -0.16070127760370573, -0.1563688768655993, 0.06997537761829638, 0.3739016520480315, -0.2934504299191758, -0.3360925044553975, 0.05290976838344553, -0.2576238999453684, -0.1922938634486248, 0.23120078762682775, -0.10846962666837498, 0.04559414324273045, 0.14450835106739154, -0.009305553666005531, -0.06343260433034932, -0.2196010532982958, 0.3444199303475519, 0.024338872416410594, 0.29535758354589536, 0.09594079466381421, 0.09774440402397885, 0.027710563340224325, -0.07692847276339307, 0.03195353865497357, -0.10548648193938183, 0.1555708500077041, 0.30945054313003006, 0.24533630917042804, 0.3086736513456951, -0.42845190286946794, -0.17454893017032494, 0.03650533828573922, 0.14742981381714343, 0.1342746329328899, -0.044343608658527954, -0.3092269789330506, 0.1504680297257437, -0.1912973236447821, -0.053626475323108026, -0.18956194384178768, -0.0504000839292227, -0.011005570355337113, -0.23553919812742, -0.02480400861071151, 0.09075709437796226, 0.05978007836189742, -0.017924511797415714, -0.1060205433893619, 0.020858782609381402, 0.15529999238206074, 0.019443112190492683, -0.004691810125950724, 0.13806079678082217, -0.06093349072270939, -0.1704636488391164, 0.36451910194785647, -0.031213229106894384, -0.17787682928610593, 0.2347932921218065, -0.023584061197470873, -0.21582936935592442, 0.09018416149386516, 0.19962247636770675, 0.12135766874998807, -0.15868947297664515, 0.04248241735428261, 0.0017939071966490397, 0.23568594735503817, 0.05207160998446246, 0.028690765087958425, 0.19681186774978415, 0.1727159339352511, 0.036084617080147534, 0.17366876240897303, -0.03968274833944937, -0.08648833603753397, -0.2644327969251511, -0.15777702283424636, -0.11215612173546105, -0.06148770437272712, -0.06828415290947305, -0.16789519590868926, 0.37507717772386967, 0.271912386706875, 0.17697891575905184, 0.10638073032120397, 0.34716017267201094, 0.018331413066092258, 0.10692660873755813, 0.10215714751878598, 0.16156972269915665, 0.017850013374118134, 0.12378528332240725, -0.18650222322030457, 0.11437898403964937, 0.014122795061363528] |
1,802.06552 | Are Generative Classifiers More Robust to Adversarial Attacks? | There is a rising interest in studying the robustness of deep neural network
classifiers against adversaries, with both advanced attack and defence
techniques being actively developed. However, most recent work focuses on
discriminative classifiers, which only model the conditional distribution of
the labels given the inputs. In this paper, we propose and investigate the deep
Bayes classifier, which improves classical naive Bayes with conditional deep
generative models. We further develop detection methods for adversarial
examples, which reject inputs with low likelihood under the generative model.
Experimental results suggest that deep Bayes classifiers are more robust than
deep discriminative classifiers, and that the proposed detection methods are
effective against many recently proposed attacks.
| cs.LG stat.ML | there is a rising interest in studying the robustness of deep neural network classifiers against adversaries with both advanced attack and defence techniques being actively developed however most recent work focuses on discriminative classifiers which only model the conditional distribution of the labels given the inputs in this paper we propose and investigate the deep bayes classifier which improves classical naive bayes with conditional deep generative models we further develop detection methods for adversarial examples which reject inputs with low likelihood under the generative model experimental results suggest that deep bayes classifiers are more robust than deep discriminative classifiers and that the proposed detection methods are effective against many recently proposed attacks | [['there', 'is', 'a', 'rising', 'interest', 'in', 'studying', 'the', 'robustness', 'of', 'deep', 'neural', 'network', 'classifiers', 'against', 'adversaries', 'with', 'both', 'advanced', 'attack', 'and', 'defence', 'techniques', 'being', 'actively', 'developed', 'however', 'most', 'recent', 'work', 'focuses', 'on', 'discriminative', 'classifiers', 'which', 'only', 'model', 'the', 'conditional', 'distribution', 'of', 'the', 'labels', 'given', 'the', 'inputs', 'in', 'this', 'paper', 'we', 'propose', 'and', 'investigate', 'the', 'deep', 'bayes', 'classifier', 'which', 'improves', 'classical', 'naive', 'bayes', 'with', 'conditional', 'deep', 'generative', 'models', 'we', 'further', 'develop', 'detection', 'methods', 'for', 'adversarial', 'examples', 'which', 'reject', 'inputs', 'with', 'low', 'likelihood', 'under', 'the', 'generative', 'model', 'experimental', 'results', 'suggest', 'that', 'deep', 'bayes', 'classifiers', 'are', 'more', 'robust', 'than', 'deep', 'discriminative', 'classifiers', 'and', 'that', 'the', 'proposed', 'detection', 'methods', 'are', 'effective', 'against', 'many', 'recently', 'proposed', 'attacks']] | [0.0021027601043377736, -0.022150906310084144, -0.06324444981458198, 0.1243351595309962, -0.0945357220501007, -0.28785641249019783, 0.0633444952057159, 0.44458426945493557, -0.20582374880593438, -0.2977694481877344, 0.057894715061203375, -0.29538136131928433, -0.26736984566585825, 0.17752202373685577, -0.16998295395335714, 0.15369659936342422, 0.1016582682412783, 0.03567439533695246, -0.03387267401142578, -0.35539262304415126, 0.33592761795236065, 0.08892632645516382, 0.40366711023411234, -0.05050767212118704, 0.11652659670965347, -0.01619687530702712, -0.03308664511392375, -0.006594344413315412, -0.05890312685746072, 0.2081020032700118, 0.3244526475915401, 0.254401354838462, 0.38673527335881125, -0.40145671497365193, -0.29397143663871766, 0.1330609145474487, 0.10522900967875362, 0.14571539586281038, -0.045541777782351085, -0.3775802838083889, 0.10329521447160264, -0.2175682368397247, 0.046655084089642126, -0.21098435150841915, -0.0623008177831902, 0.010498453175906823, -0.29912609141423935, 0.01134458454362175, 0.11283048117236051, 0.07009748428494536, -0.048043686611760804, -0.146191688088168, 0.026585319548238267, 0.061184836397712515, 0.08833566039850536, 0.05537931843511095, 0.1525038297529266, -0.24063631945214833, -0.1757887447394231, 0.2319476278831384, -0.06404824436490994, -0.1901413428173068, 0.21367032317877083, 0.019511518234919225, -0.19140149553173355, 0.07703716208093933, 0.25744136279848007, 0.13929441776625545, -0.16177783817485242, -0.03629535795360945, -0.041532567047397606, 0.13424384616519092, -0.003960182050442589, -0.025448541921962584, 0.18148607732395508, 0.2876667800342797, 0.01599489544865459, 0.1503909764682508, -0.19430223873808114, -0.07693827058704171, -0.1981205402158334, -0.020912717537222698, -0.1705766615507725, -0.044867367250844836, -0.10059794987280059, -0.16680603656069642, 0.37586941196163287, 0.2921963730742781, 0.20959036286304972, 0.17937708411045605, 0.3999672997243969, 0.04080164859936174, 0.10917712517091006, 0.1677932615940725, 0.2746930242459972, 0.07093967967167762, 0.019601805397542194, -0.09133450103503751, 0.17957381431915564, 0.034385402275282625] |
1,802.06553 | On the quantum improved Schwarzschild black hole | Deriving the gravitational effective action directly from exact
renormalization group is very complicated, if not impossible. Hence, to study
the effects of running gravitational coupling which tends to a non--Gaussian UV
fixed point (as it is supposed by the asymptotic safety conjecture), two steps
are usually adopted. Cutoff identification and improvement of the gravitational
coupling to the running one. As suggested in [1], a function of all independent
curvature invariants seems to be the best choice for cutoff identification of
gravitational quantum fluctuations in curved spacetime and makes the action
improvement, which saves the general covariance of theory, possible. Here, we
choose Ricci tensor square for this purpose and then the equation of motion of
improved gravitational action and its spherically symmetric vacuum solution are
obtained. Indeed, its effect on the massive particles' trajectory and the black
hole thermodynamics are studied.
| gr-qc | deriving the gravitational effective action directly from exact renormalization group is very complicated if not impossible hence to study the effects of running gravitational coupling which tends to a nongaussian uv fixed point as it is supposed by the asymptotic safety conjecture two steps are usually adopted cutoff identification and improvement of the gravitational coupling to the running one as suggested in 1 a function of all independent curvature invariants seems to be the best choice for cutoff identification of gravitational quantum fluctuations in curved spacetime and makes the action improvement which saves the general covariance of theory possible here we choose ricci tensor square for this purpose and then the equation of motion of improved gravitational action and its spherically symmetric vacuum solution are obtained indeed its effect on the massive particles trajectory and the black hole thermodynamics are studied | [['deriving', 'the', 'gravitational', 'effective', 'action', 'directly', 'from', 'exact', 'renormalization', 'group', 'is', 'very', 'complicated', 'if', 'not', 'impossible', 'hence', 'to', 'study', 'the', 'effects', 'of', 'running', 'gravitational', 'coupling', 'which', 'tends', 'to', 'a', 'nongaussian', 'uv', 'fixed', 'point', 'as', 'it', 'is', 'supposed', 'by', 'the', 'asymptotic', 'safety', 'conjecture', 'two', 'steps', 'are', 'usually', 'adopted', 'cutoff', 'identification', 'and', 'improvement', 'of', 'the', 'gravitational', 'coupling', 'to', 'the', 'running', 'one', 'as', 'suggested', 'in', '1', 'a', 'function', 'of', 'all', 'independent', 'curvature', 'invariants', 'seems', 'to', 'be', 'the', 'best', 'choice', 'for', 'cutoff', 'identification', 'of', 'gravitational', 'quantum', 'fluctuations', 'in', 'curved', 'spacetime', 'and', 'makes', 'the', 'action', 'improvement', 'which', 'saves', 'the', 'general', 'covariance', 'of', 'theory', 'possible', 'here', 'we', 'choose', 'ricci', 'tensor', 'square', 'for', 'this', 'purpose', 'and', 'then', 'the', 'equation', 'of', 'motion', 'of', 'improved', 'gravitational', 'action', 'and', 'its', 'spherically', 'symmetric', 'vacuum', 'solution', 'are', 'obtained', 'indeed', 'its', 'effect', 'on', 'the', 'massive', 'particles', 'trajectory', 'and', 'the', 'black', 'hole', 'thermodynamics', 'are', 'studied']] | [-0.1462382414256031, 0.12405304155305874, -0.11748713972575381, 0.09613297205064975, -0.1271461532764956, -0.14818249051690313, -0.00998059932905388, 0.3230960100413637, -0.21750093029204307, -0.3061881374686639, 0.11477962117113755, -0.25276786603978074, -0.14257127081839935, 0.14901649093929123, -0.028762589941950554, 0.05984887034807301, 0.010999044612320867, 0.07488457813977878, -0.07177404544550714, -0.24368329266257954, 0.3341792177917528, 0.10350196982208798, 0.24966503517926797, 0.053393825895238854, 0.10631642762756517, -0.0011446700226647635, -0.03572501991842444, 0.028810180469369846, -0.10200818216573473, 0.0595611853785945, 0.20095024316353685, 0.09289322219699653, 0.2396080263936562, -0.37690911262382004, -0.2193134212288477, 0.10956125757623966, 0.1446876552464533, 0.1412955630910814, -0.03204446792658683, -0.2828285960870273, 0.06143138076654298, -0.1713744962343563, -0.17765614761209697, -0.05124197818391712, 0.054534473422591094, -0.05220340838546845, -0.2677388849456841, 0.07244405117284684, 0.027574927219130258, -0.03558928408851543, -0.06215310187561186, -0.07375441745158073, -0.006751568979709178, 0.1275079137916472, 0.12822984096904597, 0.054021442358560386, 0.17371723724773536, -0.13072508150143614, -0.07246152723393014, 0.411918716458934, -0.10307672346367482, -0.2434319160806002, 0.1614193583587647, -0.14126260622391307, -0.12855340424819406, 0.12256130800707966, 0.11836376352605561, 0.15885202210489, -0.15696051039448972, 0.12515813189662717, 0.03409425189251292, 0.1390524032884459, 0.10189371812652717, 0.05598114283486263, 0.22270118118864848, 0.10213304884361883, 0.07293050413858806, 0.10389430235315061, -0.024291403035151093, -0.11362870477828534, -0.3480570766255788, -0.12488418989501074, -0.19999724794724125, 0.11299763384932761, -0.15411989287510827, -0.17866027473260696, 0.3563898599818877, 0.13855394510988225, 0.1117523232435086, 0.0685155975635672, 0.2766233824048165, 0.11965303486526832, 0.048222173358716654, 0.08386474545939383, 0.3143038246021045, 0.1334846731562643, 0.0607092801303147, -0.24250138239400026, -0.00553100267821487, 0.09402357668001601] |
1,802.06554 | Speed Limit for Classical Stochastic Processes | Speed limit for classical stochastic Markov processes with discrete states is
studied. We find that a trade-off inequality exists between the speed of the
state transformation and the entropy production. The dynamical activity
determines the time scale and plays a crucial role in the inequality. For
systems with stationary current, a similar trade-off inequality with the
Hatano-Sasa entropy production gives a much better bound on the speed of the
state transformation. Our inequalities contain only physically well-defined
quantities, and thus the physical picture of these inequalities is clear.
| cond-mat.stat-mech quant-ph | speed limit for classical stochastic markov processes with discrete states is studied we find that a tradeoff inequality exists between the speed of the state transformation and the entropy production the dynamical activity determines the time scale and plays a crucial role in the inequality for systems with stationary current a similar tradeoff inequality with the hatanosasa entropy production gives a much better bound on the speed of the state transformation our inequalities contain only physically welldefined quantities and thus the physical picture of these inequalities is clear | [['speed', 'limit', 'for', 'classical', 'stochastic', 'markov', 'processes', 'with', 'discrete', 'states', 'is', 'studied', 'we', 'find', 'that', 'a', 'tradeoff', 'inequality', 'exists', 'between', 'the', 'speed', 'of', 'the', 'state', 'transformation', 'and', 'the', 'entropy', 'production', 'the', 'dynamical', 'activity', 'determines', 'the', 'time', 'scale', 'and', 'plays', 'a', 'crucial', 'role', 'in', 'the', 'inequality', 'for', 'systems', 'with', 'stationary', 'current', 'a', 'similar', 'tradeoff', 'inequality', 'with', 'the', 'hatanosasa', 'entropy', 'production', 'gives', 'a', 'much', 'better', 'bound', 'on', 'the', 'speed', 'of', 'the', 'state', 'transformation', 'our', 'inequalities', 'contain', 'only', 'physically', 'welldefined', 'quantities', 'and', 'thus', 'the', 'physical', 'picture', 'of', 'these', 'inequalities', 'is', 'clear']] | [-0.14418823844012382, 0.1478940551380881, -0.11812286248790439, 0.10903948962169868, -0.011989828199148178, -0.15597014390964017, 0.0912221548020501, 0.2872457255355336, -0.28210924129995296, -0.2963997727598656, 0.07476970833853226, -0.28293312062636355, -0.10103284784550355, 0.2285745828253725, -0.031233023486989128, 0.08263420769733122, 0.04375942502255467, 0.06797001058955422, -0.07242078297581016, -0.17574421387292782, 0.30008061877875164, 0.045265983636702666, 0.31947439002000133, 0.0893981413934274, 0.12997100760086058, -0.006083639386237006, 0.020001406683480705, -0.02212092876222662, -0.1563766177044024, 0.11223510867288992, 0.2004402294432194, 0.17530988808721304, 0.25960076361132617, -0.39385899279097264, -0.21635153818087102, 0.14157014796827835, 0.10179542353216675, 0.0730054716219787, -0.06836518680872607, -0.24861079259690913, -0.02143777898428115, -0.0986099007608242, -0.141057031649821, -0.08247975889720362, 0.047500238118862566, -0.008064498776961542, -0.2826128651405187, 0.19175595790701747, 0.09022817962679917, 0.018589536169946023, -0.0478012525815178, -0.033749609159051695, -0.03599412677100521, 0.11799980614292012, 0.030793901876842774, 0.050162620360920715, 0.1302030512650328, -0.11515334865808571, -0.12885362028398298, 0.3309516443087804, -0.03864494305691386, -0.23750034865753894, 0.2025066820523617, -0.14876644262536007, -0.14969678061209957, 0.07557854990326715, 0.13707833212207665, 0.08442906044762243, -0.13443055972245269, 0.07558156791558511, -0.041498375283977526, 0.19098824076354504, 0.040354035731235686, 0.12783012885748493, 0.15567852011140945, 0.1552788131150671, 0.10860193077347834, 0.15669958310371096, -0.027501254621628588, -0.20646559084310534, -0.34206563704223797, -0.22564365109230328, -0.1364209570191716, 0.08206441833383658, -0.1709634090599469, -0.13247662294783036, 0.3384666209378999, 0.10171280192166292, 0.1894663259524598, 0.07388351006441306, 0.23701522408704145, 0.18838117258565035, 0.02287060961614109, 0.0988685489018363, 0.28049538940699265, 0.15535216785395856, 0.12251468460520053, -0.22216108411190694, 0.14501344151689077, 0.09378676375755193] |
1,802.06555 | On an Algebraic Structure of Dimensionally Reduced Magical Supergravity
Theories | We study an algebraic structure of magical supergravities in three
dimensions. We show that if the commutation relations among the generators of
the quasi-conformal group in the super-Ehlers decomposition are in a particular
form, then one can always find a parameterization of the group element in terms
of various 3d bosonic fields that reproduces the 3d reduced Lagrangian of the
corresponding magical supergravity. This provides a unified treatment of all
the magical supergravity theories in finding explicit relations between the 3d
dimensionally reduced Lagrangians and particular coset nonlinear sigma models.
We also verify that the commutation relations of $E_{6(+2)}$, the
quasi-conformal group for $\mathbb{A}=\mathbb{C}$, indeed satisfy this
property, allowing the algebraic interpretation of the structure constants and
scalar field functions as was done in the $F_{4(+4)}$ magical supergravity.
| hep-th | we study an algebraic structure of magical supergravities in three dimensions we show that if the commutation relations among the generators of the quasiconformal group in the superehlers decomposition are in a particular form then one can always find a parameterization of the group element in terms of various 3d bosonic fields that reproduces the 3d reduced lagrangian of the corresponding magical supergravity this provides a unified treatment of all the magical supergravity theories in finding explicit relations between the 3d dimensionally reduced lagrangians and particular coset nonlinear sigma models we also verify that the commutation relations of e_62 the quasiconformal group for mathbbamathbbc indeed satisfy this property allowing the algebraic interpretation of the structure constants and scalar field functions as was done in the f_44 magical supergravity | [['we', 'study', 'an', 'algebraic', 'structure', 'of', 'magical', 'supergravities', 'in', 'three', 'dimensions', 'we', 'show', 'that', 'if', 'the', 'commutation', 'relations', 'among', 'the', 'generators', 'of', 'the', 'quasiconformal', 'group', 'in', 'the', 'superehlers', 'decomposition', 'are', 'in', 'a', 'particular', 'form', 'then', 'one', 'can', 'always', 'find', 'a', 'parameterization', 'of', 'the', 'group', 'element', 'in', 'terms', 'of', 'various', '3d', 'bosonic', 'fields', 'that', 'reproduces', 'the', '3d', 'reduced', 'lagrangian', 'of', 'the', 'corresponding', 'magical', 'supergravity', 'this', 'provides', 'a', 'unified', 'treatment', 'of', 'all', 'the', 'magical', 'supergravity', 'theories', 'in', 'finding', 'explicit', 'relations', 'between', 'the', '3d', 'dimensionally', 'reduced', 'lagrangians', 'and', 'particular', 'coset', 'nonlinear', 'sigma', 'models', 'we', 'also', 'verify', 'that', 'the', 'commutation', 'relations', 'of', 'e_62', 'the', 'quasiconformal', 'group', 'for', 'mathbbamathbbc', 'indeed', 'satisfy', 'this', 'property', 'allowing', 'the', 'algebraic', 'interpretation', 'of', 'the', 'structure', 'constants', 'and', 'scalar', 'field', 'functions', 'as', 'was', 'done', 'in', 'the', 'f_44', 'magical', 'supergravity']] | [-0.14098034701531842, 0.1052072395586514, -0.07587399641938862, 0.09008082957006991, -0.10945373203694111, -0.09169319990859737, -0.030927042550747356, 0.31179616512362995, -0.2199837967369055, -0.2634729628953787, 0.06202268291316512, -0.25413601797088864, -0.21703766726164353, 0.169444213961325, -0.06356676021916052, 0.019852964020895935, -0.003708819239003037, 0.06857013040857893, -0.1751422593480952, -0.24289476957600858, 0.34797602587024723, -0.027267723211220334, 0.26626768969147213, -0.011708305690378423, 0.1343986857756381, -0.011872677697933145, -0.013927478553904664, 0.010379385095947082, -0.12772296878987588, 0.15541349123010323, 0.25493765456938866, 0.12009266891058475, 0.1143729684704412, -0.4394675318506502, -0.19751487133492315, 0.11980936038012188, 0.15789740489581452, 0.09640001656398886, -0.01399652974306798, -0.23964208100981538, 0.06658090888300822, -0.16946612250444198, -0.16413683695570816, -0.10745780885456101, 0.014729759941387567, -0.06428297094091595, -0.24728895490527122, 0.038059681757225745, 0.06521025990664456, 0.0773818918784696, -0.07800188309158243, -0.06569641380799963, -0.07473975377959302, 0.11288646795964312, 0.04772506940773585, -0.00015775075307973322, 0.05396557060099902, -0.17662644635013763, -0.10647559666540474, 0.408197362382438, -0.03337648652848743, -0.2622993513128705, 0.1265114088859668, -0.14897043518869887, -0.1980573312741601, 0.07432574784338829, 0.10462109234538816, 0.11470431917243534, -0.15767533240547876, 0.21996587407608917, -0.10643421629783771, 0.10959710422459812, 0.06360780400046635, 0.025327032127062835, 0.16513738457468294, 0.07392870200546606, 0.01872815500200164, 0.11730683185086245, 0.04122775167019831, -0.0735951695768606, -0.41426055982620236, -0.19730696938784112, -0.08094733845098831, 0.058954047611526526, -0.1717222360087954, -0.1604843179026382, 0.4047609978218725, 0.10947572438061119, 0.14659491634561814, 0.09014626660399021, 0.1870921372421204, 0.10709109187536385, 0.10090973781096557, 0.05345543100321222, 0.2586959784421774, 0.17365224372285107, -0.008324048788626753, -0.220986952048002, -0.08328386799003633, 0.19144905603209894] |
1,802.06556 | Plasma boosted electron beams for driving Free Electron Lasers | In this paper, we report results of simulations, in the framework of both
EuPRAXIA \cite{Walk2017} and EuPRAXIA@SPARC\_LAB \cite{Ferr2017} projects,
aimed at delivering a high brightness electron bunch for driving a Free
Electron Laser (FEL) by employing a plasma post acceleration scheme. The
boosting plasma wave is driven by a tens of \SI{}{\tera\watt} class laser and
doubles the energy of an externally injected beam up to \GeV{1}. The injected
bunch is simulated starting from a photoinjector, matched to plasma, boosted
and finally matched to an undulator, where its ability to produce FEL radiation
is verified to yield $O(\num{e11})$ photons per shot at \nm{2.7}.
| physics.acc-ph | in this paper we report results of simulations in the framework of both eupraxia citewalk2017 and eupraxiasparc_lab citeferr2017 projects aimed at delivering a high brightness electron bunch for driving a free electron laser fel by employing a plasma post acceleration scheme the boosting plasma wave is driven by a tens of siterawatt class laser and doubles the energy of an externally injected beam up to gev1 the injected bunch is simulated starting from a photoinjector matched to plasma boosted and finally matched to an undulator where its ability to produce fel radiation is verified to yield onume11 photons per shot at nm27 | [['in', 'this', 'paper', 'we', 'report', 'results', 'of', 'simulations', 'in', 'the', 'framework', 'of', 'both', 'eupraxia', 'citewalk2017', 'and', 'eupraxiasparc_lab', 'citeferr2017', 'projects', 'aimed', 'at', 'delivering', 'a', 'high', 'brightness', 'electron', 'bunch', 'for', 'driving', 'a', 'free', 'electron', 'laser', 'fel', 'by', 'employing', 'a', 'plasma', 'post', 'acceleration', 'scheme', 'the', 'boosting', 'plasma', 'wave', 'is', 'driven', 'by', 'a', 'tens', 'of', 'siterawatt', 'class', 'laser', 'and', 'doubles', 'the', 'energy', 'of', 'an', 'externally', 'injected', 'beam', 'up', 'to', 'gev1', 'the', 'injected', 'bunch', 'is', 'simulated', 'starting', 'from', 'a', 'photoinjector', 'matched', 'to', 'plasma', 'boosted', 'and', 'finally', 'matched', 'to', 'an', 'undulator', 'where', 'its', 'ability', 'to', 'produce', 'fel', 'radiation', 'is', 'verified', 'to', 'yield', 'onume11', 'photons', 'per', 'shot', 'at', 'nm27']] | [-0.0728850140471549, 0.2045660119089082, -0.07402241070149947, 0.022851580137041274, 0.01657634199904182, -0.13712315495034738, 0.015333881055619376, 0.45435914109201775, -0.21323301495513736, -0.34736442909643206, 0.0191332081851271, -0.28749584683130697, 0.06838349247178466, 0.3130236072369765, 0.0010114712328602052, 0.06139387254610408, 0.05038498160573318, -0.03714213918740909, 0.004877463684023656, -0.17965404394553186, 0.2534278734327899, 0.22251109077988826, 0.27600726140807047, 0.0625169802668322, 0.18805324712998628, -0.007397630014312789, -0.0007800048207576127, -0.03577976608552884, -0.07489419088848344, 0.06199876695976967, 0.22418400073980854, 0.055406642499255, 0.3115315857564205, -0.450029679161218, -0.21603418209172362, -0.009391799905174171, 0.13710404451955685, 0.11307847678910979, -0.10591498769090041, -0.23394994118932597, 0.05631807787324657, -0.22782965320325696, -0.16028382491858043, 0.014783859869810878, -0.061401428289941905, 0.07984135910561405, -0.3123679066883381, -0.01421386626616274, -0.009306124056276587, -0.005144129219205724, -0.01598813653366698, -0.007862417312991834, 0.013313035154235117, 0.023755005153961787, 0.03439973289214228, 0.14618591496663302, 0.2192287804875715, -0.15060574173226415, -0.10325406297810913, 0.39081769990590737, -0.06448171477219973, -0.09029042102473299, 0.14438919399951383, -0.19443401296325413, -0.02074045869857841, 0.23233676439189574, 0.18530643368427901, 0.09952691918450225, -0.14977828822741956, -0.02862581043424968, 0.03518702224699286, 0.1842605755040326, 0.1592302274525396, -0.0054191910258503916, 0.2363411526858192, 0.2087255188062326, 0.012341474134897449, 0.1817604080538659, -0.14830032242558053, 0.03915686480048084, -0.28810899681651714, -0.06005718130330296, -0.15801716511397018, 0.0400271820120175, 0.0010996712376207555, -0.10973491772742865, 0.4617035499638227, 0.1719358497558488, 0.09236391847857188, -0.028970872954532656, 0.35318422206130223, 0.14012175904990165, -0.007329556793358522, 0.08633161940103032, 0.2374965459703631, 0.1291391553222826, 0.10587827686566054, -0.22802817716128818, -0.05916541287694702, 0.0034579879018602913] |
1,802.06557 | Symmetry and Contextuality | The general concept of symmetry is realized in manifold ways in different
realms of reality, such as plants, animals, minerals, mathematical objects or
human artefacts in literature, fine arts and society. In order to arrive at a
common ground for this variedness a very general conceptualization of symmetry
is proposed: Existence of substitutions, which, in the given context, do not
lead to an essential change. This simple definition has multiple consequences:
-The context dependence of the notion of symmetry is evident in the humanities
but by no means irrelevant yet often neglected in science. The subtle
problematic of concept formation and the ontological status of similarities
opens up. -In general, the substitutions underlying the concept of symmetry are
not really performed but remain in a state of virtuality. Counterfactuality,
freedom and creativity come into focus. The detection of previously hidden
symmetries may provide deep and surprising insights. -Related to this, due
attention is devoted to the aesthetic dimension of symmetry and the breaking of
it. -Finally, we point out to what extent life is based on the interplay
between order and freedom, between full and broken symmetry.
| physics.hist-ph | the general concept of symmetry is realized in manifold ways in different realms of reality such as plants animals minerals mathematical objects or human artefacts in literature fine arts and society in order to arrive at a common ground for this variedness a very general conceptualization of symmetry is proposed existence of substitutions which in the given context do not lead to an essential change this simple definition has multiple consequences the context dependence of the notion of symmetry is evident in the humanities but by no means irrelevant yet often neglected in science the subtle problematic of concept formation and the ontological status of similarities opens up in general the substitutions underlying the concept of symmetry are not really performed but remain in a state of virtuality counterfactuality freedom and creativity come into focus the detection of previously hidden symmetries may provide deep and surprising insights related to this due attention is devoted to the aesthetic dimension of symmetry and the breaking of it finally we point out to what extent life is based on the interplay between order and freedom between full and broken symmetry | [['the', 'general', 'concept', 'of', 'symmetry', 'is', 'realized', 'in', 'manifold', 'ways', 'in', 'different', 'realms', 'of', 'reality', 'such', 'as', 'plants', 'animals', 'minerals', 'mathematical', 'objects', 'or', 'human', 'artefacts', 'in', 'literature', 'fine', 'arts', 'and', 'society', 'in', 'order', 'to', 'arrive', 'at', 'a', 'common', 'ground', 'for', 'this', 'variedness', 'a', 'very', 'general', 'conceptualization', 'of', 'symmetry', 'is', 'proposed', 'existence', 'of', 'substitutions', 'which', 'in', 'the', 'given', 'context', 'do', 'not', 'lead', 'to', 'an', 'essential', 'change', 'this', 'simple', 'definition', 'has', 'multiple', 'consequences', 'the', 'context', 'dependence', 'of', 'the', 'notion', 'of', 'symmetry', 'is', 'evident', 'in', 'the', 'humanities', 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1,802.06558 | Slowest kinetic modes revealed by metabasin renormalization | Understanding the slowest relaxations of complex systems, such as relaxation
of glass-forming materials, diffusion in nanoclusters, and folding of
biomolecules, is important for physics, chemistry, and biology. For a kinetic
system, the relaxation modes are determined by diagonalizing its transition
rate matrix. However, for realistic systems of interest, numerical
diagonalization, as well as extracting physical understanding from the
diagonalization results, is difficult due to the high dimensionality. Here, we
develop an alternative and generally applicable method of extracting the
long-time scale relaxation dynamics by combining the metabasin analysis of
Okushima et al. [Phys. Rev. E 80, 036112 (2009)] and a Jacobi method. We test
the method on a illustrative model of a four-funnel model, for which we obtain
a renormalized kinematic equation of much lower dimension sufficient for
determining slow relaxation modes precisely. The method is successfully applied
to the vacancy transport problem in ionic nanoparticles [Niiyama et al. Chem.
Phys. Lett. 654, 52 (2016)], allowing a clear physical interpretation that the
final relaxation consists of two successive, characteristic processes.
| cond-mat.mes-hall cond-mat.dis-nn | understanding the slowest relaxations of complex systems such as relaxation of glassforming materials diffusion in nanoclusters and folding of biomolecules is important for physics chemistry and biology for a kinetic system the relaxation modes are determined by diagonalizing its transition rate matrix however for realistic systems of interest numerical diagonalization as well as extracting physical understanding from the diagonalization results is difficult due to the high dimensionality here we develop an alternative and generally applicable method of extracting the longtime scale relaxation dynamics by combining the metabasin analysis of okushima et al phys rev e 80 036112 2009 and a jacobi method we test the method on a illustrative model of a fourfunnel model for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely the method is successfully applied to the vacancy transport problem in ionic nanoparticles niiyama et al chem phys lett 654 52 2016 allowing a clear physical interpretation that the final relaxation consists of two successive characteristic processes | [['understanding', 'the', 'slowest', 'relaxations', 'of', 'complex', 'systems', 'such', 'as', 'relaxation', 'of', 'glassforming', 'materials', 'diffusion', 'in', 'nanoclusters', 'and', 'folding', 'of', 'biomolecules', 'is', 'important', 'for', 'physics', 'chemistry', 'and', 'biology', 'for', 'a', 'kinetic', 'system', 'the', 'relaxation', 'modes', 'are', 'determined', 'by', 'diagonalizing', 'its', 'transition', 'rate', 'matrix', 'however', 'for', 'realistic', 'systems', 'of', 'interest', 'numerical', 'diagonalization', 'as', 'well', 'as', 'extracting', 'physical', 'understanding', 'from', 'the', 'diagonalization', 'results', 'is', 'difficult', 'due', 'to', 'the', 'high', 'dimensionality', 'here', 'we', 'develop', 'an', 'alternative', 'and', 'generally', 'applicable', 'method', 'of', 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0.053332754779685604, 0.08056351205289185] |
1,802.06559 | Remarks on BMS${}_3$ invariant field theories: correlation functions and
nonunitary CFTs | We use the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras to
reconsider some generic aspects of CFTs with the BMS${}_3$ algebra defined as a
chiral symmetry. For unitarity theories, it is known that the extended symmetry
generator acts trivially, and the resulting theory is equivalent to a CFT with
a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending
on a nilpotent variable, and we organize the Verma module through the action of
this new operator. Finally, we find the conditions imposed by the modified Ward
identity.
| hep-th | we use the isomorphism between the bms_3 and the w22 algebras to reconsider some generic aspects of cfts with the bms_3 algebra defined as a chiral symmetry for unitarity theories it is known that the extended symmetry generator acts trivially and the resulting theory is equivalent to a cft with a virasoro symmetry only for nonunitary cfts we define an operator depending on a nilpotent variable and we organize the verma module through the action of this new operator finally we find the conditions imposed by the modified ward identity | [['we', 'use', 'the', 'isomorphism', 'between', 'the', 'bms_3', 'and', 'the', 'w22', 'algebras', 'to', 'reconsider', 'some', 'generic', 'aspects', 'of', 'cfts', 'with', 'the', 'bms_3', 'algebra', 'defined', 'as', 'a', 'chiral', 'symmetry', 'for', 'unitarity', 'theories', 'it', 'is', 'known', 'that', 'the', 'extended', 'symmetry', 'generator', 'acts', 'trivially', 'and', 'the', 'resulting', 'theory', 'is', 'equivalent', 'to', 'a', 'cft', 'with', 'a', 'virasoro', 'symmetry', 'only', 'for', 'nonunitary', 'cfts', 'we', 'define', 'an', 'operator', 'depending', 'on', 'a', 'nilpotent', 'variable', 'and', 'we', 'organize', 'the', 'verma', 'module', 'through', 'the', 'action', 'of', 'this', 'new', 'operator', 'finally', 'we', 'find', 'the', 'conditions', 'imposed', 'by', 'the', 'modified', 'ward', 'identity']] | [-0.15369860261368254, 0.13567098898234287, -0.09761103492023217, 0.052801942231599244, -0.14855006183756309, -0.17435227068555023, -0.03319449604411299, 0.32712115100067524, -0.291186087537143, -0.17972456488447885, 0.1444445377940105, -0.2567254557377762, -0.18038039669497974, 0.1030978098925617, -0.08041682371921423, 0.019774977655874357, 0.012695320923295285, 0.11426294427882466, -0.1657053415844631, -0.21977062709629536, 0.39156848317943516, 0.029475474505064388, 0.25705317080331347, 0.05933733135009081, 0.14760192153820148, 0.0428155332751986, 0.023539913818240166, -0.04120073817256424, -0.1321670982292239, 0.10165067662795385, 0.21920270046490867, 0.07263394824436141, 0.12893977138317295, -0.4261852312238059, -0.1349041352643528, 0.11971766429875667, 0.11923055263857046, 0.09183577112853528, -0.03629970306970386, -0.31115820614828005, 0.05465168725285265, -0.2370469237988194, -0.16081621226233742, -0.08326401182760795, 0.017426286798177495, -0.10765529147659739, -0.2774573483866536, 0.04609155124829461, 0.06391218652327856, 0.07126986572725905, -0.09009161143460208, -0.020169294572001995, -0.1251344353477988, 0.09359385554885699, 0.04637061229700016, 0.012405681734283766, 0.1387957734405063, -0.1463097817549068, -0.14355303598050442, 0.3691691449532906, -0.014927550372279559, -0.2660787449011372, 0.14366894992482332, -0.11686931199833958, -0.20091589409857988, -0.013109074271697965, 0.045564637829860054, 0.14485113244089814, -0.10678138734979761, 0.2116338515013922, -0.11423127750555674, 0.08767574943938396, 0.04746364784530467, 0.010639514789606135, 0.17850854658625193, 0.04847708228820314, 0.07253544544801116, 0.17618863275792035, 0.05629417693190691, -0.059456221583402816, -0.45215919125411247, -0.17508191832522343, -0.10462104867522916, 0.09412705320088814, -0.10380418347663686, -0.15704723562941783, 0.42365743649295634, 0.1821840429652689, 0.1881879926950205, 0.09529950322790279, 0.1681365904631093, 0.16648171267653297, 0.1888073686988921, 0.05934776227093405, 0.16864633256110312, 0.21862858737974117, 0.011808026933835612, -0.24396576391300187, -0.09744199349855383, 0.22457560396546292] |
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