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1,802.0756 | Critical yield numbers and limiting yield surfaces of particle arrays
settling in a Bingham fluid | We consider the flow of multiple particles in a Bingham fluid in an
anti-plane shear flow configuration. The limiting situation in which the
internal and applied forces balance and the fluid and particles stop flowing,
that is, when the flow settles, is formulated as finding the optimal ratio
between the total variation functional and a linear functional. The minimal
value for this quotient is referred to as the critical yield number or, in
analogy to Rayleigh quotients, generalized eigenvalue. This minimum value can
in general only be attained by discontinuous, hence not physical, velocities.
However, we prove that these generalized eigenfunctions, whose jumps we refer
to as limiting yield surfaces, appear as rescaled limits of the physical
velocities. Then, we show the existence of geometrically simple minimizers.
Furthermore, a numerical method for the minimization is then considered. It is
based on a nonlinear finite difference discretization, whose consistency is
proven, and a standard primal-dual descent scheme. Finally, numerical examples
show a variety of geometric solutions exhibiting the properties discussed in
the theoretical sections.
| math.OC | we consider the flow of multiple particles in a bingham fluid in an antiplane shear flow configuration the limiting situation in which the internal and applied forces balance and the fluid and particles stop flowing that is when the flow settles is formulated as finding the optimal ratio between the total variation functional and a linear functional the minimal value for this quotient is referred to as the critical yield number or in analogy to rayleigh quotients generalized eigenvalue this minimum value can in general only be attained by discontinuous hence not physical velocities however we prove that these generalized eigenfunctions whose jumps we refer to as limiting yield surfaces appear as rescaled limits of the physical velocities then we show the existence of geometrically simple minimizers furthermore a numerical method for the minimization is then considered it is based on a nonlinear finite difference discretization whose consistency is proven and a standard primaldual descent scheme finally numerical examples show a variety of geometric solutions exhibiting the properties discussed in the theoretical sections | [['we', 'consider', 'the', 'flow', 'of', 'multiple', 'particles', 'in', 'a', 'bingham', 'fluid', 'in', 'an', 'antiplane', 'shear', 'flow', 'configuration', 'the', 'limiting', 'situation', 'in', 'which', 'the', 'internal', 'and', 'applied', 'forces', 'balance', 'and', 'the', 'fluid', 'and', 'particles', 'stop', 'flowing', 'that', 'is', 'when', 'the', 'flow', 'settles', 'is', 'formulated', 'as', 'finding', 'the', 'optimal', 'ratio', 'between', 'the', 'total', 'variation', 'functional', 'and', 'a', 'linear', 'functional', 'the', 'minimal', 'value', 'for', 'this', 'quotient', 'is', 'referred', 'to', 'as', 'the', 'critical', 'yield', 'number', 'or', 'in', 'analogy', 'to', 'rayleigh', 'quotients', 'generalized', 'eigenvalue', 'this', 'minimum', 'value', 'can', 'in', 'general', 'only', 'be', 'attained', 'by', 'discontinuous', 'hence', 'not', 'physical', 'velocities', 'however', 'we', 'prove', 'that', 'these', 'generalized', 'eigenfunctions', 'whose', 'jumps', 'we', 'refer', 'to', 'as', 'limiting', 'yield', 'surfaces', 'appear', 'as', 'rescaled', 'limits', 'of', 'the', 'physical', 'velocities', 'then', 'we', 'show', 'the', 'existence', 'of', 'geometrically', 'simple', 'minimizers', 'furthermore', 'a', 'numerical', 'method', 'for', 'the', 'minimization', 'is', 'then', 'considered', 'it', 'is', 'based', 'on', 'a', 'nonlinear', 'finite', 'difference', 'discretization', 'whose', 'consistency', 'is', 'proven', 'and', 'a', 'standard', 'primaldual', 'descent', 'scheme', 'finally', 'numerical', 'examples', 'show', 'a', 'variety', 'of', 'geometric', 'solutions', 'exhibiting', 'the', 'properties', 'discussed', 'in', 'the', 'theoretical', 'sections']] | [-0.1255977571944604, 0.11740856095578191, -0.11272225652772912, 0.06876022762059089, -0.058886211693846766, -0.11649609184850847, 0.01740564687602825, 0.33269633655974673, -0.3233273341158954, -0.26678464779727207, 0.12143999178936932, -0.23718108430052595, -0.15119792543610053, 0.1814624041876072, -0.0853276644211607, 0.0860333507705609, 0.044484699452484316, 0.0432503917173757, -0.06410416622102433, -0.20975679801602046, 0.29185918947907885, -0.0007799021708590619, 0.28378302678788847, 0.07398406922281585, 0.12797952092096554, -0.02470370239478595, 0.012835149028785311, 0.09741863649273884, -0.167544849230817, 0.0723151040204257, 0.2437525070110885, 0.057310246898808835, 0.25782680818595727, -0.40625948860509203, -0.2158309550891291, 0.12614880047329416, 0.14537942965078904, 0.08087310644143901, -0.03376567202439865, -0.2089333144807919, 0.08970774861585586, -0.1453562674026484, -0.15365284382274128, -0.0679229981658948, 0.004807927303899058, 0.07235518908814521, -0.27787569922400435, 0.09876303152165058, 0.0628346030821087, 0.048204530100472744, -0.07600374090636008, -0.09301750214347843, -0.041329990894765176, 0.0710590706374079, 0.07485387326726917, -0.030419670039992457, 0.1157632553526012, -0.12064266221791592, -0.06295994658970591, 0.4148851873170089, -0.0711799972152978, -0.28591912988078044, 0.1722665725584072, -0.08714321629424186, -0.08223394400607041, 0.11745837294480446, 0.17124635478309383, 0.15167050176055166, -0.1165759067790148, 0.06869083312252601, -0.07453125287547191, 0.11796031764242798, 0.08586789285925599, -0.029117078720551588, 0.15208446624758787, 0.13772026896126827, 0.13306072026335047, 0.14746874980991867, -0.06605830257139411, -0.13505444680798173, -0.3560922103399018, -0.1623180534507584, -0.18498357478764738, 0.06583131814916884, -0.11095738202840497, -0.18943780028083593, 0.3478146723029431, 0.09072581505419072, 0.2148197113470352, 0.07835372441125774, 0.2695747256881929, 0.165797145253941, 0.016831464183279934, 0.10232721131047331, 0.26905816159684837, 0.16430321445747822, 0.06312072360780456, -0.22348991047585587, 0.04494847545118981, 0.12077225007606682] |
1,802.07561 | $L_p$ Minkowski Valuations on polytopes | For $1 \leq p < \infty$, Ludwig, Haberl and Parapatits classified $L_p$
Minkowski valuations intertwining the special linear group with additional
conditions such as homogeneity and continuity. In this paper,a complete
classification of $L_p$ Minkowski valuations intertwining the special linear
group on polytopes without any additional conditions is established for $p \geq
1$ including $p = \infty$. For $n=3$ and $p=1$, there exist valuations not
mentioned before.
| math.MG | for 1 leq p infty ludwig haberl and parapatits classified l_p minkowski valuations intertwining the special linear group with additional conditions such as homogeneity and continuity in this papera complete classification of l_p minkowski valuations intertwining the special linear group on polytopes without any additional conditions is established for p geq 1 including p infty for n3 and p1 there exist valuations not mentioned before | [['for', '1', 'leq', 'p', 'infty', 'ludwig', 'haberl', 'and', 'parapatits', 'classified', 'l_p', 'minkowski', 'valuations', 'intertwining', 'the', 'special', 'linear', 'group', 'with', 'additional', 'conditions', 'such', 'as', 'homogeneity', 'and', 'continuity', 'in', 'this', 'papera', 'complete', 'classification', 'of', 'l_p', 'minkowski', 'valuations', 'intertwining', 'the', 'special', 'linear', 'group', 'on', 'polytopes', 'without', 'any', 'additional', 'conditions', 'is', 'established', 'for', 'p', 'geq', '1', 'including', 'p', 'infty', 'for', 'n3', 'and', 'p1', 'there', 'exist', 'valuations', 'not', 'mentioned', 'before']] | [-0.1384649303436163, 0.09902756131486967, -0.03142756858142093, 0.12108535345760174, -0.07116086279711453, -0.23944778117584065, 0.0016977296472759917, 0.37004374276148155, -0.29655683404416777, -0.2021098673576489, 0.11079998649620393, -0.29222374353412306, -0.0625319077516906, 0.13822739068200462, -0.10636696646542987, 0.07611938068293966, -0.07411636371398345, 0.08090402859670576, -0.1240855247961008, -0.343341094767311, 0.3313190790358931, -0.05195962905418128, 0.21373677246447187, 0.007925746642285958, 0.07097386812347395, 0.08896494537475519, 0.02567672422810574, -0.04088449331902666, -0.2344886411810876, 0.014238674790249206, 0.31450754590878205, 0.11083037273419905, 0.2654539610230131, -0.3647734136611689, -0.17462456862267572, 0.2453519987902837, 0.09684922615997493, -0.0758322541587404, -0.02617522154650942, -0.2506891936791362, 0.09460805424168939, -0.06640742684248835, -0.15584237111033872, -0.105058416898828, 0.13199913123389706, 0.013941785131464712, -0.3123856582751614, 0.06117129778431263, 0.2200796619799803, 0.15586928839911707, -0.16515293695920263, -0.23400412790942937, -0.050160508741100784, 0.07025013800193847, 0.02829212550932425, 0.09347839040856343, 0.01410197232326027, -0.06779451292459271, -0.10982372830039822, 0.37763028386689257, 0.010529680948820896, -0.2362445500693866, 0.11195925049833022, -0.18832564882541192, -0.2180948903915123, 0.08880763231536548, 0.07852471803198569, 0.15137400967796566, -0.028703367162961513, 0.23633493826946506, -0.12283495254450827, 0.07257925797603093, 0.17871339844714385, 0.036350173366372474, 0.016589431470492855, 0.019921333907404914, 0.11095441169891274, 0.07816185971023515, 0.05540611817923491, 0.01583758945344016, -0.4326334406650858, -0.1698322832962731, -0.1601573465159163, 0.1636642395681065, -0.15942672410096748, -0.08489153833943419, 0.21731001567786734, 0.0026155202358495444, 0.14704524214903358, 0.12599083682289347, 0.14682316905236803, 0.048835959589268896, 0.029100253974320367, 0.09516831120708957, 0.15228705905610695, 0.1079118066263618, 0.01043291076348396, -0.09914042055515893, -0.013419110058748629, 0.15069018743088236] |
1,802.07562 | Early warning signals in plant disease outbreaks | Summary
1. Infectious disease outbreaks in plants threaten ecosystems, agricultural
crops and food trade. Currently, several fungal diseases are affecting forests
worldwide, posing a major risk to tree species, habitats and consequently
ecosystem decay. Prediction and control of disease spread are difficult, mainly
due to the complexity of the interaction between individual components
involved.
2. In this work, we introduce a lattice-based epidemic model coupled with a
stochastic process that mimics, in a very simplified way, the interaction
between the hosts and pathogen. We studied the disease spread by measuring the
propagation velocity of the pathogen on the susceptible hosts. Quantitative
results indicate the occurrence of a critical transition between two stable
phases: local confinement and an extended epiphytotic outbreak that depends on
the density of the susceptible individuals.
3. Quantitative predictions of epiphytotics are performed using the framework
early-warning indicators for impending regime shifts, widely applied on
dynamical systems. These signals forecast successfully the outcome of the
critical shift between the two stable phases before the system enters the
epiphytotic regime.
4. Synthesis: Our study demonstrates that early-warning indicators could be
useful for the prediction of forest disease epidemics through mathematical and
computational models suited to more specific pathogen-host-environmental
interactions.
| q-bio.PE | summary 1 infectious disease outbreaks in plants threaten ecosystems agricultural crops and food trade currently several fungal diseases are affecting forests worldwide posing a major risk to tree species habitats and consequently ecosystem decay prediction and control of disease spread are difficult mainly due to the complexity of the interaction between individual components involved 2 in this work we introduce a latticebased epidemic model coupled with a stochastic process that mimics in a very simplified way the interaction between the hosts and pathogen we studied the disease spread by measuring the propagation velocity of the pathogen on the susceptible hosts quantitative results indicate the occurrence of a critical transition between two stable phases local confinement and an extended epiphytotic outbreak that depends on the density of the susceptible individuals 3 quantitative predictions of epiphytotics are performed using the framework earlywarning indicators for impending regime shifts widely applied on dynamical systems these signals forecast successfully the outcome of the critical shift between the two stable phases before the system enters the epiphytotic regime 4 synthesis our study demonstrates that earlywarning indicators could be useful for the prediction of forest disease epidemics through mathematical and computational models suited to more specific pathogenhostenvironmental interactions | [['summary', '1', 'infectious', 'disease', 'outbreaks', 'in', 'plants', 'threaten', 'ecosystems', 'agricultural', 'crops', 'and', 'food', 'trade', 'currently', 'several', 'fungal', 'diseases', 'are', 'affecting', 'forests', 'worldwide', 'posing', 'a', 'major', 'risk', 'to', 'tree', 'species', 'habitats', 'and', 'consequently', 'ecosystem', 'decay', 'prediction', 'and', 'control', 'of', 'disease', 'spread', 'are', 'difficult', 'mainly', 'due', 'to', 'the', 'complexity', 'of', 'the', 'interaction', 'between', 'individual', 'components', 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1,802.07563 | Laplace transforms and valuations | It is proved that the classical Laplace transform is a continuous valuation
which is positively GL$(n)$ covariant and logarithmic translation covariant.
Conversely, these properties turn out to be sufficient to characterize this
transform.
| math.MG math.FA | it is proved that the classical laplace transform is a continuous valuation which is positively gln covariant and logarithmic translation covariant conversely these properties turn out to be sufficient to characterize this transform | [['it', 'is', 'proved', 'that', 'the', 'classical', 'laplace', 'transform', 'is', 'a', 'continuous', 'valuation', 'which', 'is', 'positively', 'gln', 'covariant', 'and', 'logarithmic', 'translation', 'covariant', 'conversely', 'these', 'properties', 'turn', 'out', 'to', 'be', 'sufficient', 'to', 'characterize', 'this', 'transform']] | [-0.08421459794044495, 0.09920225738350189, -0.20404847896178113, 0.15207662874352978, -0.18106354722245174, -0.16073253255506809, -0.04971695237944721, 0.3910664322249817, -0.3768593768278758, -0.12197557001402884, 0.10573919515732225, -0.20357448870852363, -0.1747844543195132, 0.17778696819688333, -0.12161404258486899, 0.03300239766637484, -0.03669717174136278, 0.07956733616689841, -0.10651219909248705, -0.3239008527474873, 0.2747917834556464, 0.033581501324519966, 0.3031056878918951, 0.03271813517097722, 0.08751356751291138, -0.022352764326514618, -0.05667772403015106, -0.03547643356476769, -0.09130039905082385, 0.12030552731206019, 0.25724407319318165, 0.08925901436613816, 0.2465718218097181, -0.3502123485121763, -0.19948857562672911, 0.17874547060240398, 0.0744854249342373, -0.005052961186844517, 0.030128473253694898, -0.3060899113276691, 0.13948922631133234, -0.11546802747938217, -0.1540320466808749, -0.2076328651923122, 0.07024895439319538, -0.02611946983432228, -0.27958612894695817, 0.04944137512057117, 0.14559359792055507, 0.012185271236706863, -0.06845862040239753, -0.02946033658967777, -0.019890147190766806, 0.03557909431048867, 0.02095170081310877, 0.12280915117342815, 0.14081730119263133, -0.027333603141772928, -0.04546628601736191, 0.3785133269248587, -0.029357999083444927, -0.3170880761251531, 0.13311381872997366, -0.1939924212285515, -0.1412131775622115, 0.11125559792995002, 0.0791878356513652, 0.12544208503977367, -0.2244361782107841, 0.14694236659014484, -0.11870284079376495, 0.136813261969523, 0.13002131992217267, 0.007771750954403119, 0.14235573634505272, -0.02044748452802499, 0.1292589201281468, 0.16013890196865593, 0.045389244220021996, -0.14256682365455411, -0.3462691583924673, -0.2429181392671484, -0.15823868659296722, 0.12096992358000892, -0.008952738025320948, -0.1795776431646311, 0.3404433207981514, 0.05813937423094599, 0.11651025997531234, 0.1229236810926743, 0.2377016647634181, 0.23777496192964132, 0.07506365027052886, 0.05310778978816939, 0.1425448004720789, 0.20665666404547114, 0.022640678375451403, -0.19410304684248386, -0.004528063716310443, 0.12468396808782761] |
1,802.07564 | Clipped Action Policy Gradient | Many continuous control tasks have bounded action spaces. When policy
gradient methods are applied to such tasks, out-of-bound actions need to be
clipped before execution, while policies are usually optimized as if the
actions are not clipped. We propose a policy gradient estimator that exploits
the knowledge of actions being clipped to reduce the variance in estimation. We
prove that our estimator, named clipped action policy gradient (CAPG), is
unbiased and achieves lower variance than the conventional estimator that
ignores action bounds. Experimental results demonstrate that CAPG generally
outperforms the conventional estimator, indicating that it is a better policy
gradient estimator for continuous control tasks. The source code is available
at https://github.com/pfnet-research/capg.
| cs.LG cs.AI stat.ML | many continuous control tasks have bounded action spaces when policy gradient methods are applied to such tasks outofbound actions need to be clipped before execution while policies are usually optimized as if the actions are not clipped we propose a policy gradient estimator that exploits the knowledge of actions being clipped to reduce the variance in estimation we prove that our estimator named clipped action policy gradient capg is unbiased and achieves lower variance than the conventional estimator that ignores action bounds experimental results demonstrate that capg generally outperforms the conventional estimator indicating that it is a better policy gradient estimator for continuous control tasks the source code is available at httpsgithubcompfnetresearchcapg | [['many', 'continuous', 'control', 'tasks', 'have', 'bounded', 'action', 'spaces', 'when', 'policy', 'gradient', 'methods', 'are', 'applied', 'to', 'such', 'tasks', 'outofbound', 'actions', 'need', 'to', 'be', 'clipped', 'before', 'execution', 'while', 'policies', 'are', 'usually', 'optimized', 'as', 'if', 'the', 'actions', 'are', 'not', 'clipped', 'we', 'propose', 'a', 'policy', 'gradient', 'estimator', 'that', 'exploits', 'the', 'knowledge', 'of', 'actions', 'being', 'clipped', 'to', 'reduce', 'the', 'variance', 'in', 'estimation', 'we', 'prove', 'that', 'our', 'estimator', 'named', 'clipped', 'action', 'policy', 'gradient', 'capg', 'is', 'unbiased', 'and', 'achieves', 'lower', 'variance', 'than', 'the', 'conventional', 'estimator', 'that', 'ignores', 'action', 'bounds', 'experimental', 'results', 'demonstrate', 'that', 'capg', 'generally', 'outperforms', 'the', 'conventional', 'estimator', 'indicating', 'that', 'it', 'is', 'a', 'better', 'policy', 'gradient', 'estimator', 'for', 'continuous', 'control', 'tasks', 'the', 'source', 'code', 'is', 'available', 'at', 'httpsgithubcompfnetresearchcapg']] | [-0.050210281000049276, 0.03161366748284887, -0.15160987351343713, 0.07196929596406831, -0.133406944132664, -0.21055660873905502, 0.053124361008998346, 0.5375661875713955, -0.2702980153262615, -0.2766546459360556, 0.16432227892272006, -0.2639779188162224, -0.1751357546499507, 0.2427335444245149, -0.21537427849305624, 0.0750480103137141, 0.09315215098057789, 0.06034806130284613, -0.10561318454459648, -0.3126376699656248, 0.21458950847895308, 0.05128922560252249, 0.3655897136692974, -0.03523123130593872, 0.1670495495443571, -0.0360329409299249, 0.0062694731554736125, 0.005782652870667252, -0.02824112263631171, 0.0970413919961588, 0.28956055318598045, 0.1748652553757314, 0.36361138341440397, -0.3135726749727672, -0.23709371012042868, 0.15841312863525342, 0.12869951619597322, 0.09064950290855697, -0.015648592219010674, -0.2712890341454609, 0.10589865175583824, -0.17541476919908416, 0.006975938375531273, -0.14228613306609492, -0.10774715939875354, 0.0023586529756853864, -0.3833793395156549, 0.08168933378871192, 0.041806485862682825, 0.037119288126599384, -0.07522935045205734, -0.16202102002941748, -0.0007885659219358455, 0.14636477540083104, 0.07007315061266788, 0.08850625945805488, 0.22123353326354514, -0.08889627123082226, -0.16657508471134033, 0.31105527114123105, -0.08575845085870241, -0.25171059041538024, 0.10759226492161608, -0.0715986240866848, -0.11604864484291863, 0.11470730207352475, 0.1849859685637057, 0.13035095322623172, -0.14445912473774197, 0.054391306341858583, -0.013264993764460086, 0.17751847316447475, 0.0042855089826678685, 0.018687482889402997, 0.08541089989752933, 0.12776842133607716, 0.2439340075070504, 0.12189011237774552, -0.041230565309524535, -0.11434767872931181, -0.256387908028608, -0.0688605223105035, -0.19868528734553945, -0.07213432732744629, -0.12755272089151815, -0.15888052924684334, 0.3036347695033659, 0.21341674646193332, 0.12849581409669059, 0.19057824620977043, 0.3992983022535389, 0.11815766656178642, 0.1264755807647651, 0.1995495093774728, 0.21458740920590405, 0.03220281202811748, 0.035729901676214385, -0.21889914871532132, 0.15198279973966153, 0.08931976321235363] |
1,802.07565 | Fluctuation Analysis of the Atmospheric Energy Cycle | The atmosphere gains available potential energy by solar radiation and
dissipates kinetic energy mainly in the atmospheric boundary layer. We analyze
the fluctuations of the global mean energy cycle defined by Lorenz (1955) in a
simulation with a simplified hydrostatic model. The energy current densities
are well approximated by the generalized Gumbel distribution (Bramwell,
Holdsworth and Pinton, 1998) and the Generalized Extreme Value (GEV)
distribution. In an attempt to assess the fluctuation relation of Evans, Cohen,
and Morriss (1993) we define entropy production by the injected power and use
the GEV location parameter as a reference state. The fluctuation ratio reveals
a linear behavior in a finite range.
| physics.ao-ph | the atmosphere gains available potential energy by solar radiation and dissipates kinetic energy mainly in the atmospheric boundary layer we analyze the fluctuations of the global mean energy cycle defined by lorenz 1955 in a simulation with a simplified hydrostatic model the energy current densities are well approximated by the generalized gumbel distribution bramwell holdsworth and pinton 1998 and the generalized extreme value gev distribution in an attempt to assess the fluctuation relation of evans cohen and morriss 1993 we define entropy production by the injected power and use the gev location parameter as a reference state the fluctuation ratio reveals a linear behavior in a finite range | [['the', 'atmosphere', 'gains', 'available', 'potential', 'energy', 'by', 'solar', 'radiation', 'and', 'dissipates', 'kinetic', 'energy', 'mainly', 'in', 'the', 'atmospheric', 'boundary', 'layer', 'we', 'analyze', 'the', 'fluctuations', 'of', 'the', 'global', 'mean', 'energy', 'cycle', 'defined', 'by', 'lorenz', '1955', 'in', 'a', 'simulation', 'with', 'a', 'simplified', 'hydrostatic', 'model', 'the', 'energy', 'current', 'densities', 'are', 'well', 'approximated', 'by', 'the', 'generalized', 'gumbel', 'distribution', 'bramwell', 'holdsworth', 'and', 'pinton', '1998', 'and', 'the', 'generalized', 'extreme', 'value', 'gev', 'distribution', 'in', 'an', 'attempt', 'to', 'assess', 'the', 'fluctuation', 'relation', 'of', 'evans', 'cohen', 'and', 'morriss', '1993', 'we', 'define', 'entropy', 'production', 'by', 'the', 'injected', 'power', 'and', 'use', 'the', 'gev', 'location', 'parameter', 'as', 'a', 'reference', 'state', 'the', 'fluctuation', 'ratio', 'reveals', 'a', 'linear', 'behavior', 'in', 'a', 'finite', 'range']] | [-0.10645065873307791, 0.15553899101799307, -0.07914019459507095, 0.13218185619257813, -0.015598348939334447, -0.05832442275318756, 0.0606553784422225, 0.28359898959971824, -0.2679264178095421, -0.35971992218620935, 0.053511007403392555, -0.2691416396706734, -0.04620347674145311, 0.14411023379751603, -0.04745635670557056, 0.07855004401776483, 0.03811657825651807, 0.0002835735959826775, -0.02967450135927823, -0.16711003793719806, 0.28184482341034794, 0.15767379358349332, 0.2915397030740695, 0.05909446810420497, 0.09092706427821573, -0.0016251402810426815, -0.008994504340972646, 0.01197009024107038, -0.18705013401164972, 0.04479471220687594, 0.17324196808215864, 0.06646105127830831, 0.24816888945950372, -0.3631416342730792, -0.2710678055794593, 0.10591362385938102, 0.071083022066269, 0.001157699236294852, -0.013375247086240154, -0.2330652540725357, 0.024176174317890743, -0.23325829664992062, -0.1619759661514523, -0.01225491862454153, 0.020430308142852672, 0.07477639288474577, -0.282528894285689, 0.14588042378495886, 0.02280150865586826, 0.07733789428558974, -0.08093279215533568, -0.12812295814378644, -0.09618737341018992, 0.060617059688874576, 0.04236242917414649, 0.013491385453819947, 0.16589726009933314, -0.11632021604861431, -0.05585119059915602, 0.3335334571816449, -0.13049212127774604, -0.16663257176724244, 0.12830443185631116, -0.12442867586582478, -0.05549277829990353, 0.12306238368223861, 0.13518463336985628, 0.06426783518883276, -0.18037281082591639, 0.09702893336608848, -0.012901624452700522, 0.15177491529765627, 0.08179732192008984, -0.0498745532723952, 0.2101393312343203, 0.12252779868167807, 0.03408638585604868, 0.149684024298177, -0.13216682529694154, -0.13688667487563952, -0.2905523637090019, -0.12572440164128565, -0.1868662832487146, 0.08674467706455374, -0.08132437907776, -0.11863676108033308, 0.4191814207884852, 0.1369890621643654, 0.2004116169915025, 0.04553529315294241, 0.2906414693955086, 0.19144375492128948, -0.006468303974955079, 0.14311221977783684, 0.2817509501583804, 0.17059359905960145, 0.18270227639004588, -0.2158265471599012, 0.023343724909761287, 0.06670522016806985] |
1,802.07566 | Electron-impact excitation of diatomic hydride cations II: OH$^+$ and
SH$^+$ | R-matrix calculations combined with the adiabatic-nuclei-rotation and
Coulomb-Born approximations are used to compute electron-impact rotational rate
coefficients for two open-shell diatomic cations of astrophysical interest: the
hydoxyl and sulphanyl ions, OH$^+$ and SH$^+$. Hyperfine resolved rate
coefficients are deduced using the infinite-order-sudden approximation. The
propensity rule $\Delta F=\Delta j=\Delta N=\pm 1$ is observed, as is expected
for cations with a large dipole moment. A model for OH$^+$ excitation in the
Orion Bar photon-dominated region (PDR) is presented which nicely reproduces
Herschel observations for an electron fraction $x_e=10^{-4}$ and an OH$^+$
column density of $3\times 10^{13}$~cm$^{-2}$. Electron impact electronic
excitation cross sections and rate coefficients for the ions are also
presented.
| astro-ph.SR astro-ph.GA | rmatrix calculations combined with the adiabaticnucleirotation and coulombborn approximations are used to compute electronimpact rotational rate coefficients for two openshell diatomic cations of astrophysical interest the hydoxyl and sulphanyl ions oh and sh hyperfine resolved rate coefficients are deduced using the infiniteordersudden approximation the propensity rule delta fdelta jdelta npm 1 is observed as is expected for cations with a large dipole moment a model for oh excitation in the orion bar photondominated region pdr is presented which nicely reproduces herschel observations for an electron fraction x_e104 and an oh column density of 3times 1013cm2 electron impact electronic excitation cross sections and rate coefficients for the ions are also presented | [['rmatrix', 'calculations', 'combined', 'with', 'the', 'adiabaticnucleirotation', 'and', 'coulombborn', 'approximations', 'are', 'used', 'to', 'compute', 'electronimpact', 'rotational', 'rate', 'coefficients', 'for', 'two', 'openshell', 'diatomic', 'cations', 'of', 'astrophysical', 'interest', 'the', 'hydoxyl', 'and', 'sulphanyl', 'ions', 'oh', 'and', 'sh', 'hyperfine', 'resolved', 'rate', 'coefficients', 'are', 'deduced', 'using', 'the', 'infiniteordersudden', 'approximation', 'the', 'propensity', 'rule', 'delta', 'fdelta', 'jdelta', 'npm', '1', 'is', 'observed', 'as', 'is', 'expected', 'for', 'cations', 'with', 'a', 'large', 'dipole', 'moment', 'a', 'model', 'for', 'oh', 'excitation', 'in', 'the', 'orion', 'bar', 'photondominated', 'region', 'pdr', 'is', 'presented', 'which', 'nicely', 'reproduces', 'herschel', 'observations', 'for', 'an', 'electron', 'fraction', 'x_e104', 'and', 'an', 'oh', 'column', 'density', 'of', '3times', '1013cm2', 'electron', 'impact', 'electronic', 'excitation', 'cross', 'sections', 'and', 'rate', 'coefficients', 'for', 'the', 'ions', 'are', 'also', 'presented']] | [-0.07363623864498464, 0.11723800748600383, 0.06252908760260018, 0.08117314690684478, 0.026238664431181155, -0.11276421607647724, 0.03840857319685385, 0.43196039369224376, -0.1865532651350324, -0.23186553237994886, -0.03946380195634018, -0.2889716578296052, -0.000245529519095314, 0.15159105920103239, 0.09011767654133881, 0.008998474532316596, 0.01294546703289632, -0.06233242462512176, -0.023324334835809358, -0.16197904763426982, 0.22084864668266954, 0.13125716043715277, 0.17058272637374136, 0.11946241854567011, 0.05138243444017925, -0.09142952133299571, 0.009299175365704973, -0.07250899719601532, -0.1953083494159762, 0.1229316071115153, 0.3219670934035917, 0.026306506900889974, 0.12978379352991293, -0.4124689503520165, -0.16302910359260045, 0.00312817821615235, 0.14801136070405538, 0.11198038576535424, -0.032736216531187856, -0.23969934748503258, -0.0054258018707909255, -0.19790583836652761, -0.16070380605282789, -0.06705338185442225, 0.05900090477069102, 0.09951428950430369, -0.3609660129387641, 0.11791989286534514, -0.03614999070095847, 0.0830974741591078, -0.145961518342308, -0.25611268243102253, -0.05847652138316266, 0.02484064149661517, 0.011633088760613903, 0.08823770911977538, 0.22534373580623102, -0.07960116962972537, -0.04861967665811052, 0.41478595594471357, -0.11455302087168368, -0.1237133939240901, 0.1423001190260896, -0.20220549528284948, -0.16748722289460446, 0.23802800009132558, 0.07034887517978139, 0.12138768965554125, -0.11774262480156601, 0.0770418792013035, -0.029523495739580678, 0.2016787364077315, 0.1018112078001547, 0.04913582168695218, 0.15336890670142514, 0.025663509323560405, 0.01837642877450529, 0.05348213416752669, -0.22031894775617095, -0.09016677451249704, -0.23717833834893579, -0.149422983182067, -0.13972537234460689, 0.0436671972099059, -0.0836669999378775, -0.07468192463626487, 0.2991548005210341, 0.005653758010528279, 0.22143194286969825, -0.01922569804460267, 0.2801897008112579, 0.1506504540810502, 0.01960786104527355, 0.05952025946001259, 0.23628618392900055, 0.23404701279898016, 0.02948732830403935, -0.3028741754143376, 0.11469106785601603, 0.09031146345989567] |
1,802.07567 | Measurement of optical to electrical and electrical to optical delays
with ps-level uncertainty | We present a new measurement principle to determine the absolute time delay
of a waveform from an optical reference plane to an electrical reference plane
and vice versa. We demonstrate a method based on this principle with 2 ps
uncertainty. This method can be used to perform accurate time delay
determinations of optical transceivers used in fibre-optic time-dissemination
equipment. As a result the time scales in optical and electrical domain can be
related to each other with the same uncertainty. We expect this method to break
new grounds in high-accuracy time transfer and absolute calibration of
time-transfer equipment.
| physics.optics | we present a new measurement principle to determine the absolute time delay of a waveform from an optical reference plane to an electrical reference plane and vice versa we demonstrate a method based on this principle with 2 ps uncertainty this method can be used to perform accurate time delay determinations of optical transceivers used in fibreoptic timedissemination equipment as a result the time scales in optical and electrical domain can be related to each other with the same uncertainty we expect this method to break new grounds in highaccuracy time transfer and absolute calibration of timetransfer equipment | [['we', 'present', 'a', 'new', 'measurement', 'principle', 'to', 'determine', 'the', 'absolute', 'time', 'delay', 'of', 'a', 'waveform', 'from', 'an', 'optical', 'reference', 'plane', 'to', 'an', 'electrical', 'reference', 'plane', 'and', 'vice', 'versa', 'we', 'demonstrate', 'a', 'method', 'based', 'on', 'this', 'principle', 'with', '2', 'ps', 'uncertainty', 'this', 'method', 'can', 'be', 'used', 'to', 'perform', 'accurate', 'time', 'delay', 'determinations', 'of', 'optical', 'transceivers', 'used', 'in', 'fibreoptic', 'timedissemination', 'equipment', 'as', 'a', 'result', 'the', 'time', 'scales', 'in', 'optical', 'and', 'electrical', 'domain', 'can', 'be', 'related', 'to', 'each', 'other', 'with', 'the', 'same', 'uncertainty', 'we', 'expect', 'this', 'method', 'to', 'break', 'new', 'grounds', 'in', 'highaccuracy', 'time', 'transfer', 'and', 'absolute', 'calibration', 'of', 'timetransfer', 'equipment']] | [-0.09943145566581528, 0.05027258154466873, -0.11189885897869148, 0.019796648870471903, -0.10110351341517315, -0.14011579084200496, 0.11416841704235173, 0.44496849947368977, -0.28223608608943285, -0.3330909161607629, 0.10953018933501017, -0.21107726519178485, -0.08387352454658482, 0.2608732716324403, -0.09233621570771348, 0.07112603793976847, 0.05480963821743721, 0.017002289385064363, -0.09649139670319087, -0.1648884237235047, 0.20834900761388012, 0.06059139364005364, 0.29456690336894437, 0.022876999464567713, 0.10081544333166376, 0.012438802437415136, -0.048177311148916935, 0.004449832882040862, -0.1033010282649745, 0.12887174680291377, 0.25722072085308045, 0.1088756145372358, 0.22027360846662952, -0.43109574579854604, -0.19571758906558617, 0.12465782865723499, 0.10639360253267068, 0.16083648995995597, -0.015309620425393133, -0.25810938226731167, 0.037691989558336046, -0.16189477190413734, -0.12959892487095803, -0.04950133499871824, -0.001049641865430419, 0.044500825955465284, -0.2725884829619035, 0.07831275312364408, -0.01848661160269349, 0.05841613843192145, -0.061846986225777376, -0.07382817293238855, 0.03872017560469121, 0.17611095667864704, -0.015159584053782458, 0.06461490809283767, 0.11722267698016517, -0.03369812937405383, -0.12943781944971108, 0.4053762169391608, -0.09756884154456802, -0.19478123589927696, 0.14743894741140767, -0.13846369398777017, -0.08743398547287762, 0.08731604454145987, 0.22313067000167272, 0.12291815498430934, -0.17195167590038293, -0.038387102551983916, 0.049721347715359986, 0.24849380712149685, 0.03335225362733928, 0.057374349759277146, 0.17193284104626202, 0.18966271881417363, 0.09321164134313766, 0.1073500598599587, -0.131357698966557, 0.035308117618227434, -0.30106733998610186, -0.1698237513442531, -0.19003349861619784, 0.052027139116616286, -0.08537212554224378, -0.0907589188325651, 0.3747308676865566, 0.2043077664488216, 0.1780277007984324, 0.05460818345207222, 0.3790183054456084, 0.1422003046165403, 0.07047525549441883, 0.026400237228990216, 0.2789936230527525, 0.07883884922898922, 0.14542046865237127, -0.23058208113430625, 0.02058545564848584, 0.03683008917741785] |
1,802.07568 | CABS-flex 2.0: a web server for fast simulations of flexibility of
protein structures | Classical simulations of protein flexibility remain computationally
expensive, especially for large proteins. A few years ago, we developed a fast
method for predicting protein structure fluctuations that uses a single protein
model as the input. The method has been made available as the CABS-flex web
server and applied in numerous studies of protein structure-function
relationships. Here, we present a major update of the CABS-flex web server to
version 2.0. The new features include: extension of the method to significantly
larger and multimeric proteins, customizable distance restraints and simulation
parameters, contact maps and a new, enhanced web server interface. CABS-flex
2.0 is freely available at http://biocomp.chem.uw.edu.pl/CABSflex2
| q-bio.BM | classical simulations of protein flexibility remain computationally expensive especially for large proteins a few years ago we developed a fast method for predicting protein structure fluctuations that uses a single protein model as the input the method has been made available as the cabsflex web server and applied in numerous studies of protein structurefunction relationships here we present a major update of the cabsflex web server to version 20 the new features include extension of the method to significantly larger and multimeric proteins customizable distance restraints and simulation parameters contact maps and a new enhanced web server interface cabsflex 20 is freely available at httpbiocompchemuweduplcabsflex2 | [['classical', 'simulations', 'of', 'protein', 'flexibility', 'remain', 'computationally', 'expensive', 'especially', 'for', 'large', 'proteins', 'a', 'few', 'years', 'ago', 'we', 'developed', 'a', 'fast', 'method', 'for', 'predicting', 'protein', 'structure', 'fluctuations', 'that', 'uses', 'a', 'single', 'protein', 'model', 'as', 'the', 'input', 'the', 'method', 'has', 'been', 'made', 'available', 'as', 'the', 'cabsflex', 'web', 'server', 'and', 'applied', 'in', 'numerous', 'studies', 'of', 'protein', 'structurefunction', 'relationships', 'here', 'we', 'present', 'a', 'major', 'update', 'of', 'the', 'cabsflex', 'web', 'server', 'to', 'version', '20', 'the', 'new', 'features', 'include', 'extension', 'of', 'the', 'method', 'to', 'significantly', 'larger', 'and', 'multimeric', 'proteins', 'customizable', 'distance', 'restraints', 'and', 'simulation', 'parameters', 'contact', 'maps', 'and', 'a', 'new', 'enhanced', 'web', 'server', 'interface', 'cabsflex', '20', 'is', 'freely', 'available', 'at', 'httpbiocompchemuweduplcabsflex2']] | [-0.09565082037275155, 0.04900798942141522, -0.04830830528562029, 0.0867346658498998, -0.09076054639836702, -0.20244446123251691, 0.06786014719713981, 0.4207782440890486, -0.28026867346264994, -0.3370168710915515, 0.06868777858303823, -0.2572202904758832, -0.142292498342263, 0.2205913661141844, -0.005910210058433362, 0.06755466239141802, 0.1411412046290934, 0.0011134238358443747, 0.0032640531638977476, -0.23212558614390078, 0.20130278216227174, 0.12093043963362177, 0.2791886567362011, 0.06837728941956392, 0.10141648671840532, -0.005655582665125481, -0.05562743016232092, 0.0010291249133073366, -0.15952738686813134, 0.18201074070440462, 0.25577043889475487, 0.15239706161082722, 0.2766634592128237, -0.4279783374289624, -0.21883657306002882, 0.041394029336515814, 0.16899325153253114, 0.15269721624925017, -0.07072348117183608, -0.2651892631995277, 0.10145166448245828, -0.20829985634638712, -0.07791408055149637, -0.08528590992276665, 0.02154245421451588, 0.03992081252195371, -0.1934062058734036, 0.07351298124278681, -0.04357475286143689, 0.09764948847273794, -0.024056511568442848, -0.11077069032650727, -0.003909245505033491, 0.1785329897997704, 0.024484714402485855, 0.06586656944665055, 0.22977256829751871, -0.1074837322633427, -0.09162671648888275, 0.37478394821608585, -0.036038890030340553, -0.16809500864026353, 0.22369829026194146, -0.022627568163443357, -0.21517061037817398, 0.15311751974961504, 0.17714971931351242, 0.12245816000414869, -0.22600799495446083, 0.050240740607618, -0.0023912238225770686, 0.24108591242335164, 0.04753919050115375, -0.051505564841835834, 0.16632246215326282, 0.24039085491452938, -0.0019236853113397956, 0.15081775513513443, -0.09004979552208589, -0.10163825666173719, -0.18444922561040863, -0.17286187998923616, -0.18825231281852423, -0.008286985277663916, -0.09762826488384654, -0.1815553442754138, 0.37783896473522943, 0.14541839915406085, 0.1548934310513477, 0.06682310838592596, 0.2890727364664109, -0.052834577296520226, 0.14836832599338287, 0.06295653524844405, 0.13526127156980622, 0.06037764570031028, 0.15312606013881472, -0.12819918419923992, 0.1169834507006901, 0.024871133061913915] |
1,802.07569 | Continual Lifelong Learning with Neural Networks: A Review | Humans and animals have the ability to continually acquire, fine-tune, and
transfer knowledge and skills throughout their lifespan. This ability, referred
to as lifelong learning, is mediated by a rich set of neurocognitive mechanisms
that together contribute to the development and specialization of our
sensorimotor skills as well as to long-term memory consolidation and retrieval.
Consequently, lifelong learning capabilities are crucial for autonomous agents
interacting in the real world and processing continuous streams of information.
However, lifelong learning remains a long-standing challenge for machine
learning and neural network models since the continual acquisition of
incrementally available information from non-stationary data distributions
generally leads to catastrophic forgetting or interference. This limitation
represents a major drawback for state-of-the-art deep neural network models
that typically learn representations from stationary batches of training data,
thus without accounting for situations in which information becomes
incrementally available over time. In this review, we critically summarize the
main challenges linked to lifelong learning for artificial learning systems and
compare existing neural network approaches that alleviate, to different
extents, catastrophic forgetting. We discuss well-established and emerging
research motivated by lifelong learning factors in biological systems such as
structural plasticity, memory replay, curriculum and transfer learning,
intrinsic motivation, and multisensory integration.
| cs.LG q-bio.NC stat.ML | humans and animals have the ability to continually acquire finetune and transfer knowledge and skills throughout their lifespan this ability referred to as lifelong learning is mediated by a rich set of neurocognitive mechanisms that together contribute to the development and specialization of our sensorimotor skills as well as to longterm memory consolidation and retrieval consequently lifelong learning capabilities are crucial for autonomous agents interacting in the real world and processing continuous streams of information however lifelong learning remains a longstanding challenge for machine learning and neural network models since the continual acquisition of incrementally available information from nonstationary data distributions generally leads to catastrophic forgetting or interference this limitation represents a major drawback for stateoftheart deep neural network models that typically learn representations from stationary batches of training data thus without accounting for situations in which information becomes incrementally available over time in this review we critically summarize the main challenges linked to lifelong learning for artificial learning systems and compare existing neural network approaches that alleviate to different extents catastrophic forgetting we discuss wellestablished and emerging research motivated by lifelong learning factors in biological systems such as structural plasticity memory replay curriculum and transfer learning intrinsic motivation and multisensory integration | [['humans', 'and', 'animals', 'have', 'the', 'ability', 'to', 'continually', 'acquire', 'finetune', 'and', 'transfer', 'knowledge', 'and', 'skills', 'throughout', 'their', 'lifespan', 'this', 'ability', 'referred', 'to', 'as', 'lifelong', 'learning', 'is', 'mediated', 'by', 'a', 'rich', 'set', 'of', 'neurocognitive', 'mechanisms', 'that', 'together', 'contribute', 'to', 'the', 'development', 'and', 'specialization', 'of', 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1,802.0757 | Influence of chemical potential on the Casimir-Polder interaction
between an atom and gapped graphene or graphene-coated substrate | We present a formalism based on first principles of quantum electrodynamics
at nonzero temperature which permits to calculate the Casimir-Polder
interaction between an atom and a graphene sheet with arbitrary mass gap and
chemical potential, including graphene-coated substrates. The free energy and
force of the Casimir-Polder interaction are expressed via the polarization
tensor of graphene in (2+1)-dimensional space-time in the framework of the
Dirac model. The obtained expressions are used to investigate the influence of
the chemical potential of graphene on the Casimir-Polder interaction.
Computations are performed for an atom of metastable helium interacting with
either a free-standing graphene sheet or a graphene-coated substrate made of
amorphous silica. It is shown that the impacts of the nonzero chemical
potential and the mass gap on the Casimir-Polder interaction are in opposite
directions by increasing and decreasing the magnitudes of the free energy and
force, respectively. It turns out, however, that the temperature-dependent part
of the Casimir-Polder interaction is decreased by a nonzero chemical potential,
whereas the mass gap increases it compared to the case of undoped, gapless
graphene. The physical explanation for these effects is provided. Numerical
computations of the Casimir-Polder interaction are performed at various
temperatures and atom-graphene separations.
| cond-mat.mes-hall | we present a formalism based on first principles of quantum electrodynamics at nonzero temperature which permits to calculate the casimirpolder interaction between an atom and a graphene sheet with arbitrary mass gap and chemical potential including graphenecoated substrates the free energy and force of the casimirpolder interaction are expressed via the polarization tensor of graphene in 21dimensional spacetime in the framework of the dirac model the obtained expressions are used to investigate the influence of the chemical potential of graphene on the casimirpolder interaction computations are performed for an atom of metastable helium interacting with either a freestanding graphene sheet or a graphenecoated substrate made of amorphous silica it is shown that the impacts of the nonzero chemical potential and the mass gap on the casimirpolder interaction are in opposite directions by increasing and decreasing the magnitudes of the free energy and force respectively it turns out however that the temperaturedependent part of the casimirpolder interaction is decreased by a nonzero chemical potential whereas the mass gap increases it compared to the case of undoped gapless graphene the physical explanation for these effects is provided numerical computations of the casimirpolder interaction are performed at various temperatures and atomgraphene separations | [['we', 'present', 'a', 'formalism', 'based', 'on', 'first', 'principles', 'of', 'quantum', 'electrodynamics', 'at', 'nonzero', 'temperature', 'which', 'permits', 'to', 'calculate', 'the', 'casimirpolder', 'interaction', 'between', 'an', 'atom', 'and', 'a', 'graphene', 'sheet', 'with', 'arbitrary', 'mass', 'gap', 'and', 'chemical', 'potential', 'including', 'graphenecoated', 'substrates', 'the', 'free', 'energy', 'and', 'force', 'of', 'the', 'casimirpolder', 'interaction', 'are', 'expressed', 'via', 'the', 'polarization', 'tensor', 'of', 'graphene', 'in', '21dimensional', 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1,802.07571 | Norm estimates and asymptotic faithfulness of the quantum $SU(n)$
representations of the mapping class groups | We give a direct proof for the asymptotic faithfulness of the quantum $SU(n)$
representations of the mapping class groups using peak sections in Kodaira
embedding. We give also estimates on the norm of the parallell transport of the
projective connection on the Verlinde bundle. The faithfulness has been proved
earlier in [1] using Toeplitz operators of compact K\"ahler manifolds and in
[10] using skein theory.
| math.DG math.RT | we give a direct proof for the asymptotic faithfulness of the quantum sun representations of the mapping class groups using peak sections in kodaira embedding we give also estimates on the norm of the parallell transport of the projective connection on the verlinde bundle the faithfulness has been proved earlier in 1 using toeplitz operators of compact kahler manifolds and in 10 using skein theory | [['we', 'give', 'a', 'direct', 'proof', 'for', 'the', 'asymptotic', 'faithfulness', 'of', 'the', 'quantum', 'sun', 'representations', 'of', 'the', 'mapping', 'class', 'groups', 'using', 'peak', 'sections', 'in', 'kodaira', 'embedding', 'we', 'give', 'also', 'estimates', 'on', 'the', 'norm', 'of', 'the', 'parallell', 'transport', 'of', 'the', 'projective', 'connection', 'on', 'the', 'verlinde', 'bundle', 'the', 'faithfulness', 'has', 'been', 'proved', 'earlier', 'in', '1', 'using', 'toeplitz', 'operators', 'of', 'compact', 'kahler', 'manifolds', 'and', 'in', '10', 'using', 'skein', 'theory']] | [-0.14231040957383811, 0.01586983066249209, -0.1185572575309869, 0.10431740453036932, -0.07136386366775976, -0.10793885506259707, -0.009010327304713428, 0.3544153601217728, -0.224597876604933, -0.2355962708305854, 0.11564174049999565, -0.25052977171905627, -0.1546639241851293, 0.21373223970429256, -0.1298327930414906, 0.03771366722022112, 0.054221648561696596, 0.10475000471163254, -0.1517799104205691, -0.2749211907118129, 0.4459638285307357, 0.022538353694387926, 0.24548940071119713, 0.09384921287687925, 0.11341271952797587, 0.01873726905681766, -0.03418377242409266, -0.06909710285612024, -0.1503888707393064, 0.1799988756601054, 0.24927222505570032, 0.08465658293392223, 0.1522061702544586, -0.4074664857811653, -0.1920443767699628, 0.16820822403264735, 0.11717232732961957, 0.02996419109404087, -0.06083056267279272, -0.3210659504438249, 0.084847639200206, -0.1654516175102729, -0.10040535398114186, -0.06769907412907251, 0.033714668538707956, -0.02941383452942738, -0.19376237555048786, 0.024880033476690117, 0.09215264801795665, 0.1416760869180927, -0.09268057698097366, -0.09945676217858608, -0.02819886416769945, 0.09430607576460506, -0.016413682306077905, 0.012131755261753615, 0.11487205007041876, -0.06589551574478929, -0.1374018406853653, 0.3064771635314593, -0.08596104410691903, -0.23742694185616878, 0.1279661779363568, -0.1658275700102632, -0.1874536918906065, 0.08994620744712077, 0.09523574327333616, 0.16607928213018638, -0.02518497918947385, 0.18557634112120677, -0.11643408758995624, 0.05877783380699559, 0.0881662879855587, 0.026030920445919037, 0.08389134786736507, 0.11455787945395479, 0.08390619195997714, 0.1106618181659052, -0.06465244143484877, -0.04975055645291622, -0.34145254825170224, -0.25935409427978673, -0.14755039256281005, 0.17653504113953275, -0.15208466902415518, -0.12464687328857298, 0.41042952193663673, 0.06056804758711503, 0.2048804025667218, 0.15503787841074743, 0.1980117161113482, 0.07492695482662665, 0.0816810149484529, 0.05456455313385679, 0.2443777746735857, 0.3027636586760099, 0.03386508977183929, -0.11932011950187958, -0.032189007938051455, 0.2773338786254709] |
1,802.07572 | Information Theoretic Co-Training | This paper introduces an information theoretic co-training objective for
unsupervised learning. We consider the problem of predicting the future. Rather
than predict future sensations (image pixels or sound waves) we predict
"hypotheses" to be confirmed by future sensations. More formally, we assume a
population distribution on pairs $(x,y)$ where we can think of $x$ as a past
sensation and $y$ as a future sensation. We train both a predictor model
$P_\Phi(z|x)$ and a confirmation model $P_\Psi(z|y)$ where we view $z$ as
hypotheses (when predicted) or facts (when confirmed). For a population
distribution on pairs $(x,y)$ we focus on the problem of measuring the mutual
information between $x$ and $y$. By the data processing inequality this mutual
information is at least as large as the mutual information between $x$ and $z$
under the distribution on triples $(x,z,y)$ defined by the confirmation model
$P_\Psi(z|y)$. The information theoretic training objective for $P_\Phi(z|x)$
and $P_\Psi(z|y)$ can be viewed as a form of co-training where we want the
prediction from $x$ to match the confirmation from $y$.
| cs.LG stat.ML | this paper introduces an information theoretic cotraining objective for unsupervised learning we consider the problem of predicting the future rather than predict future sensations image pixels or sound waves we predict hypotheses to be confirmed by future sensations more formally we assume a population distribution on pairs xy where we can think of x as a past sensation and y as a future sensation we train both a predictor model p_phizx and a confirmation model p_psizy where we view z as hypotheses when predicted or facts when confirmed for a population distribution on pairs xy we focus on the problem of measuring the mutual information between x and y by the data processing inequality this mutual information is at least as large as the mutual information between x and z under the distribution on triples xzy defined by the confirmation model p_psizy the information theoretic training objective for p_phizx and p_psizy can be viewed as a form of cotraining where we want the prediction from x to match the confirmation from y | [['this', 'paper', 'introduces', 'an', 'information', 'theoretic', 'cotraining', 'objective', 'for', 'unsupervised', 'learning', 'we', 'consider', 'the', 'problem', 'of', 'predicting', 'the', 'future', 'rather', 'than', 'predict', 'future', 'sensations', 'image', 'pixels', 'or', 'sound', 'waves', 'we', 'predict', 'hypotheses', 'to', 'be', 'confirmed', 'by', 'future', 'sensations', 'more', 'formally', 'we', 'assume', 'a', 'population', 'distribution', 'on', 'pairs', 'xy', 'where', 'we', 'can', 'think', 'of', 'x', 'as', 'a', 'past', 'sensation', 'and', 'y', 'as', 'a', 'future', 'sensation', 'we', 'train', 'both', 'a', 'predictor', 'model', 'p_phizx', 'and', 'a', 'confirmation', 'model', 'p_psizy', 'where', 'we', 'view', 'z', 'as', 'hypotheses', 'when', 'predicted', 'or', 'facts', 'when', 'confirmed', 'for', 'a', 'population', 'distribution', 'on', 'pairs', 'xy', 'we', 'focus', 'on', 'the', 'problem', 'of', 'measuring', 'the', 'mutual', 'information', 'between', 'x', 'and', 'y', 'by', 'the', 'data', 'processing', 'inequality', 'this', 'mutual', 'information', 'is', 'at', 'least', 'as', 'large', 'as', 'the', 'mutual', 'information', 'between', 'x', 'and', 'z', 'under', 'the', 'distribution', 'on', 'triples', 'xzy', 'defined', 'by', 'the', 'confirmation', 'model', 'p_psizy', 'the', 'information', 'theoretic', 'training', 'objective', 'for', 'p_phizx', 'and', 'p_psizy', 'can', 'be', 'viewed', 'as', 'a', 'form', 'of', 'cotraining', 'where', 'we', 'want', 'the', 'prediction', 'from', 'x', 'to', 'match', 'the', 'confirmation', 'from', 'y']] | [-0.08164825205732247, 0.04783399861437775, -0.09183703949811924, 0.11265795392134939, -0.07904033071142347, -0.1622635422685348, 0.08622536601512419, 0.3855836526435964, -0.28319457195260944, -0.30522868901162464, 0.08809189464732567, -0.32740200023879024, -0.12430510695968919, 0.15881086667205263, -0.07906706898801905, 0.005127604912045439, 0.05078454556573621, 0.09613411128247047, -0.058843177788452626, -0.2309316411628114, 0.30697522961452384, 0.010135668390156592, 0.266719133771189, 0.008038545540629832, 0.1391593382933506, 0.07142987464116339, -0.012176350547986872, 0.013062358247664045, -0.13011782678487874, 0.11960827318047557, 0.265742125811384, 0.19211741132552132, 0.3089691233602079, -0.3768100894220612, -0.21769760220914203, 0.1268367606721928, 0.14768013213213313, 0.06376972343389165, -0.02582962832264671, -0.3082322749802295, 0.07394306091446197, -0.13613804247613778, -0.04168652318801512, -0.046867144241439423, 0.007924151124761384, 0.00015936790253309643, -0.33179173392298467, 0.05653800695367596, 0.06746634907801362, 0.08368100170046092, -0.032299233247142504, -0.10789488749047878, -0.045228393855230774, 0.12575375723878524, 0.05506428441662779, 0.08664476814446971, 0.10643323058372035, -0.1525121368248673, -0.11636671472395606, 0.35740807538523395, -0.0879999632047496, -0.21300556716673513, 0.1341379043290063, -0.12659714889493498, -0.119407036270508, 0.030934115997789537, 0.20852473893901333, 0.11859336120131261, -0.15333563741929965, 0.00855920424184981, -0.05932117025641834, 0.17431962918216254, 0.0267564250046716, 0.042588118184357884, 0.27623371595468865, 0.19292231378118124, 0.027775013441329495, 0.10835270269034321, -0.11379584620487602, -0.01574849581126781, -0.29420712795108556, -0.1617527280893067, -0.19333585709990825, 0.08264848441433381, -0.0708962872346199, -0.09535919012611403, 0.3187069157289122, 0.1889250886544366, 0.26633931748185524, 0.06753722645671052, 0.2709295244038324, 0.0571642128380892, 0.019895319446154375, 0.0506625477635466, 0.18119992368909366, 0.08069546062033624, 0.05994977583999143, -0.10885740668266354, 0.13240561779752813, 0.03306934261311065] |
1,802.07573 | Asymmetric Cryptography with Physical Unclonable Keys | Secure communication is of paramount importance in modern society. Asymmetric
cryptography methods such as the widely used RSA method allow secure exchange
of information between parties who have not shared secret keys. However, the
existing asymmetric cryptographic schemes rely on unproven mathematical
assumptions for security. Further, the digital keys used in their
implementation are susceptible to copying that might remain unnoticed. Here we
introduce a secure communication method that overcomes these two limitations by
employing Physical Unclonable Keys (PUKs). Using optical PUKs realized in
opaque scattering materials and employing off-the-shelf equipment, we transmit
messages in an error-corrected way. Information is transmitted as patterned
wavefronts of few-photon wavepackets which can be successfully decrypted only
with the receiver's PUK. The security of PUK-Enabled Asymmetric Communication
(PEAC) is not based on any stored secret but on the hardness of distinguishing
between different few-photon wavefronts.
| physics.optics quant-ph | secure communication is of paramount importance in modern society asymmetric cryptography methods such as the widely used rsa method allow secure exchange of information between parties who have not shared secret keys however the existing asymmetric cryptographic schemes rely on unproven mathematical assumptions for security further the digital keys used in their implementation are susceptible to copying that might remain unnoticed here we introduce a secure communication method that overcomes these two limitations by employing physical unclonable keys puks using optical puks realized in opaque scattering materials and employing offtheshelf equipment we transmit messages in an errorcorrected way information is transmitted as patterned wavefronts of fewphoton wavepackets which can be successfully decrypted only with the receivers puk the security of pukenabled asymmetric communication peac is not based on any stored secret but on the hardness of distinguishing between different fewphoton wavefronts | [['secure', 'communication', 'is', 'of', 'paramount', 'importance', 'in', 'modern', 'society', 'asymmetric', 'cryptography', 'methods', 'such', 'as', 'the', 'widely', 'used', 'rsa', 'method', 'allow', 'secure', 'exchange', 'of', 'information', 'between', 'parties', 'who', 'have', 'not', 'shared', 'secret', 'keys', 'however', 'the', 'existing', 'asymmetric', 'cryptographic', 'schemes', 'rely', 'on', 'unproven', 'mathematical', 'assumptions', 'for', 'security', 'further', 'the', 'digital', 'keys', 'used', 'in', 'their', 'implementation', 'are', 'susceptible', 'to', 'copying', 'that', 'might', 'remain', 'unnoticed', 'here', 'we', 'introduce', 'a', 'secure', 'communication', 'method', 'that', 'overcomes', 'these', 'two', 'limitations', 'by', 'employing', 'physical', 'unclonable', 'keys', 'puks', 'using', 'optical', 'puks', 'realized', 'in', 'opaque', 'scattering', 'materials', 'and', 'employing', 'offtheshelf', 'equipment', 'we', 'transmit', 'messages', 'in', 'an', 'errorcorrected', 'way', 'information', 'is', 'transmitted', 'as', 'patterned', 'wavefronts', 'of', 'fewphoton', 'wavepackets', 'which', 'can', 'be', 'successfully', 'decrypted', 'only', 'with', 'the', 'receivers', 'puk', 'the', 'security', 'of', 'pukenabled', 'asymmetric', 'communication', 'peac', 'is', 'not', 'based', 'on', 'any', 'stored', 'secret', 'but', 'on', 'the', 'hardness', 'of', 'distinguishing', 'between', 'different', 'fewphoton', 'wavefronts']] | [-0.19705315304557136, 0.057569878945501196, -0.10675214274841197, 0.07311965673323036, -0.07144514956128072, -0.3333101862226613, 0.09661887759541381, 0.43313392553725005, -0.3007957029895967, -0.28990207961075665, 0.12350144669899772, -0.23944418873596826, -0.13109885505914196, 0.23418765092569896, -0.14492279795162819, 0.11899296611355727, -0.016161141366704695, -0.050016058851992166, 0.014122796939987251, -0.2981221392315895, 0.31539820209453706, 0.019672302806558198, 0.34491293023080183, 0.04476779406575267, 0.05817274792998967, 0.07115973891717765, -0.041555436903282124, -0.09922584829687633, -0.06068043638697418, 0.13455223901923197, 0.34908248828415867, 0.18224240319378784, 0.28550516887609023, -0.49327191509826873, -0.20141592041096268, 0.11548594401820618, 0.1905503575998249, 0.15761791301209835, -0.09212063180251896, -0.29400396353209063, 0.06360952320563443, -0.1920546981992255, -0.043308238159892536, -0.05726605691426598, -0.06262527893105631, 0.06688017821922104, -0.22017014941529317, 0.010734848417889546, -0.005643853592439829, 0.07307217152350966, 0.07298703431254527, -0.03808778658618822, 0.008399595592088778, 0.19711945534971378, -0.03954300269833766, -0.049452186032901996, 0.16411601868115694, -0.10857372867415988, -0.1694095238737298, 0.38463944808566286, 0.03421906504937557, -0.18436025178251678, 0.1544870399435133, 0.0018600031343179151, -0.0880953907411929, 0.12674965169229407, 0.1990687049966415, 0.05446062611607725, -0.16517241503906382, 0.010398820298980675, -0.03189615778940018, 0.2606414497610839, 0.12442248076652451, 0.20494120418237904, 0.1967565742550719, 0.1063057839158265, 0.023055058945079938, 0.07615209517141064, -0.05273167498286485, -0.11935203649131033, -0.22553529846824377, -0.13496566670672858, -0.2681918518809492, 0.028807234882098035, -0.05904454940590607, -0.10099049040239633, 0.31906333950567334, 0.22701987214317984, 0.059887085421531296, -0.00820913270495914, 0.44443889900781763, 0.013274177047766416, 0.13367931541185551, 0.15699684728101335, 0.24444344395990758, 0.09479119977057802, 0.11166001137633644, -0.10190329366185538, 0.2023549608865698, -0.010895245273679714] |
1,802.07574 | Higher Hochschild homology and exponential functors | We study higher Hochschild homology evaluated on wedges of circles, viewed as
a functor on the category of free groups. The main results use coefficients
arising from square-zero extensions; this is motivated by work of Turchin and
Willwacher in relation to hairy graph cohomology. The functorial point of view
allows us to exploit tools such as the theory of polynomial functors and
exponential functors. We also introduce and make essential use of the category
of outer functors, the full subcategory of functors on free groups on which
inner automorphisms act trivially. We give a description of higher Hochschild
homology in terms of intrinsically defined polynomial outer functors; we also
obtain several explicit computations of these outer functors, working over a
field of characteristic zero. In particular, higher Hochschild homology gives a
natural source of non-trivial polynomial outer functors.
| math.AT | we study higher hochschild homology evaluated on wedges of circles viewed as a functor on the category of free groups the main results use coefficients arising from squarezero extensions this is motivated by work of turchin and willwacher in relation to hairy graph cohomology the functorial point of view allows us to exploit tools such as the theory of polynomial functors and exponential functors we also introduce and make essential use of the category of outer functors the full subcategory of functors on free groups on which inner automorphisms act trivially we give a description of higher hochschild homology in terms of intrinsically defined polynomial outer functors we also obtain several explicit computations of these outer functors working over a field of characteristic zero in particular higher hochschild homology gives a natural source of nontrivial polynomial outer functors | [['we', 'study', 'higher', 'hochschild', 'homology', 'evaluated', 'on', 'wedges', 'of', 'circles', 'viewed', 'as', 'a', 'functor', 'on', 'the', 'category', 'of', 'free', 'groups', 'the', 'main', 'results', 'use', 'coefficients', 'arising', 'from', 'squarezero', 'extensions', 'this', 'is', 'motivated', 'by', 'work', 'of', 'turchin', 'and', 'willwacher', 'in', 'relation', 'to', 'hairy', 'graph', 'cohomology', 'the', 'functorial', 'point', 'of', 'view', 'allows', 'us', 'to', 'exploit', 'tools', 'such', 'as', 'the', 'theory', 'of', 'polynomial', 'functors', 'and', 'exponential', 'functors', 'we', 'also', 'introduce', 'and', 'make', 'essential', 'use', 'of', 'the', 'category', 'of', 'outer', 'functors', 'the', 'full', 'subcategory', 'of', 'functors', 'on', 'free', 'groups', 'on', 'which', 'inner', 'automorphisms', 'act', 'trivially', 'we', 'give', 'a', 'description', 'of', 'higher', 'hochschild', 'homology', 'in', 'terms', 'of', 'intrinsically', 'defined', 'polynomial', 'outer', 'functors', 'we', 'also', 'obtain', 'several', 'explicit', 'computations', 'of', 'these', 'outer', 'functors', 'working', 'over', 'a', 'field', 'of', 'characteristic', 'zero', 'in', 'particular', 'higher', 'hochschild', 'homology', 'gives', 'a', 'natural', 'source', 'of', 'nontrivial', 'polynomial', 'outer', 'functors']] | [-0.17584505163646047, 0.001326660375934148, -0.11387952489346481, 0.10235714353621006, -0.12773190768084663, -0.09531337599796445, -0.02610280433335625, 0.34067982720022183, -0.39801332030607306, -0.2384524582716488, 0.08431586243323577, -0.16827812466310232, -0.16565002517629604, 0.18609250211359366, -0.19471298512813728, -0.05456329201199654, 0.04341855643830006, 0.09587013368845741, -0.09495868049292029, -0.232879282841906, 0.44496020387547713, 0.01694703934903162, 0.18405380319007605, 0.06492367397109722, 0.08935392126980898, -0.021027240493888225, -0.07714720121483602, -0.03618341847660317, -0.1969691730370961, 0.15290459386491473, 0.3523585132012765, 0.022257545807709295, 0.16311754823850672, -0.43040506489089003, -0.0626564815588147, 0.16111982101911976, 0.14966757545261172, 0.040038537950275226, -0.014585906252487684, -0.28811163430277636, 0.10336137840362347, -0.26866604389784776, -0.09326979369971146, -0.08138589084157265, 0.035166315246791834, -0.003908156037695058, -0.2023616185739967, -0.021057704079346193, 0.10530121358006263, 0.16098358181467198, -0.09375428665552518, -0.08035798420609934, -0.088541866209277, 0.1526084959851173, -0.023757873049085585, 0.0026442508476421885, 0.17149117166189937, -0.103742493503808, -0.14774838150850078, 0.3840317432464951, -0.09330904428455708, -0.1888934634828373, 0.16502979673121287, -0.14794822546157418, -0.18189946557327674, 0.13624002966031, 0.038194734395643616, 0.17693448061987327, 0.003995350015390179, 0.21049152501475782, -0.11078791487692059, 0.07276433162442644, 0.12982477726873712, 0.04852696952234576, 0.1506379769568372, 0.053442362107107066, 0.08025132972693098, 0.20277547267555812, 0.043575996840102736, -0.06823109730443769, -0.33754276013190765, -0.21173195463294783, -0.06603668325418688, 0.10092216754919323, -0.1293823183443527, -0.20363168079284547, 0.41746417325718893, 0.13826556245296978, 0.1772195265925341, 0.18415443363546333, 0.26270833673576516, 0.026661642420483564, 0.10115812652730856, -0.014840430331062542, 0.11115421487045461, 0.2768983919598648, -0.004763508793405271, -0.07555195285796958, -0.031116983969695866, 0.25960529056728643] |
1,802.07575 | Emulating dynamic non-linear simulators using Gaussian processes | The dynamic emulation of non-linear deterministic computer codes where the
output is a time series, possibly multivariate, is examined. Such computer
models simulate the evolution of some real-world phenomenon over time, for
example models of the climate or the functioning of the human brain. The models
we are interested in are highly non-linear and exhibit tipping points,
bifurcations and chaotic behaviour. However, each simulation run could be too
time-consuming to perform analyses that require many runs, including
quantifying the variation in model output with respect to changes in the
inputs. Therefore, Gaussian process emulators are used to approximate the
output of the code. To do this, the flow map of the system under study is
emulated over a short time period. Then, it is used in an iterative way to
predict the whole time series. A number of ways are proposed to take into
account the uncertainty of inputs to the emulators, after fixed initial
conditions, and the correlation between them through the time series. The
methodology is illustrated with two examples: the highly non-linear dynamical
systems described by the Lorenz and Van der Pol equations. In both cases, the
predictive performance is relatively high and the measure of uncertainty
provided by the method reflects the extent of predictability in each system.
| stat.ML math.DS stat.AP | the dynamic emulation of nonlinear deterministic computer codes where the output is a time series possibly multivariate is examined such computer models simulate the evolution of some realworld phenomenon over time for example models of the climate or the functioning of the human brain the models we are interested in are highly nonlinear and exhibit tipping points bifurcations and chaotic behaviour however each simulation run could be too timeconsuming to perform analyses that require many runs including quantifying the variation in model output with respect to changes in the inputs therefore gaussian process emulators are used to approximate the output of the code to do this the flow map of the system under study is emulated over a short time period then it is used in an iterative way to predict the whole time series a number of ways are proposed to take into account the uncertainty of inputs to the emulators after fixed initial conditions and the correlation between them through the time series the methodology is illustrated with two examples the highly nonlinear dynamical systems described by the lorenz and van der pol equations in both cases the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system | [['the', 'dynamic', 'emulation', 'of', 'nonlinear', 'deterministic', 'computer', 'codes', 'where', 'the', 'output', 'is', 'a', 'time', 'series', 'possibly', 'multivariate', 'is', 'examined', 'such', 'computer', 'models', 'simulate', 'the', 'evolution', 'of', 'some', 'realworld', 'phenomenon', 'over', 'time', 'for', 'example', 'models', 'of', 'the', 'climate', 'or', 'the', 'functioning', 'of', 'the', 'human', 'brain', 'the', 'models', 'we', 'are', 'interested', 'in', 'are', 'highly', 'nonlinear', 'and', 'exhibit', 'tipping', 'points', 'bifurcations', 'and', 'chaotic', 'behaviour', 'however', 'each', 'simulation', 'run', 'could', 'be', 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1,802.07576 | A note on $\mathfrak{gl}_2$-invariant Bethe vectors | We consider $\mathfrak{gl}_2$-invariant quantum integrable models solvable by
the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is
preserved under certain twist transformations of the monodromy matrix. We also
derive the actions of the twisted monodromy matrix entries onto twisted
off-shell Bethe vectors.
| math-ph hep-th math.MP | we consider mathfrakgl_2invariant quantum integrable models solvable by the algebraic bethe ansatz we show that the form of onshell bethe vectors is preserved under certain twist transformations of the monodromy matrix we also derive the actions of the twisted monodromy matrix entries onto twisted offshell bethe vectors | [['we', 'consider', 'mathfrakgl_2invariant', 'quantum', 'integrable', 'models', 'solvable', 'by', 'the', 'algebraic', 'bethe', 'ansatz', 'we', 'show', 'that', 'the', 'form', 'of', 'onshell', 'bethe', 'vectors', 'is', 'preserved', 'under', 'certain', 'twist', 'transformations', 'of', 'the', 'monodromy', 'matrix', 'we', 'also', 'derive', 'the', 'actions', 'of', 'the', 'twisted', 'monodromy', 'matrix', 'entries', 'onto', 'twisted', 'offshell', 'bethe', 'vectors']] | [-0.25109810600786103, 0.2061267729808131, -0.03954858917985921, 0.10533872246995325, -0.11558187485713026, -0.14181605797595062, -0.006099677184070258, 0.36725187965709233, -0.3256142826133367, -0.09800040191444366, 0.09214575407500177, -0.23824688946099384, -0.22713752003872525, 0.07100496623847309, 0.0005333940666194236, 0.09535885108229906, 0.12847766196658916, 0.11484559139479762, -0.2911447225411868, -0.302864214693925, 0.4087147176589655, -0.05236004041153532, 0.2736854694945657, -0.03138167932047509, 0.17647907583285932, 0.11008921658377284, 0.04244141398078721, -0.11136692108424462, -0.11227837071893863, 0.14444060480910476, 0.2410224140454849, 0.11783644783756007, 0.021764696616193523, -0.4575771234686608, -0.10384986795100343, 0.11572520685908587, 0.18424712512237224, 0.12958466336536018, 0.051930832798066345, -0.31514687014176795, 0.04934678294027791, -0.24522479599260766, -0.22659699204782752, -0.14461294846082834, -0.03979281627613565, -0.06356598380143227, -0.22564876975957304, 0.05243636645900551, 0.020217298145365457, 0.05275183212182563, -0.06873311203621003, -0.14732758792714498, -0.04988375966153715, 0.04695182307825788, 0.06375372432344391, -0.06765142950715254, 0.12474102351774016, -0.12962876649006552, -0.07297484643514389, 0.31990999566472095, -0.02044775486296124, -0.2988869366843415, 0.03389740553077148, -0.08919049936103755, -0.2109023884910604, 0.10031595304810806, 0.05542322604552559, 0.06973909380157357, -0.15229713864138592, 0.2639670379905273, -0.20248502252987868, 0.06135730279366607, 0.09750739181333262, -0.04405929082397209, 0.15161142882931491, -0.06078781997380049, -0.002087207045406103, 0.204830940509134, 0.09917644278713218, -0.13518358283149806, -0.3784180243054162, -0.12699122545714286, -0.1683133518444779, 0.2306239515259538, -0.17605124533419375, -0.2334550956223646, 0.42427599279756617, 0.1445646359807933, 0.21235028854773744, 0.12638791313435396, 0.1524641796865541, 0.20640604627197204, 0.07554245821159819, 0.07987131799935647, 0.1250448765476113, 0.2739879186720709, -0.06600098182325778, -0.2485293278004974, -0.0750967936043668, 0.3163281219970921] |
1,802.07577 | Complex Cellular Structures | We introduce the notion of a complex cell, a complexification of the
cells/cylinders used in real tame geometry. For $\delta\in(0,1)$ and a complex
cell $\mathcal{C}$ we define its holomorphic extension
$\mathcal{C}\subset\mathcal{C}^\delta$, which is again a complex cell. The
hyperbolic geometry of $\mathcal{C}$ within $\mathcal{C}^\delta$ provides the
class of complex cells with a rich geometric function theory absent in the real
case. We use this to prove a complex analog of the cellular decomposition
theorem of real tame geometry. In the algebraic case we show that the
complexity of such decompositions depends polynomially on the degrees of the
equations involved.
Using this theory, we refine the Yomdin-Gromov algebraic lemma on
$C^r$-smooth parametrizations of semialgebraic sets: we show that the number of
$C^r$ charts can be taken to be polynomial in the smoothness order $r$ and in
the complexity of the set. The algebraic lemma was initially invented in the
work of Yomdin and Gromov to produce estimates for the topological entropy of
$C^\infty$ maps. For analytic maps our refined version, combined with work of
Burguet, Liao and Yang, establishes an optimal refinement of these estimates in
the form of tight bounds on the tail entropy and volume growth. This settles a
conjecture of Yomdin who proved the same result in dimension two in 1991. A
self-contained proof of these estimates using the refined algebraic lemma is
given in an appendix by Yomdin.
The algebraic lemma has more recently been used in the study of rational
points on algebraic and transcendental varieties. We use the theory of complex
cells in these two directions. In the algebraic context we refine a result of
Heath-Brown on interpolating rational points in algebraic varieties. In the
transcendental context we prove an interpolation result for (unrestricted)
logarithmic images of subanalytic sets.
| math.CV math.AG math.DS math.LO math.NT | we introduce the notion of a complex cell a complexification of the cellscylinders used in real tame geometry for deltain01 and a complex cell mathcalc we define its holomorphic extension mathcalcsubsetmathcalcdelta which is again a complex cell the hyperbolic geometry of mathcalc within mathcalcdelta provides the class of complex cells with a rich geometric function theory absent in the real case we use this to prove a complex analog of the cellular decomposition theorem of real tame geometry in the algebraic case we show that the complexity of such decompositions depends polynomially on the degrees of the equations involved using this theory we refine the yomdingromov algebraic lemma on crsmooth parametrizations of semialgebraic sets we show that the number of cr charts can be taken to be polynomial in the smoothness order r and in the complexity of the set the algebraic lemma was initially invented in the work of yomdin and gromov to produce estimates for the topological entropy of cinfty maps for analytic maps our refined version combined with work of burguet liao and yang establishes an optimal refinement of these estimates in the form of tight bounds on the tail entropy and volume growth this settles a conjecture of yomdin who proved the same result in dimension two in 1991 a selfcontained proof of these estimates using the refined algebraic lemma is given in an appendix by yomdin the algebraic lemma has more recently been used in the study of rational points on algebraic and transcendental varieties we use the theory of complex cells in these two directions in the algebraic context we refine a result of heathbrown on interpolating rational points in algebraic varieties in the transcendental context we prove an interpolation result for unrestricted logarithmic images of subanalytic sets | [['we', 'introduce', 'the', 'notion', 'of', 'a', 'complex', 'cell', 'a', 'complexification', 'of', 'the', 'cellscylinders', 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1,802.07578 | Improving Recommender Systems Beyond the Algorithm | Recommender systems rely heavily on the predictive accuracy of the learning
algorithm. Most work on improving accuracy has focused on the learning
algorithm itself. We argue that this algorithmic focus is myopic. In
particular, since learning algorithms generally improve with more and better
data, we propose shaping the feedback generation process as an alternate and
complementary route to improving accuracy. To this effect, we explore how
changes to the user interface can impact the quality and quantity of feedback
data -- and therefore the learning accuracy. Motivated by information foraging
theory, we study how feedback quality and quantity are influenced by interface
design choices along two axes: information scent and information access cost.
We present a user study of these interface factors for the common task of
picking a movie to watch, showing that these factors can effectively shape and
improve the implicit feedback data that is generated while maintaining the user
experience.
| cs.HC cs.IR | recommender systems rely heavily on the predictive accuracy of the learning algorithm most work on improving accuracy has focused on the learning algorithm itself we argue that this algorithmic focus is myopic in particular since learning algorithms generally improve with more and better data we propose shaping the feedback generation process as an alternate and complementary route to improving accuracy to this effect we explore how changes to the user interface can impact the quality and quantity of feedback data and therefore the learning accuracy motivated by information foraging theory we study how feedback quality and quantity are influenced by interface design choices along two axes information scent and information access cost we present a user study of these interface factors for the common task of picking a movie to watch showing that these factors can effectively shape and improve the implicit feedback data that is generated while maintaining the user experience | [['recommender', 'systems', 'rely', 'heavily', 'on', 'the', 'predictive', 'accuracy', 'of', 'the', 'learning', 'algorithm', 'most', 'work', 'on', 'improving', 'accuracy', 'has', 'focused', 'on', 'the', 'learning', 'algorithm', 'itself', 'we', 'argue', 'that', 'this', 'algorithmic', 'focus', 'is', 'myopic', 'in', 'particular', 'since', 'learning', 'algorithms', 'generally', 'improve', 'with', 'more', 'and', 'better', 'data', 'we', 'propose', 'shaping', 'the', 'feedback', 'generation', 'process', 'as', 'an', 'alternate', 'and', 'complementary', 'route', 'to', 'improving', 'accuracy', 'to', 'this', 'effect', 'we', 'explore', 'how', 'changes', 'to', 'the', 'user', 'interface', 'can', 'impact', 'the', 'quality', 'and', 'quantity', 'of', 'feedback', 'data', 'and', 'therefore', 'the', 'learning', 'accuracy', 'motivated', 'by', 'information', 'foraging', 'theory', 'we', 'study', 'how', 'feedback', 'quality', 'and', 'quantity', 'are', 'influenced', 'by', 'interface', 'design', 'choices', 'along', 'two', 'axes', 'information', 'scent', 'and', 'information', 'access', 'cost', 'we', 'present', 'a', 'user', 'study', 'of', 'these', 'interface', 'factors', 'for', 'the', 'common', 'task', 'of', 'picking', 'a', 'movie', 'to', 'watch', 'showing', 'that', 'these', 'factors', 'can', 'effectively', 'shape', 'and', 'improve', 'the', 'implicit', 'feedback', 'data', 'that', 'is', 'generated', 'while', 'maintaining', 'the', 'user', 'experience']] | [-0.08449100098790184, 0.02730981555645198, -0.09028383274562657, 0.047778806799322796, -0.16207152995354446, -0.1643766711747862, 0.10096358687013363, 0.45316442282331226, -0.25787298020517674, -0.36729206541885534, 0.09806527522682461, -0.27076729880890954, -0.1871724207119673, 0.1950798740144819, -0.12573787212482115, 0.04719149057315295, 0.07852758452492326, 0.039411223248431555, -0.03983920990791184, -0.30148327467031777, 0.33322171090357616, 0.12686544300155028, 0.33551714676554856, 0.07303808046823465, 0.1043624042121289, 0.021351035270766403, -0.056975184437377674, -0.0046070132337167466, -0.113492480199583, 0.16970560984272628, 0.2784887310515746, 0.2147912100404746, 0.3350131642318478, -0.40918996040464234, -0.20702550198123054, 0.05817180802420664, 0.17678146195708236, 0.09064309577929396, -0.0991380961538533, -0.271523796757193, 0.06489285267276787, -0.15034730801064716, -0.023941887530351157, -0.11210686228342208, -0.0600383678377655, 0.0007887968656512768, -0.2960686463936183, 0.008713259981289556, 0.0657616926274434, 0.0535099856910835, -0.015503758690197413, -0.08529679819720944, 0.01649670365977248, 0.2175304085494166, 0.05086654076321314, 0.04714437171519661, 0.2004746524567293, -0.18877378648367563, -0.15455084342485, 0.3722936525989912, -0.009168609040850578, -0.22277300584583395, 0.19059286379304372, -0.07797551186338655, -0.1424620114848949, 0.09354206321816157, 0.27157540019145116, 0.08227495330778, -0.1547514350854487, -0.0002826025007188467, 0.01982543467985172, 0.20825712682103345, 0.028139116372346364, 0.04750173304331072, 0.1545661986486888, 0.22585322190609172, 0.05642390463158096, 0.09599349363117271, -0.016915852867226164, -0.06721186283730755, -0.16362062200144128, -0.1289924421825593, -0.16117656998042212, -0.01860621820455172, -0.10064092598747122, -0.09248261617521118, 0.37680568001968295, 0.24175616123370433, 0.18210083317305698, 0.044697421062186264, 0.359256410272792, 0.06451946271408815, 0.030670787397723057, 0.10335171259564384, 0.2114312575324316, -0.019246135418621923, 0.12193431553130626, -0.24045220169385798, 0.14910875597821646, 0.027452315739968692] |
1,802.07579 | Spin Hartree-Fock approach to quantum Heisenberg antiferromagnets in low
dimensions | We construct a new mean-field theory for quantum (spin-1/2) Heisenberg
antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock
decoupling of the four-point correlation functions. We show that the solution
to the self-consistency equations based on two-point correlation functions does
not produce any unphysical finite-temperature phase transition in accord with
Mermin-Wagner theorem, unlike the common approach based on the mean-field
equation for the order parameter. The next-neighbor spin-spin correlation
functions, calculated within this approach, reproduce closely the strong
renormalization by quantum fluctuations obtained via Bethe ansatz in 1D and a
small renormalization of the classical antiferromagnetic state in 2D. The heat
capacity approximates with reasonable accuracy the full Bethe ansatz result at
all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the
heat capacity at a finite temperature that is accessible by high-order $1/T$
expansions.
| cond-mat.mes-hall cond-mat.str-el | we construct a new meanfield theory for quantum spin12 heisenberg antiferromagnet in one 1d and two 2d dimensions using a hartreefock decoupling of the fourpoint correlation functions we show that the solution to the selfconsistency equations based on twopoint correlation functions does not produce any unphysical finitetemperature phase transition in accord with merminwagner theorem unlike the common approach based on the meanfield equation for the order parameter the nextneighbor spinspin correlation functions calculated within this approach reproduce closely the strong renormalization by quantum fluctuations obtained via bethe ansatz in 1d and a small renormalization of the classical antiferromagnetic state in 2d the heat capacity approximates with reasonable accuracy the full bethe ansatz result at all temperatures in 1d in 2d we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by highorder 1t expansions | [['we', 'construct', 'a', 'new', 'meanfield', 'theory', 'for', 'quantum', 'spin12', 'heisenberg', 'antiferromagnet', 'in', 'one', '1d', 'and', 'two', '2d', 'dimensions', 'using', 'a', 'hartreefock', 'decoupling', 'of', 'the', 'fourpoint', 'correlation', 'functions', 'we', 'show', 'that', 'the', 'solution', 'to', 'the', 'selfconsistency', 'equations', 'based', 'on', 'twopoint', 'correlation', 'functions', 'does', 'not', 'produce', 'any', 'unphysical', 'finitetemperature', 'phase', 'transition', 'in', 'accord', 'with', 'merminwagner', 'theorem', 'unlike', 'the', 'common', 'approach', 'based', 'on', 'the', 'meanfield', 'equation', 'for', 'the', 'order', 'parameter', 'the', 'nextneighbor', 'spinspin', 'correlation', 'functions', 'calculated', 'within', 'this', 'approach', 'reproduce', 'closely', 'the', 'strong', 'renormalization', 'by', 'quantum', 'fluctuations', 'obtained', 'via', 'bethe', 'ansatz', 'in', '1d', 'and', 'a', 'small', 'renormalization', 'of', 'the', 'classical', 'antiferromagnetic', 'state', 'in', '2d', 'the', 'heat', 'capacity', 'approximates', 'with', 'reasonable', 'accuracy', 'the', 'full', 'bethe', 'ansatz', 'result', 'at', 'all', 'temperatures', 'in', '1d', 'in', '2d', 'we', 'obtain', 'a', 'reduction', 'of', 'the', 'peak', 'height', 'in', 'the', 'heat', 'capacity', 'at', 'a', 'finite', 'temperature', 'that', 'is', 'accessible', 'by', 'highorder', '1t', 'expansions']] | [-0.1275023343985887, 0.13162791229079485, -0.08742658047636863, 0.1000134085819542, -0.018104783751044448, -0.13968852424173506, 0.04686151321414025, 0.3276859588816866, -0.21209903622788567, -0.21207022494180583, 0.029350313104011795, -0.31817788211303155, -0.11412787687675938, 0.16435246037358378, 0.10119885174798539, 0.09286331394166275, 0.010726532506450386, 0.03720354215995819, -0.1950056703192983, -0.20587989108122468, 0.3019078104509288, 0.006445083775316606, 0.31446899022333896, 0.07852644855123977, 0.07058344403659547, 0.04947453564996798, 0.08134483458422176, 0.02564510198349094, -0.17494102880259785, 0.04677633329952409, 0.23044926506284807, -0.028000262650576504, 0.2024857710030946, -0.42460341002609764, -0.24761700753523103, 0.028759175664875528, 0.14687133376760134, 0.1771524302479062, -0.011642926357934003, -0.26278203870397765, 0.017417859728936547, -0.19063010260501836, -0.16779892801484614, -0.14462185930460691, -0.07108605901508794, 0.0077721779723163254, -0.27401476545207254, 0.18086968600697867, 0.03025274090892212, 0.057338360117396694, -0.06328331085794664, -0.1069081166948003, -0.021427396266848187, 0.08588209954396515, -0.010304905607697222, 0.060234873236476125, 0.05607879887924406, -0.12510661619480934, -0.09825616756859529, 0.3437476749263274, -0.11787665709999709, -0.2043238627379174, 0.15077388910185938, -0.18560604398444921, -0.1300275534231841, 0.13563349058402221, 0.08579384512430825, 0.0968359605689253, -0.17478709546784005, 0.13635136052832605, -0.036379834249537515, 0.18282440844499928, 0.019582901900582067, 0.013933021418906592, 0.1617168276863811, 0.11381149692200385, 0.020996947023835217, 0.15481544208185344, -0.048798367885833645, -0.19687487789384134, -0.30376154429220653, -0.11994659326566787, -0.2638427615825126, 0.07437441166064139, -0.15212280627554184, -0.22951723618263548, 0.37878487503703134, 0.1997783419694849, 0.17072102440833734, 0.07939055441370742, 0.2585754669662174, 0.18128664712779796, 0.0745949954839775, 0.09360237005394656, 0.21672048828063104, 0.17464089873116595, 0.0880268816998997, -0.29461070327283617, -0.009040809389516399, 0.16857319795428874] |
1,802.0758 | Numerical Investigation on Local Non-equilibrium Flows Using a Diatomic
Nonlinear Constitutive Model | The linear Navier-Stokes-Fourier (NSF) constitutive relations are capable of
simulating the near-continuum flows, but fail in description of those flows
which are removed far away from local equilibrium. In this paper, a diatomic
nonlinear model named as nonlinear coupled constitutive relations (NCCR),
derived from Eu's generalized hydrodynamics and proposed by Myong, is presented
as an alternative for simulating these hypersonic gas flows with a goal of
recovering NSF's solutions in continuum regime and being superior in transition
regime. To guarantee stable computation, a reliable and efficient coupled
algorithm is proposed for this diatomic nonlinear constitutive model.
Constitutive-curve analysis is carried out in detail to compare this coupled
algorithm with Myong's previous algorithm. Local flow regions are investigated
carefully in these hypersonic flows past a cone tip, a hollow cylinder-flare
and a HTV-type vehicle. The convergent solutions of NCCR model are compared
with NSF, DSMC calculations and experiment. It is demonstrated that the NCCR
model works as efficiently as the NSF model in continuum regime, but more
accurately compared with DSMC and experiment than NSF in non-equilibrium flows.
The discrepancies of flow- field and surface parameters, imply a potential for
remedying NSF's deficiency in local non-equilibrium regions.
| physics.flu-dyn physics.comp-ph | the linear navierstokesfourier nsf constitutive relations are capable of simulating the nearcontinuum flows but fail in description of those flows which are removed far away from local equilibrium in this paper a diatomic nonlinear model named as nonlinear coupled constitutive relations nccr derived from eus generalized hydrodynamics and proposed by myong is presented as an alternative for simulating these hypersonic gas flows with a goal of recovering nsfs solutions in continuum regime and being superior in transition regime to guarantee stable computation a reliable and efficient coupled algorithm is proposed for this diatomic nonlinear constitutive model constitutivecurve analysis is carried out in detail to compare this coupled algorithm with myongs previous algorithm local flow regions are investigated carefully in these hypersonic flows past a cone tip a hollow cylinderflare and a htvtype vehicle the convergent solutions of nccr model are compared with nsf dsmc calculations and experiment it is demonstrated that the nccr model works as efficiently as the nsf model in continuum regime but more accurately compared with dsmc and experiment than nsf in nonequilibrium flows the discrepancies of flow field and surface parameters imply a potential for remedying nsfs deficiency in local nonequilibrium regions | [['the', 'linear', 'navierstokesfourier', 'nsf', 'constitutive', 'relations', 'are', 'capable', 'of', 'simulating', 'the', 'nearcontinuum', 'flows', 'but', 'fail', 'in', 'description', 'of', 'those', 'flows', 'which', 'are', 'removed', 'far', 'away', 'from', 'local', 'equilibrium', 'in', 'this', 'paper', 'a', 'diatomic', 'nonlinear', 'model', 'named', 'as', 'nonlinear', 'coupled', 'constitutive', 'relations', 'nccr', 'derived', 'from', 'eus', 'generalized', 'hydrodynamics', 'and', 'proposed', 'by', 'myong', 'is', 'presented', 'as', 'an', 'alternative', 'for', 'simulating', 'these', 'hypersonic', 'gas', 'flows', 'with', 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1,802.07581 | Universal Hypothesis Testing with Kernels: Asymptotically Optimal Tests
for Goodness of Fit | We characterize the asymptotic performance of nonparametric goodness of fit
testing. The exponential decay rate of the type-II error probability is used as
the asymptotic performance metric, and a test is optimal if it achieves the
maximum rate subject to a constant level constraint on the type-I error
probability. We show that two classes of Maximum Mean Discrepancy (MMD) based
tests attain this optimality on $\mathbb R^d$, while the quadratic-time Kernel
Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate
under a relaxed level constraint. Under the same performance metric, we proceed
to show that the quadratic-time MMD based two-sample tests are also optimal for
general two-sample problems, provided that kernels are bounded continuous and
characteristic. Key to our approach are Sanov's theorem from large deviation
theory and the weak metrizable properties of the MMD and KSD.
| stat.ML cs.IT cs.LG math.IT | we characterize the asymptotic performance of nonparametric goodness of fit testing the exponential decay rate of the typeii error probability is used as the asymptotic performance metric and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the typei error probability we show that two classes of maximum mean discrepancy mmd based tests attain this optimality on mathbb rd while the quadratictime kernel stein discrepancy ksd based tests achieve the maximum exponential decay rate under a relaxed level constraint under the same performance metric we proceed to show that the quadratictime mmd based twosample tests are also optimal for general twosample problems provided that kernels are bounded continuous and characteristic key to our approach are sanovs theorem from large deviation theory and the weak metrizable properties of the mmd and ksd | [['we', 'characterize', 'the', 'asymptotic', 'performance', 'of', 'nonparametric', 'goodness', 'of', 'fit', 'testing', 'the', 'exponential', 'decay', 'rate', 'of', 'the', 'typeii', 'error', 'probability', 'is', 'used', 'as', 'the', 'asymptotic', 'performance', 'metric', 'and', 'a', 'test', 'is', 'optimal', 'if', 'it', 'achieves', 'the', 'maximum', 'rate', 'subject', 'to', 'a', 'constant', 'level', 'constraint', 'on', 'the', 'typei', 'error', 'probability', 'we', 'show', 'that', 'two', 'classes', 'of', 'maximum', 'mean', 'discrepancy', 'mmd', 'based', 'tests', 'attain', 'this', 'optimality', 'on', 'mathbb', 'rd', 'while', 'the', 'quadratictime', 'kernel', 'stein', 'discrepancy', 'ksd', 'based', 'tests', 'achieve', 'the', 'maximum', 'exponential', 'decay', 'rate', 'under', 'a', 'relaxed', 'level', 'constraint', 'under', 'the', 'same', 'performance', 'metric', 'we', 'proceed', 'to', 'show', 'that', 'the', 'quadratictime', 'mmd', 'based', 'twosample', 'tests', 'are', 'also', 'optimal', 'for', 'general', 'twosample', 'problems', 'provided', 'that', 'kernels', 'are', 'bounded', 'continuous', 'and', 'characteristic', 'key', 'to', 'our', 'approach', 'are', 'sanovs', 'theorem', 'from', 'large', 'deviation', 'theory', 'and', 'the', 'weak', 'metrizable', 'properties', 'of', 'the', 'mmd', 'and', 'ksd']] | [-0.06972900618088813, 0.010652887129070733, -0.11651815666663025, 0.16527020130323233, -0.059956083884931725, -0.17446645219616003, 0.11084519558261223, 0.36714787763818135, -0.2618582929558248, -0.2584238836019159, 0.10971530517161214, -0.23269302641852296, -0.11086432706135854, 0.22265041196088997, -0.11150507894914141, 0.1580839540521286, 0.08159332716060307, 0.06359990605776258, -0.11789887541362333, -0.34084335417091416, 0.28493988701886086, 0.07648650251610352, 0.3741320642649377, 0.0398177386063868, 0.11981797194202169, -0.0688182635018401, 0.03326776749688944, 0.04036527949137439, -0.18704688503726666, 0.11775565924618742, 0.18549656897964184, 0.1885691837293746, 0.32350743044730573, -0.33245769310608614, -0.16368993563119408, 0.17530644614343271, 0.05696804502982271, -0.004064642129090729, -0.025709718119071648, -0.25838174737936304, 0.12751782284178537, -0.10002058727680135, -0.08734932889920666, -0.04817612483936677, -0.043192461547575785, 0.05008419538075908, -0.38150145768744054, 0.13481292344454723, 0.09985686268108032, 0.022857660521491827, -0.024633117716947046, -0.14086910085702356, 0.06964328879885805, 0.08982120992836924, 0.10040864203771804, 0.040394381369571304, 0.0910008363727239, -0.05490849180843869, -0.13299161664096357, 0.31081910840094945, -0.1255449067567569, -0.236496239240623, 0.1444946545755772, -0.13990721940029438, -0.12501951720793364, 0.0976990695670917, 0.20162741847925905, 0.11512280059241348, -0.1414320453023203, 0.11175465010099864, -0.0495143821261984, 0.15991036674985998, 0.07633446247765807, 0.030933910145394157, 0.10402102801084465, 0.1621124938816308, 0.11757056371529968, 0.13019272119557257, -0.12709885912029434, -0.10351776080407041, -0.3477598569094599, -0.1483515885611661, -0.20527685466624473, 0.043408606375614514, -0.1627800444150662, -0.16355405801408018, 0.3515211693396484, 0.13295234294554634, 0.149327727282594, 0.19932973554371286, 0.25769073530870806, 0.11619317448168671, -0.003785760321138467, 0.13522276114000312, 0.26007378648752144, 0.1470853323719913, -0.05591304452583971, -0.23341961368196476, 0.11292371765891318, 0.09834707435251887] |
1,802.07582 | Axisymmetric inertial modes in a spherical shell at low Ekman numbers | We investigate the asymptotic properties of axisymmetric inertial modes
propagating in a spherical shell when viscosity tends to zero. We identify
three kinds of eigenmodes whose eigenvalues follow very different laws as the
Ekman number $E$ becomes very small. First are modes associated with attractors
of characteristics that are made of thin shear layers closely following the
periodic orbit traced by the characteristic attractor. Second are modes made of
shear layers that connect the critical latitude singularities of the two
hemispheres of the inner boundary of the spherical shell. Third are
quasi-regular modes associated with the frequency of neutral periodic orbits of
characteristics. We thoroughly analyse a subset of attractor modes for which
numerical solutions point to an asymptotic law governing the eigenvalues. We
show that three length scales proportional to $E^{1/6}$, $E^{1/4}$ and
$E^{1/3}$ control the shape of the shear layers that are associated with these
modes. These scales point out the key role of the small parameter $E^{1/12}$ in
these oscillatory flows. With a simplified model of the viscous Poincar\'e
equation, we can give an approximate analytical formula that reproduces the
velocity field in such shear layers. Finally, we also present an analysis of
the quasi-regular modes whose frequencies are close to $\sin(\pi/4)$ and
explain why a fluid inside a spherical shell cannot respond to any periodic
forcing at this frequency when viscosity vanishes.
| physics.flu-dyn astro-ph.EP astro-ph.SR | we investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero we identify three kinds of eigenmodes whose eigenvalues follow very different laws as the ekman number e becomes very small first are modes associated with attractors of characteristics that are made of thin shear layers closely following the periodic orbit traced by the characteristic attractor second are modes made of shear layers that connect the critical latitude singularities of the two hemispheres of the inner boundary of the spherical shell third are quasiregular modes associated with the frequency of neutral periodic orbits of characteristics we thoroughly analyse a subset of attractor modes for which numerical solutions point to an asymptotic law governing the eigenvalues we show that three length scales proportional to e16 e14 and e13 control the shape of the shear layers that are associated with these modes these scales point out the key role of the small parameter e112 in these oscillatory flows with a simplified model of the viscous poincare equation we can give an approximate analytical formula that reproduces the velocity field in such shear layers finally we also present an analysis of the quasiregular modes whose frequencies are close to sinpi4 and explain why a fluid inside a spherical shell cannot respond to any periodic forcing at this frequency when viscosity vanishes | [['we', 'investigate', 'the', 'asymptotic', 'properties', 'of', 'axisymmetric', 'inertial', 'modes', 'propagating', 'in', 'a', 'spherical', 'shell', 'when', 'viscosity', 'tends', 'to', 'zero', 'we', 'identify', 'three', 'kinds', 'of', 'eigenmodes', 'whose', 'eigenvalues', 'follow', 'very', 'different', 'laws', 'as', 'the', 'ekman', 'number', 'e', 'becomes', 'very', 'small', 'first', 'are', 'modes', 'associated', 'with', 'attractors', 'of', 'characteristics', 'that', 'are', 'made', 'of', 'thin', 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1,802.07583 | Time-series analysis of fissure-fed multi-vent activity: a snapshot from
the July 2014 eruption of Etna volcano (Italy) | On 5 July 2014, an eruptive fissure opened on the eastern flank of Etna
volcano (Italy) at ~3.000 m a.s.l. Strombolian activity and lava effusion
occurred simultaneously at two neighbouring vents. In the following weeks,
eruptive activity led to the build-up of two cones, tens of meters high, here
named Crater N and Crater S. To characterize the short-term (days) dynamics of
this multi-vent system, we performed a multi-parametric investigation by means
of a dense instrumental network. The experimental setup, deployed on July
15-16th at ca. 300 m from the eruption site, comprised two broadband
seismometers and three microphones as well as high speed video and thermal
cameras. Thermal analyses enabled us to characterize the style of eruptive
activity at each vent. In particular, explosive activity at Crater N featured
higher thermal amplitudes and a lower explosion frequency than at Crater S.
Several episodes of switching between puffing and Strombolian activity were
noted at Crater S through both visual observation and thermal data; oppositely,
Crater N exhibited a quasi-periodic activity. The quantification of the
eruptive style of each vent enabled us to infer the geometry of the eruptive
system: a branched conduit, prone to rapid changes of gas flux accommodated at
the most inclined conduit (i.e. Crater S). Accordingly, we were able to
correctly interpret acoustic data and thereby extend the characterization of
this twovent system.
| physics.geo-ph | on 5 july 2014 an eruptive fissure opened on the eastern flank of etna volcano italy at 3000 m asl strombolian activity and lava effusion occurred simultaneously at two neighbouring vents in the following weeks eruptive activity led to the buildup of two cones tens of meters high here named crater n and crater s to characterize the shortterm days dynamics of this multivent system we performed a multiparametric investigation by means of a dense instrumental network the experimental setup deployed on july 1516th at ca 300 m from the eruption site comprised two broadband seismometers and three microphones as well as high speed video and thermal cameras thermal analyses enabled us to characterize the style of eruptive activity at each vent in particular explosive activity at crater n featured higher thermal amplitudes and a lower explosion frequency than at crater s several episodes of switching between puffing and strombolian activity were noted at crater s through both visual observation and thermal data oppositely crater n exhibited a quasiperiodic activity the quantification of the eruptive style of each vent enabled us to infer the geometry of the eruptive system a branched conduit prone to rapid changes of gas flux accommodated at the most inclined conduit ie crater s accordingly we were able to correctly interpret acoustic data and thereby extend the characterization of this twovent system | [['on', '5', 'july', '2014', 'an', 'eruptive', 'fissure', 'opened', 'on', 'the', 'eastern', 'flank', 'of', 'etna', 'volcano', 'italy', 'at', '3000', 'm', 'asl', 'strombolian', 'activity', 'and', 'lava', 'effusion', 'occurred', 'simultaneously', 'at', 'two', 'neighbouring', 'vents', 'in', 'the', 'following', 'weeks', 'eruptive', 'activity', 'led', 'to', 'the', 'buildup', 'of', 'two', 'cones', 'tens', 'of', 'meters', 'high', 'here', 'named', 'crater', 'n', 'and', 'crater', 's', 'to', 'characterize', 'the', 'shortterm', 'days', 'dynamics', 'of', 'this', 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1,802.07584 | DeepASL: Enabling Ubiquitous and Non-Intrusive Word and Sentence-Level
Sign Language Translation | There is an undeniable communication barrier between deaf people and people
with normal hearing ability. Although innovations in sign language translation
technology aim to tear down this communication barrier, the majority of
existing sign language translation systems are either intrusive or constrained
by resolution or ambient lighting conditions. Moreover, these existing systems
can only perform single-sign ASL translation rather than sentence-level
translation, making them much less useful in daily-life communication
scenarios. In this work, we fill this critical gap by presenting DeepASL, a
transformative deep learning-based sign language translation technology that
enables ubiquitous and non-intrusive American Sign Language (ASL) translation
at both word and sentence levels. DeepASL uses infrared light as its sensing
mechanism to non-intrusively capture the ASL signs. It incorporates a novel
hierarchical bidirectional deep recurrent neural network (HB-RNN) and a
probabilistic framework based on Connectionist Temporal Classification (CTC)
for word-level and sentence-level ASL translation respectively. To evaluate its
performance, we have collected 7,306 samples from 11 participants, covering 56
commonly used ASL words and 100 ASL sentences. DeepASL achieves an average
94.5% word-level translation accuracy and an average 8.2% word error rate on
translating unseen ASL sentences. Given its promising performance, we believe
DeepASL represents a significant step towards breaking the communication
barrier between deaf people and hearing majority, and thus has the significant
potential to fundamentally change deaf people's lives.
| cs.CV | there is an undeniable communication barrier between deaf people and people with normal hearing ability although innovations in sign language translation technology aim to tear down this communication barrier the majority of existing sign language translation systems are either intrusive or constrained by resolution or ambient lighting conditions moreover these existing systems can only perform singlesign asl translation rather than sentencelevel translation making them much less useful in dailylife communication scenarios in this work we fill this critical gap by presenting deepasl a transformative deep learningbased sign language translation technology that enables ubiquitous and nonintrusive american sign language asl translation at both word and sentence levels deepasl uses infrared light as its sensing mechanism to nonintrusively capture the asl signs it incorporates a novel hierarchical bidirectional deep recurrent neural network hbrnn and a probabilistic framework based on connectionist temporal classification ctc for wordlevel and sentencelevel asl translation respectively to evaluate its performance we have collected 7306 samples from 11 participants covering 56 commonly used asl words and 100 asl sentences deepasl achieves an average 945 wordlevel translation accuracy and an average 82 word error rate on translating unseen asl sentences given its promising performance we believe deepasl represents a significant step towards breaking the communication barrier between deaf people and hearing majority and thus has the significant potential to fundamentally change deaf peoples lives | [['there', 'is', 'an', 'undeniable', 'communication', 'barrier', 'between', 'deaf', 'people', 'and', 'people', 'with', 'normal', 'hearing', 'ability', 'although', 'innovations', 'in', 'sign', 'language', 'translation', 'technology', 'aim', 'to', 'tear', 'down', 'this', 'communication', 'barrier', 'the', 'majority', 'of', 'existing', 'sign', 'language', 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1,802.07585 | Maximising Bernoulli measures and dimension gaps for countable branched
systems | Kifer, Peres, and Weiss proved that there exists $c_0>0,$ such that $\dim
\mu\leq 1-c_0$ for any probability measure $\mu$ which makes the digits of the
continued fraction expansion i.i.d. random variables. In this paper we prove
that amongst this class of measures, there exists one whose dimension is
maximal. Our results also apply in the more general setting of countable
branched systems.
| math.DS | kifer peres and weiss proved that there exists c_00 such that dim muleq 1c_0 for any probability measure mu which makes the digits of the continued fraction expansion iid random variables in this paper we prove that amongst this class of measures there exists one whose dimension is maximal our results also apply in the more general setting of countable branched systems | [['kifer', 'peres', 'and', 'weiss', 'proved', 'that', 'there', 'exists', 'c_00', 'such', 'that', 'dim', 'muleq', '1c_0', 'for', 'any', 'probability', 'measure', 'mu', 'which', 'makes', 'the', 'digits', 'of', 'the', 'continued', 'fraction', 'expansion', 'iid', 'random', 'variables', 'in', 'this', 'paper', 'we', 'prove', 'that', 'amongst', 'this', 'class', 'of', 'measures', 'there', 'exists', 'one', 'whose', 'dimension', 'is', 'maximal', 'our', 'results', 'also', 'apply', 'in', 'the', 'more', 'general', 'setting', 'of', 'countable', 'branched', 'systems']] | [-0.14456619927468786, 0.15886748734037162, -0.06254358130094946, 0.07010135688765555, -0.02888190478361288, -0.15588168885375633, 0.10350158806035265, 0.3400694346208064, -0.2523875698508298, -0.13676414399820028, 0.09212164407534922, -0.30673989233728804, -0.19422279218723235, 0.20848850630410778, -0.13401147533116525, 0.011824299329433774, 0.06240999619247484, 0.08368786934335701, -0.0032791104434882518, -0.31883376644405187, 0.3423048271664006, -0.08404263060112468, 0.20736732033127156, 0.02825057332510831, 0.1339212471054348, 0.020485132131114848, -0.020311389958150076, 0.01090486077439101, -0.19616589710280036, 0.08179828770397628, 0.2914321002107663, 0.15766103607297066, 0.28674364138822084, -0.2775362855525779, -0.19180292414203592, 0.2708003196224082, 0.10968777719030126, 0.01139953638404058, -0.04631792148694465, -0.23243672892329145, 0.13553343171284335, -0.14932531497029009, -0.1746913608102525, -0.11127209855762661, 0.1441298754366695, 0.009602485835307935, -0.31201467467624633, 0.060481558423622926, 0.16494897387341642, 0.04900733331126756, -0.009204865120290244, -0.11070412780410137, 0.01905059520170459, 0.08731737248714036, 0.05893669257200033, 0.09456182525447401, 0.0327940949193034, -0.039954437820821025, -0.13974690025092149, 0.3409325470766205, -0.06219910534068209, -0.22183760475046688, 0.19330886868973735, -0.23357464661096514, -0.24165607622412386, 0.09664947666956844, 0.06972166396616424, 0.11697692221763437, -0.0927444484435999, 0.1504204218251035, -0.15360006045733318, 0.18070675909030634, 0.13875222222146685, 0.028987737942189284, 0.08222302148637713, 0.08203376405185363, 0.1511424229381087, 0.13527961113856588, -0.00895058798802192, -0.06405750152151116, -0.3020353371002635, -0.18013147267772525, -0.21894733688687204, 0.13693032503799826, -0.14563202575497047, -0.1993861974934574, 0.2853288256303697, 0.1406233790177913, 0.15886728633500513, 0.14861390211230113, 0.19984409701247074, 0.10247988150012298, -0.005826085002436379, 0.1254661266279758, 0.13069192460570178, 0.15305027368738025, 0.028218300606612665, -0.09872621190199843, 0.07222591750476448, 0.09437809017349462] |
1,802.07586 | Global Spherical Tropicalization via Toric Embeddings | The first steps in defining tropicalization for spherical varieties have been
taken in the last few years. There are two parts to this theory: tropicalizing
subvarieties of homogeneous spaces and tropicalizing their closures in
spherical embeddings. In this paper, we obtain a new description of spherical
tropicalization that is equivalent to the other theories. This works by
embedding in a toric variety, tropicalizing there, and then applying a
particular piecewise projection map. We use this theory to prove that taking
closures commutes with the spherical tropicalization operation.
| math.AG | the first steps in defining tropicalization for spherical varieties have been taken in the last few years there are two parts to this theory tropicalizing subvarieties of homogeneous spaces and tropicalizing their closures in spherical embeddings in this paper we obtain a new description of spherical tropicalization that is equivalent to the other theories this works by embedding in a toric variety tropicalizing there and then applying a particular piecewise projection map we use this theory to prove that taking closures commutes with the spherical tropicalization operation | [['the', 'first', 'steps', 'in', 'defining', 'tropicalization', 'for', 'spherical', 'varieties', 'have', 'been', 'taken', 'in', 'the', 'last', 'few', 'years', 'there', 'are', 'two', 'parts', 'to', 'this', 'theory', 'tropicalizing', 'subvarieties', 'of', 'homogeneous', 'spaces', 'and', 'tropicalizing', 'their', 'closures', 'in', 'spherical', 'embeddings', 'in', 'this', 'paper', 'we', 'obtain', 'a', 'new', 'description', 'of', 'spherical', 'tropicalization', 'that', 'is', 'equivalent', 'to', 'the', 'other', 'theories', 'this', 'works', 'by', 'embedding', 'in', 'a', 'toric', 'variety', 'tropicalizing', 'there', 'and', 'then', 'applying', 'a', 'particular', 'piecewise', 'projection', 'map', 'we', 'use', 'this', 'theory', 'to', 'prove', 'that', 'taking', 'closures', 'commutes', 'with', 'the', 'spherical', 'tropicalization', 'operation']] | [-0.09159625358023178, 0.04282068385175247, -0.11580002964099591, 0.06393925086782452, -0.060965462405791225, -0.09140530656273851, -0.048579934140099965, 0.37891749774330646, -0.32646849914721543, -0.186879626180891, 0.08791650773224088, -0.22961563355792527, -0.1668277527566935, 0.19017769567582798, -0.17710736333713706, -0.0021176055641095527, 0.05518133592545644, 0.008364035640896737, -0.17250805058056254, -0.32070394393442003, 0.40401823307526696, -0.04305836702857552, 0.23080208400885263, 0.02076257796337207, 0.11946274753360228, 0.002235730478390195, 0.009551880754070121, 0.03821789456836494, -0.15096977174943768, 0.17815762121316003, 0.31420014079274805, 0.1409046412659702, 0.21541275297045365, -0.4318950929646862, -0.1955330360723638, 0.18792051017610892, 0.13559657079970527, 0.0772466307677243, -0.030915412037558425, -0.24297787504934373, 0.06919457434928152, -0.19648396501039295, -0.15005066321263538, -0.11918181848000392, 0.07569950508574645, 0.002931980523227275, -0.19505083952339944, -0.07519925634333885, 0.1348586718755207, 0.13160118234782725, -0.06737533646325271, -0.07286363628146977, -0.003539114869360266, 0.07947878989701469, 0.00796438819707382, 0.07057167709558859, 0.06962650810400474, -0.067124187951672, -0.0926140567378794, 0.3746729265984105, -0.029339360174904953, -0.25170966776237746, 0.14242846195468273, -0.14890707072791184, -0.20246495819789753, 0.12956603262145286, 0.10485986973448046, 0.13614176922402849, -0.06504704761479435, 0.16330949895635205, -0.1232146052857754, 0.05690285557046019, 0.14280380798375297, -0.06277998197481208, 0.15577029960294222, 0.13455985346541408, 0.03341055327715973, 0.13834818809135313, -0.02270254558594576, -0.09463564943637293, -0.3441373911076065, -0.1576488556704302, -0.10184257433631982, 0.10078651995944052, -0.07779962577470365, -0.16200745801023883, 0.39612740017045506, 0.08519444507600248, 0.2135728734449066, 0.09420283504858099, 0.30150172628205396, 0.04768812944363246, 0.0469534738583426, 0.04013999677316724, 0.20407228609118824, 0.18847089311397025, -0.0006158065222118093, -0.06785524353898804, -0.03776403660778941, 0.19617595621545253] |
1,802.07587 | Attaining the ultimate precision limit in quantum state estimation | We derive a bound on the precision of state estimation for finite dimensional
quantum systems and prove its attainability in the generic case where the
spectrum is non-degenerate. Our results hold under an assumption called local
asymptotic covariance, which is weaker than unbiasedness or local unbiasedness.
The derivation is based on an analysis of the limiting distribution of the
estimator's deviation from the true value of the parameter, and takes advantage
of quantum local asymptotic normality, a useful asymptotic characterization of
identically prepared states in terms of Gaussian states. We first prove our
results for the mean square error of a special class of models, called
D-invariant, and then extend the results to arbitrary models, generic cost
functions, and global state estimation, where the unknown parameter is not
restricted to a local neighbourhood of the true value. The extension includes a
treatment of nuisance parameters, i.e. parameters that are not of interest to
the experimenter but nevertheless affect the precision of the estimation. As an
illustration of the general approach, we provide the optimal estimation
strategies for the joint measurement of two qubit observables, for the
estimation of qubit states in the presence of amplitude damping noise, and for
noisy multiphase estimation.
| quant-ph math-ph math.MP | we derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is nondegenerate our results hold under an assumption called local asymptotic covariance which is weaker than unbiasedness or local unbiasedness the derivation is based on an analysis of the limiting distribution of the estimators deviation from the true value of the parameter and takes advantage of quantum local asymptotic normality a useful asymptotic characterization of identically prepared states in terms of gaussian states we first prove our results for the mean square error of a special class of models called dinvariant and then extend the results to arbitrary models generic cost functions and global state estimation where the unknown parameter is not restricted to a local neighbourhood of the true value the extension includes a treatment of nuisance parameters ie parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation as an illustration of the general approach we provide the optimal estimation strategies for the joint measurement of two qubit observables for the estimation of qubit states in the presence of amplitude damping noise and for noisy multiphase estimation | [['we', 'derive', 'a', 'bound', 'on', 'the', 'precision', 'of', 'state', 'estimation', 'for', 'finite', 'dimensional', 'quantum', 'systems', 'and', 'prove', 'its', 'attainability', 'in', 'the', 'generic', 'case', 'where', 'the', 'spectrum', 'is', 'nondegenerate', 'our', 'results', 'hold', 'under', 'an', 'assumption', 'called', 'local', 'asymptotic', 'covariance', 'which', 'is', 'weaker', 'than', 'unbiasedness', 'or', 'local', 'unbiasedness', 'the', 'derivation', 'is', 'based', 'on', 'an', 'analysis', 'of', 'the', 'limiting', 'distribution', 'of', 'the', 'estimators', 'deviation', 'from', 'the', 'true', 'value', 'of', 'the', 'parameter', 'and', 'takes', 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1,802.07588 | W-Types with Reductions and the Small Object Argument | We define a simple kind of higher inductive type generalising dependent
$W$-types, which we refer to as $W$-types with reductions. Just as dependent
$W$-types can be characterised as initial algebras of certain endofunctors
(referred to as polynomial endofunctors), we will define our generalisation as
initial algebras of certain pointed endofunctors, which we will refer to as
pointed polynomial endofunctors.
We will show that $W$-types with reductions exist in all $\Pi W$-pretoposes
that satisfy a weak choice axiom, known as weakly initial set of covers (WISC).
This includes all Grothendieck toposes and realizability toposes as long as
WISC holds in the background universe.
We will show that a large class of $W$-types with reductions in internal
presheaf categories can be constructed without using WISC.
We will show that $W$-types with reductions suffice to construct some
interesting examples of algebraic weak factorisation systems (awfs's).
Specifically, we will see how to construct awfs's that are cofibrantly
generated with respect to a codomain fibration, as defined in a previous paper
by the author.
| math.CT math.LO | we define a simple kind of higher inductive type generalising dependent wtypes which we refer to as wtypes with reductions just as dependent wtypes can be characterised as initial algebras of certain endofunctors referred to as polynomial endofunctors we will define our generalisation as initial algebras of certain pointed endofunctors which we will refer to as pointed polynomial endofunctors we will show that wtypes with reductions exist in all pi wpretoposes that satisfy a weak choice axiom known as weakly initial set of covers wisc this includes all grothendieck toposes and realizability toposes as long as wisc holds in the background universe we will show that a large class of wtypes with reductions in internal presheaf categories can be constructed without using wisc we will show that wtypes with reductions suffice to construct some interesting examples of algebraic weak factorisation systems awfss specifically we will see how to construct awfss that are cofibrantly generated with respect to a codomain fibration as defined in a previous paper by the author | [['we', 'define', 'a', 'simple', 'kind', 'of', 'higher', 'inductive', 'type', 'generalising', 'dependent', 'wtypes', 'which', 'we', 'refer', 'to', 'as', 'wtypes', 'with', 'reductions', 'just', 'as', 'dependent', 'wtypes', 'can', 'be', 'characterised', 'as', 'initial', 'algebras', 'of', 'certain', 'endofunctors', 'referred', 'to', 'as', 'polynomial', 'endofunctors', 'we', 'will', 'define', 'our', 'generalisation', 'as', 'initial', 'algebras', 'of', 'certain', 'pointed', 'endofunctors', 'which', 'we', 'will', 'refer', 'to', 'as', 'pointed', 'polynomial', 'endofunctors', 'we', 'will', 'show', 'that', 'wtypes', 'with', 'reductions', 'exist', 'in', 'all', 'pi', 'wpretoposes', 'that', 'satisfy', 'a', 'weak', 'choice', 'axiom', 'known', 'as', 'weakly', 'initial', 'set', 'of', 'covers', 'wisc', 'this', 'includes', 'all', 'grothendieck', 'toposes', 'and', 'realizability', 'toposes', 'as', 'long', 'as', 'wisc', 'holds', 'in', 'the', 'background', 'universe', 'we', 'will', 'show', 'that', 'a', 'large', 'class', 'of', 'wtypes', 'with', 'reductions', 'in', 'internal', 'presheaf', 'categories', 'can', 'be', 'constructed', 'without', 'using', 'wisc', 'we', 'will', 'show', 'that', 'wtypes', 'with', 'reductions', 'suffice', 'to', 'construct', 'some', 'interesting', 'examples', 'of', 'algebraic', 'weak', 'factorisation', 'systems', 'awfss', 'specifically', 'we', 'will', 'see', 'how', 'to', 'construct', 'awfss', 'that', 'are', 'cofibrantly', 'generated', 'with', 'respect', 'to', 'a', 'codomain', 'fibration', 'as', 'defined', 'in', 'a', 'previous', 'paper', 'by', 'the', 'author']] | [-0.13451221395683075, 0.10073403260737125, -0.07928718042066543, 0.13994406366241274, -0.14249021699652076, -0.14957468157600878, -0.024117443909441743, 0.3757413027231537, -0.34246263597604065, -0.2521875230307896, 0.09054425721738621, -0.1965136769382904, -0.14350890345494485, 0.20474794781434216, -0.17766832206619992, -0.04488420132769361, 0.06614521314345655, 0.04980595872482462, -0.10248474476117865, -0.28099670354415485, 0.4008460246647398, -0.0027709054577696535, 0.19210991893002452, 0.003960866056981364, 0.1206322092025186, 0.008380576510154199, -0.017684701031872203, 0.0928509298634405, -0.1541189485187715, 0.05938402187097208, 0.33576698782936937, 0.1517438920619454, 0.19852161391394302, -0.3593076332860316, -0.1107586893485859, 0.16909798751432736, 0.13558760949222015, 0.099647059422707, 0.026931386135402136, -0.2783360799131471, 0.12103060530595637, -0.24421008921317047, -0.12909408933981986, -0.1566037131082599, 0.03838161433010273, 0.10504070404706345, -0.24242249423904078, -0.034687251601662, 0.11563760103447185, 0.057894802057749724, -0.06285697812494445, -0.07798195576885648, -0.06281919556481409, 0.07414484436421412, -0.034721557749435306, 0.024781140318650398, 0.0995881275240598, -0.06749327827682941, -0.1589939668005432, 0.37659330419929965, -0.11060434280495558, -0.21840578030484417, 0.1796572277089581, -0.0949252286601612, -0.20582277754632136, 0.03921314247002426, 0.058837206197148634, 0.10311242891475558, -0.061398218579900764, 0.11598308376622819, -0.14199715390090464, 0.12348987447053549, 0.13947928672201843, 0.08422956521445442, 0.12884837997678136, 0.09496501600092631, 0.06900520171412998, 0.1740858746856074, 0.030927065676743432, -0.039655328911196976, -0.4020943664058688, -0.13197061296419374, -0.04877789113171665, 0.16714756688036556, -0.024152152132089776, -0.2051577992471201, 0.3059504498239784, 0.14910774995362208, 0.20287003565768136, 0.1292271583945313, 0.16763912345049903, 0.06233780810734537, 0.09369302654106702, 0.002148691369386922, 0.15451807934611375, 0.14688175040923634, 0.05036347670552675, -0.06460082760202654, 0.003959366752366934, 0.15117550748289518] |
1,802.07589 | Collaboratively Weighting Deep and Classic Representation via L2
Regularization for Image Classification | Deep convolutional neural networks provide a powerful feature learning
capability for image classification. The deep image features can be utilized to
deal with many image understanding tasks like image classification and object
recognition. However, the robustness obtained in one dataset can be hardly
reproduced in the other domain, which leads to inefficient models far from
state-of-the-art. We propose a deep collaborative weight-based classification
(DeepCWC) method to resolve this problem, by providing a novel option to fully
take advantage of deep features in classic machine learning. It firstly
performs the L2-norm based collaborative representation on the original images,
as well as the deep features extracted by deep CNN models. Then, two distance
vectors, obtained based on the pair of linear representations, are fused
together via a novel collaborative weight. This collaborative weight enables
deep and classic representations to weigh each other. We observed the
complementarity between two representations in a series of experiments on 10
facial and object datasets. The proposed DeepCWC produces very promising
classification results, and outperforms many other benchmark methods,
especially the ones claimed for Fashion-MNIST. The code is going to be
published in our public repository.
| cs.CV | deep convolutional neural networks provide a powerful feature learning capability for image classification the deep image features can be utilized to deal with many image understanding tasks like image classification and object recognition however the robustness obtained in one dataset can be hardly reproduced in the other domain which leads to inefficient models far from stateoftheart we propose a deep collaborative weightbased classification deepcwc method to resolve this problem by providing a novel option to fully take advantage of deep features in classic machine learning it firstly performs the l2norm based collaborative representation on the original images as well as the deep features extracted by deep cnn models then two distance vectors obtained based on the pair of linear representations are fused together via a novel collaborative weight this collaborative weight enables deep and classic representations to weigh each other we observed the complementarity between two representations in a series of experiments on 10 facial and object datasets the proposed deepcwc produces very promising classification results and outperforms many other benchmark methods especially the ones claimed for fashionmnist the code is going to be published in our public repository | [['deep', 'convolutional', 'neural', 'networks', 'provide', 'a', 'powerful', 'feature', 'learning', 'capability', 'for', 'image', 'classification', 'the', 'deep', 'image', 'features', 'can', 'be', 'utilized', 'to', 'deal', 'with', 'many', 'image', 'understanding', 'tasks', 'like', 'image', 'classification', 'and', 'object', 'recognition', 'however', 'the', 'robustness', 'obtained', 'in', 'one', 'dataset', 'can', 'be', 'hardly', 'reproduced', 'in', 'the', 'other', 'domain', 'which', 'leads', 'to', 'inefficient', 'models', 'far', 'from', 'stateoftheart', 'we', 'propose', 'a', 'deep', 'collaborative', 'weightbased', 'classification', 'deepcwc', 'method', 'to', 'resolve', 'this', 'problem', 'by', 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1,802.0759 | Batch Normalization and the impact of batch structure on the behavior of
deep convolution networks | Batch normalization was introduced in 2015 to speed up training of deep
convolution networks by normalizing the activations across the current batch to
have zero mean and unity variance. The results presented here show an
interesting aspect of batch normalization, where controlling the shape of the
training batches can influence what the network will learn. If training batches
are structured as balanced batches (one image per class), and inference is also
carried out on balanced test batches, using the batch's own means and
variances, then the conditional results will improve considerably. The network
uses the strong information about easy images in a balanced batch, and
propagates it through the shared means and variances to help decide the
identity of harder images on the same batch. Balancing the test batches
requires the labels of the test images, which are not available in practice,
however further investigation can be done using batch structures that are less
strict and might not require the test image labels. The conditional results
show the error rate almost reduced to zero for nontrivial datasets with small
number of classes such as the CIFAR10.
| cs.CV | batch normalization was introduced in 2015 to speed up training of deep convolution networks by normalizing the activations across the current batch to have zero mean and unity variance the results presented here show an interesting aspect of batch normalization where controlling the shape of the training batches can influence what the network will learn if training batches are structured as balanced batches one image per class and inference is also carried out on balanced test batches using the batchs own means and variances then the conditional results will improve considerably the network uses the strong information about easy images in a balanced batch and propagates it through the shared means and variances to help decide the identity of harder images on the same batch balancing the test batches requires the labels of the test images which are not available in practice however further investigation can be done using batch structures that are less strict and might not require the test image labels the conditional results show the error rate almost reduced to zero for nontrivial datasets with small number of classes such as the cifar10 | [['batch', 'normalization', 'was', 'introduced', 'in', '2015', 'to', 'speed', 'up', 'training', 'of', 'deep', 'convolution', 'networks', 'by', 'normalizing', 'the', 'activations', 'across', 'the', 'current', 'batch', 'to', 'have', 'zero', 'mean', 'and', 'unity', 'variance', 'the', 'results', 'presented', 'here', 'show', 'an', 'interesting', 'aspect', 'of', 'batch', 'normalization', 'where', 'controlling', 'the', 'shape', 'of', 'the', 'training', 'batches', 'can', 'influence', 'what', 'the', 'network', 'will', 'learn', 'if', 'training', 'batches', 'are', 'structured', 'as', 'balanced', 'batches', 'one', 'image', 'per', 'class', 'and', 'inference', 'is', 'also', 'carried', 'out', 'on', 'balanced', 'test', 'batches', 'using', 'the', 'batchs', 'own', 'means', 'and', 'variances', 'then', 'the', 'conditional', 'results', 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1,802.07591 | Least Square Error Method Robustness of Computation: What is not usually
considered and taught | There are many practical applications based on the Least Square Error (LSE)
approximation. It is based on a square error minimization 'on a vertical' axis.
The LSE method is simple and easy also for analytical purposes. However, if
data span is large over several magnitudes or non-linear LSE is used, severe
numerical instability can be expected. The presented contribution describes a
simple method for large span of data LSE computation. It is especially
convenient if large span of data are to be processed, when the 'standard'
pseudoinverse matrix is ill conditioned. It is actually based on a LSE solution
using orthogonal basis vectors instead of orthonormal basis vectors. The
presented approach has been used for a linear regression as well as for
approximation using radial basis functions.
| cs.GR cs.CV | there are many practical applications based on the least square error lse approximation it is based on a square error minimization on a vertical axis the lse method is simple and easy also for analytical purposes however if data span is large over several magnitudes or nonlinear lse is used severe numerical instability can be expected the presented contribution describes a simple method for large span of data lse computation it is especially convenient if large span of data are to be processed when the standard pseudoinverse matrix is ill conditioned it is actually based on a lse solution using orthogonal basis vectors instead of orthonormal basis vectors the presented approach has been used for a linear regression as well as for approximation using radial basis functions | [['there', 'are', 'many', 'practical', 'applications', 'based', 'on', 'the', 'least', 'square', 'error', 'lse', 'approximation', 'it', 'is', 'based', 'on', 'a', 'square', 'error', 'minimization', 'on', 'a', 'vertical', 'axis', 'the', 'lse', 'method', 'is', 'simple', 'and', 'easy', 'also', 'for', 'analytical', 'purposes', 'however', 'if', 'data', 'span', 'is', 'large', 'over', 'several', 'magnitudes', 'or', 'nonlinear', 'lse', 'is', 'used', 'severe', 'numerical', 'instability', 'can', 'be', 'expected', 'the', 'presented', 'contribution', 'describes', 'a', 'simple', 'method', 'for', 'large', 'span', 'of', 'data', 'lse', 'computation', 'it', 'is', 'especially', 'convenient', 'if', 'large', 'span', 'of', 'data', 'are', 'to', 'be', 'processed', 'when', 'the', 'standard', 'pseudoinverse', 'matrix', 'is', 'ill', 'conditioned', 'it', 'is', 'actually', 'based', 'on', 'a', 'lse', 'solution', 'using', 'orthogonal', 'basis', 'vectors', 'instead', 'of', 'orthonormal', 'basis', 'vectors', 'the', 'presented', 'approach', 'has', 'been', 'used', 'for', 'a', 'linear', 'regression', 'as', 'well', 'as', 'for', 'approximation', 'using', 'radial', 'basis', 'functions']] | [-0.06573238628586446, 0.013465052303733436, -0.09048604001850256, 0.10326820742943889, -0.1031044884566511, -0.14218400069604092, -0.002879456682937352, 0.43807296014911545, -0.2683271381446696, -0.22762646287034347, 0.23228130492062754, -0.25571250153900726, -0.16361331480085908, 0.26501363017009644, -0.05085408094675486, 0.1130305126228729, 0.11125299119295215, 0.04470926123179906, -0.09951908630868933, -0.2864871230489743, 0.23882880080931299, 0.05646332297620811, 0.30742040880053767, -0.01090284094111774, 0.14599994417760287, 0.023451767322849336, -0.00741217636290615, 0.029160304919002563, -0.05416255088625696, 0.09284337289360037, 0.26762213334661183, 0.17082101973616995, 0.32600535909593925, -0.37937231692228846, -0.16212865018733139, 0.08858031521397312, 0.159090006518669, 0.10271472076878069, -0.0010558682105203314, -0.19557497894582082, 0.07654617187075728, -0.14495351256007022, -0.12474785348438057, -0.12638685485076775, 0.01824768946513416, 0.031380204567282396, -0.3472770576137961, 0.10734133760231239, 0.00029819782577660377, 0.07678736315116169, -0.016453071702711694, -0.20826584003557722, 0.027485897946061464, 0.07550391936642631, 0.04237787844429863, 0.045748171905526804, 0.08071329874741867, -0.010057368095758863, -0.05672018876753923, 0.4023746896212495, -0.0740361565780848, -0.28481687524715277, 0.1452947578440589, -0.08346478370436299, -0.08659799693254974, 0.13871519757053397, 0.21408006432282878, 0.09899742872358894, -0.15372436409635107, 0.08871820879188975, -0.06750297081825418, 0.16207461614403726, 0.024412032136121604, -0.011363840826941052, 0.1578157235479613, 0.19434608078165727, 0.10194071877965938, 0.07436590084226757, -0.0844858615387847, -0.06683498500721662, -0.29684357788032434, -0.10305613564606023, -0.2842681614579413, 0.01753747802389067, -0.10924930058364246, -0.18161149116555655, 0.3591969164132368, 0.10773042674491724, 0.17182941914455394, 0.03551410181873192, 0.33682842678793773, 0.17849603027983488, 0.09886850216829283, 0.11053432014910138, 0.2086125224440058, 0.12483217362424462, 0.021530873614260707, -0.13903193969800187, 0.08335145826884142, 0.0913085088163145] |
1,802.07592 | "How to squash a mathematical tomato", Rubic's cube-like surfaces and
their connection to reversible computation | Here we show how reversible computation processes, like Margolus diffusion,
can be envisioned as physical turning operations on a 2-dimensional rigid
surface that is cut by a regular pattern of intersecting circles. We then
briefly explore the design-space of these patterns, and report on the discovery
of an interesting fractal subdivision of space by iterative circle packings. We
devise two different ways for creating this fractal, both showing interesting
properties, some resembling properties of the dragon curve. The patterns
presented here can have interesting applications to the engineering of modular,
kinetic, active surfaces.
| cs.GR | here we show how reversible computation processes like margolus diffusion can be envisioned as physical turning operations on a 2dimensional rigid surface that is cut by a regular pattern of intersecting circles we then briefly explore the designspace of these patterns and report on the discovery of an interesting fractal subdivision of space by iterative circle packings we devise two different ways for creating this fractal both showing interesting properties some resembling properties of the dragon curve the patterns presented here can have interesting applications to the engineering of modular kinetic active surfaces | [['here', 'we', 'show', 'how', 'reversible', 'computation', 'processes', 'like', 'margolus', 'diffusion', 'can', 'be', 'envisioned', 'as', 'physical', 'turning', 'operations', 'on', 'a', '2dimensional', 'rigid', 'surface', 'that', 'is', 'cut', 'by', 'a', 'regular', 'pattern', 'of', 'intersecting', 'circles', 'we', 'then', 'briefly', 'explore', 'the', 'designspace', 'of', 'these', 'patterns', 'and', 'report', 'on', 'the', 'discovery', 'of', 'an', 'interesting', 'fractal', 'subdivision', 'of', 'space', 'by', 'iterative', 'circle', 'packings', 'we', 'devise', 'two', 'different', 'ways', 'for', 'creating', 'this', 'fractal', 'both', 'showing', 'interesting', 'properties', 'some', 'resembling', 'properties', 'of', 'the', 'dragon', 'curve', 'the', 'patterns', 'presented', 'here', 'can', 'have', 'interesting', 'applications', 'to', 'the', 'engineering', 'of', 'modular', 'kinetic', 'active', 'surfaces']] | [-0.14837224912198801, 0.15706828837573994, -0.12645094251881042, 0.08399627402534969, -0.09351128283687817, -0.12725495777383286, 0.03792994575554966, 0.38586156358641965, -0.3120338853889255, -0.27775376724700135, 0.1365339716455789, -0.24546848178430591, -0.26417894076596027, 0.22352419940814858, -0.06696374472499805, 0.05214108460112124, 0.01325851528634948, -0.024801234163904704, -0.06506121042184532, -0.225841469441851, 0.32425199149637135, 0.02057933969603431, 0.25425041011304306, 0.035597535591292126, 0.07561157388432373, 0.001814380763799593, -0.02412975868911192, 0.044694388249916554, -0.18351357248250297, 0.15381253660426183, 0.21738021934945737, 0.11111348302614305, 0.16894648489992944, -0.45248846599571807, -0.2326259327481591, 0.08466698153705526, 0.18704168177560293, 0.06679182001940345, -0.0878805223807332, -0.22889516475580393, 0.049012891036928984, -0.09244253144909938, -0.1684005570207392, -0.11466425144544212, 0.0668333724782031, 0.05769406290103992, -0.15033287440817203, -0.017251525504855057, 0.09175573391539435, 0.06493080840996837, 0.0007514179977137715, -0.09908826845467732, -0.020375637222401877, 0.09495535055776277, -0.020295554874665153, -0.038891368160044314, 0.14973339353818246, -0.09746264977010108, -0.17229327428785543, 0.3811792531476346, 0.009466502179581952, -0.18651545203981862, 0.21614628278159648, -0.10605689129161258, -0.16840497370288576, 0.09737460787648396, 0.18456320250557073, 0.10430706872464589, -0.14237451381100122, 0.07713823705368365, -0.07706741168369008, 0.10907704678554368, 0.10627729172307637, 0.015810554002171323, 0.22893869590955557, 0.18602674102951441, 0.056182900005550956, 0.19595331213842596, -0.0755557499485471, -0.09197976754888171, -0.29051110824389803, -0.17353787486471475, -0.145256776236228, 0.061603696806536566, -0.1069528420043606, -0.1847863852006373, 0.4178872676566243, 0.10903990037879475, 0.21339709607143237, -0.004112637906444199, 0.2494154743479705, 0.04972682916183745, 0.05051466539472101, 0.06365301295293756, 0.19186964078514676, 0.06477634189149706, 0.038803335053906325, -0.17374159642044576, 0.030167741916312645, 0.08186309739586807] |
1,802.07593 | From Hamiltonian to zero curvature formulation for classical integrable
boundary conditions | We reconcile the Hamiltonian formalism and the zero curvature representation
in the approach to integrable boundary conditions for a classical integrable
system in 1+1 space-time dimensions. We start from an ultralocal Poisson
algebra involving a Lax matrix and two (dynamical) boundary matrices.
Sklyanin's formula for the double-row transfer matrix is used to derive
Hamilton's equations of motion for both the Lax matrix {\bf and} the boundary
matrices in the form of zero curvature equations. A key ingredient of the
method is a boundary version of the Semenov-Tian-Shansky formula for the
generating function of the time-part of a Lax pair. The procedure is
illustrated on the finite Toda chain for which we derive Lax pairs of size
$2\times 2$ for previously known Hamiltonians of type $BC_N$ and $D_N$
corresponding to constant and dynamical boundary matrices respectively.
| math-ph hep-th math.MP nlin.SI | we reconcile the hamiltonian formalism and the zero curvature representation in the approach to integrable boundary conditions for a classical integrable system in 11 spacetime dimensions we start from an ultralocal poisson algebra involving a lax matrix and two dynamical boundary matrices sklyanins formula for the doublerow transfer matrix is used to derive hamiltons equations of motion for both the lax matrix bf and the boundary matrices in the form of zero curvature equations a key ingredient of the method is a boundary version of the semenovtianshansky formula for the generating function of the timepart of a lax pair the procedure is illustrated on the finite toda chain for which we derive lax pairs of size 2times 2 for previously known hamiltonians of type bc_n and d_n corresponding to constant and dynamical boundary matrices respectively | [['we', 'reconcile', 'the', 'hamiltonian', 'formalism', 'and', 'the', 'zero', 'curvature', 'representation', 'in', 'the', 'approach', 'to', 'integrable', 'boundary', 'conditions', 'for', 'a', 'classical', 'integrable', 'system', 'in', '11', 'spacetime', 'dimensions', 'we', 'start', 'from', 'an', 'ultralocal', 'poisson', 'algebra', 'involving', 'a', 'lax', 'matrix', 'and', 'two', 'dynamical', 'boundary', 'matrices', 'sklyanins', 'formula', 'for', 'the', 'doublerow', 'transfer', 'matrix', 'is', 'used', 'to', 'derive', 'hamiltons', 'equations', 'of', 'motion', 'for', 'both', 'the', 'lax', 'matrix', 'bf', 'and', 'the', 'boundary', 'matrices', 'in', 'the', 'form', 'of', 'zero', 'curvature', 'equations', 'a', 'key', 'ingredient', 'of', 'the', 'method', 'is', 'a', 'boundary', 'version', 'of', 'the', 'semenovtianshansky', 'formula', 'for', 'the', 'generating', 'function', 'of', 'the', 'timepart', 'of', 'a', 'lax', 'pair', 'the', 'procedure', 'is', 'illustrated', 'on', 'the', 'finite', 'toda', 'chain', 'for', 'which', 'we', 'derive', 'lax', 'pairs', 'of', 'size', '2times', '2', 'for', 'previously', 'known', 'hamiltonians', 'of', 'type', 'bc_n', 'and', 'd_n', 'corresponding', 'to', 'constant', 'and', 'dynamical', 'boundary', 'matrices', 'respectively']] | [-0.14542179252542278, 0.08786705237782452, -0.060745237735725606, 0.09277106791911925, -0.06817447684302147, -0.1633729597939345, -0.04096996050272415, 0.2850484633266599, -0.2793793942007834, -0.2212222566960185, 0.10748249109410472, -0.2426734037815468, -0.1738748107115919, 0.14250475459092699, -0.03351060668729357, 0.07904103858424212, 0.061173538474101966, 0.08078292737812248, -0.1852878586166719, -0.20169997017191194, 0.3886680136028149, -0.03945723538801296, 0.21907337835586782, 0.027946086808927913, 0.17281680100653043, 0.03291470699104369, -0.0007597257786277515, -0.06951673279530299, -0.12134425068941357, 0.10339830433630555, 0.21522327907619748, 0.07699105740045267, 0.15720695735010973, -0.3983555658331224, -0.15131141323207029, 0.09907942420695283, 0.15316139924715258, 0.12100810041380074, 0.00569493703304359, -0.29600135853632226, 0.06951466569357287, -0.1790813574351982, -0.2079813243932466, -0.025675815093998255, 0.0597371591512225, -0.013507323944246146, -0.3301575339343677, 0.11571380015420936, 0.09375133509174295, 0.04463481855120009, -0.11755718978177478, -0.12745223919176427, -0.03658655742461334, 0.0731490874113932, -0.018325221107980766, -0.020642207907651786, 0.04770733571590494, -0.07849351571001453, -0.08416117715246196, 0.34730206267324404, -0.05269573918550706, -0.3042022413782664, 0.13225199534807966, -0.09628204212162587, -0.12140327329928083, 0.11089314941539248, 0.11698601485243929, 0.1319326090473515, -0.19349822566024402, 0.15166420434078604, -0.053543927935959856, 0.09311879641001126, 0.06454332297973668, -0.029157774705342504, 0.14410235912108155, 0.07570011460625414, 0.07768120482536171, 0.13447859187944056, -0.007136948049631414, -0.1724434055026565, -0.36833435883606547, -0.2084298140763615, -0.20734173525298544, 0.12457454796018663, -0.15456057568860446, -0.19910680750079118, 0.38835970898473343, 0.12169131734118079, 0.19118866091246592, 0.10134833168547684, 0.18537086799546187, 0.19565853131795996, 0.0675827152175662, 0.03613056994126693, 0.12050631344874403, 0.29191766750352427, 0.08852704805878005, -0.22660617456152868, -0.07101714113247651, 0.24531875771067257] |
1,802.07594 | Constructions of Unextendible Maximally Entangled Bases in \(\mathbb
{C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) | We study unextendible maximally entangled bases (UMEBs) in \(\mathbb
{C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to
construct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors is
established, and two UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and
\(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore,
a systematic way of constructing UMEBs containing $d(d^{\prime}-r)$ maximally
entangled vectors in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) is
presented for $r=1,2,\cdots, d-1$. Correspondingly, two UMEBs in \(\mathbb
{C}^{3}\otimes \mathbb {C}^{10}\) are obtained.
| quant-ph | we study unextendible maximally entangled bases umebs in mathbb cdotimes mathbb cdprime dd an operational method to construct umebs containing ddprime1 maximally entangled vectors is established and two umebs in mathbb c5otimes mathbb c6 and mathbb c5otimes mathbb c12 are given as examples furthermore a systematic way of constructing umebs containing ddprimer maximally entangled vectors in mathbb cdotimes mathbb cdprime is presented for r12cdots d1 correspondingly two umebs in mathbb c3otimes mathbb c10 are obtained | [['we', 'study', 'unextendible', 'maximally', 'entangled', 'bases', 'umebs', 'in', 'mathbb', 'cdotimes', 'mathbb', 'cdprime', 'dd', 'an', 'operational', 'method', 'to', 'construct', 'umebs', 'containing', 'ddprime1', 'maximally', 'entangled', 'vectors', 'is', 'established', 'and', 'two', 'umebs', 'in', 'mathbb', 'c5otimes', 'mathbb', 'c6', 'and', 'mathbb', 'c5otimes', 'mathbb', 'c12', 'are', 'given', 'as', 'examples', 'furthermore', 'a', 'systematic', 'way', 'of', 'constructing', 'umebs', 'containing', 'ddprimer', 'maximally', 'entangled', 'vectors', 'in', 'mathbb', 'cdotimes', 'mathbb', 'cdprime', 'is', 'presented', 'for', 'r12cdots', 'd1', 'correspondingly', 'two', 'umebs', 'in', 'mathbb', 'c3otimes', 'mathbb', 'c10', 'are', 'obtained']] | [-0.20397954938166282, 0.15901966226781095, 0.07433896056061391, -0.028645604961853036, 0.07533600707949303, -0.21497998113559066, -0.10255244280458153, 0.39385994501850186, -0.22487005536608837, -0.05712642211823121, 0.09366287881344118, -0.3581042297951439, -0.03348643660052296, 0.17007225855965824, -0.11000148765742779, 0.06344831491001326, -0.033581349296796625, 0.04232761994524695, -0.143730621689054, -0.33044895300340343, 0.2737168475766392, -0.1818889589048922, 0.2170066452886471, -0.034224340110085905, 0.08025940710349995, -0.003775178050786695, 0.0154388512703864, -0.08708772268694114, -0.19815695613129614, 0.12760250881547108, 0.3160727622864001, 0.13611622795681744, 0.16497065404923084, -0.38152345111045766, -0.1295188914381844, 0.2684575502678533, 0.22269321085118196, 0.04114361615468036, -0.02838407814338365, -0.3187376220902318, 0.03419801814015955, -0.16272869256242892, -0.16297107493258356, -0.12020528135711656, 0.1508917967610828, -0.02727848295848269, -0.3923453772029675, 0.06863342869259856, 0.07552262470947907, 0.06279998421942924, -0.05032672434497405, -0.14064808344632826, -0.12563969368142458, 0.0032861144350403372, -0.1298438170034548, 0.22437623575644786, 0.04644133532008923, 0.07062990012619753, -0.15078774699941278, 0.3441246967379223, -0.03507877021397957, -0.34605657917392607, 0.09055156725020531, -0.14890833366114428, -0.17990922826849035, 0.07257224805653095, 0.09409946571652066, 0.1910013006452252, -0.0634644844377523, 0.18675102047478398, -0.15509349392959848, 0.10506220267373412, 0.11625697378836133, 0.10940357586642836, 0.13391180440564365, 0.00773545221925494, 0.0296809165738523, 0.2010976118994329, 0.029180767980185065, -0.06406811159788905, -0.3960466602926745, -0.1455684460233897, -0.14219166269792957, 0.1932399595183704, -0.08422619847688646, -0.117726633010213, 0.2865077327279484, 0.001235584180582972, 0.11842441903290284, 0.06368487526881783, 0.12609006045386195, -0.04323623550076531, -0.007798808188561131, 0.08116858020452235, 0.08874830567647758, 0.1675329154686016, -0.12053076465449789, -0.0555820019559606, -0.07204912853536799, 0.16291612748960582] |
1,802.07595 | Smooth Loss Functions for Deep Top-k Classification | The top-k error is a common measure of performance in machine learning and
computer vision. In practice, top-k classification is typically performed with
deep neural networks trained with the cross-entropy loss. Theoretical results
indeed suggest that cross-entropy is an optimal learning objective for such a
task in the limit of infinite data. In the context of limited and noisy data
however, the use of a loss function that is specifically designed for top-k
classification can bring significant improvements. Our empirical evidence
suggests that the loss function must be smooth and have non-sparse gradients in
order to work well with deep neural networks. Consequently, we introduce a
family of smoothed loss functions that are suited to top-k optimization via
deep learning. The widely used cross-entropy is a special case of our family.
Evaluating our smooth loss functions is computationally challenging: a na\"ive
algorithm would require $\mathcal{O}(\binom{n}{k})$ operations, where n is the
number of classes. Thanks to a connection to polynomial algebra and a
divide-and-conquer approach, we provide an algorithm with a time complexity of
$\mathcal{O}(k n)$. Furthermore, we present a novel approximation to obtain
fast and stable algorithms on GPUs with single floating point precision. We
compare the performance of the cross-entropy loss and our margin-based losses
in various regimes of noise and data size, for the predominant use case of k=5.
Our investigation reveals that our loss is more robust to noise and overfitting
than cross-entropy.
| cs.LG | the topk error is a common measure of performance in machine learning and computer vision in practice topk classification is typically performed with deep neural networks trained with the crossentropy loss theoretical results indeed suggest that crossentropy is an optimal learning objective for such a task in the limit of infinite data in the context of limited and noisy data however the use of a loss function that is specifically designed for topk classification can bring significant improvements our empirical evidence suggests that the loss function must be smooth and have nonsparse gradients in order to work well with deep neural networks consequently we introduce a family of smoothed loss functions that are suited to topk optimization via deep learning the widely used crossentropy is a special case of our family evaluating our smooth loss functions is computationally challenging a naive algorithm would require mathcalobinomnk operations where n is the number of classes thanks to a connection to polynomial algebra and a divideandconquer approach we provide an algorithm with a time complexity of mathcalok n furthermore we present a novel approximation to obtain fast and stable algorithms on gpus with single floating point precision we compare the performance of the crossentropy loss and our marginbased losses in various regimes of noise and data size for the predominant use case of k5 our investigation reveals that our loss is more robust to noise and overfitting than crossentropy | [['the', 'topk', 'error', 'is', 'a', 'common', 'measure', 'of', 'performance', 'in', 'machine', 'learning', 'and', 'computer', 'vision', 'in', 'practice', 'topk', 'classification', 'is', 'typically', 'performed', 'with', 'deep', 'neural', 'networks', 'trained', 'with', 'the', 'crossentropy', 'loss', 'theoretical', 'results', 'indeed', 'suggest', 'that', 'crossentropy', 'is', 'an', 'optimal', 'learning', 'objective', 'for', 'such', 'a', 'task', 'in', 'the', 'limit', 'of', 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1,802.07596 | Maximal depth property of finitely generated modules | Let $(R,\mathfrak{m})$ be a Noetherian local ring and $M$ a finitely
generated $R$-module. We say $M$ has maximal depth if there is an associated
prime $\mathfrak{p}$ of $M$ such that depth $M=\dim R/\mathfrak{p}$. In this
paper, we study finitely generated modules with maximal depth. It is shown that
the maximal depth property is preserved under some important module operations.
Generalized Cohen--Macaulay modules with maximal depth are classified. Finally,
the attached primes of $H^i_{\mathfrak{m}}(M)$ are considered for
$i<\mathrm{dim} M$.
| math.AC | let rmathfrakm be a noetherian local ring and m a finitely generated rmodule we say m has maximal depth if there is an associated prime mathfrakp of m such that depth mdim rmathfrakp in this paper we study finitely generated modules with maximal depth it is shown that the maximal depth property is preserved under some important module operations generalized cohenmacaulay modules with maximal depth are classified finally the attached primes of hi_mathfrakmm are considered for imathrmdim m | [['let', 'rmathfrakm', 'be', 'a', 'noetherian', 'local', 'ring', 'and', 'm', 'a', 'finitely', 'generated', 'rmodule', 'we', 'say', 'm', 'has', 'maximal', 'depth', 'if', 'there', 'is', 'an', 'associated', 'prime', 'mathfrakp', 'of', 'm', 'such', 'that', 'depth', 'mdim', 'rmathfrakp', 'in', 'this', 'paper', 'we', 'study', 'finitely', 'generated', 'modules', 'with', 'maximal', 'depth', 'it', 'is', 'shown', 'that', 'the', 'maximal', 'depth', 'property', 'is', 'preserved', 'under', 'some', 'important', 'module', 'operations', 'generalized', 'cohenmacaulay', 'modules', 'with', 'maximal', 'depth', 'are', 'classified', 'finally', 'the', 'attached', 'primes', 'of', 'hi_mathfrakmm', 'are', 'considered', 'for', 'imathrmdim', 'm']] | [-0.2203929126737517, 0.12348286838345016, -0.055175066165822115, 0.0009601193780422603, -0.024897360083598056, -0.24086611476530762, -0.14265810911341473, 0.4023903389951508, -0.4163557815757629, -0.14774642971851312, 0.11644960363168809, -0.25132151244600354, -0.10024877588607763, 0.2210588172249692, -0.17597058051155487, -0.042675467940218946, 0.07848111840308104, 0.1569265439783952, -0.0028598931385204196, -0.35827608024211305, 0.36303661023511696, -0.005323372458071007, 0.21383459355044915, 0.021677710081444514, 0.1388888466907175, 0.009641155496386713, -0.029279638700628358, 0.0809207028605191, -0.20924409401796815, 0.08215882578913711, 0.3385210164920672, 0.11933974744629507, 0.23442288203851172, -0.3732488909001021, -0.07735448641592245, 0.29755418818738116, 0.14010135628479092, -0.11263797957891304, -0.029474995273631066, -0.2265444631247144, 0.2390613005876443, -0.19508121184710608, -0.15232071052550486, -0.04585362077494593, 0.15575832927501515, -0.003250189336923588, -0.3152187844511661, -0.04192498945753629, 0.12551333887600585, 0.18377528903319648, -0.011649405874777585, -0.07998059935389872, -0.07511601622804608, 0.0464696917425547, -0.07068108154252466, 0.01738506383078761, 0.0912462490194134, -0.0846907995414528, -0.06616516919128021, 0.3250455166164197, -0.05935391259615579, -0.20066006318359686, 0.12789200367038384, -0.18868142997502887, -0.07160169728051283, 0.10331094233123095, -0.026760447635560444, 0.1309775769416439, -0.030360564748805604, 0.2294608319636226, -0.24570434348118542, 0.11607193005712409, 0.1192479842881623, 0.05682714527325803, 0.1587000940926373, 0.12472170559186979, 0.1290989622269224, 0.12923628888184843, -0.020608677627598427, 0.15035859040768915, -0.3587112628095048, -0.17449890532971998, -0.1783464562000805, 0.15824911705414324, -0.04587462007073459, -0.09538306935658176, 0.3808046683767124, 0.10750832154391039, 0.16276439930018233, 0.09115492244937311, 0.2429459602572024, 0.056123684301335165, 0.11597752493291505, 0.12403882079831276, 0.034623534916854146, 0.21519056631644307, -0.10004594912262339, -0.09277909030482222, 0.01531561993454632, 0.16474612973826497] |
1,802.07597 | On a problem of S\'ark\"ozy and S\'os for multivariate linear forms | We prove that for pairwise co-prime numbers $k_1,\dots,k_d \geq 2$ there does
not exist any infinite set of positive integers $A$ such that the
representation function $r_A (n) = \{ (a_1, \dots, a_d) \in A^d : k_1 a_1 +
\dots + k_d a_d = n \}$ becomes constant for $n$ large enough. This result is a
particular case of our main theorem, which poses a further step towards
answering a question of S\'ark\"ozy and S\'os and widely extends a previous
result of Cilleruelo and Ru\'e for bivariate linear forms.
| math.CO | we prove that for pairwise coprime numbers k_1dotsk_d geq 2 there does not exist any infinite set of positive integers a such that the representation function r_a n a_1 dots a_d in ad k_1 a_1 dots k_d a_d n becomes constant for n large enough this result is a particular case of our main theorem which poses a further step towards answering a question of sarkozy and sos and widely extends a previous result of cilleruelo and rue for bivariate linear forms | [['we', 'prove', 'that', 'for', 'pairwise', 'coprime', 'numbers', 'k_1dotsk_d', 'geq', '2', 'there', 'does', 'not', 'exist', 'any', 'infinite', 'set', 'of', 'positive', 'integers', 'a', 'such', 'that', 'the', 'representation', 'function', 'r_a', 'n', 'a_1', 'dots', 'a_d', 'in', 'ad', 'k_1', 'a_1', 'dots', 'k_d', 'a_d', 'n', 'becomes', 'constant', 'for', 'n', 'large', 'enough', 'this', 'result', 'is', 'a', 'particular', 'case', 'of', 'our', 'main', 'theorem', 'which', 'poses', 'a', 'further', 'step', 'towards', 'answering', 'a', 'question', 'of', 'sarkozy', 'and', 'sos', 'and', 'widely', 'extends', 'a', 'previous', 'result', 'of', 'cilleruelo', 'and', 'rue', 'for', 'bivariate', 'linear', 'forms']] | [-0.20728002073542204, 0.13910265317054488, -0.023330222240384713, 0.02240784910082081, -0.037114936858415604, -0.22200721375253282, 0.017659222465698367, 0.31357086288892194, -0.2692264366613264, -0.22827241833057302, 0.05935793336521098, -0.28633984842878063, -0.14849220015637485, 0.19168680093975532, -0.042572730409782156, 0.014225740675572996, 0.048969922501041936, 0.04440137368546408, 0.014309278459368665, -0.28155310692288626, 0.2991470746152724, -0.1138022590233128, 0.15330664661172547, 0.09623379846689878, 0.077619408355037, 0.047126811589861727, 0.017083518856699453, -0.00814280197898179, -0.2096237781995485, 0.0886394995506163, 0.31622531567987655, 0.14423661916746677, 0.3215362773173385, -0.3359453692618344, -0.11922973811764408, 0.2263063798488957, 0.20973786367333414, 0.045151555173409484, -0.03046662248613566, -0.1849855420921274, 0.17065419402709345, -0.14038318286385434, -0.1332702312193075, -0.02512213903663243, 0.16633740155440238, -0.016100597763319076, -0.3980973927637585, 0.05899611746685372, 0.20844004556168744, 0.06329182733172252, 0.022131454895170016, -0.20478742122132745, 0.03814507774824714, 0.08250433587710615, 0.0021891366592665883, 0.1136579073327421, 0.013612643108461742, -0.055240700803237196, -0.10943272143004486, 0.31137205545365076, -0.052658915197775685, -0.21064030092761474, 0.10625826890499872, -0.17445574918428414, -0.19233330347529257, 0.06316054066252193, 0.0771015706575579, 0.1695985602012643, 0.0009805760806265436, 0.1918006004100194, -0.17009471318925973, 0.18160200332877813, 0.1483651658543098, -0.006320978842537712, 0.13265838342385344, 0.04605556130811664, 0.09188248311962795, 0.07116239243129521, 0.04350259924238479, 0.004448116101600506, -0.3178558247393848, -0.18597314993126524, -0.22518682853537209, 0.1909840355232361, -0.16019681814636166, -0.16874305407206217, 0.29649928406478815, 0.08373764149246761, 0.25744222907096515, 0.14360432990361005, 0.207757584589683, 0.06375018891861899, 0.04318086374953481, 0.06864231017153756, 0.07731308167179425, 0.1654764255422547, 0.012909144048153617, -0.11785796706573348, 0.01869735866210159, 0.10155575428399499] |
1,802.07598 | Design of Irregular SC-LDPC Codes With Non-Uniform Degree Distributions
by Linear Programing | In this paper, we propose a new design method of irregular spatially-coupled
low-density parity-check (SC-LDPC) codes with non-uniform degree distributions
by linear programming (LP). In general, irregular SC-LDPC codes with
non-uniform degree distributions is difficult to design with low complexity
because their density evolution equations are multi-dimensional. To solve the
problem, the proposed method is based on two main ideas: A local design of the
degree distributions and pre-computation of the input/output message
relationship. These ideas make it possible to design the degree distributions
of irregular SC-LDPC codes by solving low complexity LP problems over the
binary erasure channel. We also find a proper objective function for the
proposed design methodology to improve the performance of SC-LDPC codes. It is
shown that the irregular SC-LDPC codes obtained by the proposed method are
superior to regular SC-LDPC codes in terms of both asymptotic and finite-length
performances.
| cs.IT math.IT | in this paper we propose a new design method of irregular spatiallycoupled lowdensity paritycheck scldpc codes with nonuniform degree distributions by linear programming lp in general irregular scldpc codes with nonuniform degree distributions is difficult to design with low complexity because their density evolution equations are multidimensional to solve the problem the proposed method is based on two main ideas a local design of the degree distributions and precomputation of the inputoutput message relationship these ideas make it possible to design the degree distributions of irregular scldpc codes by solving low complexity lp problems over the binary erasure channel we also find a proper objective function for the proposed design methodology to improve the performance of scldpc codes it is shown that the irregular scldpc codes obtained by the proposed method are superior to regular scldpc codes in terms of both asymptotic and finitelength performances | [['in', 'this', 'paper', 'we', 'propose', 'a', 'new', 'design', 'method', 'of', 'irregular', 'spatiallycoupled', 'lowdensity', 'paritycheck', 'scldpc', 'codes', 'with', 'nonuniform', 'degree', 'distributions', 'by', 'linear', 'programming', 'lp', 'in', 'general', 'irregular', 'scldpc', 'codes', 'with', 'nonuniform', 'degree', 'distributions', 'is', 'difficult', 'to', 'design', 'with', 'low', 'complexity', 'because', 'their', 'density', 'evolution', 'equations', 'are', 'multidimensional', 'to', 'solve', 'the', 'problem', 'the', 'proposed', 'method', 'is', 'based', 'on', 'two', 'main', 'ideas', 'a', 'local', 'design', 'of', 'the', 'degree', 'distributions', 'and', 'precomputation', 'of', 'the', 'inputoutput', 'message', 'relationship', 'these', 'ideas', 'make', 'it', 'possible', 'to', 'design', 'the', 'degree', 'distributions', 'of', 'irregular', 'scldpc', 'codes', 'by', 'solving', 'low', 'complexity', 'lp', 'problems', 'over', 'the', 'binary', 'erasure', 'channel', 'we', 'also', 'find', 'a', 'proper', 'objective', 'function', 'for', 'the', 'proposed', 'design', 'methodology', 'to', 'improve', 'the', 'performance', 'of', 'scldpc', 'codes', 'it', 'is', 'shown', 'that', 'the', 'irregular', 'scldpc', 'codes', 'obtained', 'by', 'the', 'proposed', 'method', 'are', 'superior', 'to', 'regular', 'scldpc', 'codes', 'in', 'terms', 'of', 'both', 'asymptotic', 'and', 'finitelength', 'performances']] | [-0.1595927043199732, 0.02229297567191052, -0.10757834621030708, 0.07524393777812606, -0.026605489933542135, -0.23188865955854798, 0.01906824135783546, 0.4107697217307728, -0.31761692141921355, -0.27714143008644015, 0.10498763352455892, -0.18450113875341825, -0.2169910347346088, 0.18214343620528434, -0.13363159777403905, 0.15413715098823966, 0.10083776666493766, -0.032992993725527976, -0.178353675043387, -0.37635210754253484, 0.2935779561802488, 0.1607981012299143, 0.3076913481449773, -0.03945813430152063, 0.08165188162539411, 0.0068450573960254935, -0.0034507361047997555, -0.016067250940049516, -0.15093062387740216, 0.1331461188279028, 0.31038020931441207, 0.179090064189172, 0.2378776857436731, -0.3790750258955462, -0.2429287623228698, 0.056796290547233716, 0.12552713586402864, 0.1499405646760916, -0.05540892824345943, -0.20922478006205297, 0.1482303762069807, -0.18902704531752407, -0.062257166010937816, -0.0005677125256123214, -0.04055512520195595, 0.10245603373242093, -0.2995363372923999, -0.006148173433832889, 0.07104174953339429, 0.02363413168952383, 0.0034450037533353115, -0.1694228724215244, 0.061449708921256764, 0.05495961153687074, -0.027243945469822863, 0.00882242625129634, 0.025601566945812827, -0.04291866075665016, -0.11287572029978037, 0.32260043082501866, -0.015696926084186498, -0.2628116999383502, 0.17714851285884928, -0.08252069261888492, -0.08799481450194685, 0.1793693600928989, 0.27576360550693013, 0.1469144636508206, -0.1416348166121491, 0.07695156908714501, -0.03166625634686829, 0.16989045261309066, 0.06492871686912559, 0.08772559196343004, 0.1483256545383483, 0.1400984724084365, 0.05186291461617782, 0.20960008567359684, -0.06594074660558896, -0.12489431627969867, -0.19912991924532528, -0.06580930927061829, -0.18815104955614642, -0.02544317437528536, -0.15509537785968358, -0.18552714673669785, 0.3991547750839, 0.13923986695128782, 0.12344108045639085, 0.1520442615423737, 0.30545596011496823, 0.06835340188238127, 0.07489972737946965, 0.18649494839382583, 0.13210360533397258, 0.20966883146300397, 0.024501243676058947, -0.26954899706139135, 0.09170544111844281, 0.08386406284307354] |
1,802.07599 | Graphene-enabled, directed nanomaterial placement from solution for
large-scale device integration | Controlled placement of nanomaterials at predefined locations with nanoscale
precision remains among the most challenging problems that inhibit their
large-scale integration in the field of semiconductor process technology.
Methods based on surface functionalization have a drawback where undesired
chemical modifications can occur and deteriorate the deposited material. The
application of electric-field assisted placement techniques eliminates the
element of chemical treatment; however, it requires an incorporation of
conductive placement electrodes that limit the performance, scaling, and
density of integrated electronic devices. Here, we report a method for
electric-field assisted placement of solution-processed nanomaterials by using
large-scale graphene layers featuring nanoscale deposition sites. The
structured graphene layers are prepared via either transfer or synthesis on
standard substrates, then are removed without residue once nanomaterial
deposition is completed, yielding material assemblies with nanoscale resolution
that cover surface areas larger than 1mm2. In order to demonstrate the broad
applicability, we have assembled representative zero-, one-, and
two-dimensional semiconductors at predefined substrate locations and integrated
them into nanoelectronic devices. This graphene-based placement technique
affords nanoscale resolution at wafer scale, and could enable mass
manufacturing of nanoelectronics and optoelectronics involving a wide range of
nanomaterials prepared via solution-based approaches.
| physics.app-ph cond-mat.mes-hall | controlled placement of nanomaterials at predefined locations with nanoscale precision remains among the most challenging problems that inhibit their largescale integration in the field of semiconductor process technology methods based on surface functionalization have a drawback where undesired chemical modifications can occur and deteriorate the deposited material the application of electricfield assisted placement techniques eliminates the element of chemical treatment however it requires an incorporation of conductive placement electrodes that limit the performance scaling and density of integrated electronic devices here we report a method for electricfield assisted placement of solutionprocessed nanomaterials by using largescale graphene layers featuring nanoscale deposition sites the structured graphene layers are prepared via either transfer or synthesis on standard substrates then are removed without residue once nanomaterial deposition is completed yielding material assemblies with nanoscale resolution that cover surface areas larger than 1mm2 in order to demonstrate the broad applicability we have assembled representative zero one and twodimensional semiconductors at predefined substrate locations and integrated them into nanoelectronic devices this graphenebased placement technique affords nanoscale resolution at wafer scale and could enable mass manufacturing of nanoelectronics and optoelectronics involving a wide range of nanomaterials prepared via solutionbased approaches | [['controlled', 'placement', 'of', 'nanomaterials', 'at', 'predefined', 'locations', 'with', 'nanoscale', 'precision', 'remains', 'among', 'the', 'most', 'challenging', 'problems', 'that', 'inhibit', 'their', 'largescale', 'integration', 'in', 'the', 'field', 'of', 'semiconductor', 'process', 'technology', 'methods', 'based', 'on', 'surface', 'functionalization', 'have', 'a', 'drawback', 'where', 'undesired', 'chemical', 'modifications', 'can', 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1,802.076 | Randomized sliding window algorithms for regular languages | A sliding window algorithm receives a stream of symbols and has to output at
each time instant a certain value which only depends on the last $n$ symbols.
If the algorithm is randomized, then at each time instant it produces an
incorrect output with probability at most $\epsilon$, which is a constant error
bound. This work proposes a more relaxed definition of correctness which is
parameterized by the error bound $\epsilon$ and the failure ratio $\phi$: A
randomized sliding window algorithm is required to err with probability at most
$\epsilon$ at a portion of $1-\phi$ of all time instants of an input stream.
This work continues the investigation of sliding window algorithms for regular
languages. In previous works a trichotomy theorem was shown for deterministic
algorithms: the optimal space complexity is either constant, logarithmic or
linear in the window size. The main results of this paper concerns three
natural settings (randomized algorithms with failure ratio zero and
randomized/deterministic algorithms with bounded failure ratio) and provide
natural language theoretic characterizations of the space complexity classes.
| cs.FL cs.DS | a sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last n symbols if the algorithm is randomized then at each time instant it produces an incorrect output with probability at most epsilon which is a constant error bound this work proposes a more relaxed definition of correctness which is parameterized by the error bound epsilon and the failure ratio phi a randomized sliding window algorithm is required to err with probability at most epsilon at a portion of 1phi of all time instants of an input stream this work continues the investigation of sliding window algorithms for regular languages in previous works a trichotomy theorem was shown for deterministic algorithms the optimal space complexity is either constant logarithmic or linear in the window size the main results of this paper concerns three natural settings randomized algorithms with failure ratio zero and randomizeddeterministic algorithms with bounded failure ratio and provide natural language theoretic characterizations of the space complexity classes | [['a', 'sliding', 'window', 'algorithm', 'receives', 'a', 'stream', 'of', 'symbols', 'and', 'has', 'to', 'output', 'at', 'each', 'time', 'instant', 'a', 'certain', 'value', 'which', 'only', 'depends', 'on', 'the', 'last', 'n', 'symbols', 'if', 'the', 'algorithm', 'is', 'randomized', 'then', 'at', 'each', 'time', 'instant', 'it', 'produces', 'an', 'incorrect', 'output', 'with', 'probability', 'at', 'most', 'epsilon', 'which', 'is', 'a', 'constant', 'error', 'bound', 'this', 'work', 'proposes', 'a', 'more', 'relaxed', 'definition', 'of', 'correctness', 'which', 'is', 'parameterized', 'by', 'the', 'error', 'bound', 'epsilon', 'and', 'the', 'failure', 'ratio', 'phi', 'a', 'randomized', 'sliding', 'window', 'algorithm', 'is', 'required', 'to', 'err', 'with', 'probability', 'at', 'most', 'epsilon', 'at', 'a', 'portion', 'of', '1phi', 'of', 'all', 'time', 'instants', 'of', 'an', 'input', 'stream', 'this', 'work', 'continues', 'the', 'investigation', 'of', 'sliding', 'window', 'algorithms', 'for', 'regular', 'languages', 'in', 'previous', 'works', 'a', 'trichotomy', 'theorem', 'was', 'shown', 'for', 'deterministic', 'algorithms', 'the', 'optimal', 'space', 'complexity', 'is', 'either', 'constant', 'logarithmic', 'or', 'linear', 'in', 'the', 'window', 'size', 'the', 'main', 'results', 'of', 'this', 'paper', 'concerns', 'three', 'natural', 'settings', 'randomized', 'algorithms', 'with', 'failure', 'ratio', 'zero', 'and', 'randomizeddeterministic', 'algorithms', 'with', 'bounded', 'failure', 'ratio', 'and', 'provide', 'natural', 'language', 'theoretic', 'characterizations', 'of', 'the', 'space', 'complexity', 'classes']] | [-0.1506905162698896, 0.10109293910373955, -0.08666831381199074, 0.023108247555846166, -0.08203756682994652, -0.19448165782334315, 0.11879767576179391, 0.3456055287357872, -0.28781671531503816, -0.28934652816418105, 0.09186780831919218, -0.22290393276236994, -0.12934438364292264, 0.19378692681653523, -0.10794470689092585, 0.11394168698024328, 0.053453279411517125, 0.1069999722929771, -0.06336605753022855, -0.32167770769285586, 0.2718694418597417, 0.07255072524566526, 0.25365933742524915, 0.009597553723529412, 0.10586157013699843, -0.007470759740799149, -0.009975189413078603, 0.010583174483234203, -0.1623880834119513, 0.05748055523229128, 0.25824063282589177, 0.17887172312879493, 0.3710357045264904, -0.34990876448486063, -0.14618718037058767, 0.11836466821168974, 0.12083584935582012, 0.10766867944779618, -0.004245569974986831, -0.23000030616982006, 0.13548852345230586, -0.09444955799249512, -0.056314758869625545, 0.031398767551590254, 0.07438375252282861, -0.020557867131610483, -0.3229700104095246, 0.039142812085418685, 0.08621486291461597, 0.016937140553026874, -0.02338304199316038, -0.10837240278656256, 0.07300322842811142, 0.10785146705628604, 0.05439649518401594, 0.10194216145611654, 0.12604851658978214, -0.07313100067694063, -0.13805747759458475, 0.33684771058467256, -0.05745498292320381, -0.17974716051336312, 0.15694536522536867, -0.09955173119568841, -0.15217154217760126, 0.1754405095021246, 0.1685273889802138, 0.1217078705906405, -0.09224354368069268, 0.12187491181828727, -0.0383552092186719, 0.22438178687676721, 0.13327295055903624, 0.04751609919075935, 0.11457100104152984, 0.17275728476960536, 0.13525343284507502, 0.13553960979485485, -0.03844169660362366, -0.06586289888307065, -0.3188435472682592, -0.14303793994820208, -0.19307224088310765, -0.019102688742844615, -0.13183070584085926, -0.18001606969975037, 0.37569772733127793, 0.08440142198374247, 0.21263503708009948, 0.1807341371532368, 0.3406358846393279, 0.13220068460298068, 0.018631672688539144, 0.14528819763322356, 0.1397414668705422, 0.05961008412047489, 0.08257847422373217, -0.16255502797652446, 0.1550992800116625, 0.10074836041432109] |
1,802.07601 | Coupling non-conforming discretizations of PDEs by spectral
approximation of the Lagrange multiplier space | This work focuses on the development of a non-conforming domain decomposition
method for the approximation of PDEs based on weakly imposed transmission
conditions: the continuity of the global solution is enforced by a discrete
number of Lagrange multipliers defined over the interfaces of adjacent
subdomains. The method falls into the class of primal hybrid methods, which
also include the well-known mortar method. Differently from the mortar method,
we discretize the space of basis functions on the interface by spectral
approximation independently of the discretization of the two adjacent domains;
one of the possible choices is to approximate the interface variational space
by Fourier basis functions. As we show in the numerical simulations, our
approach is well-suited for the solution of problems with non-conforming meshes
or with finite element basis functions with different polynomial degrees in
each subdomain. Another application of the method that still needs to be
investigated is the coupling of solutions obtained from otherwise incompatible
methods, such as the finite element method, the spectral element method or
isogeometric analysis.
| math.NA cs.CE cs.NA | this work focuses on the development of a nonconforming domain decomposition method for the approximation of pdes based on weakly imposed transmission conditions the continuity of the global solution is enforced by a discrete number of lagrange multipliers defined over the interfaces of adjacent subdomains the method falls into the class of primal hybrid methods which also include the wellknown mortar method differently from the mortar method we discretize the space of basis functions on the interface by spectral approximation independently of the discretization of the two adjacent domains one of the possible choices is to approximate the interface variational space by fourier basis functions as we show in the numerical simulations our approach is wellsuited for the solution of problems with nonconforming meshes or with finite element basis functions with different polynomial degrees in each subdomain another application of the method that still needs to be investigated is the coupling of solutions obtained from otherwise incompatible methods such as the finite element method the spectral element method or isogeometric analysis | [['this', 'work', 'focuses', 'on', 'the', 'development', 'of', 'a', 'nonconforming', 'domain', 'decomposition', 'method', 'for', 'the', 'approximation', 'of', 'pdes', 'based', 'on', 'weakly', 'imposed', 'transmission', 'conditions', 'the', 'continuity', 'of', 'the', 'global', 'solution', 'is', 'enforced', 'by', 'a', 'discrete', 'number', 'of', 'lagrange', 'multipliers', 'defined', 'over', 'the', 'interfaces', 'of', 'adjacent', 'subdomains', 'the', 'method', 'falls', 'into', 'the', 'class', 'of', 'primal', 'hybrid', 'methods', 'which', 'also', 'include', 'the', 'wellknown', 'mortar', 'method', 'differently', 'from', 'the', 'mortar', 'method', 'we', 'discretize', 'the', 'space', 'of', 'basis', 'functions', 'on', 'the', 'interface', 'by', 'spectral', 'approximation', 'independently', 'of', 'the', 'discretization', 'of', 'the', 'two', 'adjacent', 'domains', 'one', 'of', 'the', 'possible', 'choices', 'is', 'to', 'approximate', 'the', 'interface', 'variational', 'space', 'by', 'fourier', 'basis', 'functions', 'as', 'we', 'show', 'in', 'the', 'numerical', 'simulations', 'our', 'approach', 'is', 'wellsuited', 'for', 'the', 'solution', 'of', 'problems', 'with', 'nonconforming', 'meshes', 'or', 'with', 'finite', 'element', 'basis', 'functions', 'with', 'different', 'polynomial', 'degrees', 'in', 'each', 'subdomain', 'another', 'application', 'of', 'the', 'method', 'that', 'still', 'needs', 'to', 'be', 'investigated', 'is', 'the', 'coupling', 'of', 'solutions', 'obtained', 'from', 'otherwise', 'incompatible', 'methods', 'such', 'as', 'the', 'finite', 'element', 'method', 'the', 'spectral', 'element', 'method', 'or', 'isogeometric', 'analysis']] | [-0.08475598137368236, 0.03709667746783697, -0.11984158019203017, -0.0035003691771113973, -0.06651378533944531, -0.11101086708384822, 0.028506854762818817, 0.36867881551036363, -0.327824465355874, -0.259932674867869, 0.1417718307436471, -0.229343048596417, -0.11420245207464921, 0.18103985022481162, -0.02966976843022725, 0.08949726980658826, 0.08161191237077378, -0.01970771294243243, -0.10813686209329137, -0.21073543384932636, 0.3656881514893115, -0.03804790697398198, 0.2959017689116517, 0.036849625551956026, 0.12471295658727749, -0.019779842785336295, -0.05568318579847004, 0.042100910799596894, -0.09222442980424933, 0.15274110388682, 0.2363711180361478, 0.10369619719237524, 0.3257611339192903, -0.4411470758625203, -0.21484629287553286, 0.06147661729210618, 0.14409448745066833, 0.06724255279554817, -0.04225342775278382, -0.2586236365741304, 0.07555665950459695, -0.11717595253548209, -0.14001839921118048, -0.06344059893414813, -0.06432855186564576, 0.07928648876973934, -0.30675346988160707, 0.049623762149661944, 0.02748067203190243, 0.04122576478607299, -0.09534153368389398, -0.14712004092854192, -0.012193350111167029, 0.07750685384145758, 0.03221979267263447, 0.013621339884897074, 0.052084384358090444, -0.048864010778631554, -0.06955155131695738, 0.4070514772599291, -0.043366845038158505, -0.329822651529957, 0.19256546387138465, -0.1005019476699877, -0.08490291631600835, 0.11961897515129483, 0.15415111193583178, 0.20851355734994712, -0.1174619572879801, 0.1306295858298521, -0.031767725150716325, 0.14767546428650705, 0.04957555046533806, -0.013598485838905064, 0.10067100623726016, 0.17456141531832342, 0.1449838212653123, 0.12487384762866177, -0.04649173795097175, -0.09653683218659767, -0.34165210012354674, -0.16446833787159176, -0.23684782495487983, -0.07848560565208461, -0.14927726165985156, -0.2384037186925392, 0.4097205456666245, 0.1323346262035227, 0.11890769110752912, 0.012876803472730718, 0.3149150179328713, 0.1372402095915314, 0.07795176540136511, 0.05661362826780618, 0.1823774213897206, 0.12625417419251772, 0.0742754223613526, -0.229962872263665, 0.050671250218993914, 0.22237483877960962] |
1,802.07602 | Wake of inertial waves of a horizontal cylinder in horizontal
translation | We analyze theoretically and experimentally the wake behind a horizontal
cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a
fluid rotating about the vertical axis at a rate $\Omega$. Using particle image
velocimetry measurements in the rotating frame, we show that the wake is
stabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger than
in a non-rotating fluid. Over the explored range of parameters, the limit of
stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm
Ro}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process is
governed by the Ekman pumping in the boundary layer. At low Rossby number, the
wake takes the form of a stationary pattern of inertial waves, similar to the
wake of surface gravity waves behind a ship. We compare this steady wake
pattern to a model, originally developed by [Johnson, J. Fluid Mech. 120, 359
(1982)], assuming a free-slip boundary condition and a weak streamwise
perturbation. Our measurements show a quantitative agreement with this model
for ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the
wake is close to the prediction for an infinitely small line object. However,
the wake amplitude and phase origin are not correctly described by the
weak-streamwise-perturbation model, calling for an alternative model for the
boundary condition at moderate rotation rate.
| physics.flu-dyn physics.geo-ph | we analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter d horizontally translated at constant velocity u in a fluid rotating about the vertical axis at a rate omega using particle image velocimetry measurements in the rotating frame we show that the wake is stabilized by rotation for reynolds number rm reudnu much larger than in a nonrotating fluid over the explored range of parameters the limit of stability is rm re simeq 275 pm 25 rm ro with rm rou2omega d the rossby number indicating that the stabilizing process is governed by the ekman pumping in the boundary layer at low rossby number the wake takes the form of a stationary pattern of inertial waves similar to the wake of surface gravity waves behind a ship we compare this steady wake pattern to a model originally developed by johnson j fluid mech 120 359 1982 assuming a freeslip boundary condition and a weak streamwise perturbation our measurements show a quantitative agreement with this model for rm rolesssim 03 at larger rossby number the phase pattern of the wake is close to the prediction for an infinitely small line object however the wake amplitude and phase origin are not correctly described by the weakstreamwiseperturbation model calling for an alternative model for the boundary condition at moderate rotation rate | [['we', 'analyze', 'theoretically', 'and', 'experimentally', 'the', 'wake', 'behind', 'a', 'horizontal', 'cylinder', 'of', 'diameter', 'd', 'horizontally', 'translated', 'at', 'constant', 'velocity', 'u', 'in', 'a', 'fluid', 'rotating', 'about', 'the', 'vertical', 'axis', 'at', 'a', 'rate', 'omega', 'using', 'particle', 'image', 'velocimetry', 'measurements', 'in', 'the', 'rotating', 'frame', 'we', 'show', 'that', 'the', 'wake', 'is', 'stabilized', 'by', 'rotation', 'for', 'reynolds', 'number', 'rm', 'reudnu', 'much', 'larger', 'than', 'in', 'a', 'nonrotating', 'fluid', 'over', 'the', 'explored', 'range', 'of', 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1,802.07603 | RichMol: A general variational approach for rovibrational molecular
dynamics in external electric fields | A general variational approach for computing the rovibrational dynamics of
polyatomic molecules in the presence of external electric fields is presented.
Highly accurate, full-dimensional variational calculations provide a basis of
field-free rovibrational states for evaluating the rovibrational matrix
elements of high-rank Cartesian tensor operators, and for solving the
time-dependent Schr\"odinger equation. The effect of the external electric
field is treated as a multipole moment expansion truncated at the second
hyperpolarizability interaction term. Our fully numerical and computationally
efficient method has been implemented in a new program, RichMol, which can
simulate the effects of multiple external fields of arbitrary strength,
polarization, pulse shape and duration. Illustrative calculations of two-color
orientation and rotational excitation with an optical centrifuge of NH$_3$ are
discussed.
| physics.chem-ph | a general variational approach for computing the rovibrational dynamics of polyatomic molecules in the presence of external electric fields is presented highly accurate fulldimensional variational calculations provide a basis of fieldfree rovibrational states for evaluating the rovibrational matrix elements of highrank cartesian tensor operators and for solving the timedependent schrodinger equation the effect of the external electric field is treated as a multipole moment expansion truncated at the second hyperpolarizability interaction term our fully numerical and computationally efficient method has been implemented in a new program richmol which can simulate the effects of multiple external fields of arbitrary strength polarization pulse shape and duration illustrative calculations of twocolor orientation and rotational excitation with an optical centrifuge of nh_3 are discussed | [['a', 'general', 'variational', 'approach', 'for', 'computing', 'the', 'rovibrational', 'dynamics', 'of', 'polyatomic', 'molecules', 'in', 'the', 'presence', 'of', 'external', 'electric', 'fields', 'is', 'presented', 'highly', 'accurate', 'fulldimensional', 'variational', 'calculations', 'provide', 'a', 'basis', 'of', 'fieldfree', 'rovibrational', 'states', 'for', 'evaluating', 'the', 'rovibrational', 'matrix', 'elements', 'of', 'highrank', 'cartesian', 'tensor', 'operators', 'and', 'for', 'solving', 'the', 'timedependent', 'schrodinger', 'equation', 'the', 'effect', 'of', 'the', 'external', 'electric', 'field', 'is', 'treated', 'as', 'a', 'multipole', 'moment', 'expansion', 'truncated', 'at', 'the', 'second', 'hyperpolarizability', 'interaction', 'term', 'our', 'fully', 'numerical', 'and', 'computationally', 'efficient', 'method', 'has', 'been', 'implemented', 'in', 'a', 'new', 'program', 'richmol', 'which', 'can', 'simulate', 'the', 'effects', 'of', 'multiple', 'external', 'fields', 'of', 'arbitrary', 'strength', 'polarization', 'pulse', 'shape', 'and', 'duration', 'illustrative', 'calculations', 'of', 'twocolor', 'orientation', 'and', 'rotational', 'excitation', 'with', 'an', 'optical', 'centrifuge', 'of', 'nh_3', 'are', 'discussed']] | [-0.1434929342392613, 0.12619038329749788, -0.03547059479678253, 0.03527567647162731, -0.03624828376400308, -0.09342925239182195, -0.0117360529653188, 0.4229127884756367, -0.22513166684344285, -0.2838421607499613, 0.02478337780368992, -0.20041116699772035, -0.07898078896613996, 0.15820507772908615, 0.0974057393164194, 0.05662224331025441, 0.05911728122639431, -0.01743247122244573, -0.03958533289025444, -0.1588838867793748, 0.28071279120983694, 0.05995001284671681, 0.23425948288792572, 0.07351398147924357, 0.11111394516701083, 0.002070376504713497, 0.01783836296047358, -0.013042858840913331, -0.05258304927646801, 0.14508423464227968, 0.23069300608241836, 0.03469459617612179, 0.24650837293974742, -0.48764301197869436, -0.21648891019720992, 0.03599567705874934, 0.13555809932549587, 0.21303583303086868, -0.05488347532931997, -0.2989037637442288, -0.04192268781700492, -0.16955949692055583, -0.1939011195228443, -0.19047267468325293, 0.06942809291698523, 0.06526692875293123, -0.34736275398994193, 0.07974990119007141, -0.006199554667393325, 0.11040881731899108, -0.13941602948113901, -0.14927151902019195, -0.026454295192164284, 0.06681725397870383, -0.02589599174220397, 0.06037521698050389, 0.1540878921661119, -0.1146726523107309, -0.10157127934703682, 0.4187336960228301, -0.09799759915321596, -0.20549364960478508, 0.10368185261843585, -0.11269812929217055, -0.11548191024589219, 0.17631855336244867, 0.1711929459300894, 0.21196304523863463, -0.1444449083128271, 0.08340201976595588, 0.018796247635584545, 0.15748503586637372, 0.05792001016954539, 0.026338593935018733, 0.16065983665214867, 0.10449596302693381, 0.01813001960062054, 0.16780281118156404, -0.09898166132292577, -0.1267476989144162, -0.27776372996638254, -0.12404802949605569, -0.216452671437986, 0.04554710306712434, -0.07459823650791224, -0.19164140814007455, 0.40846638666747626, 0.1073646157972139, 0.07244571205081825, -0.03117469385043256, 0.3571154846801978, 0.1814802542383618, 0.018736511711500772, 0.05098750112781755, 0.25688985705438283, 0.22834828489718317, 0.06141899099393489, -0.2953937126642989, 0.034134461434886736, 0.06535231971921508] |
1,802.07604 | Long gaps in sieved sets | For each prime $p$, let $I_p \subset \mathbb{Z}/p\mathbb{Z}$ denote a
collection of residue classes modulo $p$ such that the cardinalities $|I_p|$
are bounded and about $1$ on average. We show that for sufficiently large $x$,
the sifted set $\{ n \in \mathbb{Z}: n \pmod{p} \not \in I_p \hbox{ for all }p
\leq x\}$ contains gaps of size at least $x (\log x)^{\delta} $ where
$\delta>0$ depends only on the density of primes for which $I_p\ne \emptyset$.
This improves on the "trivial" bound of $\gg x$. As a consequence, for any
non-constant polynomial $f:\mathbb{Z}\to \mathbb{Z}$ with positive leading
coefficient, the set $\{ n \leq X: f(n) \hbox{ composite}\}$ contains an
interval of consecutive integers of length $\ge (\log X) (\log\log X)^{\delta}$
for sufficiently large $X$, where $\delta>0$ depends only on the degree of $f$.
| math.NT | for each prime p let i_p subset mathbbzpmathbbz denote a collection of residue classes modulo p such that the cardinalities i_p are bounded and about 1 on average we show that for sufficiently large x the sifted set n in mathbbz n pmodp not in i_p hbox for all p leq x contains gaps of size at least x log xdelta where delta0 depends only on the density of primes for which i_pne emptyset this improves on the trivial bound of gg x as a consequence for any nonconstant polynomial fmathbbzto mathbbz with positive leading coefficient the set n leq x fn hbox composite contains an interval of consecutive integers of length ge log x loglog xdelta for sufficiently large x where delta0 depends only on the degree of f | [['for', 'each', 'prime', 'p', 'let', 'i_p', 'subset', 'mathbbzpmathbbz', 'denote', 'a', 'collection', 'of', 'residue', 'classes', 'modulo', 'p', 'such', 'that', 'the', 'cardinalities', 'i_p', 'are', 'bounded', 'and', 'about', '1', 'on', 'average', 'we', 'show', 'that', 'for', 'sufficiently', 'large', 'x', 'the', 'sifted', 'set', 'n', 'in', 'mathbbz', 'n', 'pmodp', 'not', 'in', 'i_p', 'hbox', 'for', 'all', 'p', 'leq', 'x', 'contains', 'gaps', 'of', 'size', 'at', 'least', 'x', 'log', 'xdelta', 'where', 'delta0', 'depends', 'only', 'on', 'the', 'density', 'of', 'primes', 'for', 'which', 'i_pne', 'emptyset', 'this', 'improves', 'on', 'the', 'trivial', 'bound', 'of', 'gg', 'x', 'as', 'a', 'consequence', 'for', 'any', 'nonconstant', 'polynomial', 'fmathbbzto', 'mathbbz', 'with', 'positive', 'leading', 'coefficient', 'the', 'set', 'n', 'leq', 'x', 'fn', 'hbox', 'composite', 'contains', 'an', 'interval', 'of', 'consecutive', 'integers', 'of', 'length', 'ge', 'log', 'x', 'loglog', 'xdelta', 'for', 'sufficiently', 'large', 'x', 'where', 'delta0', 'depends', 'only', 'on', 'the', 'degree', 'of', 'f']] | [-0.25538480255818286, 0.1556587442247519, 0.008089057777397102, -0.017138736800006882, 0.01938714505013195, -0.22773025016795145, 0.044666126334050205, 0.29450094274943694, -0.287284869227733, -0.22988313620953704, 0.007985321955857216, -0.36332714529999066, -0.0034912777118734084, 0.19550741623243084, -0.04933001676181448, -0.02648194470202725, -0.015398189749248559, 0.16437760629924014, -0.06218556627936778, -0.3216870716480571, 0.2898369489976176, -0.14140936929152303, 0.11787613218984916, 0.0434781607837067, 0.12115303488826612, 0.04543360306706745, 0.07987420693098102, -0.023007675601547817, -0.22974334215962244, 0.006148759723146213, 0.2766456370118249, 0.1048823213277501, 0.2729565018962603, -0.31979441372095607, -0.1042213351247483, 0.2620280792179983, 0.17938674339893623, -0.13425115142035793, 0.04884271853006794, -0.18368945108159096, 0.24112419782250072, -0.08275887428601436, -0.12358762944859336, -0.015540875345323002, 0.23193376597919269, 0.05837465745571535, -0.39473531932526384, 0.025270055986766238, 0.13025543172261678, 0.09350216059101513, 0.043987367336740135, -0.27931593356333906, -0.055924256914295256, 0.04469712302670814, -0.018372593622189015, 0.14175395783695421, 0.020134219094870787, -0.06038641690656732, -0.0017048953304765746, 0.3144303070148453, -0.08608489721882506, -0.18324181076604873, 0.04610687970125582, -0.23928060397156514, -0.18022166855735122, 0.16179463255684823, 0.11075791692564962, 0.2163686585695359, 0.05354457323483075, 0.29826620940320936, -0.15190463917406305, 0.26097601710353047, 0.14468115930139902, 0.039668641382377245, 0.0799857028232509, 0.09263522436231142, 0.11713046990553266, 0.025006609237607336, -0.05809076079458464, 0.08481461499104626, -0.43894078975426964, -0.15969902192455265, -0.23535593392170995, 0.23537283100370132, -0.1846171283576723, -0.15381629960666032, 0.2650584080911358, 0.04700358224727097, 0.26163171474263436, 0.13705958666923834, 0.14705033275822643, 0.05589107241871716, -0.014072164216486271, 0.14058983206996345, -0.027385052264435217, 0.08159012084524875, -0.09728305416501826, -0.16123341479215014, 0.07896903395521804, 0.13060250803971485] |
1,802.07605 | Accelerating crystal structure prediction by machine-learning
interatomic potentials with active learning | In this letter we propose a new methodology for crystal structure prediction,
which is based on the evolutionary algorithm USPEX and the machine-learning
interatomic potentials actively learning on-the-fly. Our methodology allows for
an automated construction of an interatomic interaction model from scratch
replacing the expensive DFT with a speedup of several orders of magnitude.
Predicted low-energy structures are then tested on DFT, ensuring that our
machine-learning model does not introduce any prediction error. We tested our
methodology on a problem of prediction of carbon allotropes, dense sodium
structures and boron allotropes including those which have more than 100 atoms
in the primitive cell. All the the main allotropes have been reproduced and a
new 54-atom structure of boron have been found at very modest computational
efforts.
| cond-mat.mtrl-sci | in this letter we propose a new methodology for crystal structure prediction which is based on the evolutionary algorithm uspex and the machinelearning interatomic potentials actively learning onthefly our methodology allows for an automated construction of an interatomic interaction model from scratch replacing the expensive dft with a speedup of several orders of magnitude predicted lowenergy structures are then tested on dft ensuring that our machinelearning model does not introduce any prediction error we tested our methodology on a problem of prediction of carbon allotropes dense sodium structures and boron allotropes including those which have more than 100 atoms in the primitive cell all the the main allotropes have been reproduced and a new 54atom structure of boron have been found at very modest computational efforts | [['in', 'this', 'letter', 'we', 'propose', 'a', 'new', 'methodology', 'for', 'crystal', 'structure', 'prediction', 'which', 'is', 'based', 'on', 'the', 'evolutionary', 'algorithm', 'uspex', 'and', 'the', 'machinelearning', 'interatomic', 'potentials', 'actively', 'learning', 'onthefly', 'our', 'methodology', 'allows', 'for', 'an', 'automated', 'construction', 'of', 'an', 'interatomic', 'interaction', 'model', 'from', 'scratch', 'replacing', 'the', 'expensive', 'dft', 'with', 'a', 'speedup', 'of', 'several', 'orders', 'of', 'magnitude', 'predicted', 'lowenergy', 'structures', 'are', 'then', 'tested', 'on', 'dft', 'ensuring', 'that', 'our', 'machinelearning', 'model', 'does', 'not', 'introduce', 'any', 'prediction', 'error', 'we', 'tested', 'our', 'methodology', 'on', 'a', 'problem', 'of', 'prediction', 'of', 'carbon', 'allotropes', 'dense', 'sodium', 'structures', 'and', 'boron', 'allotropes', 'including', 'those', 'which', 'have', 'more', 'than', '100', 'atoms', 'in', 'the', 'primitive', 'cell', 'all', 'the', 'the', 'main', 'allotropes', 'have', 'been', 'reproduced', 'and', 'a', 'new', '54atom', 'structure', 'of', 'boron', 'have', 'been', 'found', 'at', 'very', 'modest', 'computational', 'efforts']] | [-0.031071374795399606, 0.056493659950094297, -0.09084635874070227, 0.024410510286688804, -0.02628976881422568, -0.15394948979467155, 0.07573478785902261, 0.45828965765237806, -0.23900954972207547, -0.3298055467233062, 0.023109562030062078, -0.2584871224035742, -0.18255977695062756, 0.197511833390221, -0.008602156989276409, 0.08050292221829296, 0.08629565670341253, -0.018159929394721986, -0.08355508197285234, -0.2853861418766901, 0.24867808147519826, 0.07534065376222134, 0.28969532331079245, 0.041322159925475714, 0.05226504350081086, -0.07320013481937349, 0.015255964040756225, 0.0077303690016269685, -0.13124043235956925, 0.1952901054592803, 0.21740265771048142, 0.06345745854265988, 0.27655265110824256, -0.4647766502276063, -0.25663116545765663, 0.04990512024797499, 0.13441992062702776, 0.16819669790565966, -0.09966232526081148, -0.25587739249318836, 0.10895629375986755, -0.19306671902537345, -0.062194032499566676, -0.13276073432341218, 0.001735474357381463, -0.0035627967566251753, -0.24242117980495095, 0.028067247541621328, 0.002388930570334196, 0.08587183222174645, -0.09773749809013679, -0.19783244138769807, 0.010404003510251641, 0.0729428990939632, -0.013548847809433938, 0.03143749184906483, 0.14245229136943818, -0.08694572921656073, -0.14146053037419914, 0.44995240116119384, -0.053019752240390516, -0.1348525173291564, 0.21136538177542388, -0.04373534625954926, -0.18729170767962933, 0.14991601955890654, 0.14728228826774284, 0.13920532121136783, -0.17385179740656168, 0.06618013349035755, -0.011660997837781906, 0.19961602457612754, 0.0579703729711473, -0.008695124331861735, 0.19232058009132744, 0.26303564419504255, 0.015143620295450091, 0.08179844474047422, -0.09071518136747181, -0.05256139553897083, -0.2015649588536471, -0.15043976868898606, -0.1861514441529289, -0.0008036101086763665, -0.09030525591562036, -0.2149675814397633, 0.4166746094301343, 0.16458186300843955, 0.13496866802871227, 0.0490084821972996, 0.27026915685459973, 0.027863657041452824, 0.13820350125432015, 0.0455802315287292, 0.24846523953229188, 0.08860463000833989, 0.04006459609046578, -0.17946179847512395, 0.11973696854710579, 0.05454146630316973] |
1,802.07606 | Ordered Preference Elicitation Strategies for Supporting Multi-Objective
Decision Making | In multi-objective decision planning and learning, much attention is paid to
producing optimal solution sets that contain an optimal policy for every
possible user preference profile. We argue that the step that follows, i.e,
determining which policy to execute by maximising the user's intrinsic utility
function over this (possibly infinite) set, is under-studied. This paper aims
to fill this gap. We build on previous work on Gaussian processes and pairwise
comparisons for preference modelling, extend it to the multi-objective decision
support scenario, and propose new ordered preference elicitation strategies
based on ranking and clustering. Our main contribution is an in-depth
evaluation of these strategies using computer and human-based experiments. We
show that our proposed elicitation strategies outperform the currently used
pairwise methods, and found that users prefer ranking most. Our experiments
further show that utilising monotonicity information in GPs by using a linear
prior mean at the start and virtual comparisons to the nadir and ideal points,
increases performance. We demonstrate our decision support framework in a
real-world study on traffic regulation, conducted with the city of Amsterdam.
| cs.LG cs.AI stat.ML | in multiobjective decision planning and learning much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile we argue that the step that follows ie determining which policy to execute by maximising the users intrinsic utility function over this possibly infinite set is understudied this paper aims to fill this gap we build on previous work on gaussian processes and pairwise comparisons for preference modelling extend it to the multiobjective decision support scenario and propose new ordered preference elicitation strategies based on ranking and clustering our main contribution is an indepth evaluation of these strategies using computer and humanbased experiments we show that our proposed elicitation strategies outperform the currently used pairwise methods and found that users prefer ranking most our experiments further show that utilising monotonicity information in gps by using a linear prior mean at the start and virtual comparisons to the nadir and ideal points increases performance we demonstrate our decision support framework in a realworld study on traffic regulation conducted with the city of amsterdam | [['in', 'multiobjective', 'decision', 'planning', 'and', 'learning', 'much', 'attention', 'is', 'paid', 'to', 'producing', 'optimal', 'solution', 'sets', 'that', 'contain', 'an', 'optimal', 'policy', 'for', 'every', 'possible', 'user', 'preference', 'profile', 'we', 'argue', 'that', 'the', 'step', 'that', 'follows', 'ie', 'determining', 'which', 'policy', 'to', 'execute', 'by', 'maximising', 'the', 'users', 'intrinsic', 'utility', 'function', 'over', 'this', 'possibly', 'infinite', 'set', 'is', 'understudied', 'this', 'paper', 'aims', 'to', 'fill', 'this', 'gap', 'we', 'build', 'on', 'previous', 'work', 'on', 'gaussian', 'processes', 'and', 'pairwise', 'comparisons', 'for', 'preference', 'modelling', 'extend', 'it', 'to', 'the', 'multiobjective', 'decision', 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1,802.07607 | Regularity of minimal surfaces with lower dimensional obstacles | We study the Plateau problem with a lower dimensional obstacle in
$\mathbb{R}^n$. Intuitively, in $\mathbb{R}^3$ this corresponds to a soap film
(spanning a given contour) that is pushed from below by a "vertical" 2D
half-space (or some smooth deformation of it). We establish almost optimal
$C^{1,1/2-}$ estimates for the solutions near points on the free boundary of
the contact set, in any dimension $n\ge 2$.
The $C^{1,1/2-}$ estimates follow from an $\varepsilon$-regularity result for
minimal surfaces with thin obstacles in the spirit of the De Giorgi's
improvement of flatness. To prove it, we follow Savin's small perturbations
method. A nontrivial difficulty in using Savin's approach for minimal surfaces
with thin obstacles is that near a typical contact point the solution consists
of two smooth surfaces that intersect transversally, and hence it is not very
flat at small scales. Via a new "dichotomy approach" based on barrier arguments
we are able to overcome this difficulty and prove the desired result.
| math.AP | we study the plateau problem with a lower dimensional obstacle in mathbbrn intuitively in mathbbr3 this corresponds to a soap film spanning a given contour that is pushed from below by a vertical 2d halfspace or some smooth deformation of it we establish almost optimal c112 estimates for the solutions near points on the free boundary of the contact set in any dimension nge 2 the c112 estimates follow from an varepsilonregularity result for minimal surfaces with thin obstacles in the spirit of the de giorgis improvement of flatness to prove it we follow savins small perturbations method a nontrivial difficulty in using savins approach for minimal surfaces with thin obstacles is that near a typical contact point the solution consists of two smooth surfaces that intersect transversally and hence it is not very flat at small scales via a new dichotomy approach based on barrier arguments we are able to overcome this difficulty and prove the desired result | [['we', 'study', 'the', 'plateau', 'problem', 'with', 'a', 'lower', 'dimensional', 'obstacle', 'in', 'mathbbrn', 'intuitively', 'in', 'mathbbr3', 'this', 'corresponds', 'to', 'a', 'soap', 'film', 'spanning', 'a', 'given', 'contour', 'that', 'is', 'pushed', 'from', 'below', 'by', 'a', 'vertical', '2d', 'halfspace', 'or', 'some', 'smooth', 'deformation', 'of', 'it', 'we', 'establish', 'almost', 'optimal', 'c112', 'estimates', 'for', 'the', 'solutions', 'near', 'points', 'on', 'the', 'free', 'boundary', 'of', 'the', 'contact', 'set', 'in', 'any', 'dimension', 'nge', '2', 'the', 'c112', 'estimates', 'follow', 'from', 'an', 'varepsilonregularity', 'result', 'for', 'minimal', 'surfaces', 'with', 'thin', 'obstacles', 'in', 'the', 'spirit', 'of', 'the', 'de', 'giorgis', 'improvement', 'of', 'flatness', 'to', 'prove', 'it', 'we', 'follow', 'savins', 'small', 'perturbations', 'method', 'a', 'nontrivial', 'difficulty', 'in', 'using', 'savins', 'approach', 'for', 'minimal', 'surfaces', 'with', 'thin', 'obstacles', 'is', 'that', 'near', 'a', 'typical', 'contact', 'point', 'the', 'solution', 'consists', 'of', 'two', 'smooth', 'surfaces', 'that', 'intersect', 'transversally', 'and', 'hence', 'it', 'is', 'not', 'very', 'flat', 'at', 'small', 'scales', 'via', 'a', 'new', 'dichotomy', 'approach', 'based', 'on', 'barrier', 'arguments', 'we', 'are', 'able', 'to', 'overcome', 'this', 'difficulty', 'and', 'prove', 'the', 'desired', 'result']] | [-0.12889616970418008, 0.06660075925384669, -0.09379831398105097, 0.04715256153169504, -0.05990369685591673, -0.14966999150156599, 0.03646374340959877, 0.35640422028120394, -0.26921633618104757, -0.2590291829415123, 0.12398606987374267, -0.2763550871479436, -0.13383467681266648, 0.22852841267836685, -0.1265132353471229, 0.06815289943801157, 0.045984739715192444, -0.005279517873137627, -0.06517858164232669, -0.21413423209019158, 0.3838994358929823, -0.05345934808675973, 0.25706094925719425, 0.07029519381247601, 0.10406235869938754, -0.008657162311013185, 0.05792853228730273, 0.03789659312475215, -0.20453471896664566, 0.13051385206606755, 0.22792138017334393, 0.011386482061162216, 0.24977899476323487, -0.4183652470116767, -0.20672149410904767, 0.10580250337345046, 0.12528097681677755, 0.10590822029999404, -0.039768769208828, -0.23550221703817728, 0.1313700572925813, -0.06571865321353734, -0.24061134483360644, -0.004379649327353299, -0.0008209844723156413, -0.02133845528089822, -0.2315498905266641, 0.056771673499342964, 0.11900575687441062, 0.0427230825734108, -0.09087046999125536, -0.0656029785743112, -0.018646283152823646, 0.09514869221284072, 0.04215004333037203, 0.0794789713423746, 0.07830708339494073, -0.09987749234406583, -0.05735446568637055, 0.3344950411416028, -0.09014957710960002, -0.2430490554389456, 0.19006882531937422, -0.14340238898125646, -0.09348561290546127, 0.1733016552551468, 0.12454464690138896, 0.16298273723841933, -0.10500816056657138, 0.14167729102927348, -0.06251284047747441, 0.1338045106647586, 0.14353063241315056, -0.06350304128356138, 0.16573011258371034, 0.16144985787178032, 0.18971860800641324, 0.12672151201668214, -0.06029286137899185, -0.06100229935650275, -0.3484885112013457, -0.16711204260245036, -0.19631595704880245, 0.07826153234786971, -0.1140998193271877, -0.21616859244235423, 0.31809450700035635, 0.10390196928465974, 0.24392607433533986, 0.09789401504837866, 0.25140053231222265, 0.08169084793747822, 0.03953347227436566, 0.12025826883029321, 0.20966501208113758, 0.0790349559524571, 0.06025159428113597, -0.13979012628361207, 0.0224116331803958, 0.10641242035242887] |
1,802.07608 | Learning to Synthesize | In many scenarios we need to find the most likely program under a local
context, where the local context can be an incomplete program, a partial
specification, natural language description, etc. We call such problem program
estimation. In this paper we propose an abstract framework, learning to
synthesis, or L2S in short, to address this problem. L2S combines four tools to
achieve this: syntax is used to define the search space and search steps,
constraints are used to prune off invalid candidates at each search step,
machine-learned models are used to estimate conditional probabilities for the
candidates at each search step, and search algorithms are used to find the best
possible solution. The main goal of L2S is to lay out the design space to
motivate the research on program estimation.
We have performed a preliminary evaluation by instantiating this framework
for synthesizing conditions of an automated program repair (APR) system. The
training data are from the project itself and related JDK packages. Compared to
ACS, a state-of-the-art condition synthesis system for program repair, our
approach could deal with a larger search space such that we fixed 4 additional
bugs outside the search space of ACS, and relies only on the source code of the
current projects.
| cs.SE | in many scenarios we need to find the most likely program under a local context where the local context can be an incomplete program a partial specification natural language description etc we call such problem program estimation in this paper we propose an abstract framework learning to synthesis or l2s in short to address this problem l2s combines four tools to achieve this syntax is used to define the search space and search steps constraints are used to prune off invalid candidates at each search step machinelearned models are used to estimate conditional probabilities for the candidates at each search step and search algorithms are used to find the best possible solution the main goal of l2s is to lay out the design space to motivate the research on program estimation we have performed a preliminary evaluation by instantiating this framework for synthesizing conditions of an automated program repair apr system the training data are from the project itself and related jdk packages compared to acs a stateoftheart condition synthesis system for program repair our approach could deal with a larger search space such that we fixed 4 additional bugs outside the search space of acs and relies only on the source code of the current projects | [['in', 'many', 'scenarios', 'we', 'need', 'to', 'find', 'the', 'most', 'likely', 'program', 'under', 'a', 'local', 'context', 'where', 'the', 'local', 'context', 'can', 'be', 'an', 'incomplete', 'program', 'a', 'partial', 'specification', 'natural', 'language', 'description', 'etc', 'we', 'call', 'such', 'problem', 'program', 'estimation', 'in', 'this', 'paper', 'we', 'propose', 'an', 'abstract', 'framework', 'learning', 'to', 'synthesis', 'or', 'l2s', 'in', 'short', 'to', 'address', 'this', 'problem', 'l2s', 'combines', 'four', 'tools', 'to', 'achieve', 'this', 'syntax', 'is', 'used', 'to', 'define', 'the', 'search', 'space', 'and', 'search', 'steps', 'constraints', 'are', 'used', 'to', 'prune', 'off', 'invalid', 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1,802.07609 | Distribution of Large Gaps Between Primes | We survey some past conditional results on the distribution of large
differences between consecutive primes and examine how the Hardy-Littlewood
prime k-tuples conjecture can be applied to this question.
| math.NT | we survey some past conditional results on the distribution of large differences between consecutive primes and examine how the hardylittlewood prime ktuples conjecture can be applied to this question | [['we', 'survey', 'some', 'past', 'conditional', 'results', 'on', 'the', 'distribution', 'of', 'large', 'differences', 'between', 'consecutive', 'primes', 'and', 'examine', 'how', 'the', 'hardylittlewood', 'prime', 'ktuples', 'conjecture', 'can', 'be', 'applied', 'to', 'this', 'question']] | [-0.1687838600563078, 0.10434979982352977, -0.1590483171287282, 0.18357879878423208, -0.08237935435669176, -0.05228587246403612, 0.025953439289125902, 0.3690231391710454, -0.32782280804782077, -0.3345307432885828, 0.05283738908775408, -0.3125591681354904, -0.12331217363605211, 0.2038016606941177, -0.1534568483716455, 0.03212628231769235, 0.08364430850307489, -3.777797622927304e-05, -0.013059632916902673, -0.4298180490732193, 0.3589630534165892, -0.04240588855062579, 0.21725148848932366, 0.0840592098839838, 0.019945106336622144, 0.027738282456994057, -1.35166699002529e-05, -0.024468155770466245, -0.19971995799127837, 0.1538567423563579, 0.30788325181166676, 0.1960975681110446, 0.3472191995844759, -0.41328358984199065, -0.09304866632286074, 0.25096734921480046, 0.1628620557101636, -0.004692625350736338, -0.015498424386445048, -0.23753897049303713, 0.11421308428819837, -0.133979462894033, -0.13340604844792137, -0.09015067101552568, 0.030982818775649727, 0.11051054173630886, -0.24718253680601202, 0.04706477283917625, 0.06066094685731263, 0.14078698496751743, -0.01809744869262494, -0.1744857059213622, 0.0881669251890532, 0.15153694835266676, 0.12537859871598153, 0.009826030534017703, 0.03290733857208799, -0.06143765523226868, -0.14778874146527257, 0.2612147694774743, -0.04280496799740298, -0.14545934056413584, 0.09775913866429493, -0.24534724363736038, -0.18250428146586337, 0.0023084732198060073, 0.14933844225416923, 0.09498938320782678, -0.04964914190550816, 0.055565229069104355, -0.21391301961808368, 0.16106684268291654, 0.1712755466136953, 0.013655793499843827, 0.21609987507991749, 0.021654906265180688, 0.04406658206777326, 0.13220819301405473, -0.11552876962252476, -0.030166193714429593, -0.30709495042161694, -0.13855933998550835, -0.22521023208211208, 0.11426039175772719, -0.09071861385670892, -0.10450147741056721, 0.39231591157872103, 0.2317191331229847, 0.21970899442435596, 0.09429306925499234, 0.21000212225420722, 0.0628917443662368, 0.0458014499524544, 0.0259281726040203, 0.11636409438556414, 0.15604778899457947, -0.02776993719603995, -0.1757106213862526, 0.06543196423043465, 0.10949202260837473] |
1,802.0761 | Homotopy Theory of Bicomplexes | We define two model structures on the category of bicomplexes concentrated in
the right half plane. The first model structure has weak equivalences detected
by the totalisation functor. The second model structure's weak equivalences are
detected by the $E^2$-term of the spectral sequence associated to the
filtration of the total complex by the horizontal degree. We then extend this
result to twisted complexes.
| math.AT math.KT | we define two model structures on the category of bicomplexes concentrated in the right half plane the first model structure has weak equivalences detected by the totalisation functor the second model structures weak equivalences are detected by the e2term of the spectral sequence associated to the filtration of the total complex by the horizontal degree we then extend this result to twisted complexes | [['we', 'define', 'two', 'model', 'structures', 'on', 'the', 'category', 'of', 'bicomplexes', 'concentrated', 'in', 'the', 'right', 'half', 'plane', 'the', 'first', 'model', 'structure', 'has', 'weak', 'equivalences', 'detected', 'by', 'the', 'totalisation', 'functor', 'the', 'second', 'model', 'structures', 'weak', 'equivalences', 'are', 'detected', 'by', 'the', 'e2term', 'of', 'the', 'spectral', 'sequence', 'associated', 'to', 'the', 'filtration', 'of', 'the', 'total', 'complex', 'by', 'the', 'horizontal', 'degree', 'we', 'then', 'extend', 'this', 'result', 'to', 'twisted', 'complexes']] | [-0.16004923926365952, 0.0725137030315255, -0.027539648806616183, 0.09545390074133812, -0.05172536564209769, -0.05863144501082359, -0.014488524139573376, 0.3981982680908855, -0.38770229093760494, -0.2540916879961808, 0.08369788011318192, -0.22174087239733536, -0.1340219743790165, 0.11554699661135073, -0.056807610882265915, -0.05133108217682269, 0.036374136189659755, 0.06396048773650921, -0.028293329644046964, -0.2089142330073481, 0.4310347299812542, 0.019031039101161783, 0.2416705876108139, -0.0020530456080920093, 0.07271960353659045, -0.03970166057678721, -0.027888954857424382, -0.00847085337004354, -0.15604906854212225, 0.18116837164627447, 0.16736362945108163, 0.06109425019202454, 0.19522744148872012, -0.3888891779727513, -0.13940775326468172, 0.12922805318638922, 0.078680734322857, 0.02918253060910971, 0.016891846979682844, -0.3279328407839902, 0.15629784007286351, -0.1525914472597745, -0.13566371799266386, -0.0030483452963732905, 0.002792034057840224, 0.03962955143182508, -0.1671137751292272, 0.025170958443214337, 0.10292717177541025, 0.0665543993574477, -0.08437212923121068, -0.05420351363418083, -0.12414977139222526, 0.11930772353474411, -0.011748391870153887, 0.011306211382390992, 0.08817803573554321, -0.11545633887796994, -0.11192155730790429, 0.3499185883950803, -0.10543905236127396, -0.17331613136094906, 0.14701645301594848, -0.18767984634295345, -0.17512956319466955, 0.1716488371603191, 0.06346273739191313, 0.17429631912419874, -0.07941824037134798, 0.12467472301796079, -0.10310933829074906, 0.11937016468014448, 0.08274567803938783, -0.023544169699532852, 0.166354414413593, 0.10541849381350461, 0.057861335170004635, 0.17965522931978828, -0.09898336128530753, -0.07339981800666259, -0.28374467874246256, -0.14034071393431194, -0.08117084239136367, 0.052488153173462414, -0.0672920571054302, -0.14105420056430082, 0.42981242616811105, 0.12165553250440186, 0.24500662729805034, 0.08125874040377958, 0.2797690679942588, 0.09918780358988911, 0.08174645151161859, -0.04014676630557064, 0.213373985945157, 0.2262571874457682, 0.034835208545348814, -0.10704800011561959, 0.060315534577614835, 0.18187350318616918] |
1,802.07611 | H.E.S.S. discovery of very high energy gamma-ray emission from PKS
0625-354 | PKS 0625-354 (z=0.055) was observed with the four H.E.S.S. telescopes in 2012
during 5.5 hours. The source was detected above an energy threshold of 200 GeV
at a significance level of 6.1$\sigma$. No significant variability is found in
these observations. The source is well described with a power-law spectrum with
photon index $\Gamma =2.84 \pm 0.50_{stat} \pm 0.10_{syst}$ and normalization
(at $E_0$=1.0 TeV) $N_0(E_0)=(0.58 \pm 0.22_{stat} \pm
0.12_{syst})\times10^{-12}$ TeV$^{-1}$cm$^{-2}$s$^{-1}$. Multi-wavelength data
collected with Fermi-LAT, Swift-XRT, Swift-UVOT, ATOM and WISE are also
analysed. Significant variability is observed only in the Fermi-LAT
$\gamma$-ray and Swift-XRT X-ray energy bands. Having a good multi-wavelength
coverage from radio to very high energy, we performed a broadband modelling
from two types of emission scenarios. The results from a one zone
lepto-hadronic, and a multi-zone leptonic models are compared and discussed. On
the grounds of energetics, our analysis favours a leptonic multi-zone model.
Models associated to the X-ray variability constraint supports previous results
suggesting a BL Lac nature of PKS 0625-354, with, however, a large-scale jet
structure typical of a radio galaxy.
| astro-ph.HE | pks 0625354 z0055 was observed with the four hess telescopes in 2012 during 55 hours the source was detected above an energy threshold of 200 gev at a significance level of 61sigma no significant variability is found in these observations the source is well described with a powerlaw spectrum with photon index gamma 284 pm 050_stat pm 010_syst and normalization at e_010 tev n_0e_0058 pm 022_stat pm 012_systtimes1012 tev1cm2s1 multiwavelength data collected with fermilat swiftxrt swiftuvot atom and wise are also analysed significant variability is observed only in the fermilat gammaray and swiftxrt xray energy bands having a good multiwavelength coverage from radio to very high energy we performed a broadband modelling from two types of emission scenarios the results from a one zone leptohadronic and a multizone leptonic models are compared and discussed on the grounds of energetics our analysis favours a leptonic multizone model models associated to the xray variability constraint supports previous results suggesting a bl lac nature of pks 0625354 with however a largescale jet structure typical of a radio galaxy | [['pks', '0625354', 'z0055', 'was', 'observed', 'with', 'the', 'four', 'hess', 'telescopes', 'in', '2012', 'during', '55', 'hours', 'the', 'source', 'was', 'detected', 'above', 'an', 'energy', 'threshold', 'of', '200', 'gev', 'at', 'a', 'significance', 'level', 'of', '61sigma', 'no', 'significant', 'variability', 'is', 'found', 'in', 'these', 'observations', 'the', 'source', 'is', 'well', 'described', 'with', 'a', 'powerlaw', 'spectrum', 'with', 'photon', 'index', 'gamma', '284', 'pm', '050_stat', 'pm', '010_syst', 'and', 'normalization', 'at', 'e_010', 'tev', 'n_0e_0058', 'pm', '022_stat', 'pm', '012_systtimes1012', 'tev1cm2s1', 'multiwavelength', 'data', 'collected', 'with', 'fermilat', 'swiftxrt', 'swiftuvot', 'atom', 'and', 'wise', 'are', 'also', 'analysed', 'significant', 'variability', 'is', 'observed', 'only', 'in', 'the', 'fermilat', 'gammaray', 'and', 'swiftxrt', 'xray', 'energy', 'bands', 'having', 'a', 'good', 'multiwavelength', 'coverage', 'from', 'radio', 'to', 'very', 'high', 'energy', 'we', 'performed', 'a', 'broadband', 'modelling', 'from', 'two', 'types', 'of', 'emission', 'scenarios', 'the', 'results', 'from', 'a', 'one', 'zone', 'leptohadronic', 'and', 'a', 'multizone', 'leptonic', 'models', 'are', 'compared', 'and', 'discussed', 'on', 'the', 'grounds', 'of', 'energetics', 'our', 'analysis', 'favours', 'a', 'leptonic', 'multizone', 'model', 'models', 'associated', 'to', 'the', 'xray', 'variability', 'constraint', 'supports', 'previous', 'results', 'suggesting', 'a', 'bl', 'lac', 'nature', 'of', 'pks', '0625354', 'with', 'however', 'a', 'largescale', 'jet', 'structure', 'typical', 'of', 'a', 'radio', 'galaxy']] | [-0.04943660957300488, 0.09973703790601576, -0.05724271332899875, 0.13800952822339776, -0.09154367021367173, -0.13834836560520616, 0.06598475503680461, 0.48538184082683394, -0.13496662632781356, -0.4102523234727628, 0.05469429502606063, -0.34900299680028934, 0.02708033889751224, 0.23720072470468415, -0.0002985092746230828, 0.004551044035264675, 0.11395584686440141, -0.10823775886229295, -0.0031561872778076896, -0.1540288126013954, 0.18345470276442083, 0.16109828103799373, 0.23944901391754256, 0.016339418224935585, 0.07869776975404581, -0.07382965464939309, -0.08399451369871659, -0.06964217217310387, -0.07727316558525404, 0.04562708349651931, 0.21525027234957259, 0.06266909728155416, 0.1534847534093869, -0.2794396955410347, -0.2514088375740411, 0.09305634781006067, 0.1090438932132469, -0.06259142659494982, -0.011757637196740903, -0.320074091152556, 0.06278132398284095, -0.22082393499200834, -0.15890621990787193, 0.09346879287280471, 0.019702534774756607, 0.00023415713392965057, -0.21865030873929808, 0.1439516113672118, -0.06351170452989582, 0.10890363355043947, -0.18274875359664508, -0.08888835896710481, -0.07838906643583494, 0.006233482769526103, 0.07445500248988324, 0.07513529985598699, 0.09271005097064464, -0.10673570235615924, -0.1651357493828982, 0.38425465826602545, -0.04036674950107494, 0.019301977800890147, 0.19532289830830823, -0.18223291335024816, -0.26504152181887014, 0.20855100415099193, 0.13519286763963892, 0.05295328318675542, -0.1585664052163552, 0.03759987372738097, -0.03266064047364874, 0.2839928836315213, 0.012003889526514447, 0.030389516357664594, 0.26620435836752326, 0.16553291077177754, -0.028300718765924958, 0.11925832826116889, -0.28527817830121527, 0.024056647660429864, -0.30481994716888844, 0.0055978139287189525, -0.14300352925201879, 0.12883824785650871, -0.09703217603442574, -0.06006158869165708, 0.4374767958296134, 0.03974881354198955, 0.22107921246548787, 0.02460620796910542, 0.2948948448414312, 0.09719010279856294, 0.032803363611866886, 0.14502347088008025, 0.3548653087551322, 0.09558615492355517, 0.15333446575712192, -0.15014216840294572, 0.026716485052533885, -0.056164819778710164] |
1,802.07612 | WQO dichotomy for 3-graphs | We investigate data-enriched models, like Petri nets with data, where
executability of a transition is conditioned by a relation between data values
involved. Decidability status of various decision problems in such models may
depend on the structure of data domain. According to the WQO Dichotomy
Conjecture, if a data domain is homogeneous then it either exhibits a well
quasi-order (in which case decidability follows by standard arguments), or
essentially all the decision problems are undecidable for Petri nets over that
data domain. We confirm the conjecture for data domains being 3-graphs (graphs
with 2-colored edges). On the technical level, this results is a significant
step beyond known classification results for homogeneous structures.
| cs.LO | we investigate dataenriched models like petri nets with data where executability of a transition is conditioned by a relation between data values involved decidability status of various decision problems in such models may depend on the structure of data domain according to the wqo dichotomy conjecture if a data domain is homogeneous then it either exhibits a well quasiorder in which case decidability follows by standard arguments or essentially all the decision problems are undecidable for petri nets over that data domain we confirm the conjecture for data domains being 3graphs graphs with 2colored edges on the technical level this results is a significant step beyond known classification results for homogeneous structures | [['we', 'investigate', 'dataenriched', 'models', 'like', 'petri', 'nets', 'with', 'data', 'where', 'executability', 'of', 'a', 'transition', 'is', 'conditioned', 'by', 'a', 'relation', 'between', 'data', 'values', 'involved', 'decidability', 'status', 'of', 'various', 'decision', 'problems', 'in', 'such', 'models', 'may', 'depend', 'on', 'the', 'structure', 'of', 'data', 'domain', 'according', 'to', 'the', 'wqo', 'dichotomy', 'conjecture', 'if', 'a', 'data', 'domain', 'is', 'homogeneous', 'then', 'it', 'either', 'exhibits', 'a', 'well', 'quasiorder', 'in', 'which', 'case', 'decidability', 'follows', 'by', 'standard', 'arguments', 'or', 'essentially', 'all', 'the', 'decision', 'problems', 'are', 'undecidable', 'for', 'petri', 'nets', 'over', 'that', 'data', 'domain', 'we', 'confirm', 'the', 'conjecture', 'for', 'data', 'domains', 'being', '3graphs', 'graphs', 'with', '2colored', 'edges', 'on', 'the', 'technical', 'level', 'this', 'results', 'is', 'a', 'significant', 'step', 'beyond', 'known', 'classification', 'results', 'for', 'homogeneous', 'structures']] | [-0.09754102593203923, 0.07264861539174039, -0.04553931859229599, 0.10374335970872224, -0.12449159361589868, -0.1381377139682504, 0.0879896533851688, 0.3846229960521062, -0.2959506247393988, -0.28284609211222816, 0.18032725698834806, -0.2998800683926019, -0.11748899598312271, 0.19134414095960156, -0.10965420799497683, 0.03691983421719612, 0.11849268051367756, 0.037457473571873734, -0.01759574522667036, -0.2621456855417204, 0.37783752484163186, -0.04564464754248793, 0.2735900469292123, 0.06073534142997888, 0.061990685641413204, 0.0034778650162053536, 0.003389895993792494, 0.033176181201761704, -0.13596838488074928, 0.053386594940748835, 0.3106677843169818, 0.18080995674035302, 0.24960180078549227, -0.4050695185574728, -0.18221971438148873, 0.1444688587783005, 0.09950113033053574, 0.10100448088246389, 0.0005851735010625677, -0.2737420144310506, 0.10338364299890157, -0.0912093596935675, -0.08465956684269078, -0.048961580705803795, 0.039259194004714386, 0.021474986471369997, -0.25318862376829004, 0.029396013986017253, 0.16887757486374294, 0.08792375861289534, -0.08081619196460238, -0.09764684338583024, -0.023370291688479483, 0.09738442040392542, 0.011612310818383924, 0.02011429278525054, 0.04953753855498927, -0.15067975748087037, -0.21743435313220363, 0.37591161586444927, -0.0324811057506448, -0.2161355641846721, 0.19009433928793212, -0.11938339322784429, -0.20449169062766004, 0.07272834218262385, 0.1209337572768532, 0.11246437858999916, -0.11621888159818293, 0.1177321044761721, -0.10820876337117977, 0.17464857251354, 0.08306883969176393, -0.030448111256601306, 0.1714965720736497, 0.22452696304566958, 0.0678363527509023, 0.13984856790200145, 0.010383496438530652, -0.09481636316490334, -0.2846153857991905, -0.09690714261687554, -0.15471922798891896, 0.0003611315041780472, -0.09639714412424746, -0.1935050046272777, 0.33159649018030446, 0.13129707486767256, 0.2001604886415104, 0.16531902335705823, 0.25777884660422934, 0.08371939481999557, 0.10403411837529626, 0.07171262575833647, 0.1277855616188734, 0.12857704465319444, 0.0697134805199279, -0.11594784869770478, 0.11975729505338513, 0.06340796394726715] |
1,802.07613 | About Kendall's regression | Conditional Kendall's tau is a measure of dependence between two random
variables, conditionally on some covariates. We assume a regression-type
relationship between conditional Kendall's tau and some covariates, in a
parametric setting with a large number of transformations of a small number of
regressors. This model may be sparse, and the underlying parameter is estimated
through a penalized criterion. We prove non-asymptotic bounds with explicit
constants that hold with high probabilities. We derive the consistency of a
two-step estimator, its asymptotic law and some oracle properties. Some
simulations and applications to real data conclude the paper.
| math.ST stat.ME stat.TH | conditional kendalls tau is a measure of dependence between two random variables conditionally on some covariates we assume a regressiontype relationship between conditional kendalls tau and some covariates in a parametric setting with a large number of transformations of a small number of regressors this model may be sparse and the underlying parameter is estimated through a penalized criterion we prove nonasymptotic bounds with explicit constants that hold with high probabilities we derive the consistency of a twostep estimator its asymptotic law and some oracle properties some simulations and applications to real data conclude the paper | [['conditional', 'kendalls', 'tau', 'is', 'a', 'measure', 'of', 'dependence', 'between', 'two', 'random', 'variables', 'conditionally', 'on', 'some', 'covariates', 'we', 'assume', 'a', 'regressiontype', 'relationship', 'between', 'conditional', 'kendalls', 'tau', 'and', 'some', 'covariates', 'in', 'a', 'parametric', 'setting', 'with', 'a', 'large', 'number', 'of', 'transformations', 'of', 'a', 'small', 'number', 'of', 'regressors', 'this', 'model', 'may', 'be', 'sparse', 'and', 'the', 'underlying', 'parameter', 'is', 'estimated', 'through', 'a', 'penalized', 'criterion', 'we', 'prove', 'nonasymptotic', 'bounds', 'with', 'explicit', 'constants', 'that', 'hold', 'with', 'high', 'probabilities', 'we', 'derive', 'the', 'consistency', 'of', 'a', 'twostep', 'estimator', 'its', 'asymptotic', 'law', 'and', 'some', 'oracle', 'properties', 'some', 'simulations', 'and', 'applications', 'to', 'real', 'data', 'conclude', 'the', 'paper']] | [-0.1013886974057338, 0.10674819798199071, -0.12638262957140492, 0.13223235631812713, -0.10833992840101321, -0.180683240032522, 0.1137622079756208, 0.3891228954695786, -0.2754641436113161, -0.26982696260286804, 0.12270995955987019, -0.2507586277934024, -0.164082539898421, 0.17359806066087913, -0.09374176753044594, 0.10839435108512892, 0.05526782730885316, 0.039912131847813725, -0.09268982323070911, -0.2697706708010325, 0.2693629518131881, 0.021370017838004667, 0.24557270134149198, -0.0026462104093904295, 0.1385941227307891, 0.012506249937966155, -0.05341721293128406, 0.027333901428695146, -0.15452207157106082, 0.11278993582042555, 0.2163903362234123, 0.156655446793593, 0.3479903668436843, -0.3562050958086426, -0.17410335812019184, 0.17954531125724316, 0.05977734805249687, 0.04997337483412897, -0.002933038649644004, -0.2561359434087838, 0.0695630860767172, -0.16622223789454438, -0.08240400258485654, -0.0840938666369766, -0.0021396736071134606, 0.07343181554460898, -0.414885902350458, 0.10568161426150861, 0.0720805140347996, 0.08872186104417779, -0.02593677364711766, -0.11999554278251405, 0.03835570423204141, 0.06657027451850202, 0.12097760700635263, -0.04402805966189286, 0.09037514201403003, -0.10449536292920432, -0.087235833760739, 0.27536446953248134, -0.0592641440598527, -0.28570076285783824, 0.15805168343225282, -0.1761276914718716, -0.18656487801733115, 0.03257833564809213, 0.20638511066014567, 0.09646722641059569, -0.16385064083927622, 0.10395538682496408, -0.09898015449289232, 0.1576822344432003, 0.014078173558421744, 0.05353394357856208, 0.1076988363735533, 0.13671925390372053, 0.06390378572784054, 0.14959361402604068, -0.11584774634441904, -0.04649337273440324, -0.3735761897017558, -0.15694215478288243, -0.2143164870600837, 0.026869761602332193, -0.23877358359883752, -0.1917918864528474, 0.35465863298547146, 0.1343442190955102, 0.28984101543513435, 0.17414209907777453, 0.2490547729927736, 0.13299494998257919, -0.03339319144045779, 0.07720395898407635, 0.15295879905291562, 0.20615900348639116, -0.022146865264706623, -0.16509501102458066, 0.17107542016310617, 0.056503641933280356] |
1,802.07614 | Light Scattering by Cholesteric Skyrmions | We study the light scattering by localized quasi planar excitations of a
Cholesteric Liquid Crystal known as spherulites. Due to the anisotropic optical
properties of the medium and the peculiar shape of the excitations, we
quantitatively evaluate the cross section of the axis-rotation of polarized
light. Because of the complexity of the system under consideration, first we
give a simplified, but analytical, description of the spherulite and we compare
the Born approximation results in this setting with those obtained by resorting
to a numerical exact solution. The effects of changing values of the driving
external static electric (or magnetic) field is considered. Possible
applications of the phenomenon are envisaged.
| cond-mat.soft | we study the light scattering by localized quasi planar excitations of a cholesteric liquid crystal known as spherulites due to the anisotropic optical properties of the medium and the peculiar shape of the excitations we quantitatively evaluate the cross section of the axisrotation of polarized light because of the complexity of the system under consideration first we give a simplified but analytical description of the spherulite and we compare the born approximation results in this setting with those obtained by resorting to a numerical exact solution the effects of changing values of the driving external static electric or magnetic field is considered possible applications of the phenomenon are envisaged | [['we', 'study', 'the', 'light', 'scattering', 'by', 'localized', 'quasi', 'planar', 'excitations', 'of', 'a', 'cholesteric', 'liquid', 'crystal', 'known', 'as', 'spherulites', 'due', 'to', 'the', 'anisotropic', 'optical', 'properties', 'of', 'the', 'medium', 'and', 'the', 'peculiar', 'shape', 'of', 'the', 'excitations', 'we', 'quantitatively', 'evaluate', 'the', 'cross', 'section', 'of', 'the', 'axisrotation', 'of', 'polarized', 'light', 'because', 'of', 'the', 'complexity', 'of', 'the', 'system', 'under', 'consideration', 'first', 'we', 'give', 'a', 'simplified', 'but', 'analytical', 'description', 'of', 'the', 'spherulite', 'and', 'we', 'compare', 'the', 'born', 'approximation', 'results', 'in', 'this', 'setting', 'with', 'those', 'obtained', 'by', 'resorting', 'to', 'a', 'numerical', 'exact', 'solution', 'the', 'effects', 'of', 'changing', 'values', 'of', 'the', 'driving', 'external', 'static', 'electric', 'or', 'magnetic', 'field', 'is', 'considered', 'possible', 'applications', 'of', 'the', 'phenomenon', 'are', 'envisaged']] | [-0.14342282782093174, 0.1362966863132358, -0.08765926402648566, 0.06559987705959766, -0.04866101445319752, -0.08438857667648268, 0.048470693097139396, 0.3644660893586223, -0.24021546144676567, -0.29626923835301705, 0.06444092782503166, -0.2517406178476112, -0.14189157037590458, 0.17667050073052654, 0.01792193027385683, 0.046070687364085136, -2.373920546637641e-05, 0.027859469908030912, -0.07077380491547822, -0.20132532141050669, 0.3157617324980459, 0.040122281034806896, 0.2872181037803077, 0.07432622456636401, 0.0663694908057719, 0.04738512511270259, -0.008126721493209954, 0.055389766725797755, -0.1436891067100482, 0.10759266067287643, 0.17911378737470066, 0.006836165423953423, 0.16675329189402638, -0.46360764830131773, -0.1913938283170056, 0.04891985065101094, 0.13276173430063795, 0.15885622021569698, -0.06576649996794812, -0.2858410554127423, 0.039672464826489215, -0.14451388660300937, -0.22117621685309266, -0.07669995660910865, -0.00787570953899477, 0.06110395531841614, -0.2380506010096589, 0.06022333233030858, 0.07132608465488172, 0.024587075103126053, -0.12261828183653523, -0.08116008157311524, -0.00013039512904705825, 0.08867333576091807, 0.07927916618710798, -0.0013789625135595324, 0.1408177859891482, -0.17713458153048123, -0.10355711534524474, 0.42802288456544, -0.06740803790442576, -0.16706305924257053, 0.16509901677448027, -0.1695753194184767, -0.04637301648337463, 0.16582583318921496, 0.16761186066745454, 0.1337121841260577, -0.12665924775851803, 0.07686204376039785, -0.044959498360252904, 0.13276271204705592, 0.06328152675888743, 0.054102817455444624, 0.1858137253180353, 0.18451928927701106, -0.021208983725281776, 0.1906266632959833, -0.09127321627197994, -0.08279728656688584, -0.2935815490264859, -0.11935539570684475, -0.14821906326418416, 0.054183520794915105, -0.06362180965408226, -0.19871305035970485, 0.40823720804689434, 0.13073175297015244, 0.16417867704553324, -0.016520397358194546, 0.31031122065528677, 0.12182240583826098, 0.023111741476761247, 0.027051237079797796, 0.30715817264798617, 0.17577226513337033, 0.10250907597407975, -0.26061641763145516, 0.055653776494889624, 0.026633745309448353] |
1,802.07615 | Resonant optical pulses on a continuous wave background in two-level
active media | We present exact N-soliton optical pulses riding on a continuous-wave (c.w.)
beam that propagate through and interact with a two-level active optical
medium. Their representation is derived via an appropriate generalization of
the inverse scattering transform for the corresponding Maxwell-Bloch equations.
We describe the single-soliton solutions in detail and classify them into
several distinct families. In addition to the analogues of traveling-wave
soliton pulses that arise in the absence of a c.w. beam, we obtain
breather-like structures, periodic pulse-trains and rogue-wave-type (i.e.,
rational) pulses, whose existence is directly due to the presence of the c.w.
beam. These soliton solutions are the analogues for Maxwell-Bloch systems of
the four classical solution types of the focusing nonlinear Schrodinger
equation with non-zero background, although the physical behavior of the
corresponding solutions is quite different.
| nlin.PS nlin.SI | we present exact nsoliton optical pulses riding on a continuouswave cw beam that propagate through and interact with a twolevel active optical medium their representation is derived via an appropriate generalization of the inverse scattering transform for the corresponding maxwellbloch equations we describe the singlesoliton solutions in detail and classify them into several distinct families in addition to the analogues of travelingwave soliton pulses that arise in the absence of a cw beam we obtain breatherlike structures periodic pulsetrains and roguewavetype ie rational pulses whose existence is directly due to the presence of the cw beam these soliton solutions are the analogues for maxwellbloch systems of the four classical solution types of the focusing nonlinear schrodinger equation with nonzero background although the physical behavior of the corresponding solutions is quite different | [['we', 'present', 'exact', 'nsoliton', 'optical', 'pulses', 'riding', 'on', 'a', 'continuouswave', 'cw', 'beam', 'that', 'propagate', 'through', 'and', 'interact', 'with', 'a', 'twolevel', 'active', 'optical', 'medium', 'their', 'representation', 'is', 'derived', 'via', 'an', 'appropriate', 'generalization', 'of', 'the', 'inverse', 'scattering', 'transform', 'for', 'the', 'corresponding', 'maxwellbloch', 'equations', 'we', 'describe', 'the', 'singlesoliton', 'solutions', 'in', 'detail', 'and', 'classify', 'them', 'into', 'several', 'distinct', 'families', 'in', 'addition', 'to', 'the', 'analogues', 'of', 'travelingwave', 'soliton', 'pulses', 'that', 'arise', 'in', 'the', 'absence', 'of', 'a', 'cw', 'beam', 'we', 'obtain', 'breatherlike', 'structures', 'periodic', 'pulsetrains', 'and', 'roguewavetype', 'ie', 'rational', 'pulses', 'whose', 'existence', 'is', 'directly', 'due', 'to', 'the', 'presence', 'of', 'the', 'cw', 'beam', 'these', 'soliton', 'solutions', 'are', 'the', 'analogues', 'for', 'maxwellbloch', 'systems', 'of', 'the', 'four', 'classical', 'solution', 'types', 'of', 'the', 'focusing', 'nonlinear', 'schrodinger', 'equation', 'with', 'nonzero', 'background', 'although', 'the', 'physical', 'behavior', 'of', 'the', 'corresponding', 'solutions', 'is', 'quite', 'different']] | [-0.1652790772631158, 0.10468361107192577, -0.07527647360206344, 0.06059830562958797, -0.07956225928207931, -0.13931243295976242, -0.01260678941120444, 0.40887581662440947, -0.2671498922818853, -0.23578057270641475, 0.11151070652219157, -0.29149374087131763, -0.1329555663229652, 0.22605106933042407, 0.028551006708619032, 0.05852341622316329, 0.029443187749215453, 0.005817444720702578, -0.04246563224713932, -0.15755741349818517, 0.3515824965136342, -0.04026240349725582, 0.27698392363972674, -0.044385621354864666, 0.13968509357682493, -0.00395260224941858, 0.028262202230881352, -0.07410077006707705, -0.10583020725466633, 0.10814235177136554, 0.20960616624856354, 0.05693580635079695, 0.18738162363049135, -0.46105745785631413, -0.2397092004458225, 0.11514475796544968, 0.17066321167878287, 0.17064041399952862, -0.08090146233656177, -0.3072950532515497, 0.05908973989719453, -0.11334463341031657, -0.21637638219336205, -0.06210044135029117, 0.0064952741557544515, 0.13925552635016858, -0.22174607136452845, 0.03475945917420205, 0.05726349470747072, 0.002565561578624391, -0.1255787090513884, -0.03724303271246049, -0.019805785012250953, 0.055224068401482446, 0.007976233417731385, -0.045898938515447366, 0.06584370995748991, -0.14550919727920447, -0.10024753420129996, 0.38859649320934403, -0.08845460752761641, -0.21733427082383355, 0.20581752769540734, -0.12512471734062414, -0.025483227125549502, 0.18468524944109393, 0.1642791503542211, 0.14838221141628113, -0.14004869006083223, 0.047811794550024524, -0.04332184617934647, 0.15932075334207493, 0.1721689514689465, 0.08109579978929471, 0.1878131748603065, 0.11609882303484709, 0.03562411619350314, 0.17307347389183533, -0.025263125170969816, -0.11646817363221054, -0.30100980910739694, -0.08765545566097017, -0.10263211082472184, 0.08361932502828481, -0.04869514826088223, -0.17108036884713138, 0.448886382198611, 0.09762423352091104, 0.13219236347160135, 0.003915251797613825, 0.26467823451240513, 0.19197150887993647, -0.010840222031932122, 0.021420998063819238, 0.26161329260695176, 0.1682619285307709, 0.11277067289839304, -0.2631246700292713, -0.0716883096769055, 0.0781280423709473] |
1,802.07616 | Constraining the Higgs self couplings at $e^+e^-$ colliders | We study the sensitivity to the shape of the Higgs potential of single,
double, and triple Higgs production at future $e^+e^-$ colliders. Physics
beyond the Standard Model is parameterised through the inclusion of
higher-dimensional operators $(\Phi^\dagger \Phi- v^2/2)^n/\Lambda^{(2n-4)}$
with $n=3,4$, which allows a consistent treatment of independent deviations of
the cubic and quartic self couplings beyond the tree level. We calculate the
effects induced by a modified potential up to one loop in single and double
Higgs production and at the tree level in triple Higgs production, for both $Z$
boson associated and $W$ boson fusion production mechanisms. We consider two
different scenarios. First, the dimension six operator provides the dominant
contribution (as expected, for instance, in a linear
effective-field-theory(EFT)); we find in this case that the corresponding
Wilson coefficient can be determined at $\mathcal{O}(10\%)$ accuracy by just
combining accurate measurements of single Higgs cross sections at $\sqrt{\hat
s}=$240-250 GeV and double Higgs production in $W$ boson fusion at higher
energies. Second, both operators of dimension six and eight can give effects of
similar order, i.e., independent quartic self coupling deviations are present.
Constraints on Wilson coefficients can be best tested by combining measurements
from single, double and triple Higgs production. Given that the sensitivity of
single Higgs production to the dimension eight operator is presently unknown,
we consider double and triple Higgs production and show that combining their
information colliders at higher energies will provide first coarse constraints
on the corresponding Wilson coefficient.
| hep-ph | we study the sensitivity to the shape of the higgs potential of single double and triple higgs production at future ee colliders physics beyond the standard model is parameterised through the inclusion of higherdimensional operators phidagger phi v22nlambda2n4 with n34 which allows a consistent treatment of independent deviations of the cubic and quartic self couplings beyond the tree level we calculate the effects induced by a modified potential up to one loop in single and double higgs production and at the tree level in triple higgs production for both z boson associated and w boson fusion production mechanisms we consider two different scenarios first the dimension six operator provides the dominant contribution as expected for instance in a linear effectivefieldtheoryeft we find in this case that the corresponding wilson coefficient can be determined at mathcalo10 accuracy by just combining accurate measurements of single higgs cross sections at sqrthat s240250 gev and double higgs production in w boson fusion at higher energies second both operators of dimension six and eight can give effects of similar order ie independent quartic self coupling deviations are present constraints on wilson coefficients can be best tested by combining measurements from single double and triple higgs production given that the sensitivity of single higgs production to the dimension eight operator is presently unknown we consider double and triple higgs production and show that combining their information colliders at higher energies will provide first coarse constraints on the corresponding wilson coefficient | [['we', 'study', 'the', 'sensitivity', 'to', 'the', 'shape', 'of', 'the', 'higgs', 'potential', 'of', 'single', 'double', 'and', 'triple', 'higgs', 'production', 'at', 'future', 'ee', 'colliders', 'physics', 'beyond', 'the', 'standard', 'model', 'is', 'parameterised', 'through', 'the', 'inclusion', 'of', 'higherdimensional', 'operators', 'phidagger', 'phi', 'v22nlambda2n4', 'with', 'n34', 'which', 'allows', 'a', 'consistent', 'treatment', 'of', 'independent', 'deviations', 'of', 'the', 'cubic', 'and', 'quartic', 'self', 'couplings', 'beyond', 'the', 'tree', 'level', 'we', 'calculate', 'the', 'effects', 'induced', 'by', 'a', 'modified', 'potential', 'up', 'to', 'one', 'loop', 'in', 'single', 'and', 'double', 'higgs', 'production', 'and', 'at', 'the', 'tree', 'level', 'in', 'triple', 'higgs', 'production', 'for', 'both', 'z', 'boson', 'associated', 'and', 'w', 'boson', 'fusion', 'production', 'mechanisms', 'we', 'consider', 'two', 'different', 'scenarios', 'first', 'the', 'dimension', 'six', 'operator', 'provides', 'the', 'dominant', 'contribution', 'as', 'expected', 'for', 'instance', 'in', 'a', 'linear', 'effectivefieldtheoryeft', 'we', 'find', 'in', 'this', 'case', 'that', 'the', 'corresponding', 'wilson', 'coefficient', 'can', 'be', 'determined', 'at', 'mathcalo10', 'accuracy', 'by', 'just', 'combining', 'accurate', 'measurements', 'of', 'single', 'higgs', 'cross', 'sections', 'at', 'sqrthat', 's240250', 'gev', 'and', 'double', 'higgs', 'production', 'in', 'w', 'boson', 'fusion', 'at', 'higher', 'energies', 'second', 'both', 'operators', 'of', 'dimension', 'six', 'and', 'eight', 'can', 'give', 'effects', 'of', 'similar', 'order', 'ie', 'independent', 'quartic', 'self', 'coupling', 'deviations', 'are', 'present', 'constraints', 'on', 'wilson', 'coefficients', 'can', 'be', 'best', 'tested', 'by', 'combining', 'measurements', 'from', 'single', 'double', 'and', 'triple', 'higgs', 'production', 'given', 'that', 'the', 'sensitivity', 'of', 'single', 'higgs', 'production', 'to', 'the', 'dimension', 'eight', 'operator', 'is', 'presently', 'unknown', 'we', 'consider', 'double', 'and', 'triple', 'higgs', 'production', 'and', 'show', 'that', 'combining', 'their', 'information', 'colliders', 'at', 'higher', 'energies', 'will', 'provide', 'first', 'coarse', 'constraints', 'on', 'the', 'corresponding', 'wilson', 'coefficient']] | [-0.08705193611998034, 0.19024840516185088, -0.018425586144536488, 0.11231439941730814, -0.04821048635232003, -0.1934724216179389, 0.03905659575397883, 0.3072581784026813, -0.24559161050971676, -0.26272401119934014, 0.02255594324372724, -0.31320929313876766, -0.04805935982661128, 0.19179485934106363, 0.06294150667166515, 0.06731457492390733, 0.08154985132623324, 0.06598701002764616, -0.06589740001948172, -0.27930938776319697, 0.3400963028715112, 0.06683119395709136, 0.19968107354313258, 0.11116495951082697, 0.09092102992189932, 0.07392770665237888, -0.036290761038923786, -0.04776196285340301, -0.11954575144773116, 0.12850070881166523, 0.16789631070994243, 0.04168588953826691, 0.1333218277605923, -0.3175600648111822, -0.1265476021405572, 0.14186841602479708, 0.1409226487626426, 0.07473987758041772, -0.02654720175551459, -0.23610272781278058, 0.10021891891526413, -0.20822099741177316, -0.11730423905994551, -0.059849015347219044, -0.052278961255930026, -0.07098032093290008, -0.33423536534409554, 0.07490869996976494, -0.05229486936618307, 0.030282630855642662, 0.006252246097076097, -0.16575485937339854, -0.09399406000086845, 0.050800875513775746, 0.03992320318161452, 0.011925425755074518, 0.16858338007579762, -0.17807793472236585, -0.2209409732667196, 0.38113199077021037, -0.15699968090294417, -0.18056726638704473, 0.1618375443173302, -0.2123520315848909, -0.1793736739323718, 0.14559061891239072, 0.21020768468820827, 0.0760498050710426, -0.17847580178273664, 0.16993057066565032, 0.042212179595318575, 0.1254257557602576, 0.09656012784573732, 0.03808731237171349, 0.23873418785392064, 0.16177828351414425, 0.024118932795129267, 0.08964956757666628, -0.08713185462324892, -0.08186395995896618, -0.41666058145987095, -0.1290833287465041, -0.02773019214666978, 0.043945628685946286, -0.0957449086384096, -0.10397494778605139, 0.37084108668367893, 0.0886733177662885, 0.2606465374380427, 0.020434542147044665, 0.27305442717214234, 0.14721442066172633, 0.09767184166732357, -0.005427844097347026, 0.31275803937781527, 0.12607871609956367, 0.08160348970345675, -0.2006687984930562, 0.002483903407215825, 0.10195550865288901] |
1,802.07617 | Convergence rates for smooth k-means change-point detection | In this paper, we consider the estimation of a change-point for possibly
high-dimensional data in a Gaussian model, using a k-means method. We prove
that, up to a logarithmic term, this change-point estimator has a minimax rate
of convergence. Then, considering the case of sparse data, with a Sobolev
regularity, we propose a smoothing procedure based on Lepski's method and show
that the resulting estimator attains the optimal rate of convergence. Our
results are illustrated by some simulations. As the theoretical statement
relying on Lepski's method depends on some unknown constant, practical
strategies are suggested to perform an optimal smoothing.
| math.ST stat.TH | in this paper we consider the estimation of a changepoint for possibly highdimensional data in a gaussian model using a kmeans method we prove that up to a logarithmic term this changepoint estimator has a minimax rate of convergence then considering the case of sparse data with a sobolev regularity we propose a smoothing procedure based on lepskis method and show that the resulting estimator attains the optimal rate of convergence our results are illustrated by some simulations as the theoretical statement relying on lepskis method depends on some unknown constant practical strategies are suggested to perform an optimal smoothing | [['in', 'this', 'paper', 'we', 'consider', 'the', 'estimation', 'of', 'a', 'changepoint', 'for', 'possibly', 'highdimensional', 'data', 'in', 'a', 'gaussian', 'model', 'using', 'a', 'kmeans', 'method', 'we', 'prove', 'that', 'up', 'to', 'a', 'logarithmic', 'term', 'this', 'changepoint', 'estimator', 'has', 'a', 'minimax', 'rate', 'of', 'convergence', 'then', 'considering', 'the', 'case', 'of', 'sparse', 'data', 'with', 'a', 'sobolev', 'regularity', 'we', 'propose', 'a', 'smoothing', 'procedure', 'based', 'on', 'lepskis', 'method', 'and', 'show', 'that', 'the', 'resulting', 'estimator', 'attains', 'the', 'optimal', 'rate', 'of', 'convergence', 'our', 'results', 'are', 'illustrated', 'by', 'some', 'simulations', 'as', 'the', 'theoretical', 'statement', 'relying', 'on', 'lepskis', 'method', 'depends', 'on', 'some', 'unknown', 'constant', 'practical', 'strategies', 'are', 'suggested', 'to', 'perform', 'an', 'optimal', 'smoothing']] | [-0.07405877923592925, -0.04475532276424929, -0.13806248577311636, 0.08851972126518376, -0.06403075356036425, -0.16867135206703096, 0.098923696896818, 0.4058976363763213, -0.26020232735201715, -0.24469102963339537, 0.1905172278522514, -0.22701461985241622, -0.19302753374911844, 0.23124733036151157, -0.14604922898113729, 0.1262143393466249, 0.08461988091468811, 0.028080569114536047, -0.08853885213378816, -0.3320808669948019, 0.3195673681702465, 0.07256429078057408, 0.29092312158085404, -0.005909049175679684, 0.16177395997336133, -0.0009571798844262957, -0.04739266850054264, -0.0006699535762891174, -0.18599035539737088, 0.14283991167787463, 0.21714022965403273, 0.1425119750876911, 0.3948568917810917, -0.3226503937272355, -0.21952325328253208, 0.11744557186961174, 0.1431571031268686, 0.12463317297864705, -0.07803388583590276, -0.26484201214974745, 0.09704564782092348, -0.136229805694893, -0.08239545282442123, -0.12487050835043192, -0.08691355380229653, 0.03661554453894496, -0.40343783374875786, 0.14518413554877044, 0.06317442065104842, 0.028441801597364248, -0.05455286311218515, -0.107135926829651, 0.08430196494096891, 0.02145686769508757, 0.10118832161882892, 0.014947722544893622, 0.10974979427177459, -0.0709147547883913, -0.13744089658837766, 0.3137632710300386, -0.08920819112099707, -0.25478020841255783, 0.1172504461160861, -0.08269564491230995, -0.150959418467246, 0.0930737905204296, 0.21010344832204284, 0.16738951281178743, -0.1403437374031637, 0.11013646739942487, -0.07584871326573193, 0.14008201438002288, 0.03676499427296221, -0.0210731039615348, 0.04659300319850445, 0.22021326009416953, 0.15933518360368906, 0.15206240396248177, -0.13566745087271556, -0.0768288874346763, -0.32325882025063035, -0.09519394299015403, -0.24062667451798916, -0.00321699989028275, -0.1871730795687472, -0.19221249649301173, 0.36221545793116094, 0.19124926183605567, 0.21311559991911053, 0.14798896941705608, 0.30635512731038034, 0.13349619201384486, -0.03014176708413288, 0.12818726238794625, 0.21415652190626133, 0.10329176253871993, 0.02720045727211982, -0.19447949733119457, 0.10340479214675724, 0.10177269660169258] |
1,802.07618 | On the l^{q,p} cohomology of Carnot groups | We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show
vanishing and non-vanishing results depending of the range of the (p, q) gap
with respect to the weight gaps in the Lie algebra cohomology of G.
| math.FA math.DG | we study the simplicial ell qp cohomology of carnot groups g we show vanishing and nonvanishing results depending of the range of the p q gap with respect to the weight gaps in the lie algebra cohomology of g | [['we', 'study', 'the', 'simplicial', 'ell', 'qp', 'cohomology', 'of', 'carnot', 'groups', 'g', 'we', 'show', 'vanishing', 'and', 'nonvanishing', 'results', 'depending', 'of', 'the', 'range', 'of', 'the', 'p', 'q', 'gap', 'with', 'respect', 'to', 'the', 'weight', 'gaps', 'in', 'the', 'lie', 'algebra', 'cohomology', 'of', 'g']] | [-0.27690412598447156, 0.09895524121403025, -0.07718184165274486, -0.0019397636254628499, -0.10533640001757213, -0.09916387331218292, 0.04277921919949735, 0.3450183052665148, -0.37056916503187937, -0.30469256507692477, 0.0003744617719442034, -0.2380965750139111, -0.08380402021635419, 0.15127093753275964, -0.11741841178482924, -0.02861231379210949, 0.07398095211157432, 0.15696088649714604, -0.11980666848233877, -0.2619399498575009, 0.4456901334417172, -0.023091390275229245, 0.19680783935846427, 0.08780117036822514, 0.02677114241016217, -0.030416937640462167, 0.009702447252586866, -0.03244658755377317, -0.2377308424657736, 0.11707737693228783, 0.3393502801728363, -0.06311732019560459, 0.21263411383216196, -0.30720662105924046, -0.08006045795403995, 0.22523124955403498, 0.089058195742277, -0.03322132810568198, 0.04190024158033805, -0.226304882301543, 0.18667110853279248, -0.18525512146357542, -0.12141031451905385, -0.04157572562018266, 0.11048578900786546, 0.021969295924720474, -0.20960567649215078, 0.04268928032177381, 0.10457936860620975, 0.12980468712078455, -0.10888359083746298, -0.18860627395602372, -0.09823928888027485, 0.0814684173092246, -0.02860266400071291, 0.025055225204246547, 0.1340532092950665, -0.12322652292175171, -0.1514326535547391, 0.3989756955550267, -0.09110710397362709, -0.14103523312279811, 0.09845091373874591, -0.3067015950114299, -0.16174832518952778, 0.09425218695273194, 0.06515227271339451, 0.197588095584741, 0.10679374632831568, 0.24311464583017647, -0.07600820749902572, 0.03856219709492647, 0.08818431611722097, -0.0028611618356826976, 0.09857038881343144, 0.0812327398870809, 0.12005862314254045, 0.10776100745305228, 0.013370295237296093, 0.03416373208165169, -0.4026933826315097, -0.1962370393702235, -0.18346223660195485, 0.12722465567863905, -0.15053267761406738, -0.12143060983492969, 0.4127293585393673, 0.10057756775775208, 0.21290000678840068, 0.15097883081015867, 0.1399316830226244, 0.0968810163724881, 0.08518659713892983, 0.07435512129599467, 0.11833864369262488, 0.272235183021388, -0.06696280502738097, -0.2460292065754915, -0.11078532374663971, 0.15391227962353674] |
1,802.07619 | On the local cohomology of modular invariants | We compute some numerical invariants of local cohomology of the ring of
invariants by a finite group, mainly in the modular case. Also, we present some
applications. In particular, we study Cohen-Macaulay property of modular
invariants from the viewpoints of depth, Serre's condition and the relevant
generalizations (e.g., the Buchsbaum property, etc). The situation in the local
case is different from the global case.
| math.AC | we compute some numerical invariants of local cohomology of the ring of invariants by a finite group mainly in the modular case also we present some applications in particular we study cohenmacaulay property of modular invariants from the viewpoints of depth serres condition and the relevant generalizations eg the buchsbaum property etc the situation in the local case is different from the global case | [['we', 'compute', 'some', 'numerical', 'invariants', 'of', 'local', 'cohomology', 'of', 'the', 'ring', 'of', 'invariants', 'by', 'a', 'finite', 'group', 'mainly', 'in', 'the', 'modular', 'case', 'also', 'we', 'present', 'some', 'applications', 'in', 'particular', 'we', 'study', 'cohenmacaulay', 'property', 'of', 'modular', 'invariants', 'from', 'the', 'viewpoints', 'of', 'depth', 'serres', 'condition', 'and', 'the', 'relevant', 'generalizations', 'eg', 'the', 'buchsbaum', 'property', 'etc', 'the', 'situation', 'in', 'the', 'local', 'case', 'is', 'different', 'from', 'the', 'global', 'case']] | [-0.20145421659981366, 0.03293065566685982, -0.10370343519025482, 0.08230157936668547, -0.06252820663212333, -0.10979906241846038, -0.042956355693604564, 0.29936284295399673, -0.3664446252514608, -0.21845022498746403, 0.14380204324879742, -0.24474252050276846, -0.2085215289698681, 0.1901786828530021, -0.13424691632098984, 0.027664326480589807, 0.020567658641084563, 0.08962461646297015, -0.11855259122967254, -0.29064488342555705, 0.43208078398311045, -0.003867989216814749, 0.2528730869962601, 0.0915272087440826, 0.02181314621702768, 0.026531262148637325, -0.044880618690513074, 0.02760926727205515, -0.19080103082524147, 0.1252287271854584, 0.2608093310263939, 0.09326746506849304, 0.17994546832051128, -0.4425466771062929, -0.11233434574387502, 0.1756908722454682, 0.08824964770315091, 0.06972787679660541, -0.03556311327702133, -0.25199099202654907, 0.12744777854823042, -0.18519359313359018, -0.17088506511208834, -0.07692711558775045, 0.024603986537840683, 0.040004821956244996, -0.20713285572855966, 0.027653488719352026, 0.08519753129803576, 0.17599612336198334, -0.07433635965571739, -0.06764307276171166, -0.028332820220384747, 0.08640301060950151, 0.009937498976796633, -0.07138923341335612, 0.11469703161128564, -0.18900421014404856, -0.08088487474014983, 0.39356086432235315, -0.03328480743221007, -0.21369400158437202, 0.16762351586658042, -0.15446711476397468, -0.22222464477817994, 0.05008350418211194, 0.07283260940312175, 0.20951608351242612, -0.02607348827586975, 0.16289975878953555, -0.12802930466568796, 0.019975698174675927, 0.08117800556647126, 0.05578743337537162, 0.10958241642219946, 0.051197689474065555, 0.07309816005772518, 0.20717770868213847, -0.019979109901214542, -0.044806779304053634, -0.3577150934142992, -0.20224020560272038, -0.13406400610983837, 0.07104375687777065, -0.12180653276277553, -0.11344682709022891, 0.4837994705012534, 0.14173994761222275, 0.18368217966053635, 0.07940650608361466, 0.27618518052622676, 0.049653071524517145, 0.04849584773182869, 0.027861615984875243, 0.13943218171061744, 0.1767444888864702, 0.044008702447172254, -0.14452857106334704, 0.023468355349905323, 0.17708008510817308] |
1,802.0762 | Angular and polarization trails from effective interactions of Majorana
neutrinos at the LHeC | We study the possibility of the LHeC facility to disentangle different new
physics contributions to the production of heavy sterile Majorana neutrinos in
the lepton number violating channel $e^{-}p\rightarrow l_{j}^{+} + 3 jets$
($l_j\equiv e ,\mu $). This is done investigating the angular and polarization
trails of effective operators with distinct Dirac-Lorentz structure
contributing to the Majorana neutrino production, which parameterize new
physics from a higher energy scale. We study an asymmetry in the angular
distribution of the final anti-lepton and the initial electron polarization
effect on the number of signal events produced by the vectorial and scalar
effective interactions, finding both analyses could well separate their
contributions.
| hep-ph | we study the possibility of the lhec facility to disentangle different new physics contributions to the production of heavy sterile majorana neutrinos in the lepton number violating channel eprightarrow l_j 3 jets l_jequiv e mu this is done investigating the angular and polarization trails of effective operators with distinct diraclorentz structure contributing to the majorana neutrino production which parameterize new physics from a higher energy scale we study an asymmetry in the angular distribution of the final antilepton and the initial electron polarization effect on the number of signal events produced by the vectorial and scalar effective interactions finding both analyses could well separate their contributions | [['we', 'study', 'the', 'possibility', 'of', 'the', 'lhec', 'facility', 'to', 'disentangle', 'different', 'new', 'physics', 'contributions', 'to', 'the', 'production', 'of', 'heavy', 'sterile', 'majorana', 'neutrinos', 'in', 'the', 'lepton', 'number', 'violating', 'channel', 'eprightarrow', 'l_j', '3', 'jets', 'l_jequiv', 'e', 'mu', 'this', 'is', 'done', 'investigating', 'the', 'angular', 'and', 'polarization', 'trails', 'of', 'effective', 'operators', 'with', 'distinct', 'diraclorentz', 'structure', 'contributing', 'to', 'the', 'majorana', 'neutrino', 'production', 'which', 'parameterize', 'new', 'physics', 'from', 'a', 'higher', 'energy', 'scale', 'we', 'study', 'an', 'asymmetry', 'in', 'the', 'angular', 'distribution', 'of', 'the', 'final', 'antilepton', 'and', 'the', 'initial', 'electron', 'polarization', 'effect', 'on', 'the', 'number', 'of', 'signal', 'events', 'produced', 'by', 'the', 'vectorial', 'and', 'scalar', 'effective', 'interactions', 'finding', 'both', 'analyses', 'could', 'well', 'separate', 'their', 'contributions']] | [-0.13521672140008636, 0.265554472867405, -0.05730250328612913, 0.1692771931844098, -0.06535065361032528, -0.1217505979462571, 0.0267703199138244, 0.26155328425977914, -0.24693973990423337, -0.35067559773368495, -0.03444634703697548, -0.3325542564193408, 0.005983092972920054, 0.11993619559244031, 0.10050003825731221, 0.04052452381168093, 0.0259388330425801, -0.04534634251058811, -0.027530832805981238, -0.17447154466284528, 0.3359596489440827, 0.11457388885540977, 0.24018383734815177, 0.10541792085305565, 0.06122528374461191, 0.014138689524649332, -0.11196342660003297, -0.07509848254599742, -0.09221206224922623, 0.0729963886108072, 0.16990371444927796, 0.1039961352811328, 0.1223811256600519, -0.39670357583866767, -0.14187932181216423, 0.17837189739082185, 0.15363742910502923, 0.081358958637741, -0.06859112190459633, -0.2848937879893042, 0.04177872244978235, -0.1980326416503106, -0.13444188427002657, -0.03201392928049678, 0.0015893687981934775, -0.05903899643703231, -0.32285638561394686, 0.05656926839645686, -0.027973796294758185, -0.00636156668354358, -0.003881936648949271, -0.1983232935760281, -0.03961389565263831, 0.0810556681782362, 0.14170015393534585, 0.013815373588087303, 0.15185482324367122, -0.17414579743829867, -0.15589995522695105, 0.36295584721291174, -0.07008110320062509, -0.17777001836581066, 0.1710331890382804, -0.23206503035811085, -0.1234644357602866, 0.13659767778368578, 0.2612907878078875, 0.0840291689288625, -0.18787283156610404, 0.08273392989178233, -0.010271714549855374, 0.11021991136783202, 0.04826065473524588, 0.08970491344863106, 0.27753664243168064, 0.17613216869178272, 0.03199222416040443, 0.054964814193191984, -0.13328787681557946, -0.007055627599003769, -0.3717061957610505, -0.13529571211907923, -0.1182237852719568, 0.08516486447548405, -0.050548714656144425, -0.07597304017704334, 0.46485598599188266, 0.1123304424142199, 0.2296998968791394, -0.052530500367062076, 0.2996495341793412, 0.06921974077510337, 0.06126676109921564, 0.02860551542114644, 0.277835154710781, 0.14528369946360942, 0.12272247429493638, -0.30366300252443623, 0.01588459505389134, 0.015182810436402048] |
1,802.07621 | An exact extremal result for tournaments and 4-uniform hypergraphs | In this paper, we address the following problem due to Frankl and F\"uredi
(1984). What is the maximum number of hyperedges in an $r$-uniform hypergraph
with $n$ vertices, such that every set of $r+1$ vertices contains $0$ or
exactly $2$ hyperedges? They solved this problem for $r=3$. For $r=4$, a
partial solution is given by Gunderson and Semeraro (2017) when $n=q+1$ for
some prime power number $q\equiv3\pmod{4} $. Assuming the existence of
skew-symmetric conference matrices for every order divisible by $4$, we give a
solution for $n\equiv0\pmod{4} $ and for $n\equiv3\pmod{4}$.
| math.CO | in this paper we address the following problem due to frankl and furedi 1984 what is the maximum number of hyperedges in an runiform hypergraph with n vertices such that every set of r1 vertices contains 0 or exactly 2 hyperedges they solved this problem for r3 for r4 a partial solution is given by gunderson and semeraro 2017 when nq1 for some prime power number qequiv3pmod4 assuming the existence of skewsymmetric conference matrices for every order divisible by 4 we give a solution for nequiv0pmod4 and for nequiv3pmod4 | [['in', 'this', 'paper', 'we', 'address', 'the', 'following', 'problem', 'due', 'to', 'frankl', 'and', 'furedi', '1984', 'what', 'is', 'the', 'maximum', 'number', 'of', 'hyperedges', 'in', 'an', 'runiform', 'hypergraph', 'with', 'n', 'vertices', 'such', 'that', 'every', 'set', 'of', 'r1', 'vertices', 'contains', '0', 'or', 'exactly', '2', 'hyperedges', 'they', 'solved', 'this', 'problem', 'for', 'r3', 'for', 'r4', 'a', 'partial', 'solution', 'is', 'given', 'by', 'gunderson', 'and', 'semeraro', '2017', 'when', 'nq1', 'for', 'some', 'prime', 'power', 'number', 'qequiv3pmod4', 'assuming', 'the', 'existence', 'of', 'skewsymmetric', 'conference', 'matrices', 'for', 'every', 'order', 'divisible', 'by', '4', 'we', 'give', 'a', 'solution', 'for', 'nequiv0pmod4', 'and', 'for', 'nequiv3pmod4']] | [-0.1745298345854809, 0.09259686968103187, 0.01775970755058319, 0.012986638631974889, -0.05394184418824003, -0.1852075266868396, 0.015105030533240372, 0.2998242814007194, -0.2479880332708532, -0.333199983370642, 0.10158406036938432, -0.3523307031150474, -0.1366332512792893, 0.09156494121998549, -0.12982232384058798, 0.03790318220583072, 0.05711577229505015, 0.0726910573484506, 0.054101346928333904, -0.3408203711245902, 0.32471439953850106, -0.06611919093357269, 0.10639984981389716, 0.0951004148471754, 0.0865053485342583, 0.05564151845921811, 0.03425075378279786, 0.06504579508395562, -0.1651650108374164, 0.06788092782060334, 0.2949962104822314, 0.18943212956709918, 0.28202617307041966, -0.41682639565294455, -0.12347614232634822, 0.23321122238629086, 0.12585644501256, 0.04911027985170137, -0.009184907813188295, -0.20486574499802881, 0.1736293798596815, -0.1247331460688783, -0.15610624884991625, 0.02294911803179529, 0.16566558082609675, -0.01763869663104848, -0.33278851279295807, 0.0014531057433571754, 0.12096728178737469, 0.05817239539634144, 0.011617732212640518, -0.18664776275021044, 0.018423015855490988, 0.05099061594059052, -0.026737179081930323, 0.0743775190149304, -0.04789633872556002, -0.10209768639334618, -0.1321019994008333, 0.35912843701581276, 0.0005859629627382166, -0.1859919100046851, 0.06139061273465496, -0.11249816181614648, -0.18857110624179937, 0.11816545032224683, 0.11541053423993723, 0.14798733305665232, -0.0865754719675034, 0.14864850236809551, -0.1544332082321066, 0.13984479308994704, 0.17626046271301632, -0.017194035452205773, 0.12090690069572003, 0.09665465924813044, 0.15976740120433616, 0.12737774649678274, 0.014908534534232215, 0.043279992757625015, -0.3193476850188576, -0.14265327613129344, -0.22042610655744496, 0.12050686134187895, -0.1359081826926423, -0.11714332939537112, 0.3752544250252635, 0.10159335456122535, 0.18202801897775295, 0.11368761950194142, 0.19982250413835742, 0.09425907181511595, -0.04224797519097148, 0.21458205100971944, 0.1092162215178643, 0.16158597072759687, 0.002936948372354341, -0.1168857309858986, 0.011933762970012288, 0.18154174821494623] |
1,802.07622 | Cubic Halo Bias in Eulerian and Lagrangian Space | Predictions of the next-to-leading order, i.e. one-loop, halo power spectra
depend on local and non-local bias parameters up to cubic order. The linear
bias parameter can be estimated from the large scale limit of the halo-matter
power spectrum, and the second order bias parameters from the large scale,
tree-level, bispectrum. Cubic operators would naturally be quantified using the
tree-level trispectrum. As the latter is computationally expensive, we extent
the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields
in order to estimate cubic bias parameters. We cross-correlate a basis set of
cubic bias operators with the halo field and express the result in terms of the
cross-spectra of these operators in order to cancel cosmic variance. We obtain
significant detections of local and non-local cubic bias parameters, which are
partially in tension with predictions based on local Lagrangian bias schemes.
We directly measure the Lagrangian bias parameters of the protohaloes
associated with our halo sample and clearly detect a non-local quadratic term
in Lagrangian space. We do not find a clear detection of non-local cubic
Lagrangian terms for low mass bins, but there is some mild evidence for their
presence for the highest mass bin. While the method presented here focuses on
cubic bias parameters, the approach could also be applied to quantifications of
cubic primordial non-Gaussianity.
| astro-ph.CO | predictions of the nexttoleading order ie oneloop halo power spectra depend on local and nonlocal bias parameters up to cubic order the linear bias parameter can be estimated from the large scale limit of the halomatter power spectrum and the second order bias parameters from the large scale treelevel bispectrum cubic operators would naturally be quantified using the treelevel trispectrum as the latter is computationally expensive we extent the quadratic field method proposed in schmittfull et al 2014 to cubic fields in order to estimate cubic bias parameters we crosscorrelate a basis set of cubic bias operators with the halo field and express the result in terms of the crossspectra of these operators in order to cancel cosmic variance we obtain significant detections of local and nonlocal cubic bias parameters which are partially in tension with predictions based on local lagrangian bias schemes we directly measure the lagrangian bias parameters of the protohaloes associated with our halo sample and clearly detect a nonlocal quadratic term in lagrangian space we do not find a clear detection of nonlocal cubic lagrangian terms for low mass bins but there is some mild evidence for their presence for the highest mass bin while the method presented here focuses on cubic bias parameters the approach could also be applied to quantifications of cubic primordial nongaussianity | [['predictions', 'of', 'the', 'nexttoleading', 'order', 'ie', 'oneloop', 'halo', 'power', 'spectra', 'depend', 'on', 'local', 'and', 'nonlocal', 'bias', 'parameters', 'up', 'to', 'cubic', 'order', 'the', 'linear', 'bias', 'parameter', 'can', 'be', 'estimated', 'from', 'the', 'large', 'scale', 'limit', 'of', 'the', 'halomatter', 'power', 'spectrum', 'and', 'the', 'second', 'order', 'bias', 'parameters', 'from', 'the', 'large', 'scale', 'treelevel', 'bispectrum', 'cubic', 'operators', 'would', 'naturally', 'be', 'quantified', 'using', 'the', 'treelevel', 'trispectrum', 'as', 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1,802.07623 | Explanations based on the Missing: Towards Contrastive Explanations with
Pertinent Negatives | In this paper we propose a novel method that provides contrastive
explanations justifying the classification of an input by a black box
classifier such as a deep neural network. Given an input we find what should be
%necessarily and minimally and sufficiently present (viz. important object
pixels in an image) to justify its classification and analogously what should
be minimally and necessarily \emph{absent} (viz. certain background pixels). We
argue that such explanations are natural for humans and are used commonly in
domains such as health care and criminology. What is minimally but critically
\emph{absent} is an important part of an explanation, which to the best of our
knowledge, has not been explicitly identified by current explanation methods
that explain predictions of neural networks. We validate our approach on three
real datasets obtained from diverse domains; namely, a handwritten digits
dataset MNIST, a large procurement fraud dataset and a brain activity strength
dataset. In all three cases, we witness the power of our approach in generating
precise explanations that are also easy for human experts to understand and
evaluate.
| cs.AI cs.CV cs.LG | in this paper we propose a novel method that provides contrastive explanations justifying the classification of an input by a black box classifier such as a deep neural network given an input we find what should be necessarily and minimally and sufficiently present viz important object pixels in an image to justify its classification and analogously what should be minimally and necessarily emphabsent viz certain background pixels we argue that such explanations are natural for humans and are used commonly in domains such as health care and criminology what is minimally but critically emphabsent is an important part of an explanation which to the best of our knowledge has not been explicitly identified by current explanation methods that explain predictions of neural networks we validate our approach on three real datasets obtained from diverse domains namely a handwritten digits dataset mnist a large procurement fraud dataset and a brain activity strength dataset in all three cases we witness the power of our approach in generating precise explanations that are also easy for human experts to understand and evaluate | [['in', 'this', 'paper', 'we', 'propose', 'a', 'novel', 'method', 'that', 'provides', 'contrastive', 'explanations', 'justifying', 'the', 'classification', 'of', 'an', 'input', 'by', 'a', 'black', 'box', 'classifier', 'such', 'as', 'a', 'deep', 'neural', 'network', 'given', 'an', 'input', 'we', 'find', 'what', 'should', 'be', 'necessarily', 'and', 'minimally', 'and', 'sufficiently', 'present', 'viz', 'important', 'object', 'pixels', 'in', 'an', 'image', 'to', 'justify', 'its', 'classification', 'and', 'analogously', 'what', 'should', 'be', 'minimally', 'and', 'necessarily', 'emphabsent', 'viz', 'certain', 'background', 'pixels', 'we', 'argue', 'that', 'such', 'explanations', 'are', 'natural', 'for', 'humans', 'and', 'are', 'used', 'commonly', 'in', 'domains', 'such', 'as', 'health', 'care', 'and', 'criminology', 'what', 'is', 'minimally', 'but', 'critically', 'emphabsent', 'is', 'an', 'important', 'part', 'of', 'an', 'explanation', 'which', 'to', 'the', 'best', 'of', 'our', 'knowledge', 'has', 'not', 'been', 'explicitly', 'identified', 'by', 'current', 'explanation', 'methods', 'that', 'explain', 'predictions', 'of', 'neural', 'networks', 'we', 'validate', 'our', 'approach', 'on', 'three', 'real', 'datasets', 'obtained', 'from', 'diverse', 'domains', 'namely', 'a', 'handwritten', 'digits', 'dataset', 'mnist', 'a', 'large', 'procurement', 'fraud', 'dataset', 'and', 'a', 'brain', 'activity', 'strength', 'dataset', 'in', 'all', 'three', 'cases', 'we', 'witness', 'the', 'power', 'of', 'our', 'approach', 'in', 'generating', 'precise', 'explanations', 'that', 'are', 'also', 'easy', 'for', 'human', 'experts', 'to', 'understand', 'and', 'evaluate']] | [-0.030937023077610086, 0.028371130210217324, -0.05857144591262501, 0.12176345461806848, -0.11105685361943553, -0.1553911541541515, 0.0083992717142761, 0.42758648253433157, -0.20725579290478124, -0.33021495770663023, 0.10330744260029993, -0.28706402977237877, -0.22892047070605115, 0.22094858757812422, -0.14860069419236413, 0.03370587481937915, 0.08740448849432672, 0.08850326661669304, 0.010408808138441252, -0.2800082177174895, 0.31209564535208884, 0.026600344693700238, 0.30119109006070144, 0.05495810607615649, 0.0953633003878627, -0.07128187481855472, -0.02669911665627419, 0.03332147355135777, -0.07118700144454716, 0.12340232558101101, 0.29954588466066884, 0.22320048683035199, 0.2973316256663228, -0.4193772625680385, -0.20948924264724084, 0.12724187371865167, 0.1395433313249914, 0.12656336386560194, -0.033553547832167845, -0.3059780101312764, 0.10189146899586815, -0.17788636173759953, -0.0314066784516542, -0.16926094668713304, 0.03364510053122584, -0.02931864478552107, -0.2824523663854624, 0.03386887118892006, 0.09066309293292546, 0.08528475084451938, -0.08395707248801658, -0.11447150284277924, 0.0395633911967717, 0.16577650861176296, 0.050549359246565215, 0.05426568648348866, 0.11631667466436545, -0.20113004619490946, -0.15889084108436763, 0.38440552216776636, -0.019776850211528245, -0.21063995118646325, 0.19802887132914548, -0.07957799944129322, -0.1380045930706187, 0.049727183552144956, 0.1898273612226077, 0.11927288883166869, -0.199921769587051, -0.010664258212416192, -0.07158733526208134, 0.19919950200383435, 0.0413726129315027, -0.02181668785725082, 0.22831072013699608, 0.21304298876104563, 0.00556200882354542, 0.13419647154455816, -0.10046513275154395, -0.028321851769545943, -0.2777345273434446, -0.13427693286408368, -0.1751056360074298, 0.02306449533025852, -0.08348732776717503, -0.17886643035054792, 0.3918534886259376, 0.22902496592037044, 0.21956519377051611, 0.05350056364203625, 0.32030580659250446, 0.0320793930787771, 0.09981113742105663, 0.04685176546643541, 0.19074431238329728, 0.013242384149389488, 0.07703255289862079, -0.13456514223708949, 0.08237047064683159, 0.013112534241740373] |
1,802.07624 | Endoscopic transfer for unitary Lie algebras | We give another proof of the existence of the endoscopic transfer for unitary
Lie algebras and its compatibility with Fourier transforms. By the work of
Kazhdan and Vashavsky, this implies the corresponding endoscopic fundamental
lemma (theorem of Laumon--Ng\^o). We study the compatibility between Fourier
transforms and transfers and we prove that the compatibility in the
Jacquet-Rallis setting implies the compatibility in the endoscopic setting for
unitary groups.
| math.NT | we give another proof of the existence of the endoscopic transfer for unitary lie algebras and its compatibility with fourier transforms by the work of kazhdan and vashavsky this implies the corresponding endoscopic fundamental lemma theorem of laumonngo we study the compatibility between fourier transforms and transfers and we prove that the compatibility in the jacquetrallis setting implies the compatibility in the endoscopic setting for unitary groups | [['we', 'give', 'another', 'proof', 'of', 'the', 'existence', 'of', 'the', 'endoscopic', 'transfer', 'for', 'unitary', 'lie', 'algebras', 'and', 'its', 'compatibility', 'with', 'fourier', 'transforms', 'by', 'the', 'work', 'of', 'kazhdan', 'and', 'vashavsky', 'this', 'implies', 'the', 'corresponding', 'endoscopic', 'fundamental', 'lemma', 'theorem', 'of', 'laumonngo', 'we', 'study', 'the', 'compatibility', 'between', 'fourier', 'transforms', 'and', 'transfers', 'and', 'we', 'prove', 'that', 'the', 'compatibility', 'in', 'the', 'jacquetrallis', 'setting', 'implies', 'the', 'compatibility', 'in', 'the', 'endoscopic', 'setting', 'for', 'unitary', 'groups']] | [-0.16325229254837792, 0.051599489766746186, -0.15926966031010334, 0.045356488018296656, -0.07710233069239901, -0.06217351433319541, 0.037727237650408196, 0.34800535566531693, -0.3374792690388858, -0.22621032826315898, 0.12629649027680548, -0.18266263143875852, -0.15742560792714358, 0.24830510980234696, -0.14670754745602607, 0.017695413185104442, 0.11485858164870968, 0.07124253299373846, -0.14221149573030953, -0.19861220263231258, 0.4361496158517324, -0.03241125120638082, 0.29062854574921615, 0.057437891685045685, 0.11094858741674285, 0.13876782552554057, -0.04677321762562944, -0.16268616505683614, -0.12027633725005077, 0.20409358338667796, 0.25380678997876555, 0.07821020272990259, 0.23112223876210358, -0.3679212061258463, -0.07296028126461002, 0.15603167165357332, 0.06194569579540537, 0.02710600302894958, -0.086176165440478, -0.28470595756975503, 0.11781698829279497, -0.13670465444716123, -0.12915828899265483, -0.1002821544615122, -0.021803641921052566, -0.001560317875387577, -0.2600001942079801, 0.11508373731317428, 0.1856187501205848, 0.10319834312853905, -0.14099871304351835, -0.02931117391070494, -0.0012013319020087903, 0.16992583053831298, 0.0155374713242054, -0.044150198870696704, 0.07747567391667802, -0.11254006950542904, -0.11670683010552939, 0.36622928203298494, -0.023239181276697378, -0.15871194397600796, 0.18481667683674738, -0.14530038049157995, -0.1666857498912857, 0.019291040014762145, 0.053393895551562306, 0.08679993387598257, -0.048486317020769304, 0.16343585291089346, -0.12080340524418996, 0.05840160853157823, 0.1568136828306776, 0.03852715842569104, 0.09368638229341461, 0.059777056311185545, 0.09845515203017455, 0.17536055911332368, 0.012636326196101996, -0.02749068351605764, -0.3600385322020604, -0.28974606377574114, -0.14404118200405858, 0.09002037140039297, -0.07580098647248143, -0.09436590084447884, 0.412865203160506, 0.13199644664015908, 0.19307672060452974, 0.1578125866416555, 0.23903289273954353, 0.11172659698014076, 0.0700355833539596, 0.023368693802219172, 0.20275911929515691, 0.2856178768588087, 0.0445697899048145, -0.18082240785543735, -0.046914468390437274, 0.1897226008371665] |
1,802.07625 | Fast flow-based algorithm for creating density-equalizing map
projections | Cartograms are maps that rescale geographic regions (e.g., countries,
districts) such that their areas are proportional to quantitative demographic
data (e.g., population size, gross domestic product). Unlike conventional bar
or pie charts, cartograms can represent correctly which regions share common
borders, resulting in insightful visualizations that can be the basis for
further spatial statistical analysis. Computer programs can assist data
scientists in preparing cartograms, but developing an algorithm that can
quickly transform every coordinate on the map (including points that are not
exactly on a border) while generating recognizable images has remained a
challenge. Methods that translate the cartographic deformations into
physics-inspired equations of motion have become popular, but solving these
equations with sufficient accuracy can still take several minutes on current
hardware. Here we introduce a flow-based algorithm whose equations of motion
are numerically easier to solve compared with previous methods. The equations
allow straightforward parallelization so that the calculation takes only a few
seconds even for complex and detailed input. Despite the speedup, the proposed
algorithm still keeps the advantages of previous techniques: with comparable
quantitative measures of shape distortion, it accurately scales all areas,
correctly fits the regions together and generates a map projection for every
point. We demonstrate the use of our algorithm with applications to the 2016 US
election results, the gross domestic products of Indian states and Chinese
provinces, and the spatial distribution of deaths in the London borough of
Kensington and Chelsea between 2011 and 2014.
| cs.CG | cartograms are maps that rescale geographic regions eg countries districts such that their areas are proportional to quantitative demographic data eg population size gross domestic product unlike conventional bar or pie charts cartograms can represent correctly which regions share common borders resulting in insightful visualizations that can be the basis for further spatial statistical analysis computer programs can assist data scientists in preparing cartograms but developing an algorithm that can quickly transform every coordinate on the map including points that are not exactly on a border while generating recognizable images has remained a challenge methods that translate the cartographic deformations into physicsinspired equations of motion have become popular but solving these equations with sufficient accuracy can still take several minutes on current hardware here we introduce a flowbased algorithm whose equations of motion are numerically easier to solve compared with previous methods the equations allow straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input despite the speedup the proposed algorithm still keeps the advantages of previous techniques with comparable quantitative measures of shape distortion it accurately scales all areas correctly fits the regions together and generates a map projection for every point we demonstrate the use of our algorithm with applications to the 2016 us election results the gross domestic products of indian states and chinese provinces and the spatial distribution of deaths in the london borough of kensington and chelsea between 2011 and 2014 | [['cartograms', 'are', 'maps', 'that', 'rescale', 'geographic', 'regions', 'eg', 'countries', 'districts', 'such', 'that', 'their', 'areas', 'are', 'proportional', 'to', 'quantitative', 'demographic', 'data', 'eg', 'population', 'size', 'gross', 'domestic', 'product', 'unlike', 'conventional', 'bar', 'or', 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'deaths', 'in', 'the', 'london', 'borough', 'of', 'kensington', 'and', 'chelsea', 'between', '2011', 'and', '2014']] | [-0.05333480179789032, 0.03659222985737855, -0.10702932028474742, 0.0911505959128103, -0.08692283327285494, -0.13029273860233825, 0.03604265048262312, 0.3892639109138322, -0.25498355447055765, -0.3302227787101541, 0.12142909316904456, -0.30025268401622124, -0.1504021653822426, 0.22826168884105857, -0.10594380257315006, 0.036807852621862654, 0.11568532429521525, 0.009188092074113516, -0.03661198989600252, -0.28254242166992727, 0.25707903712566677, 0.027449897403492598, 0.30739151786324953, 0.009186817224898773, 0.10909692194849964, -0.02175483681624794, -0.06076036216942323, 0.043453331017495746, -0.08340337794066742, 0.13045817616813973, 0.28222670363208197, 0.18602797038238728, 0.2840984075473181, -0.4550565046543754, -0.18525138306450795, 0.10249678751152333, 0.14979367272788754, 0.10964503989234196, 0.0005903755410292275, -0.2989835625241947, 0.04913963213238355, 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1,802.07626 | Neumann Boundary Problem for Parabolic Partial Differential Equations
with Divergence Terms | We prove an existence and uniqueness result for Neumann boundary problem of a
parabolic partial differential equation (PDE for short) with a singular
nonlinear divergence term which can only be understood in a weak sense. A
probabilistic approach is applied by studying the backward stochastic
differential equations (BSDEs for short) corresponding to the PDEs, the
solution of which turns out to be a limit of a sequence of BSDEs constructed by
penalization method.
| math.PR | we prove an existence and uniqueness result for neumann boundary problem of a parabolic partial differential equation pde for short with a singular nonlinear divergence term which can only be understood in a weak sense a probabilistic approach is applied by studying the backward stochastic differential equations bsdes for short corresponding to the pdes the solution of which turns out to be a limit of a sequence of bsdes constructed by penalization method | [['we', 'prove', 'an', 'existence', 'and', 'uniqueness', 'result', 'for', 'neumann', 'boundary', 'problem', 'of', 'a', 'parabolic', 'partial', 'differential', 'equation', 'pde', 'for', 'short', 'with', 'a', 'singular', 'nonlinear', 'divergence', 'term', 'which', 'can', 'only', 'be', 'understood', 'in', 'a', 'weak', 'sense', 'a', 'probabilistic', 'approach', 'is', 'applied', 'by', 'studying', 'the', 'backward', 'stochastic', 'differential', 'equations', 'bsdes', 'for', 'short', 'corresponding', 'to', 'the', 'pdes', 'the', 'solution', 'of', 'which', 'turns', 'out', 'to', 'be', 'a', 'limit', 'of', 'a', 'sequence', 'of', 'bsdes', 'constructed', 'by', 'penalization', 'method']] | [-0.14276803630621057, 0.0034743603895026043, -0.1236228227411231, 0.1169927036309972, -0.13459651100079287, -0.17591440871562045, -0.005686326333551272, 0.2624810806456443, -0.4095147963460178, -0.20859971608048025, 0.17284534557575792, -0.2536908610889765, -0.1252539847301294, 0.22480903644264638, -0.1155836158559645, 0.11080814914758738, 0.1214336251699659, 0.00874402606221911, -0.06816963617345445, -0.21567882800296154, 0.3529022519208797, -0.07537920428567553, 0.16846041928670585, 0.013901395933728104, 0.22394578709994276, -0.015002728691834905, -0.011094140284375786, 0.06981548579562813, -0.1343444285576219, 0.09424761306870831, 0.3106480446478275, 0.002071573931647286, 0.3682843858618544, -0.3970928671195695, -0.2143969608674923, 0.08368294124096019, 0.11353384200698849, 0.13319521456995137, -0.017681774444087115, -0.34083227598912097, 0.10321618896615628, -0.12370114273882842, -0.20039178195013985, -0.05445193355163074, -0.004398971132627905, 0.07328871689889938, -0.34427920159603126, 0.11431984488584407, 0.12237914184695237, 0.019226324425576483, -0.06996695596520623, -0.01750383422748275, -0.03537305121705549, 0.0075277647207656955, 0.0670493319949569, -0.005999229765458874, 0.0072336600493792804, -0.09375264567055114, -0.114440777133321, 0.30949249113782323, -0.15941260533075627, -0.3200074371001492, 0.11187594966031611, -0.08672239924206922, -0.0980990468077872, 0.1808102102312323, 0.14368297682743367, 0.21698398005268346, -0.2566841167512618, 0.11170269832675256, -0.06516407642430587, 0.13872141254529968, 0.08172338767206833, -0.042887394660956236, 0.09904477340870932, 0.1645208437773973, 0.18545065752600562, 0.12447052002144493, 0.03293307099733757, -0.1306869515524029, -0.3629459075323523, -0.14737351691312067, -0.10485168429066057, 0.13143595949784942, -0.09309560204525191, -0.20176245230058693, 0.3170995891145239, 0.09204218137932763, 0.16579889658876784, 0.09850545278877938, 0.2025484807266254, 0.28381115124139883, -0.02790175837604967, 0.022529293647058284, 0.2032219681431131, 0.21149854671069715, 0.1570140417020972, -0.2292523354759172, 0.06891019563573374, 0.21695466402101599] |
1,802.07627 | Readout Of Singlet-Triplet Qubits At Large Magnetic Field Gradients | Visibility of singlet-triplet qubit readout is reduced to almost zero in
large magnetic field gradients due to relaxation processes. Here we present a
new readout technique that is robust against relaxation and allows for
measurement when previously studied methods fail. This technique maps the qubit
onto spin states that are immune to relaxation using a spin dependent electron
tunneling process between the qubit and the lead. We probe this readout's
performance as a function of magnetic field gradient and applied magnetic
field, and optimize the pulse applied to the qubit through experiment and
simulation.
| cond-mat.mes-hall | visibility of singlettriplet qubit readout is reduced to almost zero in large magnetic field gradients due to relaxation processes here we present a new readout technique that is robust against relaxation and allows for measurement when previously studied methods fail this technique maps the qubit onto spin states that are immune to relaxation using a spin dependent electron tunneling process between the qubit and the lead we probe this readouts performance as a function of magnetic field gradient and applied magnetic field and optimize the pulse applied to the qubit through experiment and simulation | [['visibility', 'of', 'singlettriplet', 'qubit', 'readout', 'is', 'reduced', 'to', 'almost', 'zero', 'in', 'large', 'magnetic', 'field', 'gradients', 'due', 'to', 'relaxation', 'processes', 'here', 'we', 'present', 'a', 'new', 'readout', 'technique', 'that', 'is', 'robust', 'against', 'relaxation', 'and', 'allows', 'for', 'measurement', 'when', 'previously', 'studied', 'methods', 'fail', 'this', 'technique', 'maps', 'the', 'qubit', 'onto', 'spin', 'states', 'that', 'are', 'immune', 'to', 'relaxation', 'using', 'a', 'spin', 'dependent', 'electron', 'tunneling', 'process', 'between', 'the', 'qubit', 'and', 'the', 'lead', 'we', 'probe', 'this', 'readouts', 'performance', 'as', 'a', 'function', 'of', 'magnetic', 'field', 'gradient', 'and', 'applied', 'magnetic', 'field', 'and', 'optimize', 'the', 'pulse', 'applied', 'to', 'the', 'qubit', 'through', 'experiment', 'and', 'simulation']] | [-0.10558849507744641, 0.187253322571199, -0.06394761625399932, 0.035633596733551966, -0.012424780848495503, -0.19449897852052558, 0.039490130673004116, 0.42404523563194785, -0.26333313056842444, -0.30209901397849653, 0.050896281642750146, -0.21758935558426992, -0.10285079437109859, 0.2500991648449463, -0.012679127010298854, 0.08972486652473503, 0.0519628134417407, -0.05020032193947663, -0.08050880344842185, -0.22113918017799114, 0.26944292122696306, 0.0648373382641597, 0.3132509538517433, 0.034901222838287026, 0.14600867083533964, 0.03372823891596512, 0.06821765788295801, 0.02297726091235242, -0.10606449859373475, 0.040743180413784934, 0.25376880320254713, 0.0673861552916586, 0.20754558450364052, -0.48585588108015026, -0.15357518503244252, 0.0662131397984922, 0.13952612463246158, 0.19887203083155638, -0.06083982029652342, -0.2746776939528261, 0.03369284538116227, -0.1413218464920337, -0.06006329090512814, -0.15151020733917014, -0.010857580359678399, -0.006919115083292127, -0.30393700251117983, 0.08190914501307255, 0.058762401223499725, 0.028760749549466245, -0.04501250223813955, -0.03244810154106706, 0.042451700453269986, 0.0934740835314671, 0.021265052620289313, 0.10097500991987739, 0.22774789037499973, -0.0734474418308348, -0.14937600112480529, 0.25071938233846364, -0.11033167825773993, -0.20354900622066666, 0.1852047845939214, -0.15122122518678613, -0.05406711628026468, 0.12778336219885883, 0.14954710644025832, 0.12307691602828971, -0.17590534334158292, 0.03406438728524471, 0.07465734966396492, 0.18582267071704994, 0.01679352599572628, 0.07384582306753765, 0.17995586246995138, 0.17283663937098723, 0.15152060012630325, 0.17956805418423832, -0.17663056891104403, -0.07039381048216069, -0.23231148768830648, -0.15148961336966207, -0.21717873968164178, 0.09955882174805045, -0.008582526004713455, -0.13749419758096337, 0.4425710915003289, 0.1864593467338288, 0.16060228128620285, -0.03178140969867719, 0.3347639196968459, 0.13959513018972816, 0.10765396838789766, 0.01589548921688123, 0.23796171425504886, 0.25957425772162906, 0.10316637356919138, -0.3514872214638014, 0.048302296908235454, -0.026297307112551432] |
1,802.07628 | On the fast quenching of young low-mass galaxies up to z $\sim$ 0.6: new
spotlight on the lead role of environment | We investigate the connection between environment and the different quenching
channels that galaxies are prone to follow in the rest-frame NUVrK colour
diagram, as identified by Moutard et al. (2016b). Namely, the fast quenching
channel followed by $young$ low-mass galaxies and the slow quenching channel
followed by $old$ high-mass ones. We make use of the >22 deg$^2$ covered the
VIPERS Multi-Lambda Survey (VIPERS-MLS) to select a galaxy sample complete down
to stellar masses of $M_* > 10^{9.4} M_\odot$ at $z < 0.65$ ($M_* > 10^{8.8}
M_\odot$ at $z < 0.5$) and including 33,500 (43,000) quiescent galaxies
properly selected at $0.2 < z < 0.65$, while being characterized by reliable
photometric redshifts ($\sigma_{\delta z/(1+z)} \leq 0.04$) that we use to
measure galaxy local densities. We find that (1) the quiescence of low-mass
[$M_* \leq 10^{9.7} M_\odot$] galaxies requires a strong increase of the local
density, which confirms the lead role played by environment in their fast
quenching and, therefore, confirms that the low-mass upturn observed in the
stellar mass function of quiescent galaxies is due to $environmental$
$quenching$. We also observe that (2) the reservoir of low-mass star-forming
galaxies located in very dense regions (prone to environmental quenching) has
grown between $z \sim 0.6$ and $ z \sim 0.4$ whilst the share of low-mass
quiescent galaxies (expected to being environmentally quenched) may have
simultaneously increased, which would plead for a rising importance of
$environmental$ $quenching$ with cosmic time, compared to $mass$ $quenching$.
We finally discuss the composite picture of such environmental quenching of
low-mass galaxies and, in particular, how this picture may be consistent with a
$delayed$-$then$-$rapid$ quenching scenario.
| astro-ph.GA | we investigate the connection between environment and the different quenching channels that galaxies are prone to follow in the restframe nuvrk colour diagram as identified by moutard et al 2016b namely the fast quenching channel followed by young lowmass galaxies and the slow quenching channel followed by old highmass ones we make use of the 22 deg2 covered the vipers multilambda survey vipersmls to select a galaxy sample complete down to stellar masses of m_ 1094 m_odot at z 065 m_ 1088 m_odot at z 05 and including 33500 43000 quiescent galaxies properly selected at 02 z 065 while being characterized by reliable photometric redshifts sigma_delta z1z leq 004 that we use to measure galaxy local densities we find that 1 the quiescence of lowmass m_ leq 1097 m_odot galaxies requires a strong increase of the local density which confirms the lead role played by environment in their fast quenching and therefore confirms that the lowmass upturn observed in the stellar mass function of quiescent galaxies is due to environmental quenching we also observe that 2 the reservoir of lowmass starforming galaxies located in very dense regions prone to environmental quenching has grown between z sim 06 and z sim 04 whilst the share of lowmass quiescent galaxies expected to being environmentally quenched may have simultaneously increased which would plead for a rising importance of environmental quenching with cosmic time compared to mass quenching we finally discuss the composite picture of such environmental quenching of lowmass galaxies and in particular how this picture may be consistent with a delayedthenrapid quenching scenario | [['we', 'investigate', 'the', 'connection', 'between', 'environment', 'and', 'the', 'different', 'quenching', 'channels', 'that', 'galaxies', 'are', 'prone', 'to', 'follow', 'in', 'the', 'restframe', 'nuvrk', 'colour', 'diagram', 'as', 'identified', 'by', 'moutard', 'et', 'al', '2016b', 'namely', 'the', 'fast', 'quenching', 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1,802.07629 | Extreme cooperative swelling in topologically disordered fibre
entanglements | Entangled states are ubiquitous amongst fibrous materials, whether naturally
occurring (keratin, collagen, DNA) or synthetic (nanotube assemblies,
elastane). A key mechanical characteristic of these systems is their ability to
reorganise in response to external stimuli, as implicated in e.g.
hydration-induced swelling of keratin fibrils in human skin. During swelling,
the curvature of individual fibres changes to give a cooperative and reversible
structural reorganisation that opens up a pore network. The phenomenon is known
to be highly dependent on topology, even if the nature of this dependence is
not well understood: certain ordered entanglements (`weavings') can swell to
many times their original volume while others are entirely incapable of
swelling at all. Given this sensitivity to topology, it is puzzling how the
disordered entanglements of many real materials manage to support cooperative
dilation mechanisms. Here we use a combination of geometric and
lattice-dynamical modelling to study the effect of disorder on swelling
behaviour. The model system we devise spans a continuum of disordered
topologies and is bounded by ordered states whose swelling behaviour is already
known to be either vanishingly small or extreme. We find that while topological
disorder often quenches swelling behaviour, certain disordered states possess a
surprisingly large swelling capacity. Crucially, we show that the extreme
swelling response previously observed only for certain specific weavings can be
matched---and even superseded---by that of disordered entanglements. Our
results establish a counterintuitive link between topological disorder and
mechanical flexibility that has implications not only for polymer science but
also for our broader understanding of collective phenomena in disordered
systems.
| cond-mat.soft cond-mat.mtrl-sci | entangled states are ubiquitous amongst fibrous materials whether naturally occurring keratin collagen dna or synthetic nanotube assemblies elastane a key mechanical characteristic of these systems is their ability to reorganise in response to external stimuli as implicated in eg hydrationinduced swelling of keratin fibrils in human skin during swelling the curvature of individual fibres changes to give a cooperative and reversible structural reorganisation that opens up a pore network the phenomenon is known to be highly dependent on topology even if the nature of this dependence is not well understood certain ordered entanglements weavings can swell to many times their original volume while others are entirely incapable of swelling at all given this sensitivity to topology it is puzzling how the disordered entanglements of many real materials manage to support cooperative dilation mechanisms here we use a combination of geometric and latticedynamical modelling to study the effect of disorder on swelling behaviour the model system we devise spans a continuum of disordered topologies and is bounded by ordered states whose swelling behaviour is already known to be either vanishingly small or extreme we find that while topological disorder often quenches swelling behaviour certain disordered states possess a surprisingly large swelling capacity crucially we show that the extreme swelling response previously observed only for certain specific weavings can be matchedand even supersededby that of disordered entanglements our results establish a counterintuitive link between topological disorder and mechanical flexibility that has implications not only for polymer science but also for our broader understanding of collective phenomena in disordered systems | [['entangled', 'states', 'are', 'ubiquitous', 'amongst', 'fibrous', 'materials', 'whether', 'naturally', 'occurring', 'keratin', 'collagen', 'dna', 'or', 'synthetic', 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1,802.0763 | Diffractive shear interferometry for extreme ultraviolet high-resolution
lensless imaging | We demonstrate a novel imaging approach and associated reconstruction
algorithm for far-field coherent diffractive imaging, based on the measurement
of a pair of laterally sheared diffraction patterns. The differential phase
profile retrieved from such a measurement leads to improved reconstruction
accuracy, increased robustness against noise, and faster convergence compared
to traditional coherent diffractive imaging methods. We measure laterally
sheared diffraction patterns using Fourier-transform spectroscopy with two
phase-locked pulse pairs from a high harmonic source. Using this approach, we
demonstrate spectrally resolved imaging at extreme ultraviolet wavelengths
between 28 and 35 nm.
| physics.optics | we demonstrate a novel imaging approach and associated reconstruction algorithm for farfield coherent diffractive imaging based on the measurement of a pair of laterally sheared diffraction patterns the differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy increased robustness against noise and faster convergence compared to traditional coherent diffractive imaging methods we measure laterally sheared diffraction patterns using fouriertransform spectroscopy with two phaselocked pulse pairs from a high harmonic source using this approach we demonstrate spectrally resolved imaging at extreme ultraviolet wavelengths between 28 and 35 nm | [['we', 'demonstrate', 'a', 'novel', 'imaging', 'approach', 'and', 'associated', 'reconstruction', 'algorithm', 'for', 'farfield', 'coherent', 'diffractive', 'imaging', 'based', 'on', 'the', 'measurement', 'of', 'a', 'pair', 'of', 'laterally', 'sheared', 'diffraction', 'patterns', 'the', 'differential', 'phase', 'profile', 'retrieved', 'from', 'such', 'a', 'measurement', 'leads', 'to', 'improved', 'reconstruction', 'accuracy', 'increased', 'robustness', 'against', 'noise', 'and', 'faster', 'convergence', 'compared', 'to', 'traditional', 'coherent', 'diffractive', 'imaging', 'methods', 'we', 'measure', 'laterally', 'sheared', 'diffraction', 'patterns', 'using', 'fouriertransform', 'spectroscopy', 'with', 'two', 'phaselocked', 'pulse', 'pairs', 'from', 'a', 'high', 'harmonic', 'source', 'using', 'this', 'approach', 'we', 'demonstrate', 'spectrally', 'resolved', 'imaging', 'at', 'extreme', 'ultraviolet', 'wavelengths', 'between', '28', 'and', '35', 'nm']] | [-0.0448575310439772, 0.11224261387814205, -0.11245211744476315, 0.051310867617408246, -0.001339920338468401, -0.14654695052285116, 0.049487763858441225, 0.5140332925941918, -0.29110886891382737, -0.31912830570241907, 0.06664370239333628, -0.31514634503368905, -0.1325346030253958, 0.25716451691414977, -0.04549133550928353, 0.1170345564874319, 0.1202927778915062, -0.09547552838921547, -0.044101088761945594, -0.1008384022042974, 0.2624159520082585, 0.03856163846513072, 0.3614996058027168, 0.008563340467574832, 0.15202536706167918, 0.062290137367589135, -0.08234139165974089, 0.013917060888751031, -0.09805860667192674, 0.10997422479104589, 0.22866829700133467, 0.05985492036503914, 0.2206383218661278, -0.39561730142744195, -0.20269518164447048, 0.01780791274159328, 0.16723006308797728, 0.10206241832769752, -0.09470151639722574, -0.3257103197297061, 0.041924055583856916, -0.07714830125057763, -0.1093532323305096, -0.09280024821982606, -0.09734730954681124, 0.007028324493708519, -0.30664653496837224, 0.11042017406773763, -0.03292384135772239, 0.1232416331870379, -0.08341349769833979, -0.02192859007250313, 0.014283086899872665, 0.04431054819948398, -0.06551936792803335, 0.054674147065360466, 0.159030662670445, -0.12352226531020478, -0.14301778283993621, 0.3008682521899323, -0.10763262792306205, -0.10492916409294684, 0.19343696936074603, -0.21069622227594584, -0.03526427126029036, 0.27990910383248396, 0.16967568306283062, 0.15774352207861758, -0.11763822143017263, -0.06289378963449233, 0.03617967396033007, 0.2610073836295159, 0.17524469853634692, 0.08762988996702237, 0.16424732811871792, 0.21573096020710092, 0.04288048687094188, 0.158940892510505, -0.26195150035354153, -0.014670099633244367, -0.21482859924435616, -0.07785637149041016, -0.14653786114713813, 0.04561930659974178, -0.07961220585355397, -0.1448964789960083, 0.36831168515177876, 0.16982310331825698, 0.1493040431971447, -0.007326885945276244, 0.41154110775544095, 0.08912610383397275, 0.04790295392996376, -0.01988086649881942, 0.2563366211623281, 0.19202638712486478, 0.16062960563391282, -0.2360138844872651, -0.03367484293898547, -0.0008072844440383571] |
1,802.07631 | Koll\'ar's injectivity theorem for globally $F$-regular varieties | We prove Koll\'ar's injectivity theorem for globally $F$-regular varieties.
| math.AG math.AC | we prove kollars injectivity theorem for globally fregular varieties | [['we', 'prove', 'kollars', 'injectivity', 'theorem', 'for', 'globally', 'fregular', 'varieties']] | [-0.32115849521425033, -0.11620748156888618, -0.16274521955185467, 0.2971620372393065, -0.036204440519213676, -0.3588213407331043, -0.050003132679396205, 0.28221047669649124, -0.37319893886645633, 0.024573464670942888, 0.18470423854887486, -0.17990144880281556, -0.15143034358819327, 0.3233218482799, -0.4448141290081872, -0.07151658584674199, 0.0601347159439077, 0.016788359110554058, -0.09913307076527013, -0.4289321901483668, 0.5503838691446516, -0.2158831437474065, 0.24032637228568396, 0.3635486794842614, 0.09924461527003182, 0.09247781626052326, 0.010684468886918493, -0.10919886661900415, -0.27051594605048496, 0.09531808127131727, 0.5236544066833125, 0.15969668750444221, 0.18077574918667474, -0.30395747121009564, -0.04604891480671035, 0.42908269653303754, 0.11615319756997956, -0.0038575438989533316, -0.014905688585713506, -0.2718467571669155, 0.22724691364500257, -0.04332099730769793, -0.4475751618544261, -0.22685199665526548, 0.05201250521673097, 0.11488907515174812, -0.25474310997459626, 0.043195327950848475, 0.36561699853175217, 0.23639747572855818, -0.18899415764543745, 0.008019154270490011, -0.10766273654169506, -0.14932911015219158, -0.06697891590495904, 0.027103493507537577, 0.19561901031475928, 0.045149057689640254, -0.01944547187950876, 0.14452333942366144, -0.0667843297123909, -0.23522967182927662, 0.010297538195219304, -0.1416067828734716, -0.2681861116240422, 0.04245407920744684, -0.03305076538688607, 0.35082076655493843, 0.17375677679147986, 0.23394489329722193, -0.3111633277601666, 0.007187285150090854, 0.24064934833182228, 0.002182406269841724, 0.10556593164801598, 0.004570673737261031, 0.340005937549803, 0.11979605423079596, 0.1684284491671456, 0.15384146695335707, -0.39529014461570317, -0.2074338860499362, -0.0142613442407714, 0.35792353997627896, -0.19543873420399097, -0.23589931428432465, 0.24594918514291444, 0.033696652545283236, -0.003857566871576839, 0.5096890848750869, 0.18643702199268672, -0.09790478067265616, -0.04675823957141903, 0.16386088304635552, 0.21452647406193945, 0.44157038753231365, -0.07643588653041257, 0.0222484672235118, -0.13260302941004434, 0.5510794611440765] |
1,802.07632 | Spanning Tree Congestion and Computation of Generalized
Gy\H{o}ri-Lov\'{a}sz Partition | We study a natural problem in graph sparsification, the Spanning Tree
Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree
with no tree-edge \emph{routing} too many of the original edges. The root of
this problem dates back to at least 30 years ago, motivated by applications in
network design, parallel computing and circuit design. Variants of the problem
have also seen algorithmic applications as a preprocessing step of several
important graph algorithms.
For any general connected graph with $n$ vertices and $m$ edges, we show that
its STC is at most $\mathcal{O}(\sqrt{mn})$, which is asymptotically optimal
since we also demonstrate graphs with STC at least $\Omega(\sqrt{mn})$. We
present a polynomial-time algorithm which computes a spanning tree with
congestion $\mathcal{O}(\sqrt{mn}\cdot \log n)$. We also present another
algorithm for computing a spanning tree with congestion
$\mathcal{O}(\sqrt{mn})$; this algorithm runs in sub-exponential time when $m =
\omega(n \log^2 n)$.
For achieving the above results, an important intermediate theorem is
\emph{generalized Gy\H{o}ri-Lov\'{a}sz theorem}, for which Chen et al. gave a
non-constructive proof. We give the first elementary and constructive proof by
providing a local search algorithm with running time $\mathcal{O}^*\left( 4^n
\right)$, which is a key ingredient of the above-mentioned sub-exponential time
algorithm. We discuss a few consequences of the theorem concerning graph
partitioning, which might be of independent interest.
We also show that for any graph which satisfies certain \emph{expanding
properties}, its STC is at most $\mathcal{O}(n)$, and a corresponding spanning
tree can be computed in polynomial time. We then use this to show that a random
graph has STC $\Theta(n)$ with high probability.
| cs.DS cs.CC cs.DM | we study a natural problem in graph sparsification the spanning tree congestion stc problem informally the stc problem seeks a spanning tree with no treeedge emphrouting too many of the original edges the root of this problem dates back to at least 30 years ago motivated by applications in network design parallel computing and circuit design variants of the problem have also seen algorithmic applications as a preprocessing step of several important graph algorithms for any general connected graph with n vertices and m edges we show that its stc is at most mathcalosqrtmn which is asymptotically optimal since we also demonstrate graphs with stc at least omegasqrtmn we present a polynomialtime algorithm which computes a spanning tree with congestion mathcalosqrtmncdot log n we also present another algorithm for computing a spanning tree with congestion mathcalosqrtmn this algorithm runs in subexponential time when m omegan log2 n for achieving the above results an important intermediate theorem is emphgeneralized gyhorilovasz theorem for which chen et al gave a nonconstructive proof we give the first elementary and constructive proof by providing a local search algorithm with running time mathcaloleft 4n right which is a key ingredient of the abovementioned subexponential time algorithm we discuss a few consequences of the theorem concerning graph partitioning which might be of independent interest we also show that for any graph which satisfies certain emphexpanding properties its stc is at most mathcalon and a corresponding spanning tree can be computed in polynomial time we then use this to show that a random graph has stc thetan with high probability | [['we', 'study', 'a', 'natural', 'problem', 'in', 'graph', 'sparsification', 'the', 'spanning', 'tree', 'congestion', 'stc', 'problem', 'informally', 'the', 'stc', 'problem', 'seeks', 'a', 'spanning', 'tree', 'with', 'no', 'treeedge', 'emphrouting', 'too', 'many', 'of', 'the', 'original', 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'can', 'be', 'computed', 'in', 'polynomial', 'time', 'we', 'then', 'use', 'this', 'to', 'show', 'that', 'a', 'random', 'graph', 'has', 'stc', 'thetan', 'with', 'high', 'probability']] | [-0.14357586705866526, 0.09582822138309986, -0.08819113298792275, 0.05030113618223246, -0.08909549181510908, -0.16393451159086636, 0.0937501352196046, 0.37420044210922765, -0.280949616402307, -0.3546118190801724, 0.11823267894604529, -0.22903249097078687, -0.19230043111924966, 0.16211913063605207, -0.09224329539391352, 0.06551335018181323, 0.09792289105161482, 0.06189972635607902, -0.004677073073969406, -0.3095320178043211, 0.24249620823735943, 0.0341238162570127, 0.18620236207388238, 0.07721956091287627, 0.13049195949208198, 0.025891417070973928, -0.03804407306528819, 0.03463326167364744, -0.13042375555155522, 0.08574556585219799, 0.3019690862325145, 0.20319451189594318, 0.3046246714941336, -0.39672573109172965, -0.15735196145654723, 0.18063300467044938, 0.1483347911633346, 0.1137840029660715, 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1,802.07633 | G\^Ateaux-Differentiability of Convex Functions in Infinite Dimension | It is well known that in $R^n$ , G{\^a}teaux (hence Fr{\'e}chet)
differ-entiability of a convex continuous function at some point is equivalent
to the existence of the partial derivatives at this point. We prove that this
result extends naturally to certain infinite dimensional vector spaces, in
particular to Banach spaces having a Schauder basis.
| math.FA | it is well known that in rn gateaux hence frechet differentiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point we prove that this result extends naturally to certain infinite dimensional vector spaces in particular to banach spaces having a schauder basis | [['it', 'is', 'well', 'known', 'that', 'in', 'rn', 'gateaux', 'hence', 'frechet', 'differentiability', 'of', 'a', 'convex', 'continuous', 'function', 'at', 'some', 'point', 'is', 'equivalent', 'to', 'the', 'existence', 'of', 'the', 'partial', 'derivatives', 'at', 'this', 'point', 'we', 'prove', 'that', 'this', 'result', 'extends', 'naturally', 'to', 'certain', 'infinite', 'dimensional', 'vector', 'spaces', 'in', 'particular', 'to', 'banach', 'spaces', 'having', 'a', 'schauder', 'basis']] | [-0.0971856036768207, 0.06503699922863886, -0.08282208970730316, 0.12946358635881036, -0.11779839517372959, -0.059843040001139325, 0.031840627064120094, 0.40838439258711656, -0.37958988568411683, -0.09241410431821111, 0.1543453953378254, -0.26306245296771796, -0.14780243496709275, 0.13911155674536274, -0.16061137501097653, 0.08937092295865405, -0.002947266881336581, 0.08918355985210752, -0.1771665527661032, -0.2854975888259568, 0.42036962707720277, -0.08068854530464928, 0.17889355398925408, 0.052232120722040254, 0.17915782611817122, 0.023172002048495243, 0.04396297523910004, 0.008115719828122068, -0.14622123726728187, 0.11149007459786141, 0.3361853986697377, 0.08164440026454065, 0.35852806712940055, -0.31649392070073, -0.21248536750252517, 0.21027069114684566, 0.07389717763465531, -0.023259585635420285, -0.017820621599039098, -0.2669733192613524, 0.10425895677422578, -0.09128597596625113, -0.22901529990980085, -0.10948862633580025, 0.03656223389091638, 0.05147242031218308, -0.3233402969034494, 0.03877796652674113, 0.1417210308224279, 0.047410928349906824, -0.13861208243893003, -0.07233134233656358, -0.08056841179605503, 0.008305362258809354, 0.03429420166736785, 0.16783640644390066, 0.05000045759392516, -0.010098527477343593, -0.0929606062939988, 0.3182593688790528, -0.05647139926001711, -0.2914976040779982, 0.19773458339765948, -0.2390476362252573, -0.17893600463867188, 0.11051977380126152, 0.12027678766973177, 0.15479681923774616, -0.10932855329142427, 0.1915231612071676, -0.12415496600826956, 0.09715355135487252, 0.13299917503488515, 0.08404717655887581, 0.08657748680913223, 0.10668364601684208, 0.21375211375712785, 0.1461748521036978, 0.05998293389478382, -0.10734160354949604, -0.4052970434697169, -0.1897122929628306, -0.18614785831623692, 0.11380559697149778, -0.1203550326639022, -0.23578330376273338, 0.3150006326723774, 0.10923387271347719, 0.19638002774555166, 0.1294233537331786, 0.2308245670788412, 0.148592218088935, 0.022815710504732606, 0.061927521812184805, 0.17807374375637286, 0.13561040154693402, 0.06360441623782774, -0.06381092376936719, 0.011019810788192839, 0.21642669155877434] |
1,802.07634 | Stochastic Model Predictive Control of Air Conditioning System for
Electric Vehicles: Sensitivity Study, Comparison and Improvement | A stochastic model predictive controller (SMPC) of air conditioning (AC)
system is proposed to improve the energy efficiency of electric vehicles (EV).
A Markov-chain based velocity predictor is adopted to provide a sense of the
future disturbances over the SMPC control horizon. The sensitivity of
electrified AC plant to solar radiation, ambient temperature and relative air
flow speed is quantificationally analyzed from an energy efficiency
perspective. Three control approaches are compared in terms of the electricity
consumption, cabin temperature, and comfort fluctuation, which are (i) the
proposed SMPC method, (ii) a generally used bang-bang controller and (iii)
dynamic programming (DP) as the benchmark. Real solar radiation and ambient
temperature data are measured to validate the effectiveness of the SMPC.
Comparison results illustrate that SMPC is able to improve the AC energy
economy by 12% than rule-based controller. The cabin temperature variation is
reduced by over 50.4%, resulting with a much better cabin comfort.
| cs.SY math.OC | a stochastic model predictive controller smpc of air conditioning ac system is proposed to improve the energy efficiency of electric vehicles ev a markovchain based velocity predictor is adopted to provide a sense of the future disturbances over the smpc control horizon the sensitivity of electrified ac plant to solar radiation ambient temperature and relative air flow speed is quantificationally analyzed from an energy efficiency perspective three control approaches are compared in terms of the electricity consumption cabin temperature and comfort fluctuation which are i the proposed smpc method ii a generally used bangbang controller and iii dynamic programming dp as the benchmark real solar radiation and ambient temperature data are measured to validate the effectiveness of the smpc comparison results illustrate that smpc is able to improve the ac energy economy by 12 than rulebased controller the cabin temperature variation is reduced by over 504 resulting with a much better cabin comfort | [['a', 'stochastic', 'model', 'predictive', 'controller', 'smpc', 'of', 'air', 'conditioning', 'ac', 'system', 'is', 'proposed', 'to', 'improve', 'the', 'energy', 'efficiency', 'of', 'electric', 'vehicles', 'ev', 'a', 'markovchain', 'based', 'velocity', 'predictor', 'is', 'adopted', 'to', 'provide', 'a', 'sense', 'of', 'the', 'future', 'disturbances', 'over', 'the', 'smpc', 'control', 'horizon', 'the', 'sensitivity', 'of', 'electrified', 'ac', 'plant', 'to', 'solar', 'radiation', 'ambient', 'temperature', 'and', 'relative', 'air', 'flow', 'speed', 'is', 'quantificationally', 'analyzed', 'from', 'an', 'energy', 'efficiency', 'perspective', 'three', 'control', 'approaches', 'are', 'compared', 'in', 'terms', 'of', 'the', 'electricity', 'consumption', 'cabin', 'temperature', 'and', 'comfort', 'fluctuation', 'which', 'are', 'i', 'the', 'proposed', 'smpc', 'method', 'ii', 'a', 'generally', 'used', 'bangbang', 'controller', 'and', 'iii', 'dynamic', 'programming', 'dp', 'as', 'the', 'benchmark', 'real', 'solar', 'radiation', 'and', 'ambient', 'temperature', 'data', 'are', 'measured', 'to', 'validate', 'the', 'effectiveness', 'of', 'the', 'smpc', 'comparison', 'results', 'illustrate', 'that', 'smpc', 'is', 'able', 'to', 'improve', 'the', 'ac', 'energy', 'economy', 'by', '12', 'than', 'rulebased', 'controller', 'the', 'cabin', 'temperature', 'variation', 'is', 'reduced', 'by', 'over', '504', 'resulting', 'with', 'a', 'much', 'better', 'cabin', 'comfort']] | [-0.08890198561168136, 0.061385968676559, -0.060060660088483514, 0.03627170399637905, -0.0694420655665834, -0.14990877082839218, 0.06906587329200085, 0.3649423160389358, -0.24781956374523492, -0.3527547273803137, 0.12187971242711487, -0.27603265442855024, -0.07440042748493356, 0.26549455657558746, -0.13333058141147583, 0.09660690800085955, 0.0372228907456232, 0.029923653330698036, -0.011156291035886586, -0.22424995458800517, 0.2021438112190249, 0.13258609169899346, 0.3484646470614654, 0.04338330433101339, 0.13299392967780116, -0.06128203701281165, 0.019048722471518356, 0.07006619581136643, -0.07556787329225449, 0.09791961072463226, 0.27831531654483355, 0.12461113562393519, 0.28639645913457557, -0.40894133312128533, -0.25873720591729565, 0.08043831557619806, 0.06885516866596471, 0.01907650851781535, -0.010671566572235105, -0.2645509330787105, 0.09218849836631063, -0.2251174631695951, -0.09005949617396991, -0.06952012641799751, -0.03739196821755054, 0.0572153901661521, -0.3058661519628919, 0.05237278855882062, 0.00892967025140107, 0.07657567272267116, -0.13171665236244307, -0.12215924220314871, -0.07738251643243178, 0.10369876024976762, 0.045874649705974005, 0.008698721510644247, 0.24934512853098947, -0.07555505639897793, -0.12515467058736343, 0.3689151076307776, -0.06851801751959488, -0.18105459528567355, 0.15514760217941337, -0.07576317590923091, -0.0021121128176162444, 0.15486163471892378, 0.210488495234327, 0.07713769934767115, -0.1981756230572762, 0.029122453181413946, 0.04691905404739325, 0.2032884748202134, 0.03690175652150917, -0.031064978322878578, 0.14962056002144403, 0.24006386174366875, 0.14804963225474446, 0.11686385402933762, -0.09966232415800001, -0.1305753176140118, -0.22219748199107794, -0.11391676812024873, -0.12121795869000207, -0.0030544933747329744, -0.11515239522650875, -0.0812819706507368, 0.4029166149401587, 0.22234156632680274, 0.09058265592385498, 0.0825174607449132, 0.40965818370893303, 0.15521924848001742, 0.017099122672031324, 0.12331355520481475, 0.2603706529704866, 0.09080757719945479, 0.1969350163925293, -0.3194259449800026, 0.08286738771720016, 0.007591937426660283] |
1,802.07635 | Matrix factorizations over elementary divisor domains | We study the homotopy category $\mathrm{hmf}(R,W)$ of matrix factorizations
of non-zero elements $W\in R^\times$, where $R$ is an elementary divisor
domain. When $R$ has prime elements and $W$ factors into a square-free element
$W_0$ and a finite product of primes of multiplicity greater than one and which
do not divide $W_0$, we show that $\mathrm{hmf}(R,W)$ is triangle-equivalent
with an orthogonal sum of the triangulated categories of singularities
$\mathrm{D}_{\mathrm sing}(A_n(p))$ of the local Artinian rings
$A_n(p)=R/\langle p^n\rangle$, where $p$ runs over the prime divisors of $W$ of
order $n\geq 2$. This result holds even when $R$ is not Noetherian. The
triangulated categories $\mathrm{D}_{\mathrm sing}(A_n(p))$ are Krull-Schmidt
and we describe them explicitly. We also study the cocycle category
$\mathrm{zmf}(R,W)$, showing that it is additively generated by elementary
matrix factorizations. Finally, we discuss a few classes of examples.
| math.AC hep-th math.AG | we study the homotopy category mathrmhmfrw of matrix factorizations of nonzero elements win rtimes where r is an elementary divisor domain when r has prime elements and w factors into a squarefree element w_0 and a finite product of primes of multiplicity greater than one and which do not divide w_0 we show that mathrmhmfrw is triangleequivalent with an orthogonal sum of the triangulated categories of singularities mathrmd_mathrm singa_np of the local artinian rings a_nprlangle pnrangle where p runs over the prime divisors of w of order ngeq 2 this result holds even when r is not noetherian the triangulated categories mathrmd_mathrm singa_np are krullschmidt and we describe them explicitly we also study the cocycle category mathrmzmfrw showing that it is additively generated by elementary matrix factorizations finally we discuss a few classes of examples | [['we', 'study', 'the', 'homotopy', 'category', 'mathrmhmfrw', 'of', 'matrix', 'factorizations', 'of', 'nonzero', 'elements', 'win', 'rtimes', 'where', 'r', 'is', 'an', 'elementary', 'divisor', 'domain', 'when', 'r', 'has', 'prime', 'elements', 'and', 'w', 'factors', 'into', 'a', 'squarefree', 'element', 'w_0', 'and', 'a', 'finite', 'product', 'of', 'primes', 'of', 'multiplicity', 'greater', 'than', 'one', 'and', 'which', 'do', 'not', 'divide', 'w_0', 'we', 'show', 'that', 'mathrmhmfrw', 'is', 'triangleequivalent', 'with', 'an', 'orthogonal', 'sum', 'of', 'the', 'triangulated', 'categories', 'of', 'singularities', 'mathrmd_mathrm', 'singa_np', 'of', 'the', 'local', 'artinian', 'rings', 'a_nprlangle', 'pnrangle', 'where', 'p', 'runs', 'over', 'the', 'prime', 'divisors', 'of', 'w', 'of', 'order', 'ngeq', '2', 'this', 'result', 'holds', 'even', 'when', 'r', 'is', 'not', 'noetherian', 'the', 'triangulated', 'categories', 'mathrmd_mathrm', 'singa_np', 'are', 'krullschmidt', 'and', 'we', 'describe', 'them', 'explicitly', 'we', 'also', 'study', 'the', 'cocycle', 'category', 'mathrmzmfrw', 'showing', 'that', 'it', 'is', 'additively', 'generated', 'by', 'elementary', 'matrix', 'factorizations', 'finally', 'we', 'discuss', 'a', 'few', 'classes', 'of', 'examples']] | [-0.18557779361435678, 0.0846508532979442, -0.07965507584594889, 0.05591939021451253, -0.043100533901451854, -0.18768269902284374, -0.039970031391931116, 0.3761567090987228, -0.3694456406374229, -0.17589842287793545, 0.07072607256122865, -0.26340475668985164, -0.08306274923688761, 0.13330187141491479, -0.12592929302809353, -0.08647275873590843, 0.09079304784609121, 0.11412724551701103, -0.0708124442044209, -0.3447793978266418, 0.42642745314515196, -0.06861927351019403, 0.16512587523666866, 0.04255999827000778, 0.07624761153783766, -0.002484779512997193, -0.019257960160757648, 0.02578514382969388, -0.17851011043478593, 0.09913265739805865, 0.32927035966713447, 0.10419460345292464, 0.24192947639858176, -0.3679455269884784, -0.053590301467920654, 0.24236254932111478, 0.15937429726363916, 0.00698758015914791, 0.007033983744804573, -0.22350108077807818, 0.19610832925900468, -0.2526183059817413, -0.09860377269615128, -0.06871078208860126, 0.11928748368154629, 0.018045935576992633, -0.30909619688100065, -0.03793343824713702, 0.10834461222503933, 0.12222553063475061, -0.022841558478830848, -0.17190605411633442, -0.0248660100842244, 0.06916672055604067, 0.0044274545907683205, -0.015443593176314607, 0.08548966448870488, -0.09873018941834744, -0.09088788264534742, 0.3729924316139659, -0.0366045947649809, -0.2047019566907693, 0.0990485604343121, -0.18650718794742716, -0.10682049296337937, 0.1182757167625823, 0.02521021065331297, 0.15217503776148078, 0.016164379109568472, 0.20936144681581936, -0.168725968360377, 0.13218921455700183, 0.11120130401286588, -7.288328458798787e-05, 0.11690660863951052, 0.08258226243924582, 0.06265357263509941, 0.0867073117478867, 0.013232689516144092, 0.04408633920502325, -0.3819863701137365, -0.21003744496556465, -0.1529517834478611, 0.14924688727865032, -0.12655328906066643, -0.15918715517909732, 0.41359484470740426, 0.06708257925856742, 0.17149321432589204, 0.11358374209248723, 0.2322853245641454, 0.045082122539497504, 0.062056271388428286, 0.053585092839057324, 0.08671175757808669, 0.1938363683384523, -0.08179668243701599, -0.09933222539621056, -0.026946570578729734, 0.19129155068731052] |
1,802.07636 | The lower central and derived series of the braid groups of compact
surfaces | Let M be a compact surface, either orientable or non-orientable. We study the
lower central and derived series of the braid and pure braid groups of M in
order to determine the values of n for which B\_n(M) and P\_n(M) are residually
nilpotent or residually soluble. First, we solve this problem for the case
where M is the 2-torus. We then give a general description of these series for
an arbitrary semi-direct product that allows us to calculate explicitly the
lower central series of P\_2(K), where K is the Klein bottle, and to give an
estimate for the derived series of P\_n(K). Finally, if M is a non-orientable
compact surface without boundary, we determine the values of n for which
B\_n(M) is residually nilpotent or residually soluble in the cases that were
not already known in the literature.
| math.GT math.GR | let m be a compact surface either orientable or nonorientable we study the lower central and derived series of the braid and pure braid groups of m in order to determine the values of n for which b_nm and p_nm are residually nilpotent or residually soluble first we solve this problem for the case where m is the 2torus we then give a general description of these series for an arbitrary semidirect product that allows us to calculate explicitly the lower central series of p_2k where k is the klein bottle and to give an estimate for the derived series of p_nk finally if m is a nonorientable compact surface without boundary we determine the values of n for which b_nm is residually nilpotent or residually soluble in the cases that were not already known in the literature | [['let', 'm', 'be', 'a', 'compact', 'surface', 'either', 'orientable', 'or', 'nonorientable', 'we', 'study', 'the', 'lower', 'central', 'and', 'derived', 'series', 'of', 'the', 'braid', 'and', 'pure', 'braid', 'groups', 'of', 'm', 'in', 'order', 'to', 'determine', 'the', 'values', 'of', 'n', 'for', 'which', 'b_nm', 'and', 'p_nm', 'are', 'residually', 'nilpotent', 'or', 'residually', 'soluble', 'first', 'we', 'solve', 'this', 'problem', 'for', 'the', 'case', 'where', 'm', 'is', 'the', '2torus', 'we', 'then', 'give', 'a', 'general', 'description', 'of', 'these', 'series', 'for', 'an', 'arbitrary', 'semidirect', 'product', 'that', 'allows', 'us', 'to', 'calculate', 'explicitly', 'the', 'lower', 'central', 'series', 'of', 'p_2k', 'where', 'k', 'is', 'the', 'klein', 'bottle', 'and', 'to', 'give', 'an', 'estimate', 'for', 'the', 'derived', 'series', 'of', 'p_nk', 'finally', 'if', 'm', 'is', 'a', 'nonorientable', 'compact', 'surface', 'without', 'boundary', 'we', 'determine', 'the', 'values', 'of', 'n', 'for', 'which', 'b_nm', 'is', 'residually', 'nilpotent', 'or', 'residually', 'soluble', 'in', 'the', 'cases', 'that', 'were', 'not', 'already', 'known', 'in', 'the', 'literature']] | [-0.12400610956862784, 0.14068356124820033, -0.05630134289031443, 0.05557020748813596, -0.09496581840220893, -0.15291037335249502, 0.004372694290013633, 0.34862146896404633, -0.2424921539909058, -0.2717956457948447, 0.12416275336316017, -0.25785931470591755, -0.08434664092635723, 0.2226676701557944, -0.1122542980508339, -0.062284975618859935, 0.01413211651969755, 0.13021398600244868, -0.07433813061578658, -0.2866607248880968, 0.3632226821197116, -0.05873234330531399, 0.17897732935143987, 0.0553156867981011, 0.06273144441049384, -0.017248017985906885, -0.006513242029409477, -0.006444084403127541, -0.2104010533469103, 0.09372517783228523, 0.298765128262449, 0.03196605721013444, 0.15977649620153767, -0.4132090506778247, -0.1636141054737179, 0.18943921921427187, 0.15369526401121655, 0.02702667153325688, -0.0340455868990039, -0.23401479203881614, 0.13673843900281665, -0.18300485862014088, -0.13957558223383798, -0.04560252416716969, 0.11514177790546007, -0.060944236050683845, -0.25233400038753945, 0.01193009321645334, 0.09888953377452234, 0.05882734837739364, -0.05676361129904314, -0.11716080054094968, -0.04171175947176643, 0.17785087614691397, -0.019714263024861397, 0.0023928036241778645, 0.06907480573821542, -0.05871970150316053, -0.07472009434190957, 0.39973930934902985, -0.08585732543555871, -0.2296971651215943, 0.14415852069868235, -0.2101032180995073, -0.17794870236969512, 0.15311690117569937, 0.1117363455131704, 0.1862587397918105, -0.06761320840999269, 0.16946328334692543, -0.1398857236709918, 0.08628021203575359, 0.08993978815598656, -0.08892183130112666, 0.1257542114062876, 0.07146910949866625, 0.09630424680738318, 0.14743031934156772, 0.00977325619812515, 0.046984104210159916, -0.34278165586832643, -0.24879388717691536, -0.15944845291981607, 0.11882217981073537, -0.07202544764141498, -0.18799079782700678, 0.35265555330619647, 0.04052661943073938, 0.1575128295985253, 0.13011827426996297, 0.2121828795356703, 0.09467964548874053, 0.03977860651945736, 0.12820032889536326, 0.08154851633488484, 0.20632057242345173, -0.09740456668120148, -0.18902352006525558, -0.031730572433224406, 0.188986225100909] |
1,802.07637 | Non-Abelian extension of the aether term and the Gribov problem | In this paper, we treat the proper path integral quantization of the
Yang-Mills-aether (YM-aether) system by dealing with the extra gauge copies in
the Landau gauge. Within Gribov's prescription to get rid of such remaining
gauge copies, we explicitly derive the Gribov parameter dependence of the
coupling constant and of the Lorentz violation aether term. The ultraviolet
limit is investigated under the light of recent bounds on the magnitude of the
non-Abelian aether parameter, and we show that the Gribov parameter can be
disregarded in that limit.
| hep-th | in this paper we treat the proper path integral quantization of the yangmillsaether ymaether system by dealing with the extra gauge copies in the landau gauge within gribovs prescription to get rid of such remaining gauge copies we explicitly derive the gribov parameter dependence of the coupling constant and of the lorentz violation aether term the ultraviolet limit is investigated under the light of recent bounds on the magnitude of the nonabelian aether parameter and we show that the gribov parameter can be disregarded in that limit | [['in', 'this', 'paper', 'we', 'treat', 'the', 'proper', 'path', 'integral', 'quantization', 'of', 'the', 'yangmillsaether', 'ymaether', 'system', 'by', 'dealing', 'with', 'the', 'extra', 'gauge', 'copies', 'in', 'the', 'landau', 'gauge', 'within', 'gribovs', 'prescription', 'to', 'get', 'rid', 'of', 'such', 'remaining', 'gauge', 'copies', 'we', 'explicitly', 'derive', 'the', 'gribov', 'parameter', 'dependence', 'of', 'the', 'coupling', 'constant', 'and', 'of', 'the', 'lorentz', 'violation', 'aether', 'term', 'the', 'ultraviolet', 'limit', 'is', 'investigated', 'under', 'the', 'light', 'of', 'recent', 'bounds', 'on', 'the', 'magnitude', 'of', 'the', 'nonabelian', 'aether', 'parameter', 'and', 'we', 'show', 'that', 'the', 'gribov', 'parameter', 'can', 'be', 'disregarded', 'in', 'that', 'limit']] | [-0.18134869201766218, 0.21231586184790907, -0.07976824652184458, 0.05114789425450213, -0.11431636162759627, -0.07866353600779001, 0.07676169626442168, 0.31553689309341065, -0.1997675480403225, -0.2923818968455581, 0.06924680283649222, -0.21963118181070862, -0.10940636832486181, 0.08198680016760002, -0.09912479649955297, 0.023580060103524696, 0.025311549961128655, 0.06142269099843414, -0.042298206226790654, -0.2643901011084809, 0.35377969588426983, 0.018910251329105128, 0.23266147928421987, 0.08980494488838732, 0.14499838764176648, 0.06911877332227852, -0.047079724133672084, 0.027000696710584794, -0.15761155933775145, 0.03984210554078933, 0.1657837433357011, 0.03516703764634097, 0.21747786679907757, -0.4128403444719665, -0.22407236351248097, 0.09897430027451586, 0.14870595602209077, 0.12157394022626035, 0.019497900810914442, -0.30200095915180797, 0.01322787635247497, -0.18355336388682617, -0.1603954192059224, -0.08696698669125053, -0.03091126564232742, -0.09769181245390107, -0.2693623660789693, 0.09867455942884965, 0.020599109109710245, -0.01478967717026963, -0.07337681745343348, -0.06376231495044468, 0.0003874931703595554, 0.07883655371911386, 0.1889324744916795, 0.06311673080986914, 0.09779771288637729, -0.19961429152582935, -0.09203122907989275, 0.40474462960572805, -0.10074457151212675, -0.26039705853909256, 0.07621199601494213, -0.15750258836128256, -0.1678150939864709, 0.08760298959643799, 0.08370487834600841, 0.1013598890427281, -0.15749456005937912, 0.22331799860523247, -0.04781111771350398, 0.13432042104575564, 0.10231578650555628, 0.10246916724478497, 0.1387165625933181, 0.07131629680447718, 0.059714882656493606, 0.13603698241332657, -0.05369065069483922, -0.1128103732240989, -0.4383566337473252, -0.13963998841012226, -0.15388397677418064, 0.08471167957519783, -0.16089972139521064, -0.14003617997308646, 0.35339728845831225, 0.190073689419831, 0.17357104516807287, 0.011449899234096794, 0.2615390549578211, 0.17744357316371273, 0.10126842961865751, 0.026488697282312547, 0.30011060989516625, 0.12696836821132285, 0.022230888382696053, -0.29322279946440283, -0.05258973744725261, 0.12775943767388953] |
1,802.07638 | Energy Harvesting and Magneto-Inductive Communications with Molecular
Magnets on Vibrating Graphene and Biomedical Applications in the Kilohertz to
Terahertz Band | Magneto-inductive (MI) Terahertz (THz) wireless channels provide significant
theoretical performances for MI communications (MIC) and wireless power
transmission (WPT) in nanoscale networks. Energy harvesting (EH) and signal
generation are critical for autonomous operation in challenging medium
including biomedical channels. State of the art electromagnetic (EM)
vibrational devices have millimeter dimensions while targeting low frequency EH
without any real-time communications. In this article, graphene resonators are
combined with single molecule magnets (SMMs) to realize nanoscale EH, MIC and
WPT with novel modulation methods achieving simultaneous wireless information
and PT (SWIPT). Unique advantages of graphene including atomic thickness,
ultra-low weight, high strain and resonance frequencies in the Kilohertz to
Terahertz band are combined with high and stable magnetic moments of
Terbium(III) bis(phthalocyanine) SMMs. Numerical analyses provide tens of
nanowatts powers and efficiencies of $10^4 \, W/m^3$ in acoustic and ultrasound
frequencies comparable with vibrational EH devices while millimeter wave
carrier generation is numerically analyzed. Proposed model and communication
theoretical analysis present a practical framework for challenging applications
in the near future by promising simple mechanical design. Applications include
nanoscale biomedical tagging including human cells, sensing and communication
for diagnosis and treatment, EH and modulation for autonomous nano-robotics,
and magnetic particle imaging (MPI).
| physics.app-ph physics.med-ph | magnetoinductive mi terahertz thz wireless channels provide significant theoretical performances for mi communications mic and wireless power transmission wpt in nanoscale networks energy harvesting eh and signal generation are critical for autonomous operation in challenging medium including biomedical channels state of the art electromagnetic em vibrational devices have millimeter dimensions while targeting low frequency eh without any realtime communications in this article graphene resonators are combined with single molecule magnets smms to realize nanoscale eh mic and wpt with novel modulation methods achieving simultaneous wireless information and pt swipt unique advantages of graphene including atomic thickness ultralow weight high strain and resonance frequencies in the kilohertz to terahertz band are combined with high and stable magnetic moments of terbiumiii bisphthalocyanine smms numerical analyses provide tens of nanowatts powers and efficiencies of 104 wm3 in acoustic and ultrasound frequencies comparable with vibrational eh devices while millimeter wave carrier generation is numerically analyzed proposed model and communication theoretical analysis present a practical framework for challenging applications in the near future by promising simple mechanical design applications include nanoscale biomedical tagging including human cells sensing and communication for diagnosis and treatment eh and modulation for autonomous nanorobotics and magnetic particle imaging mpi | [['magnetoinductive', 'mi', 'terahertz', 'thz', 'wireless', 'channels', 'provide', 'significant', 'theoretical', 'performances', 'for', 'mi', 'communications', 'mic', 'and', 'wireless', 'power', 'transmission', 'wpt', 'in', 'nanoscale', 'networks', 'energy', 'harvesting', 'eh', 'and', 'signal', 'generation', 'are', 'critical', 'for', 'autonomous', 'operation', 'in', 'challenging', 'medium', 'including', 'biomedical', 'channels', 'state', 'of', 'the', 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1,802.07639 | Notes On Open Book Decompositions For Engel Structures | We relate open book decompositions of a 4-manifold M with its Engel
structures. Our main result is, given an open book decomposition of M whose
binding is a collection of 2-tori and whose monodromy preserves a framing of a
page, the construction of an En-gel structure whose isotropic foliation is
transverse to the interior of the pages and tangent to the binding. In
particular the pages are contact man-ifolds and the monodromy is a
contactomorphism. As a consequence, on a parallelizable closed 4-manifold,
every open book with toric binding carries in the previous sense an Engel
structure. Moreover, we show that amongst the supported Engel structures we
construct, there is a class of loose Engel structures.
| math.SG | we relate open book decompositions of a 4manifold m with its engel structures our main result is given an open book decomposition of m whose binding is a collection of 2tori and whose monodromy preserves a framing of a page the construction of an engel structure whose isotropic foliation is transverse to the interior of the pages and tangent to the binding in particular the pages are contact manifolds and the monodromy is a contactomorphism as a consequence on a parallelizable closed 4manifold every open book with toric binding carries in the previous sense an engel structure moreover we show that amongst the supported engel structures we construct there is a class of loose engel structures | [['we', 'relate', 'open', 'book', 'decompositions', 'of', 'a', '4manifold', 'm', 'with', 'its', 'engel', 'structures', 'our', 'main', 'result', 'is', 'given', 'an', 'open', 'book', 'decomposition', 'of', 'm', 'whose', 'binding', 'is', 'a', 'collection', 'of', '2tori', 'and', 'whose', 'monodromy', 'preserves', 'a', 'framing', 'of', 'a', 'page', 'the', 'construction', 'of', 'an', 'engel', 'structure', 'whose', 'isotropic', 'foliation', 'is', 'transverse', 'to', 'the', 'interior', 'of', 'the', 'pages', 'and', 'tangent', 'to', 'the', 'binding', 'in', 'particular', 'the', 'pages', 'are', 'contact', 'manifolds', 'and', 'the', 'monodromy', 'is', 'a', 'contactomorphism', 'as', 'a', 'consequence', 'on', 'a', 'parallelizable', 'closed', '4manifold', 'every', 'open', 'book', 'with', 'toric', 'binding', 'carries', 'in', 'the', 'previous', 'sense', 'an', 'engel', 'structure', 'moreover', 'we', 'show', 'that', 'amongst', 'the', 'supported', 'engel', 'structures', 'we', 'construct', 'there', 'is', 'a', 'class', 'of', 'loose', 'engel', 'structures']] | [-0.22460826421317098, 0.06352527982267804, -0.09679983124731044, 0.0659710400274168, -0.1319936879364581, -0.11059452870916896, -0.0031566007297630584, 0.39070618486609954, -0.29139698513558715, -0.26199943053632463, 0.07828298951338591, -0.2852260785775484, -0.16890927122259544, 0.17314491388970055, -0.14761897101034893, -0.046798960290194876, 0.11904897533581946, 0.12014785852957645, -0.07484526517760844, -0.2625936910566264, 0.4139564447104931, -0.0048627019378131835, 0.1967677586121838, 0.09180711565041465, 0.1312762099529711, -0.04115883571673827, -0.023444384890447915, 0.029588908880370957, -0.17934921098270118, 0.18992376252045406, 0.24911417709342365, 0.07115961135573813, 0.1795457518571217, -0.3326999812559044, -0.13414642279280214, 0.09140321714020784, 0.11051251003438414, 0.027594579656704747, -0.020998847386839894, -0.2821005042321209, 0.11984975807015495, -0.09874921957741427, -0.17250164272263646, -0.05549086485828819, 0.08194435692536806, 0.0006070923991501331, -0.14644213108012677, -0.031899295867709766, 0.14831875360185473, 0.06541277540462284, -0.07127855460516755, -0.05270124551567153, -0.0994008291002909, 0.12656711792304373, -0.004563836960908796, 0.09697512702229594, 0.13250688050727055, -0.05820590709657248, -0.12369242052102045, 0.4078451708834297, -0.0643326581891321, -0.26634437911983194, 0.10069542920120575, -0.08946073111066402, -0.20084232015230147, 0.13662413306582463, 0.058780416701759756, 0.11488534543743048, -0.08296728221767839, 0.195730693307645, -0.15895693550079032, 0.12721412493305378, 0.13089037263075468, -0.06244766484576695, 0.1576199669005542, 0.18529142563608636, 0.12390801430166025, 0.09828728649379878, 0.025749346889667856, -0.03944569255691022, -0.33013781078224036, -0.234630413765162, -0.14872018454178912, 0.19986704296376234, -0.07118471000900047, -0.2902961086405538, 0.39788515599151464, -0.0066895588895241765, 0.22915718001955798, 0.06735430657863617, 0.2164152981873987, -0.007139436992945085, 0.03927991145886561, 0.15276132200860643, 0.08073619526112452, 0.18946068980409925, -0.002745932770957207, -0.10841658367205347, -0.002916110703593184, 0.1291699300656609] |
1,802.0764 | Antenna Design and Implementation for the Future Space Ultra-Long
Wavelength Radio Telescope | In radio astronomy, the Ultra-Long Wavelengths (ULW) regime of longer than 10
m (frequencies below 30 MHz), remains the last virtually unexplored window of
the celestial electromagnetic spectrum. The strength of the science case for
extending radio astronomy into the ULW window is growing. However, the
opaqueness of the Earth's ionosphere makes ULW observations by ground-based
facilities practically impossible. Furthermore, the ULW spectrum is full of
anthropogenic radio frequency interference (RFI). The only radical solution for
both problems is in placing an ULW astronomy facility in space. We present a
concept of a key element of a space-borne ULW array facility, an antenna that
addresses radio astronomical specifications. A tripole-type antenna and
amplifier are analysed as a solution for ULW implementation. A receiver system
with a low power dissipation is discussed as well. The active antenna is
optimized to operate at the noise level defined by the celestial emission in
the frequency band 1 - 30 MHz. Field experiments with a prototype tripole
antenna enabled estimates of the system noise temperature. They indicated that
the proposed concept meets the requirements of a space-borne ULW array
facility.
| astro-ph.IM | in radio astronomy the ultralong wavelengths ulw regime of longer than 10 m frequencies below 30 mhz remains the last virtually unexplored window of the celestial electromagnetic spectrum the strength of the science case for extending radio astronomy into the ulw window is growing however the opaqueness of the earths ionosphere makes ulw observations by groundbased facilities practically impossible furthermore the ulw spectrum is full of anthropogenic radio frequency interference rfi the only radical solution for both problems is in placing an ulw astronomy facility in space we present a concept of a key element of a spaceborne ulw array facility an antenna that addresses radio astronomical specifications a tripoletype antenna and amplifier are analysed as a solution for ulw implementation a receiver system with a low power dissipation is discussed as well the active antenna is optimized to operate at the noise level defined by the celestial emission in the frequency band 1 30 mhz field experiments with a prototype tripole antenna enabled estimates of the system noise temperature they indicated that the proposed concept meets the requirements of a spaceborne ulw array facility | [['in', 'radio', 'astronomy', 'the', 'ultralong', 'wavelengths', 'ulw', 'regime', 'of', 'longer', 'than', '10', 'm', 'frequencies', 'below', '30', 'mhz', 'remains', 'the', 'last', 'virtually', 'unexplored', 'window', 'of', 'the', 'celestial', 'electromagnetic', 'spectrum', 'the', 'strength', 'of', 'the', 'science', 'case', 'for', 'extending', 'radio', 'astronomy', 'into', 'the', 'ulw', 'window', 'is', 'growing', 'however', 'the', 'opaqueness', 'of', 'the', 'earths', 'ionosphere', 'makes', 'ulw', 'observations', 'by', 'groundbased', 'facilities', 'practically', 'impossible', 'furthermore', 'the', 'ulw', 'spectrum', 'is', 'full', 'of', 'anthropogenic', 'radio', 'frequency', 'interference', 'rfi', 'the', 'only', 'radical', 'solution', 'for', 'both', 'problems', 'is', 'in', 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1,802.07641 | The life cycles of Be viscous decretion discs: fundamental disc
parameters of 54 SMC Be stars | Be stars are main-sequence massive stars with emission features in their
spectrum, which originates in circumstellar gaseous discs. Even though the
viscous decretion disc (VDD) model can satisfactorily explain most
observations, two important physical ingredients, namely the magnitude of the
viscosity ($\alpha$) and the disk mass injection rate, remain poorly
constrained. The light curves of Be stars that undergo events of disc formation
and dissipation offer an opportunity to constrain these quantities. A pipeline
was developed to model these events that uses a grid of synthetic light curves,
computed from coupled hydrodynamic and radiative transfer calculations. A
sample of 54 Be stars from the OGLE survey of the Small Magellanic Cloud (SMC)
was selected for this study. Because of the way our sample was selected (bright
stars with clear disc events), it likely represents the densest discs in the
SMC. Like their siblings in the Galaxy, the mass of the disc in the SMC
increases with the stellar mass. The typical mass and angular momentum loss
rates associated with the disk events are of the order of $\sim$$10^{-10}\,
M_\odot\,\mathrm{yr^{-1}}$ and $\sim$$5\times 10^{36}\, \mathrm{g\, cm^{2}\,
s^{-2}}$, respectively. The values of $\alpha$ found in this work are typically
of a few tenths, consistent with recent results in the literature and with the
ones found in dwarf novae, but larger than current theory predicts. Considering
the sample as a whole, the viscosity parameter is roughly two times larger at
build-up ($\left\langle\alpha_\mathrm{bu}\right\rangle = 0.63$) than at
dissipation ($\left\langle\alpha_\mathrm{d}\right\rangle = 0.26$). Further work
is necessary to verify whether this trend is real or a result of some of the
model assumptions.
| astro-ph.SR | be stars are mainsequence massive stars with emission features in their spectrum which originates in circumstellar gaseous discs even though the viscous decretion disc vdd model can satisfactorily explain most observations two important physical ingredients namely the magnitude of the viscosity alpha and the disk mass injection rate remain poorly constrained the light curves of be stars that undergo events of disc formation and dissipation offer an opportunity to constrain these quantities a pipeline was developed to model these events that uses a grid of synthetic light curves computed from coupled hydrodynamic and radiative transfer calculations a sample of 54 be stars from the ogle survey of the small magellanic cloud smc was selected for this study because of the way our sample was selected bright stars with clear disc events it likely represents the densest discs in the smc like their siblings in the galaxy the mass of the disc in the smc increases with the stellar mass the typical mass and angular momentum loss rates associated with the disk events are of the order of sim1010 m_odotmathrmyr1 and sim5times 1036 mathrmg cm2 s2 respectively the values of alpha found in this work are typically of a few tenths consistent with recent results in the literature and with the ones found in dwarf novae but larger than current theory predicts considering the sample as a whole the viscosity parameter is roughly two times larger at buildup leftlanglealpha_mathrmburightrangle 063 than at dissipation leftlanglealpha_mathrmdrightrangle 026 further work is necessary to verify whether this trend is real or a result of some of the model assumptions | [['be', 'stars', 'are', 'mainsequence', 'massive', 'stars', 'with', 'emission', 'features', 'in', 'their', 'spectrum', 'which', 'originates', 'in', 'circumstellar', 'gaseous', 'discs', 'even', 'though', 'the', 'viscous', 'decretion', 'disc', 'vdd', 'model', 'can', 'satisfactorily', 'explain', 'most', 'observations', 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1,802.07642 | Cofree Com-PreLie algebras | A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie
product satisfying some compatibilities with the product and the coproduct. We
here give examples of cofree Com-PreLie bialgebras, including all the ones such
that the preLie product is homogeneous of degree $\ge$ --1. We also give a
graphical description of free unitary Com-PreLie algebras, explicit their
canonical bialgebra structure and exhibit with the help of a rigidity theorem
certain cofree quotients, including the Connes-Kreimer Hopf algebra of rooted
trees. We finally prove that the dual of these bialgebras are also enveloping
algebras of preLie algebras, combinatorially described.
| math.RA | a comprelie bialgebra is a commutative bialgebra with an extra prelie product satisfying some compatibilities with the product and the coproduct we here give examples of cofree comprelie bialgebras including all the ones such that the prelie product is homogeneous of degree ge 1 we also give a graphical description of free unitary comprelie algebras explicit their canonical bialgebra structure and exhibit with the help of a rigidity theorem certain cofree quotients including the conneskreimer hopf algebra of rooted trees we finally prove that the dual of these bialgebras are also enveloping algebras of prelie algebras combinatorially described | [['a', 'comprelie', 'bialgebra', 'is', 'a', 'commutative', 'bialgebra', 'with', 'an', 'extra', 'prelie', 'product', 'satisfying', 'some', 'compatibilities', 'with', 'the', 'product', 'and', 'the', 'coproduct', 'we', 'here', 'give', 'examples', 'of', 'cofree', 'comprelie', 'bialgebras', 'including', 'all', 'the', 'ones', 'such', 'that', 'the', 'prelie', 'product', 'is', 'homogeneous', 'of', 'degree', 'ge', '1', 'we', 'also', 'give', 'a', 'graphical', 'description', 'of', 'free', 'unitary', 'comprelie', 'algebras', 'explicit', 'their', 'canonical', 'bialgebra', 'structure', 'and', 'exhibit', 'with', 'the', 'help', 'of', 'a', 'rigidity', 'theorem', 'certain', 'cofree', 'quotients', 'including', 'the', 'conneskreimer', 'hopf', 'algebra', 'of', 'rooted', 'trees', 'we', 'finally', 'prove', 'that', 'the', 'dual', 'of', 'these', 'bialgebras', 'are', 'also', 'enveloping', 'algebras', 'of', 'prelie', 'algebras', 'combinatorially', 'described']] | [-0.20453317123180143, 0.0843089501035212, -0.0261130523440257, 0.09436807279921688, -0.21936365742977632, -0.16094216692014313, -0.058446966905184854, 0.4003893688929324, -0.43041423676364426, -0.15970328146097612, 0.10328892193145442, -0.19572744864913427, -0.21910826478400552, 0.1507563925044117, -0.16197518323196516, -0.11263245413654807, 0.10881769778777142, 0.16311065437110636, -0.14550674283325823, -0.26261569413223435, 0.48410050713514186, 0.03599049653192716, 0.18406427328056674, 0.02536720647334064, 0.14662512937294586, -0.003222269704565406, -0.01916509490384131, -0.02040834167059891, -0.24938802198315044, 0.08584291734542622, 0.3367007874826692, 0.06757276971130727, 0.12852672877369867, -0.3792324453516274, 0.012109135952302995, 0.1335525446837502, 0.13621580570803157, 0.019273090195290898, -0.02070094028497305, -0.2912538082538439, 0.049231798352278075, -0.3287843955641824, -0.08089549972542695, -0.1223416412819405, 0.057264631110414556, -0.0038059832556743404, -0.23018855685475093, 0.006729727643613266, 0.15361831836136325, 0.16584593826448735, -0.10052236749277431, -0.11481605394391761, -0.1314395882749968, 0.05698478071741304, -0.14788579667576265, -0.04089203422261896, 0.13475234230994532, -0.0751617423363258, -0.23485391086670665, 0.3230945856633539, 0.05079363881104284, -0.23318088638159085, 0.11892865874866328, -0.1814759496637449, -0.22286791639041384, 0.08353548993033413, -0.06514101177073862, 0.10964765502329991, -0.034677511946492996, 0.23067361629950844, -0.1765901796633796, -0.05810714362911424, 0.1553286535769929, 0.048802044291324835, 0.1072727020910694, 0.10333818586885321, 0.028524669286395823, 0.1818247327619061, 0.12794180878209976, -0.028754497564644838, -0.37485756979761076, -0.20799953923845776, 0.005752304244586932, 0.18433500982212778, -0.1947437328407042, -0.25547934139066625, 0.3840523744952314, 0.11209640872892829, 0.1600077297082361, 0.1501369918886648, 0.16176198886669413, 0.05701057739289744, 0.1560178546268227, 0.025870521626511246, 0.08112747802509575, 0.37899182281190796, -0.01182602261364156, -0.0487581189087478, -0.08751558719145856, 0.2637448211447621] |
1,802.07643 | Floating structures in shallow water: local well-posedness in the
axisymmetric case | The floating structure problem describes the interaction between surface
water waves and a floating body, generally a boat or a wave energy converter.
As shown by Lannes in [18] the equations for the fluid motion can be reduced to
a set of two evolution equations on the surface elevation and the horizontal
discharge. The presence of the object is accounted for by a constraint on the
discharge under the object; the pressure exerted by the fluid on this object is
then the Lagrange multiplier associated to this constraint. Our goal in this
paper is to prove the well-posedness of this fluid-structure interaction
problem in the shallow water approximation under the assumption that the flow
is axisymmetric without swirl. We write the fluid equations as a quasilinear
hyperbolic mixed initial boundary value problem and the solid equation as a
second order ODE coupled to the fluid equations. Finally we prove the local in
time well-posedness for this coupled problem, provided some compatibility
conditions on the initial data are satisfied.
| math.AP physics.ao-ph physics.flu-dyn | the floating structure problem describes the interaction between surface water waves and a floating body generally a boat or a wave energy converter as shown by lannes in 18 the equations for the fluid motion can be reduced to a set of two evolution equations on the surface elevation and the horizontal discharge the presence of the object is accounted for by a constraint on the discharge under the object the pressure exerted by the fluid on this object is then the lagrange multiplier associated to this constraint our goal in this paper is to prove the wellposedness of this fluidstructure interaction problem in the shallow water approximation under the assumption that the flow is axisymmetric without swirl we write the fluid equations as a quasilinear hyperbolic mixed initial boundary value problem and the solid equation as a second order ode coupled to the fluid equations finally we prove the local in time wellposedness for this coupled problem provided some compatibility conditions on the initial data are satisfied | [['the', 'floating', 'structure', 'problem', 'describes', 'the', 'interaction', 'between', 'surface', 'water', 'waves', 'and', 'a', 'floating', 'body', 'generally', 'a', 'boat', 'or', 'a', 'wave', 'energy', 'converter', 'as', 'shown', 'by', 'lannes', 'in', '18', 'the', 'equations', 'for', 'the', 'fluid', 'motion', 'can', 'be', 'reduced', 'to', 'a', 'set', 'of', 'two', 'evolution', 'equations', 'on', 'the', 'surface', 'elevation', 'and', 'the', 'horizontal', 'discharge', 'the', 'presence', 'of', 'the', 'object', 'is', 'accounted', 'for', 'by', 'a', 'constraint', 'on', 'the', 'discharge', 'under', 'the', 'object', 'the', 'pressure', 'exerted', 'by', 'the', 'fluid', 'on', 'this', 'object', 'is', 'then', 'the', 'lagrange', 'multiplier', 'associated', 'to', 'this', 'constraint', 'our', 'goal', 'in', 'this', 'paper', 'is', 'to', 'prove', 'the', 'wellposedness', 'of', 'this', 'fluidstructure', 'interaction', 'problem', 'in', 'the', 'shallow', 'water', 'approximation', 'under', 'the', 'assumption', 'that', 'the', 'flow', 'is', 'axisymmetric', 'without', 'swirl', 'we', 'write', 'the', 'fluid', 'equations', 'as', 'a', 'quasilinear', 'hyperbolic', 'mixed', 'initial', 'boundary', 'value', 'problem', 'and', 'the', 'solid', 'equation', 'as', 'a', 'second', 'order', 'ode', 'coupled', 'to', 'the', 'fluid', 'equations', 'finally', 'we', 'prove', 'the', 'local', 'in', 'time', 'wellposedness', 'for', 'this', 'coupled', 'problem', 'provided', 'some', 'compatibility', 'conditions', 'on', 'the', 'initial', 'data', 'are', 'satisfied']] | [-0.1691813956429195, 0.08934846747710946, -0.08943175729031541, 0.031173349051858253, -0.06680696063891187, -0.08330575729598336, -0.020089361660731293, 0.2720046996525655, -0.30996322833622497, -0.3025947076080012, 0.148693084822125, -0.2598117589673382, -0.10889985370643747, 0.1640842525673742, -0.06168517378752031, 0.09611605407415136, 0.07186170895805671, 0.032843671615886534, -0.06297144456073597, -0.19253648301708468, 0.3514332463077846, -0.002970243058544362, 0.2425084244182688, 0.046879323445388026, 0.15146539439350212, -0.030345419453667654, 0.03583340563844623, 0.039231338854560385, -0.14387309941113408, 0.06662231858354062, 0.21295101766909716, 0.040038514752051835, 0.2667805659473829, -0.48520448167497915, -0.2358721776233454, 0.052275602134787255, 0.08648343915133626, 0.11864703763941568, -0.059296669536879995, -0.2719371860591872, 0.07210672770105746, -0.1304166943868733, -0.1709102306880855, 0.01834514580800065, 0.010358074203222281, 0.04489188900749598, -0.2723354479076945, 0.09460957910466407, 0.08018131185201041, 0.03177245668762009, -0.17714021683925585, -0.0467518505853756, -0.046894612275840096, 0.0629972435459162, 0.04512548602430061, 0.034669231612324006, 0.11917551974156163, -0.1623866081451221, 0.008987103109358855, 0.41627558083495214, -0.08617350304398098, -0.321324308005084, 0.187617557544616, -0.09924680481587227, -0.06593001517397906, 0.13317476064133058, 0.1851735860663688, 0.12259344024988379, -0.16882662230117212, 0.07932793577873824, -0.07217903584551962, 0.16275804675561154, 0.11266392570299406, -0.10461480113389414, 0.17715644197804586, 0.18424739690852307, 0.12271694928252448, 0.15230030407838058, -0.08210574694904997, -0.08452138988650404, -0.33405199623666704, -0.17765792398270042, -0.15747725727435732, 0.04808700482187435, -0.07062215051432542, -0.16195332924776484, 0.36700150659418707, 0.12907705173572703, 0.11437816191686406, 0.044627435316908215, 0.3070799167755814, 0.14394156599441235, 0.003576764867397114, 0.09656604498602628, 0.24209982286837267, 0.15125074669846245, 0.14439696681663572, -0.26902583063392305, 0.06375242677140272, 0.12287322531587311] |
1,802.07644 | A gauge-invariant reversible cellular automaton | Gauge-invariance is a fundamental concept in physics---known to provide the
mathematical justification for all four fundamental forces. In this paper, we
provide discrete counterparts to the main gauge theoretical concepts, directly
in terms of Cellular Automata. More precisely, we describe a step-by-step
gauging procedure to enforce local symmetries upon a given Cellular Automaton.
We apply it to a simple Reversible Cellular Automaton for concreteness. From a
Computer Science perspective, discretized gauge theories may be applied to
numerical analysis, quantum simulation, fault-tolerant (quantum) computation.
From a mathematical perspective, discreteness provides a simple yet rigorous
route straight to the core concepts.
| cs.FL nlin.CG quant-ph | gaugeinvariance is a fundamental concept in physicsknown to provide the mathematical justification for all four fundamental forces in this paper we provide discrete counterparts to the main gauge theoretical concepts directly in terms of cellular automata more precisely we describe a stepbystep gauging procedure to enforce local symmetries upon a given cellular automaton we apply it to a simple reversible cellular automaton for concreteness from a computer science perspective discretized gauge theories may be applied to numerical analysis quantum simulation faulttolerant quantum computation from a mathematical perspective discreteness provides a simple yet rigorous route straight to the core concepts | [['gaugeinvariance', 'is', 'a', 'fundamental', 'concept', 'in', 'physicsknown', 'to', 'provide', 'the', 'mathematical', 'justification', 'for', 'all', 'four', 'fundamental', 'forces', 'in', 'this', 'paper', 'we', 'provide', 'discrete', 'counterparts', 'to', 'the', 'main', 'gauge', 'theoretical', 'concepts', 'directly', 'in', 'terms', 'of', 'cellular', 'automata', 'more', 'precisely', 'we', 'describe', 'a', 'stepbystep', 'gauging', 'procedure', 'to', 'enforce', 'local', 'symmetries', 'upon', 'a', 'given', 'cellular', 'automaton', 'we', 'apply', 'it', 'to', 'a', 'simple', 'reversible', 'cellular', 'automaton', 'for', 'concreteness', 'from', 'a', 'computer', 'science', 'perspective', 'discretized', 'gauge', 'theories', 'may', 'be', 'applied', 'to', 'numerical', 'analysis', 'quantum', 'simulation', 'faulttolerant', 'quantum', 'computation', 'from', 'a', 'mathematical', 'perspective', 'discreteness', 'provides', 'a', 'simple', 'yet', 'rigorous', 'route', 'straight', 'to', 'the', 'core', 'concepts']] | [-0.09079510151178158, 0.10519835752986219, -0.12360852349511518, 0.10799563582036265, -0.15785727740683575, -0.1854125006475999, 0.11663919405617314, 0.3538638196543467, -0.2874397312347986, -0.2371784977624383, 0.05842858577284924, -0.1717540019723986, -0.22340763432605723, 0.18676075923769753, -0.1177496489809175, 0.06820616946075758, 0.04288284861653739, 0.005278321942290747, -0.05510940386353023, -0.20051602230464316, 0.22377120390325328, 0.0638897545678465, 0.32272057855805875, 0.028878308716230094, 0.0796127194130071, -0.018853270144638966, -0.05565368636910405, 0.031165697022664304, -0.15784944953130825, 0.15672108680259303, 0.3189771686661608, 0.17496902637221678, 0.26432825936650745, -0.49753796466987354, -0.24151290599636885, 0.08383768072294794, 0.13025822590475863, 0.20811773600218322, -0.045032186040028746, -0.27669501814953223, 0.09024207672693443, -0.18060209576933817, -0.13274695753946672, -0.12188166759703878, 0.0009121031866275839, -0.06580816588141214, -0.20729459991098895, 0.0027172346528125356, 0.0683412896421719, 0.12769885071344217, -0.02036273563090636, -0.03571322024324719, 0.037412993875997405, 0.1424868834081429, -0.05027188918771869, -0.0034175482483542697, 0.13899607638761932, -0.0793624099092178, -0.20524988678873193, 0.45173108195458367, 0.033137451990374496, -0.2641564304869128, 0.22875938042808247, -0.029519115128003214, -0.21906722001066165, 0.08375935731645749, 0.15199358014589442, 0.04298492569514379, -0.1937334234018487, 0.09873509204148181, -0.048448214963154525, 0.1507053846607403, 0.016173116385233492, 0.023121730595523, 0.23070394295286767, 0.18653966535871125, 0.08662653885952824, 0.13142983912851433, 0.05789147022451103, -0.17417286459964756, -0.3780397114591027, -0.17643702201716296, -0.13989107743052917, 0.09664338949606849, -0.019067827726201136, -0.168594932523366, 0.40143253456573097, 0.17539904752807997, 0.0879842821147521, 0.12005970718301072, 0.3059088038375639, 0.12568273503637437, 0.029665492869419406, 0.010292067301782722, 0.15819480215978562, 0.1835055225243678, 0.09979240651413494, -0.16678929176865792, -0.042509869917067795, 0.1698596808128059] |
1,802.07645 | Limiting behavior of solutions for Euler equations of compressible fluid
flow | We study the limiting behavior of the solutions of Euler equations of
one-dimensional compressible fluid flow as the pressure like term vanishes.
This system can be thought of as an approximation for the one dimensional model
for large scale structure formation of universe. We show that the solutions of
former equation converges to the solution of later in the sense of distribution
and agrees with the vanishing viscosity limit when the initial data is of
Riemann type. A different approximation for the one dimensional model for large
scale structure formation of universe is also studied.
| math.AP | we study the limiting behavior of the solutions of euler equations of onedimensional compressible fluid flow as the pressure like term vanishes this system can be thought of as an approximation for the one dimensional model for large scale structure formation of universe we show that the solutions of former equation converges to the solution of later in the sense of distribution and agrees with the vanishing viscosity limit when the initial data is of riemann type a different approximation for the one dimensional model for large scale structure formation of universe is also studied | [['we', 'study', 'the', 'limiting', 'behavior', 'of', 'the', 'solutions', 'of', 'euler', 'equations', 'of', 'onedimensional', 'compressible', 'fluid', 'flow', 'as', 'the', 'pressure', 'like', 'term', 'vanishes', 'this', 'system', 'can', 'be', 'thought', 'of', 'as', 'an', 'approximation', 'for', 'the', 'one', 'dimensional', 'model', 'for', 'large', 'scale', 'structure', 'formation', 'of', 'universe', 'we', 'show', 'that', 'the', 'solutions', 'of', 'former', 'equation', 'converges', 'to', 'the', 'solution', 'of', 'later', 'in', 'the', 'sense', 'of', 'distribution', 'and', 'agrees', 'with', 'the', 'vanishing', 'viscosity', 'limit', 'when', 'the', 'initial', 'data', 'is', 'of', 'riemann', 'type', 'a', 'different', 'approximation', 'for', 'the', 'one', 'dimensional', 'model', 'for', 'large', 'scale', 'structure', 'formation', 'of', 'universe', 'is', 'also', 'studied']] | [-0.14395065427218612, 0.08834876055035765, -0.10655508882513172, 0.0755781359688722, -0.027543453959821676, -0.0964074480886522, -0.05741631172989544, 0.24756759836485512, -0.2904008029126807, -0.2599243982057822, 0.1394514205069036, -0.2560994452331215, -0.09846571817209845, 0.1674595416915652, 0.014659574377889695, 0.036967378776324424, 0.04870921928239496, 0.04023092192793755, -0.06895791606634463, -0.23483510394825746, 0.39176090318513546, 0.04781616505627569, 0.278788652065161, 0.015321190498377147, 0.11967740530564792, -0.07115214845214628, 0.03626714922291668, 0.0674441592081597, -0.15923893340215345, 0.037988840639101046, 0.187420311222147, 0.051540166747413185, 0.2560570997676175, -0.41038132879490913, -0.23654445991116135, 0.07378092447393819, 0.16228694393250503, 0.13129555558491696, -0.013050763199939147, -0.21762888484487408, 0.09485495522814362, -0.16829082341374535, -0.22341539664684157, -0.06404717504782112, 0.025278208159694546, 0.04239420914826424, -0.258090000943967, 0.14881196609961703, 0.06748873131643784, -0.017118322751239725, -0.15166521024841226, -0.06763780155635782, -0.020603147690723602, 0.10976999756837215, 0.10462561723236975, 0.014957483223100242, 0.0687749651211657, -0.21507163633007287, -0.04231947314999017, 0.42673507850421105, -0.14182926029408058, -0.21377865246644145, 0.18783668812462373, -0.1653592884246456, -0.10121374388078326, 0.11971835724911407, 0.16301470392040515, 0.15907089510491412, -0.11119038486121051, 0.1214946126853312, -0.07353058014261095, 0.14519734184325084, 0.06834451733647208, -0.017330021014142976, 0.16630299909922638, 0.22228748710629972, 0.08564866391059599, 0.1294254736153801, -0.07167661030727782, -0.14835212647816853, -0.3311853281271301, -0.20372271605424191, -0.19755780430216538, 0.10841638324292083, -0.1392261209896165, -0.22400454804301262, 0.3488520330504367, 0.1175138694663091, 0.19462682320491265, 0.06038202368899396, 0.25377657389954517, 0.1668077137737878, 0.023243094019983944, 0.08424679520294855, 0.21961047794473798, 0.12838413628847584, 0.11274232995010128, -0.22124971101354612, 0.06217345396841043, 0.12260796509094929] |
1,802.07646 | Minimal cut-sets in the power graphs of certain finite non-cyclic groups | The power graph of a group is the simple graph with vertices as the group
elements, in which two distinct vertices are adjacent if and only if one of
them can be obtained as an integral power of the other. We study (minimal)
cut-sets of the power graph of a (finite) non-cyclic (nilpotent) group which
are associated with its maximal cyclic subgroups. Let $G$ be a finite
non-cyclic nilpotent group whose order is divisible by at least two distinct
primes. If $G$ has a Sylow subgroup which is neither cyclic nor a generalized
quaternion $2$-group and all other Sylow subgroups of $G$ are cyclic, then
under some conditions we prove that there is only one minimum cut-set of the
power graph of $G$. We apply this result to find the vertex connectivity of the
power graphs of certain finite non-cyclic abelian groups whose order is
divisible by at most three distinct primes.
| math.CO | the power graph of a group is the simple graph with vertices as the group elements in which two distinct vertices are adjacent if and only if one of them can be obtained as an integral power of the other we study minimal cutsets of the power graph of a finite noncyclic nilpotent group which are associated with its maximal cyclic subgroups let g be a finite noncyclic nilpotent group whose order is divisible by at least two distinct primes if g has a sylow subgroup which is neither cyclic nor a generalized quaternion 2group and all other sylow subgroups of g are cyclic then under some conditions we prove that there is only one minimum cutset of the power graph of g we apply this result to find the vertex connectivity of the power graphs of certain finite noncyclic abelian groups whose order is divisible by at most three distinct primes | [['the', 'power', 'graph', 'of', 'a', 'group', 'is', 'the', 'simple', 'graph', 'with', 'vertices', 'as', 'the', 'group', 'elements', 'in', 'which', 'two', 'distinct', 'vertices', 'are', 'adjacent', 'if', 'and', 'only', 'if', 'one', 'of', 'them', 'can', 'be', 'obtained', 'as', 'an', 'integral', 'power', 'of', 'the', 'other', 'we', 'study', 'minimal', 'cutsets', 'of', 'the', 'power', 'graph', 'of', 'a', 'finite', 'noncyclic', 'nilpotent', 'group', 'which', 'are', 'associated', 'with', 'its', 'maximal', 'cyclic', 'subgroups', 'let', 'g', 'be', 'a', 'finite', 'noncyclic', 'nilpotent', 'group', 'whose', 'order', 'is', 'divisible', 'by', 'at', 'least', 'two', 'distinct', 'primes', 'if', 'g', 'has', 'a', 'sylow', 'subgroup', 'which', 'is', 'neither', 'cyclic', 'nor', 'a', 'generalized', 'quaternion', '2group', 'and', 'all', 'other', 'sylow', 'subgroups', 'of', 'g', 'are', 'cyclic', 'then', 'under', 'some', 'conditions', 'we', 'prove', 'that', 'there', 'is', 'only', 'one', 'minimum', 'cutset', 'of', 'the', 'power', 'graph', 'of', 'g', 'we', 'apply', 'this', 'result', 'to', 'find', 'the', 'vertex', 'connectivity', 'of', 'the', 'power', 'graphs', 'of', 'certain', 'finite', 'noncyclic', 'abelian', 'groups', 'whose', 'order', 'is', 'divisible', 'by', 'at', 'most', 'three', 'distinct', 'primes']] | [-0.21805198574561233, 0.19293369852570513, -0.10329531031464667, -0.004817861264056869, -0.1463032436180296, -0.17590815857616499, 1.3335635517968944e-06, 0.382867496210996, -0.32772786457989195, -0.24807931470844014, 0.12324008869396302, -0.28774377874000684, -0.09923855555366333, 0.1408657735446468, -0.11978868170224719, -0.07305345556194784, 0.040092329028993845, 0.20937393429247955, -0.01969380310650817, -0.29501270179676603, 0.3511022583973643, -0.0908585646791739, 0.18660341194175234, 0.023989329112641587, 0.09736685572179819, -0.017630645122775797, 0.0030509182742159617, 0.048676388220261095, -0.11256303895123365, 0.04657868640864954, 0.31261592105300606, 0.06446674425234578, 0.2525823618887348, -0.39387703820523856, -0.17773265047856657, 0.30208335892836513, 0.10358333978863236, -0.03776176470426818, -0.027163349687869317, -0.17909151360417078, 0.2098133008633005, -0.2151227576633621, -0.1074323176887303, -0.005410313973889539, 0.09742804649776142, 0.015817055201439775, -0.24747081526162984, -0.013943315345769454, 0.08540043788104269, 0.11182115528768727, 0.060831009141494224, -0.14303319071558163, -0.07602856106639497, 0.1267427962386711, -0.0036324698333996103, -0.012383329156651407, 0.054297579636209105, -0.05838517784784352, -0.1572327295679746, 0.4264409720750624, -0.012141191120271719, -0.1436475640542707, 0.1175666141115423, -0.18645829264393174, -0.1896314396014388, 0.1347039713567172, 0.0612220516808233, 0.15113240117697338, -0.08606339400131746, 0.16371960034149724, -0.14511924852482289, 0.10718063116655685, 0.08720160370974459, -0.008149432137878122, 0.10791545683260713, 0.07304232028055642, 0.1458512959744487, 0.11201154615187797, 0.06321417550823658, 0.06877257975161467, -0.35646227273575376, -0.11219746367178711, -0.20394331506395247, 0.078931689439598, -0.18478359326112886, -0.18147967489417888, 0.48705060194295485, 0.029974257908945316, 0.11021444417144123, 0.09438539625338499, 0.22567824756506047, 0.08925410088513193, 0.08773453073196211, 0.17098222672326588, 0.06411176929836265, 0.21422692342649066, -0.20227650662050828, -0.1920949442642986, 0.005379165099982761, 0.18807686946207755] |
1,802.07647 | MIS in the Congested Clique Model in $O(\log \log \Delta)$ Rounds | We give a maximal independent set (MIS) algorithm that runs in $O(\log \log
\Delta)$ rounds in the congested clique model, where $\Delta$ is the maximum
degree of the input graph. This improves upon the $O(\frac{\log(\Delta) \cdot
\log \log \Delta}{\sqrt{\log n}} + \log \log \Delta )$ rounds algorithm of
[Ghaffari, PODC '17], where $n$ is the number of vertices of the input graph.
In the first stage of our algorithm, we simulate the first
$O(\frac{n}{\text{poly} \log n})$ iterations of the sequential random order
Greedy algorithm for MIS in the congested clique model in $O(\log \log \Delta)$
rounds. This thins out the input graph relatively quickly: After this stage,
the maximum degree of the residual graph is poly-logarithmic. In the second
stage, we run the MIS algorithm of [Ghaffari, PODC '17] on the residual graph,
which completes in $O(\log \log \Delta)$ rounds on graphs of poly-logarithmic
degree.
| cs.DC cs.DS | we give a maximal independent set mis algorithm that runs in olog log delta rounds in the congested clique model where delta is the maximum degree of the input graph this improves upon the ofraclogdelta cdot log log deltasqrtlog n log log delta rounds algorithm of ghaffari podc 17 where n is the number of vertices of the input graph in the first stage of our algorithm we simulate the first ofracntextpoly log n iterations of the sequential random order greedy algorithm for mis in the congested clique model in olog log delta rounds this thins out the input graph relatively quickly after this stage the maximum degree of the residual graph is polylogarithmic in the second stage we run the mis algorithm of ghaffari podc 17 on the residual graph which completes in olog log delta rounds on graphs of polylogarithmic degree | [['we', 'give', 'a', 'maximal', 'independent', 'set', 'mis', 'algorithm', 'that', 'runs', 'in', 'olog', 'log', 'delta', 'rounds', 'in', 'the', 'congested', 'clique', 'model', 'where', 'delta', 'is', 'the', 'maximum', 'degree', 'of', 'the', 'input', 'graph', 'this', 'improves', 'upon', 'the', 'ofraclogdelta', 'cdot', 'log', 'log', 'deltasqrtlog', 'n', 'log', 'log', 'delta', 'rounds', 'algorithm', 'of', 'ghaffari', 'podc', '17', 'where', 'n', 'is', 'the', 'number', 'of', 'vertices', 'of', 'the', 'input', 'graph', 'in', 'the', 'first', 'stage', 'of', 'our', 'algorithm', 'we', 'simulate', 'the', 'first', 'ofracntextpoly', 'log', 'n', 'iterations', 'of', 'the', 'sequential', 'random', 'order', 'greedy', 'algorithm', 'for', 'mis', 'in', 'the', 'congested', 'clique', 'model', 'in', 'olog', 'log', 'delta', 'rounds', 'this', 'thins', 'out', 'the', 'input', 'graph', 'relatively', 'quickly', 'after', 'this', 'stage', 'the', 'maximum', 'degree', 'of', 'the', 'residual', 'graph', 'is', 'polylogarithmic', 'in', 'the', 'second', 'stage', 'we', 'run', 'the', 'mis', 'algorithm', 'of', 'ghaffari', 'podc', '17', 'on', 'the', 'residual', 'graph', 'which', 'completes', 'in', 'olog', 'log', 'delta', 'rounds', 'on', 'graphs', 'of', 'polylogarithmic', 'degree']] | [-0.2027628507332078, 0.09626005319545844, -0.007991373711930854, -0.027635909942910077, -0.020706950154687678, -0.18253538983408363, 0.17990228940200592, 0.3288057387606906, -0.25882368915315185, -0.4256586043031088, 0.03503341306017579, -0.28422449034239566, -0.14364315820525267, 0.06650875540217385, -0.10496609807014465, 0.0725407626804164, 0.08045943790514554, 0.06836783867329359, 0.050772927886074674, -0.4215455499762486, 0.18643544712103904, 0.022572657732026918, 0.15545264494472316, -0.007947522335286651, 0.05864833360704194, 0.04772302288162921, -0.021910900961873786, -0.029740776866674423, -0.14830369116332023, 0.009641660882958343, 0.26357585188400534, 0.2095136870384262, 0.2686939957684704, -0.4190867971229766, -0.06994387195279289, 0.1794554858268904, 0.18068714183256296, 0.06191419874168267, 0.1034009557533344, -0.1665710554524724, 0.12004459599432137, -0.07531903956332826, -0.027747903494829577, 0.05531385478430561, 0.07351012873363548, -0.025218809602249946, -0.3350515557527875, 0.018975434671821338, 0.07318764658910888, -0.020401904113324626, 0.14525314143725804, -0.17145863819002574, 0.03991958708502352, 0.06174946363483157, -0.09156422790672097, 0.17873409282016967, 0.047101272943629216, -0.11317844972446826, -0.11307801434637181, 0.30928326572757214, -0.08208884184652042, -0.03911810311754899, 0.017677873294867044, -0.08616081629879772, -0.2236997754579144, 0.12863420527761005, 0.1923594597760322, 0.22306925100939615, -0.029765231667884758, 0.18948438704412962, -0.09524898144549557, 0.22801066558541996, 0.13779076396354606, -0.017647234347116736, -0.06662165207422471, 0.21624787927799582, 0.17168178444595208, 0.10637933119599308, -0.019973727538516478, -0.07233052933588624, -0.3012515054483499, -0.13208552287625416, -0.24516531291550825, 0.025727564981207252, -0.31075300209423795, -0.14093677289783954, 0.412821119052491, 0.11631271152956678, 0.2744708126943026, 0.18281418755068443, 0.3290275500887739, 0.06739057445177293, -0.021917196968570352, 0.28801765458358985, 0.10151651911437512, 0.0941287234957729, 0.04506943036935159, -0.24547432730094962, 0.13831594950087103, 0.17440828319605706] |
1,802.07648 | Scalable and Robust Sparse Subspace Clustering Using Randomized
Clustering and Multilayer Graphs | Sparse subspace clustering (SSC) is one of the current state-of-the-art
methods for partitioning data points into the union of subspaces, with strong
theoretical guarantees. However, it is not practical for large data sets as it
requires solving a LASSO problem for each data point, where the number of
variables in each LASSO problem is the number of data points. To improve the
scalability of SSC, we propose to select a few sets of anchor points using a
randomized hierarchical clustering method, and, for each set of anchor points,
solve the LASSO problems for each data point allowing only anchor points to
have a non-zero weight (this reduces drastically the number of variables). This
generates a multilayer graph where each layer corresponds to a different set of
anchor points. Using the Grassmann manifold of orthogonal matrices, the shared
connectivity among the layers is summarized within a single subspace. Finally,
we use $k$-means clustering within that subspace to cluster the data points,
similarly as done by spectral clustering in SSC. We show on both synthetic and
real-world data sets that the proposed method not only allows SSC to scale to
large-scale data sets, but that it is also much more robust as it performs
significantly better on noisy data and on data with close susbspaces and
outliers, while it is not prone to oversegmentation.
| cs.CV stat.ML | sparse subspace clustering ssc is one of the current stateoftheart methods for partitioning data points into the union of subspaces with strong theoretical guarantees however it is not practical for large data sets as it requires solving a lasso problem for each data point where the number of variables in each lasso problem is the number of data points to improve the scalability of ssc we propose to select a few sets of anchor points using a randomized hierarchical clustering method and for each set of anchor points solve the lasso problems for each data point allowing only anchor points to have a nonzero weight this reduces drastically the number of variables this generates a multilayer graph where each layer corresponds to a different set of anchor points using the grassmann manifold of orthogonal matrices the shared connectivity among the layers is summarized within a single subspace finally we use kmeans clustering within that subspace to cluster the data points similarly as done by spectral clustering in ssc we show on both synthetic and realworld data sets that the proposed method not only allows ssc to scale to largescale data sets but that it is also much more robust as it performs significantly better on noisy data and on data with close susbspaces and outliers while it is not prone to oversegmentation | [['sparse', 'subspace', 'clustering', 'ssc', 'is', 'one', 'of', 'the', 'current', 'stateoftheart', 'methods', 'for', 'partitioning', 'data', 'points', 'into', 'the', 'union', 'of', 'subspaces', 'with', 'strong', 'theoretical', 'guarantees', 'however', 'it', 'is', 'not', 'practical', 'for', 'large', 'data', 'sets', 'as', 'it', 'requires', 'solving', 'a', 'lasso', 'problem', 'for', 'each', 'data', 'point', 'where', 'the', 'number', 'of', 'variables', 'in', 'each', 'lasso', 'problem', 'is', 'the', 'number', 'of', 'data', 'points', 'to', 'improve', 'the', 'scalability', 'of', 'ssc', 'we', 'propose', 'to', 'select', 'a', 'few', 'sets', 'of', 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'method', 'not', 'only', 'allows', 'ssc', 'to', 'scale', 'to', 'largescale', 'data', 'sets', 'but', 'that', 'it', 'is', 'also', 'much', 'more', 'robust', 'as', 'it', 'performs', 'significantly', 'better', 'on', 'noisy', 'data', 'and', 'on', 'data', 'with', 'close', 'susbspaces', 'and', 'outliers', 'while', 'it', 'is', 'not', 'prone', 'to', 'oversegmentation']] | [-0.07657376557379977, 0.00281003839020276, -0.05801968538198131, 0.06236769308070589, -0.10333150224043773, -0.1631246035975484, 0.10833872744931557, 0.401205793954432, -0.3085306200675026, -0.2955189927573826, 0.11354470509525844, -0.29002792751228246, -0.1130040766691317, 0.18370636444269128, -0.0921574504097831, 0.06500140273294568, 0.13094106654118223, 0.05475590006149125, -0.04811669032013558, -0.30070178340701703, 0.3425356292058356, 0.05981881245001476, 0.30835405767503365, -0.047531650879955534, 0.1156561815557049, 0.01814860136172317, -0.01682256236756684, 0.0625163286300671, -0.019942025933697833, 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1,802.07649 | Harnack's Inequality for Parabolic Nonlocal Equations | The main result of this paper is a nonlocal version of Harnack's inequality
for a class of parabolic nonlocal equations. We additionally establish a weak
Harnack inequality as well as local boundedness of solutions. None of the
results require the solution to be globally positive.
| math.AP | the main result of this paper is a nonlocal version of harnacks inequality for a class of parabolic nonlocal equations we additionally establish a weak harnack inequality as well as local boundedness of solutions none of the results require the solution to be globally positive | [['the', 'main', 'result', 'of', 'this', 'paper', 'is', 'a', 'nonlocal', 'version', 'of', 'harnacks', 'inequality', 'for', 'a', 'class', 'of', 'parabolic', 'nonlocal', 'equations', 'we', 'additionally', 'establish', 'a', 'weak', 'harnack', 'inequality', 'as', 'well', 'as', 'local', 'boundedness', 'of', 'solutions', 'none', 'of', 'the', 'results', 'require', 'the', 'solution', 'to', 'be', 'globally', 'positive']] | [-0.1118327606883314, -0.02779257714541422, -0.07421222730643219, 0.08956959988507959, -0.09920439504914813, -0.18348586316116983, -0.025995533662434255, 0.2449564983861314, -0.3204025745391846, -0.2593295325628585, 0.18521818005893792, -0.27580361891951827, -0.14536166199379497, 0.23208847077977326, -0.10296776357831226, 0.09181674788188603, 0.06432028131352531, 0.001919350607527627, -0.07410145436103145, -0.22020232174545526, 0.3941623917884297, -0.08389233955078655, 0.18250758399566014, 0.11078991190426879, 0.0858852772663037, -0.0341006434108648, 0.028900925525360638, 0.06267726190595163, -0.18250530733623438, 0.13396639894280168, 0.2179592315107584, 0.09773372544182671, 0.3617273727224933, -0.3832536220964458, -0.17518509849905967, 0.18977076924509473, 0.0938434173249536, 0.13429078087210655, -0.07606859280106922, -0.3060575452115801, 0.1078282153647807, -0.11594856230335103, -0.2653145919657416, -0.08896270208060741, -0.03378890715539455, 0.1156098493685325, -0.33732902622885175, 0.18995477188792492, 0.17636598158472527, 0.011890902587523063, -0.15682032834738494, -0.020642264363252453, 0.012226262248845564, 0.054375910727928085, 0.06345868345556988, 0.006737174691321949, 0.015492107895099454, -0.0819436704274267, -0.09824838742820753, 0.3184801421231694, -0.14154929908820324, -0.25597007502801716, 0.1254622034728527, -0.10208321873926454, -0.15784949573377768, 0.03097832745148076, 0.14482699834431212, 0.20189398825168609, -0.19383738347225718, 0.11321626599464152, -0.1603581730276346, 0.12472752100891538, 0.06701355595141649, 0.09222145840111706, 0.0452620676615172, 0.10492167452143299, 0.25648624238868556, 0.14459027859330592, 0.026637379535370403, -0.08032514500535197, -0.44865064720312753, -0.23604238368570804, -0.16875450062151584, 0.15597883173161084, -0.10678668652350704, -0.22616045168704457, 0.3485517781641748, 0.07408649526122543, 0.14543441865179274, 0.12793996431347396, 0.20203970107767316, 0.17625123482818406, 0.05124279008143478, 0.05043906975835044, 0.25615536860293814, 0.21067376806814636, 0.17042316667632096, -0.16079374072659347, 0.07051229647153781, 0.20366854555904865] |
1,802.0765 | Relativistic Entropy Inequality | In this paper we apply the entropy principle to the relativistic version of
the differential equations describing a standard fluid flow, that is, the
equations for mass, momentum, and a system for the energy matrix. These are the
second order equations which have been introduced in [3]. Since the principle
also says that the entropy equation is a scalar equation, this implies, as we
show, that one has to take a trace in the energy part of the system. Thus one
arrives at the relativistic mass-momentum-energy system for the fluid. In the
procedure we use the well-known Liu-M\"uller sum [10] in order to deduce the
Gibbs relation and the residual entropy inequality.
| math-ph math.MP | in this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow that is the equations for mass momentum and a system for the energy matrix these are the second order equations which have been introduced in 3 since the principle also says that the entropy equation is a scalar equation this implies as we show that one has to take a trace in the energy part of the system thus one arrives at the relativistic massmomentumenergy system for the fluid in the procedure we use the wellknown liumuller sum 10 in order to deduce the gibbs relation and the residual entropy inequality | [['in', 'this', 'paper', 'we', 'apply', 'the', 'entropy', 'principle', 'to', 'the', 'relativistic', 'version', 'of', 'the', 'differential', 'equations', 'describing', 'a', 'standard', 'fluid', 'flow', 'that', 'is', 'the', 'equations', 'for', 'mass', 'momentum', 'and', 'a', 'system', 'for', 'the', 'energy', 'matrix', 'these', 'are', 'the', 'second', 'order', 'equations', 'which', 'have', 'been', 'introduced', 'in', '3', 'since', 'the', 'principle', 'also', 'says', 'that', 'the', 'entropy', 'equation', 'is', 'a', 'scalar', 'equation', 'this', 'implies', 'as', 'we', 'show', 'that', 'one', 'has', 'to', 'take', 'a', 'trace', 'in', 'the', 'energy', 'part', 'of', 'the', 'system', 'thus', 'one', 'arrives', 'at', 'the', 'relativistic', 'massmomentumenergy', 'system', 'for', 'the', 'fluid', 'in', 'the', 'procedure', 'we', 'use', 'the', 'wellknown', 'liumuller', 'sum', '10', 'in', 'order', 'to', 'deduce', 'the', 'gibbs', 'relation', 'and', 'the', 'residual', 'entropy', 'inequality']] | [-0.10998275592033793, 0.0953960136116088, -0.13571618069047192, 0.07688821418848527, -0.027703826038821322, -0.09100968736802807, -0.02451479501145481, 0.2539327005260028, -0.2973675656358938, -0.2856251276937221, 0.09651273606357642, -0.2925403043438957, -0.10019773207940497, 0.170667630569959, -0.04015323200875574, 0.05415102683410451, 0.05037361851826243, 0.10367589550269013, -0.07186536891553719, -0.2131178012444965, 0.36721349103158124, 0.013544482573329865, 0.24009538412110898, 0.07136099350949128, 0.17305603229046404, -0.006775486440322286, 0.016537168046442775, 0.041604109691573424, -0.13498123115035318, 0.0939790657952193, 0.18959946177379638, 0.09655066286968822, 0.2748947271758372, -0.38631309907010813, -0.2261049827174829, 0.10297231482308325, 0.09026004442408143, 0.14524156776328176, -0.023995576276672533, -0.20883135424574484, 0.07819841581035976, -0.20777952266219366, -0.16514967225055704, -0.05965232344235184, 0.003078861220798514, -0.005085241250895165, -0.25808513343233513, 0.13573137905698351, 0.09927722066640854, -0.026843275775480596, -0.09166888050894412, -0.06266121752665017, -0.017512856479230766, 0.07244932028960001, 0.059246547358647525, 0.01777727649387744, 0.0659508567957862, -0.09997823172844611, -0.06858563747965975, 0.40385388153361845, -0.0838624213335549, -0.23748960513789374, 0.13589584354210543, -0.1468405780374064, -0.15505258327450705, 0.09771451095186241, 0.16645989196190425, 0.11209927038876927, -0.18317402449126044, 0.09059268240250547, -0.05148450337216124, 0.14692025510845957, 0.05077104497625417, -0.008532462285009321, 0.14924511255545392, 0.10658434454586592, 0.07807524415437837, 0.14645178230093406, -0.0685751894153319, -0.13043792419311767, -0.3377777852552213, -0.25164586085792595, -0.17826907573947431, 0.06380699503629862, -0.07234298268323638, -0.12122299887558764, 0.36482566507818465, 0.15493096877308982, 0.15631416334711887, 0.05393735567833557, 0.29243780997464314, 0.21140253630168904, 0.06377200260003274, 0.10667330600522659, 0.27534998390563503, 0.17568272209583638, 0.16203171534144933, -0.21590070313431095, 0.015596729984322379, 0.15942317932038694] |
1,802.07651 | Mixed perverse sheaves on flag varieties of Coxeter groups | In this paper we construct an abelian category of "mixed perverse sheaves"
attached to any realization of a Coxeter group, in terms of the associated
Elias-Williamson diagrammatic category. This construction extends previous work
of the first two authors, where we worked with parity complexes instead of
diagrams, and we extend most of the properties known in this case to the
general setting. As an application we prove that the split Grothendieck group
of the Elias-Williamson diagrammatic category is isomorphic to the
corresponding Hecke algebra, for any choice of realization.
| math.RT | in this paper we construct an abelian category of mixed perverse sheaves attached to any realization of a coxeter group in terms of the associated eliaswilliamson diagrammatic category this construction extends previous work of the first two authors where we worked with parity complexes instead of diagrams and we extend most of the properties known in this case to the general setting as an application we prove that the split grothendieck group of the eliaswilliamson diagrammatic category is isomorphic to the corresponding hecke algebra for any choice of realization | [['in', 'this', 'paper', 'we', 'construct', 'an', 'abelian', 'category', 'of', 'mixed', 'perverse', 'sheaves', 'attached', 'to', 'any', 'realization', 'of', 'a', 'coxeter', 'group', 'in', 'terms', 'of', 'the', 'associated', 'eliaswilliamson', 'diagrammatic', 'category', 'this', 'construction', 'extends', 'previous', 'work', 'of', 'the', 'first', 'two', 'authors', 'where', 'we', 'worked', 'with', 'parity', 'complexes', 'instead', 'of', 'diagrams', 'and', 'we', 'extend', 'most', 'of', 'the', 'properties', 'known', 'in', 'this', 'case', 'to', 'the', 'general', 'setting', 'as', 'an', 'application', 'we', 'prove', 'that', 'the', 'split', 'grothendieck', 'group', 'of', 'the', 'eliaswilliamson', 'diagrammatic', 'category', 'is', 'isomorphic', 'to', 'the', 'corresponding', 'hecke', 'algebra', 'for', 'any', 'choice', 'of', 'realization']] | [-0.14472241630631216, 0.034474371342849135, -0.08454001340439564, 0.02685435546962335, -0.13495507646938054, -0.08664231733262037, -0.008986288962854345, 0.34354978879348613, -0.3350243176754794, -0.1888560623432813, 0.0717090824632016, -0.1970092559212379, -0.1660965181719721, 0.1697569117263964, -0.18698894778747907, -0.0953983920090047, 0.03655850551917814, 0.10762323922048626, -0.08825455218804686, -0.28179179104777535, 0.4419845871292473, -0.0017110646566313305, 0.25158309367265597, 0.02225196220273717, 0.060006140406881826, 0.05669239339722174, -0.013333519120187907, -0.03214553993697582, -0.1398285724935704, 0.1786112947823752, 0.3278919168109639, 0.022334065170581924, 0.1916924645716136, -0.3805764439264626, -0.08464989311740671, 0.1862062364934389, 0.14357693081072878, 0.10661137613645766, -0.03326791051115966, -0.27846376484605284, 0.08415777529223581, -0.2726996296891168, -0.1441875873656755, -0.046760512149652066, 0.031036970325944463, -0.03139593222000626, -0.22872347719548794, -0.05180883393204363, 0.06822838796449177, 0.10895733384603865, -0.09466801223533458, -0.0939215910817193, -0.01827531031678232, 0.11399087101074584, -0.03758521180526678, 0.004917537903392248, 0.07873319659716962, -0.12242697285268497, -0.18378610580406163, 0.3848096140022023, -0.06401766548744205, -0.20213091810851286, 0.1543048959738167, -0.13631212111729918, -0.22104520569398498, 0.08243401010070792, 0.04476616696946407, 0.18315445418270787, -0.039102264931111526, 0.1654282257770544, -0.158625505366912, 0.06923008580257844, 0.08877459620491843, 0.020061431058258698, 0.0746547520092657, 0.12325990027905012, 0.03099775822895966, 0.18054383731018123, 0.024449348187445548, -0.07354275631100944, -0.40068723562728153, -0.21711243715515266, -0.11285104495839457, 0.09913744962135895, -0.029640231270891132, -0.18560580325344306, 0.41359194602524296, 0.17649766767209166, 0.18688649463492152, 0.12736723266458244, 0.22264104010014052, 0.07340604873842382, 0.07044782267695063, 0.0013730786112921961, 0.12434598442501901, 0.22640877365647408, -0.04300077517681724, -0.12600533993328722, -0.013950343275170647, 0.2129798531793895] |
1,802.07652 | Landmark Placement for Localization in a GPS-denied Environment | Path planning algorithms for unmanned aerial or ground vehicles, in many
surveillance applications, rely on Global Positioning System (GPS) information
for localization. However, disruption of GPS signals, by intention or
otherwise, can render these plans and algorithms ineffective. This article
provides a way of addressing this issue by utilizing stationary landmarks to
aid localization in such GPS-disrupted or GPS-denied environment. In
particular, given the vehicle's path, we formulate a landmark-placement problem
and present algorithms to place the minimum number of landmarks while
satisfying the localization, sensing, and collision-avoidance constraints. The
performance of such a placement is also evaluated via extensive simulations on
ground robots.
| math.OC | path planning algorithms for unmanned aerial or ground vehicles in many surveillance applications rely on global positioning system gps information for localization however disruption of gps signals by intention or otherwise can render these plans and algorithms ineffective this article provides a way of addressing this issue by utilizing stationary landmarks to aid localization in such gpsdisrupted or gpsdenied environment in particular given the vehicles path we formulate a landmarkplacement problem and present algorithms to place the minimum number of landmarks while satisfying the localization sensing and collisionavoidance constraints the performance of such a placement is also evaluated via extensive simulations on ground robots | [['path', 'planning', 'algorithms', 'for', 'unmanned', 'aerial', 'or', 'ground', 'vehicles', 'in', 'many', 'surveillance', 'applications', 'rely', 'on', 'global', 'positioning', 'system', 'gps', 'information', 'for', 'localization', 'however', 'disruption', 'of', 'gps', 'signals', 'by', 'intention', 'or', 'otherwise', 'can', 'render', 'these', 'plans', 'and', 'algorithms', 'ineffective', 'this', 'article', 'provides', 'a', 'way', 'of', 'addressing', 'this', 'issue', 'by', 'utilizing', 'stationary', 'landmarks', 'to', 'aid', 'localization', 'in', 'such', 'gpsdisrupted', 'or', 'gpsdenied', 'environment', 'in', 'particular', 'given', 'the', 'vehicles', 'path', 'we', 'formulate', 'a', 'landmarkplacement', 'problem', 'and', 'present', 'algorithms', 'to', 'place', 'the', 'minimum', 'number', 'of', 'landmarks', 'while', 'satisfying', 'the', 'localization', 'sensing', 'and', 'collisionavoidance', 'constraints', 'the', 'performance', 'of', 'such', 'a', 'placement', 'is', 'also', 'evaluated', 'via', 'extensive', 'simulations', 'on', 'ground', 'robots']] | [-0.17916419646501833, 0.028999645733183213, -0.025925286977058825, 0.041793710627483535, -0.07229411241361032, -0.1407135181338983, 0.08383817760292075, 0.4231981552621423, -0.22555502915901005, -0.3695195483445537, 0.17150809223804733, -0.2500315884621266, -0.1915619065870951, 0.20851442825240904, -0.1699344633768002, 0.1263779823978742, 0.1430598783818092, 0.06413080457794279, -0.016786176142940187, -0.1865839800756315, 0.2568933767513098, 0.026837511695738808, 0.28856610905780805, 0.02744540605264917, 0.12474259056662228, 0.09557696629781276, -0.007144424177514499, 0.03334107253170919, -0.07949800862172875, 0.15451294066745094, 0.32595319801247585, 0.20340794253656092, 0.2935023812221034, -0.48940039312868727, -0.22727804189986167, 0.13857911334957415, 0.18731578900570087, 0.09915397444730807, -0.07682687038437043, -0.4142455472702197, 0.0918941727163745, -0.16803764287090184, -0.09663656063596993, -0.05684707659826267, -0.02321895576703052, 0.05856712425399261, -0.2799579051378019, -0.021451470531425074, -0.0060373020961004146, 0.10045572404074025, -0.0936872603499568, -0.03668305749306455, 0.05994991955402143, 0.22327085470383548, 0.0387145092998467, 0.006376808843639332, 0.17571406129875458, -0.17875655396503634, -0.162766325780574, 0.4312247272909564, 0.057804259786601454, -0.22065733592299855, 0.21294237730805488, -0.020465179399002855, -0.14824908807435455, 0.11244138914580439, 0.2204440788311117, 0.13643487980224045, -0.19525512050399008, 0.0404571831031182, 0.014400221449071906, 0.1163235478760565, 0.04173066528221848, 0.056497776912817474, 0.20555809241394693, 0.21394190503348248, 0.2211572455542445, 0.06850423572548464, -0.12242939734578077, -0.0589246557678516, -0.19190760114967512, -0.12022974885379274, -0.20133932949701214, 0.008659891473750273, -0.03239026338768799, -0.12382271691275687, 0.33955882707902907, 0.23647799588940746, 0.15418380482907534, 0.06657914606872581, 0.41695862166656583, 0.04525528477268595, 0.012578341790347123, 0.09326010130975834, 0.18833295665179178, -0.02740587203252111, 0.11152422419228755, -0.18099755835810713, 0.10018680716280405, 0.07300243964966606] |
1,802.07653 | Building Efficient ConvNets using Redundant Feature Pruning | This paper presents an efficient technique to prune deep and/or wide
convolutional neural network models by eliminating redundant features (or
filters). Previous studies have shown that over-sized deep neural network
models tend to produce a lot of redundant features that are either shifted
version of one another or are very similar and show little or no variations;
thus resulting in filtering redundancy. We propose to prune these redundant
features along with their connecting feature maps according to their
differentiation and based on their relative cosine distances in the feature
space, thus yielding smaller network size with reduced inference costs and
competitive performance. We empirically show on select models and CIFAR-10
dataset that inference costs can be reduced by 40% for VGG-16, 27% for
ResNet-56, and 39% for ResNet-110.
| cs.CV | this paper presents an efficient technique to prune deep andor wide convolutional neural network models by eliminating redundant features or filters previous studies have shown that oversized deep neural network models tend to produce a lot of redundant features that are either shifted version of one another or are very similar and show little or no variations thus resulting in filtering redundancy we propose to prune these redundant features along with their connecting feature maps according to their differentiation and based on their relative cosine distances in the feature space thus yielding smaller network size with reduced inference costs and competitive performance we empirically show on select models and cifar10 dataset that inference costs can be reduced by 40 for vgg16 27 for resnet56 and 39 for resnet110 | [['this', 'paper', 'presents', 'an', 'efficient', 'technique', 'to', 'prune', 'deep', 'andor', 'wide', 'convolutional', 'neural', 'network', 'models', 'by', 'eliminating', 'redundant', 'features', 'or', 'filters', 'previous', 'studies', 'have', 'shown', 'that', 'oversized', 'deep', 'neural', 'network', 'models', 'tend', 'to', 'produce', 'a', 'lot', 'of', 'redundant', 'features', 'that', 'are', 'either', 'shifted', 'version', 'of', 'one', 'another', 'or', 'are', 'very', 'similar', 'and', 'show', 'little', 'or', 'no', 'variations', 'thus', 'resulting', 'in', 'filtering', 'redundancy', 'we', 'propose', 'to', 'prune', 'these', 'redundant', 'features', 'along', 'with', 'their', 'connecting', 'feature', 'maps', 'according', 'to', 'their', 'differentiation', 'and', 'based', 'on', 'their', 'relative', 'cosine', 'distances', 'in', 'the', 'feature', 'space', 'thus', 'yielding', 'smaller', 'network', 'size', 'with', 'reduced', 'inference', 'costs', 'and', 'competitive', 'performance', 'we', 'empirically', 'show', 'on', 'select', 'models', 'and', 'cifar10', 'dataset', 'that', 'inference', 'costs', 'can', 'be', 'reduced', 'by', '40', 'for', 'vgg16', '27', 'for', 'resnet56', 'and', '39', 'for', 'resnet110']] | [-0.04180648381316132, 0.045849836396087085, -0.05834343302922207, 0.05631192228884174, -0.11106672948881169, -0.19670894001956185, 0.0690963131355602, 0.4889333663045363, -0.2823272081222967, -0.3551755723747192, 0.10124833468125871, -0.2701824011091958, -0.18200813952216777, 0.17526316991825297, -0.12531862512332737, 0.04892264824229642, 0.13204202829365386, 0.0018244296925331582, -0.08358164409037272, -0.2919616086774113, 0.2733418897169031, 0.09166951458382755, 0.30039467970709666, -0.029219344094599364, 0.08792140568402829, -0.06229155970868305, -0.08638739828529651, 0.009719662378017802, -0.026669755944965345, 0.18890742992334708, 0.25513109803088696, 0.15662880485979258, 0.3014035559608601, -0.44871616465388797, -0.22968902086631715, 0.11615842407263699, 0.15553875927435, 0.09832236031616048, 0.0016521009401913034, -0.2976298077574029, 0.1302731348987436, -0.16413324218592606, 0.012009869642497506, -0.17272484371278551, 0.0062561308695876505, 0.01252398501674179, -0.25097536070097703, 0.03676640447883983, 0.07002482631497742, 0.05123534402810037, -0.014730619473994011, -0.16722361985739553, -0.038981663794402266, 0.09588698590778222, 0.006515064422274008, 0.054107910388665914, 0.11855846843172912, -0.1653764910861355, -0.12123262706882088, 0.3199395865231054, -0.06020351110055344, -0.21652886058200238, 0.23815000037029677, 0.0020679419540101662, -0.14455336966057075, 0.14992992948100436, 0.2201183670440514, 0.08903769300377462, -0.15195481231421581, -0.027701158124273206, -0.0006549355457536876, 0.19792974206939107, 0.09022730827564374, 0.05441934600003151, 0.19496964678364748, 0.18869632439782436, 0.07105991497974173, 0.13867204550570023, -0.15233273991543683, -0.06783114268182544, -0.1721741928413394, -0.07962147202852066, -0.1341574290618155, -0.014082884277740959, -0.13885434773635552, -0.14742527313569553, 0.3650525403827487, 0.2037436520386109, 0.26969673096846236, 0.14716549934382783, 0.2746729976752249, 0.052741792333108606, 0.20115511316726042, 0.11873087353160372, 0.21023687525303103, 0.021730620912421728, 0.08692983784567332, -0.14333851273795517, 0.09384235636025551, 0.03799735914071789] |
1,802.07654 | Intersecting limit sets of Kleinian subgroups and Susskind's question | We construct a non-elementary Fuchsian group that admits two non-elementary
subgroups with trivial intersection and whose radial limit sets intersect
non-trivially. This negatively answers a question of Perry Susskind (1989) that
was stated as a conjecture by James W. Anderson (2014).
| math.DS | we construct a nonelementary fuchsian group that admits two nonelementary subgroups with trivial intersection and whose radial limit sets intersect nontrivially this negatively answers a question of perry susskind 1989 that was stated as a conjecture by james w anderson 2014 | [['we', 'construct', 'a', 'nonelementary', 'fuchsian', 'group', 'that', 'admits', 'two', 'nonelementary', 'subgroups', 'with', 'trivial', 'intersection', 'and', 'whose', 'radial', 'limit', 'sets', 'intersect', 'nontrivially', 'this', 'negatively', 'answers', 'a', 'question', 'of', 'perry', 'susskind', '1989', 'that', 'was', 'stated', 'as', 'a', 'conjecture', 'by', 'james', 'w', 'anderson', '2014']] | [-0.1804722297436944, 0.17765399521194036, -0.12241872356886543, 0.07348871088825257, -0.12374362794727814, -0.22567089954845426, 0.10470699554411467, 0.3128049266411037, -0.2126692174593123, -0.24332923986153995, 0.07771526966471135, -0.2760806679668859, -0.1322375133451892, 0.1913759788816295, -0.22012535486052312, -0.010675133410386922, 0.10231218138062281, -0.009753937719435227, 0.0016459610835626358, -0.3892229282774213, 0.34482610407398967, -0.046282214214798154, 0.19948489805002037, 0.08372770922213066, 0.09026756906518485, 0.05513896981663093, -0.030602998634028, 0.03500765470060997, -0.1768927276492965, 0.06901729849263707, 0.28190449643425824, 0.07716751793717466, 0.23080662330726115, -0.27685455503169354, -0.15947874581509427, 0.1613241678285526, 0.11764015009763037, -0.03385490746941508, -0.02090909988505811, -0.3537268626798944, 0.04197851032382104, -0.17049638505616202, -0.2101323844683243, -0.015156301488054962, 0.15267914987918807, -0.08592248271878172, -0.14931557691093852, 0.02215830207143615, 0.19729452334889552, 0.06237471060509362, -0.009763788000294349, -0.030021584899414602, -0.07550435392867501, 0.060699414660608984, -0.0036652418500857384, 0.11104067286090334, 0.051692508922026655, 0.030049840130320773, -0.21317711798474193, 0.37028655482501516, -0.10290641329682819, -0.1762519370673633, 0.17843883514131714, -0.17699596330114617, -0.19876268940761957, 0.10929899324276825, 0.06698731074064243, 0.1244946546034842, -0.05169527194031128, 0.28616612856475093, -0.27759066939626525, 0.09393514055054544, 0.2225220230430728, -0.10900392328820578, 0.1124545398804291, -0.007095170525334231, 0.0557041735070326, 0.102463427522197, 0.12346563071421371, 0.06832751723165374, -0.3055958554784699, -0.18423071178812078, -0.12201499280224486, 0.1977017872069576, -0.008197727510577818, -0.23728745480681337, 0.3304838037527189, 0.016146340362000758, 0.1529389328618602, 0.10852476652348186, 0.10806396390061553, 0.07640793394558586, -0.03899271377339596, 0.16871678056876835, 0.12184630159470367, 0.1940501430696558, -0.06171257375943952, -0.16472758716199457, -0.04661348316727615, 0.30436191837326054] |
1,802.07655 | A Riemann-Hilbert problem for uncoupled BPS structures | We study the Riemann-Hilbert problem attached to an uncoupled BPS structure
proposed by Bridgeland in "Riemann-Hilbert problems from Donaldson-Thomas
theory". We show that it has "essentially" unique meromorphic solutions given
by a product of Gamma functions. We reconstruct the corresponding connection.
| math.AG hep-th | we study the riemannhilbert problem attached to an uncoupled bps structure proposed by bridgeland in riemannhilbert problems from donaldsonthomas theory we show that it has essentially unique meromorphic solutions given by a product of gamma functions we reconstruct the corresponding connection | [['we', 'study', 'the', 'riemannhilbert', 'problem', 'attached', 'to', 'an', 'uncoupled', 'bps', 'structure', 'proposed', 'by', 'bridgeland', 'in', 'riemannhilbert', 'problems', 'from', 'donaldsonthomas', 'theory', 'we', 'show', 'that', 'it', 'has', 'essentially', 'unique', 'meromorphic', 'solutions', 'given', 'by', 'a', 'product', 'of', 'gamma', 'functions', 'we', 'reconstruct', 'the', 'corresponding', 'connection']] | [-0.12284418934865332, -0.04805446454719924, -0.1387574356503603, 0.08693302068405034, -0.08173786516006036, -0.13253435343731104, -0.026148177129670797, 0.33332080098732214, -0.3617024105496523, -0.23909800695028247, 0.08058654984442244, -0.2352319099009037, -0.27457621689068107, 0.16252368674954262, -0.12223446007999705, 0.09539124283303575, 0.08726907929507788, 0.03305026910426777, -0.12653511752965066, -0.23783017187833605, 0.4332150533772642, -0.03593513705744976, 0.2576953575878245, 0.026891628064487767, 0.1228664109210779, 0.0006939077454550964, 0.014605385785150091, -0.05215387196257347, -0.18953695123331626, 0.13688335830924986, 0.33083536610484304, 0.12920551074714196, 0.18475827972813533, -0.4081101900012028, -0.11692552154929173, 0.15251424018202758, 0.15331969827004685, 0.029444381617373082, -0.01684544528493794, -0.31773450216505583, 0.09843228235500069, -0.10842090499837224, -0.20116328584348284, -0.060566276402735125, 0.026820345634094824, -0.008516003883148476, -0.20600457690093985, 0.014719521621151305, -0.055577808945644194, -0.008129106266651212, -0.12441255256715344, -0.07047344078650562, -0.049914532715863574, 0.04712240885170858, 0.06930357996919533, 0.05081320380814737, 0.03761131197168696, -0.15314263047468735, -0.13311833865577127, 0.2685572851403821, -0.04786780301663207, -0.2705551010170361, 0.12479346150123491, -0.10664976163335689, -0.16049908518382325, 0.15868163479083194, 0.09055853799757797, 0.205704522069271, -0.0988220966594271, 0.19987333177520736, -0.17923081707118488, 0.13280497125645235, 0.17100213727027905, -0.10328375385710742, 0.17670314999796996, 0.09614516955959361, 0.08736817296821534, 0.20308585226444936, 0.021603276373863948, -0.09115333623457246, -0.33127219102731564, -0.12933094036288378, -0.14560432359576225, 0.15375571461712442, -0.09274272808078222, -0.19709080462230416, 0.4566506553077843, 0.07845935445824047, 0.19701041701454214, 0.08157590547826414, 0.1390719026690576, 0.18735576491439487, 0.02113856261641514, 0.01743524155874805, 0.17984087251853653, 0.2628398698459311, 0.062434464610726916, -0.22862372315125312, -0.07525783673882848, 0.22491166838331195] |
1,802.07656 | Effects of CO2 flushing on crystal textures and compositions:
experimental evidence from recent K trachybasalts erupted at Mt. Etna | Changes in magmatic assemblages and crystal stability as a response of CO2
flushing in basaltic systems have been never directly addressed experimentally,
making the role of CO2 in magma dynamics still controversial and object of
scientific debate. We conducted a series of experiments to understand the
response of magmas from Etna volcano to CO2 flushing. We performed a first
experiment at 300 MPa to synthesize a starting material composed of crystals of
some hundreds of m and melt pools. This material is representative of an
initial magmatic assemblage composed of plagioclase, clinopyroxene and a water
undersaturated melt. In a second step, the initial assemblage was equilibrated
at 300 and 100 MPa with fluids having different XCO2fl . Our experiments
demonstrate that flushing basaltic systems with fluids may drastically affect
crystal textures and phase equilibria depending on the amount of H2O and CO2 in
the fluid phase. Since texture and crystal proportions are among the most
important parameters governing the rheology of magmas, fluid flushing will also
influence magma ascent to the Earths surface. The experimental results open new
perspectives to decipher the textural and compositional record of minerals
observed in volcanic rocks from Mt. Etna, and at the same time offer the basis
for interpreting the information preserved in minerals from other basaltic
volcanoes erupting magmas enriched in CO2.
| physics.geo-ph | changes in magmatic assemblages and crystal stability as a response of co2 flushing in basaltic systems have been never directly addressed experimentally making the role of co2 in magma dynamics still controversial and object of scientific debate we conducted a series of experiments to understand the response of magmas from etna volcano to co2 flushing we performed a first experiment at 300 mpa to synthesize a starting material composed of crystals of some hundreds of m and melt pools this material is representative of an initial magmatic assemblage composed of plagioclase clinopyroxene and a water undersaturated melt in a second step the initial assemblage was equilibrated at 300 and 100 mpa with fluids having different xco2fl our experiments demonstrate that flushing basaltic systems with fluids may drastically affect crystal textures and phase equilibria depending on the amount of h2o and co2 in the fluid phase since texture and crystal proportions are among the most important parameters governing the rheology of magmas fluid flushing will also influence magma ascent to the earths surface the experimental results open new perspectives to decipher the textural and compositional record of minerals observed in volcanic rocks from mt etna and at the same time offer the basis for interpreting the information preserved in minerals from other basaltic volcanoes erupting magmas enriched in co2 | [['changes', 'in', 'magmatic', 'assemblages', 'and', 'crystal', 'stability', 'as', 'a', 'response', 'of', 'co2', 'flushing', 'in', 'basaltic', 'systems', 'have', 'been', 'never', 'directly', 'addressed', 'experimentally', 'making', 'the', 'role', 'of', 'co2', 'in', 'magma', 'dynamics', 'still', 'controversial', 'and', 'object', 'of', 'scientific', 'debate', 'we', 'conducted', 'a', 'series', 'of', 'experiments', 'to', 'understand', 'the', 'response', 'of', 'magmas', 'from', 'etna', 'volcano', 'to', 'co2', 'flushing', 'we', 'performed', 'a', 'first', 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1,802.07657 | DNA-Graphene Interactions During Translocation Through Nanogaps | We study how double-stranded DNA translocates through graphene nanogaps.
Nanogaps are fabricated with a novel capillary-force induced graphene nanogap
formation technique. DNA translocation signatures for nanogaps are
qualitatively different from those obtained with circular nanopores, owing to
the distinct shape of the gaps discussed here. Translocation time and
conductance values vary by $\sim 100$%, which we suggest are caused by local
gap width variations. We also observe exponentially relaxing current traces. We
suggest that slow relaxation of the graphene membrane following DNA
translocation may be responsible. We conclude that DNA-graphene interactions
are important, and need to be considered for graphene-nanogap based devices.
This work further opens up new avenues for direct read of single molecule
activitities, and possibly sequencing.
| cond-mat.mes-hall | we study how doublestranded dna translocates through graphene nanogaps nanogaps are fabricated with a novel capillaryforce induced graphene nanogap formation technique dna translocation signatures for nanogaps are qualitatively different from those obtained with circular nanopores owing to the distinct shape of the gaps discussed here translocation time and conductance values vary by sim 100 which we suggest are caused by local gap width variations we also observe exponentially relaxing current traces we suggest that slow relaxation of the graphene membrane following dna translocation may be responsible we conclude that dnagraphene interactions are important and need to be considered for graphenenanogap based devices this work further opens up new avenues for direct read of single molecule activitities and possibly sequencing | [['we', 'study', 'how', 'doublestranded', 'dna', 'translocates', 'through', 'graphene', 'nanogaps', 'nanogaps', 'are', 'fabricated', 'with', 'a', 'novel', 'capillaryforce', 'induced', 'graphene', 'nanogap', 'formation', 'technique', 'dna', 'translocation', 'signatures', 'for', 'nanogaps', 'are', 'qualitatively', 'different', 'from', 'those', 'obtained', 'with', 'circular', 'nanopores', 'owing', 'to', 'the', 'distinct', 'shape', 'of', 'the', 'gaps', 'discussed', 'here', 'translocation', 'time', 'and', 'conductance', 'values', 'vary', 'by', 'sim', '100', 'which', 'we', 'suggest', 'are', 'caused', 'by', 'local', 'gap', 'width', 'variations', 'we', 'also', 'observe', 'exponentially', 'relaxing', 'current', 'traces', 'we', 'suggest', 'that', 'slow', 'relaxation', 'of', 'the', 'graphene', 'membrane', 'following', 'dna', 'translocation', 'may', 'be', 'responsible', 'we', 'conclude', 'that', 'dnagraphene', 'interactions', 'are', 'important', 'and', 'need', 'to', 'be', 'considered', 'for', 'graphenenanogap', 'based', 'devices', 'this', 'work', 'further', 'opens', 'up', 'new', 'avenues', 'for', 'direct', 'read', 'of', 'single', 'molecule', 'activitities', 'and', 'possibly', 'sequencing']] | [-0.1433656914645563, 0.22808245601962604, -0.021957280011543925, 0.004571024355802523, -0.030981910981885765, -0.22031891512401078, 0.058312635312018836, 0.4738933715969324, -0.3135643478442469, -0.2934490189533276, -0.002519618863563823, -0.24128534933147222, -0.1839892477963788, 0.21487872737824268, -0.008069180203702949, 0.031133324137772433, 0.12116893880150241, -0.1416282941992192, 0.008010484197217485, -0.1651395352638286, 0.22915778600651285, 0.04758784787567413, 0.27451406146764107, 0.1322736045345664, 0.0024548246403751166, -0.04942475857602878, 0.032618181759734514, 0.05096777487323498, -0.22177457696538033, 0.13153662357641302, 0.20171624328941107, -0.017069050681817792, 0.22162767128775948, -0.5317630290013292, -0.20309667074647936, 0.038320391009683194, 0.2194120291620493, 0.1848944016114768, -0.09553094211264776, -0.2696724246215561, 0.11695712175442959, -0.11686306416016558, -0.07961157944810111, -0.05818343434644782, 0.013261515955926607, 0.06099147515816857, -0.20600352793850976, 0.12332547444055546, -0.0011517925552375938, 0.031013719049856857, -0.038003024156838046, -0.1241715391409462, -0.0029896498455301576, 0.10675367266749558, 0.08765248377685962, 0.002680227745567327, 0.3029856757017905, -0.05710189231853608, -0.13142703207128723, 0.3216323652021263, -0.05148069276069493, -0.13037247664254645, 0.16991179391397568, -0.14301234116858763, -0.10567605763916736, 0.16939997546496274, 0.08396578411490697, 0.10007308292729052, -0.18762288095186586, -0.004297748300672063, 0.04436775830614826, 0.17882190197908684, 0.16810451894188705, 0.0645154119256641, 0.2838053489630313, 0.2267776383087039, 0.022489909868201485, 0.1557435238794626, -0.1259287348209435, -0.06263568163849413, -0.2213063109666109, -0.17634189919791307, -0.15012773894907339, 0.09645198369398714, -0.05304373142185479, -0.13543954593655855, 0.39602952806845954, 0.12988323424234177, 0.22787561870139578, 0.03675253552020244, 0.2154003682343856, 0.05949801393663106, 0.11752663855643376, -0.019024809619978718, 0.19118456998283206, 0.08348916147066199, 0.07882868447948409, -0.2680377597920597, 0.09347889473783257, -0.05833707531792638] |
1,802.07658 | The local rotation curve of the Milky Way based on SEGUE and RAVE data | We construct the rotation curve of the Milky Way in the extended solar
neighbourhood using a sample of SEGUE (Sloan Extension for Galactic
Understanding and Exploration) G-dwarfs. We investigate the rotation curve
shape for the presence of any peculiarities just outside the solar radius as
has been reported by some authors. We approach the problem in a framework of
classical Jeans analysis. Using the most recent data from RAVE (RAdial Velocity
Experiment), we determine the solar peculiar velocity and the radial
scalelengths for the three populations of different metallicities representing
the Galactic thin disc. Then with the same binning in metallicity for the SEGUE
G-dwarfs, we construct the rotation curve in the range of Galactocentric
distances 7-10 kpc. We derive the circular velocity by correcting the mean
tangential velocity for the asymmetric drift in each distance bin. With SEGUE
data we also calculate the radial scalelength of the thick disc taking as known
the derived peculiar motion of the Sun and the slope of the rotation curve. The
rotation curve constructed through SEGUE G-dwarfs appears to be smooth in the
selected radial range. The local kinematics of the thin disc rotation as
determined in the framework of our new careful analysis does not favour the
presence of a massive overdensity ring just outside the solar radius.
| astro-ph.GA | we construct the rotation curve of the milky way in the extended solar neighbourhood using a sample of segue sloan extension for galactic understanding and exploration gdwarfs we investigate the rotation curve shape for the presence of any peculiarities just outside the solar radius as has been reported by some authors we approach the problem in a framework of classical jeans analysis using the most recent data from rave radial velocity experiment we determine the solar peculiar velocity and the radial scalelengths for the three populations of different metallicities representing the galactic thin disc then with the same binning in metallicity for the segue gdwarfs we construct the rotation curve in the range of galactocentric distances 710 kpc we derive the circular velocity by correcting the mean tangential velocity for the asymmetric drift in each distance bin with segue data we also calculate the radial scalelength of the thick disc taking as known the derived peculiar motion of the sun and the slope of the rotation curve the rotation curve constructed through segue gdwarfs appears to be smooth in the selected radial range the local kinematics of the thin disc rotation as determined in the framework of our new careful analysis does not favour the presence of a massive overdensity ring just outside the solar radius | [['we', 'construct', 'the', 'rotation', 'curve', 'of', 'the', 'milky', 'way', 'in', 'the', 'extended', 'solar', 'neighbourhood', 'using', 'a', 'sample', 'of', 'segue', 'sloan', 'extension', 'for', 'galactic', 'understanding', 'and', 'exploration', 'gdwarfs', 'we', 'investigate', 'the', 'rotation', 'curve', 'shape', 'for', 'the', 'presence', 'of', 'any', 'peculiarities', 'just', 'outside', 'the', 'solar', 'radius', 'as', 'has', 'been', 'reported', 'by', 'some', 'authors', 'we', 'approach', 'the', 'problem', 'in', 'a', 'framework', 'of', 'classical', 'jeans', 'analysis', 'using', 'the', 'most', 'recent', 'data', 'from', 'rave', 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1,802.07659 | 3D modelling of self-organized patterns of spots on anodes of DC glow
discharge | Self-organized patterns of spots on a at metallic anode in a cylindrical glow
dis- charge tube are simulated self-consistently. A standard model of a glow
discharge is used, comprising conservation and transport equations for a single
species of ion and electrons, written with the use of the drift-diffusion and
local-field approximations, and the Poisson equation. The computation domain is
the region from the anode to the discharge column; only processes in the
near-anode region are considered. Multiple solutions, existing in the same
range of discharge current and describing modes with and without anode spots,
are computed by means of a stationary solver. The computed spots exhibited
unexpected behavior. A reversal of the local anode current density in the
middle of each of the spots was found, i.e. mini-cathodes are formed inside the
spots. The solutions do not fit into the conventional pattern of
self-organization in bistable nonlinear dissipative systems; e.g. the modes are
not joined by bifurcations.
| physics.plasm-ph | selforganized patterns of spots on a at metallic anode in a cylindrical glow dis charge tube are simulated selfconsistently a standard model of a glow discharge is used comprising conservation and transport equations for a single species of ion and electrons written with the use of the driftdiffusion and localfield approximations and the poisson equation the computation domain is the region from the anode to the discharge column only processes in the nearanode region are considered multiple solutions existing in the same range of discharge current and describing modes with and without anode spots are computed by means of a stationary solver the computed spots exhibited unexpected behavior a reversal of the local anode current density in the middle of each of the spots was found ie minicathodes are formed inside the spots the solutions do not fit into the conventional pattern of selforganization in bistable nonlinear dissipative systems eg the modes are not joined by bifurcations | [['selforganized', 'patterns', 'of', 'spots', 'on', 'a', 'at', 'metallic', 'anode', 'in', 'a', 'cylindrical', 'glow', 'dis', 'charge', 'tube', 'are', 'simulated', 'selfconsistently', 'a', 'standard', 'model', 'of', 'a', 'glow', 'discharge', 'is', 'used', 'comprising', 'conservation', 'and', 'transport', 'equations', 'for', 'a', 'single', 'species', 'of', 'ion', 'and', 'electrons', 'written', 'with', 'the', 'use', 'of', 'the', 'driftdiffusion', 'and', 'localfield', 'approximations', 'and', 'the', 'poisson', 'equation', 'the', 'computation', 'domain', 'is', 'the', 'region', 'from', 'the', 'anode', 'to', 'the', 'discharge', 'column', 'only', 'processes', 'in', 'the', 'nearanode', 'region', 'are', 'considered', 'multiple', 'solutions', 'existing', 'in', 'the', 'same', 'range', 'of', 'discharge', 'current', 'and', 'describing', 'modes', 'with', 'and', 'without', 'anode', 'spots', 'are', 'computed', 'by', 'means', 'of', 'a', 'stationary', 'solver', 'the', 'computed', 'spots', 'exhibited', 'unexpected', 'behavior', 'a', 'reversal', 'of', 'the', 'local', 'anode', 'current', 'density', 'in', 'the', 'middle', 'of', 'each', 'of', 'the', 'spots', 'was', 'found', 'ie', 'minicathodes', 'are', 'formed', 'inside', 'the', 'spots', 'the', 'solutions', 'do', 'not', 'fit', 'into', 'the', 'conventional', 'pattern', 'of', 'selforganization', 'in', 'bistable', 'nonlinear', 'dissipative', 'systems', 'eg', 'the', 'modes', 'are', 'not', 'joined', 'by', 'bifurcations']] | [-0.12876521623995638, 0.14350198242120826, -0.0349966218868175, 0.025211282910253756, 0.013195187848909065, -0.14550381089644268, 0.01578335279340629, 0.33826960913407117, -0.23215077343420723, -0.278266936301803, 0.08095916199351613, -0.3013640607181841, -0.06276464164674951, 0.17559145774486332, -0.010080199920943974, 0.043057441535170375, 0.02307857194234832, -0.011028250891309327, -0.0474170531020858, -0.15171945341176185, 0.25955241119775635, 0.030995730779324777, 0.3049410730540657, 0.027977617955632292, 0.09578349464461028, -0.07070005260025844, -0.006869329092576384, 0.05361404393811543, -0.07779370592787671, 0.05536996695744351, 0.2283193610760813, 0.02130667471105997, 0.19799499126533285, -0.5148823591283499, -0.2617274586839649, 0.028892725497523013, 0.15399519963522415, 0.09554317677639819, -0.06132505167848789, -0.26336526971023816, 0.06063577845149363, -0.13015239384288016, -0.14125591779324728, 0.009573064711637413, 0.001997168653477461, 0.10975034866117848, -0.2719411746246549, 0.09134688797162081, 0.062112251809594454, 0.042654119091495, -0.09670364987463333, -0.07581869369217505, -0.07841728312763362, 0.08538645441727474, 0.017817974327138077, -0.01786781924490172, 0.20460798897562574, -0.13934919438086069, -0.07845897200212885, 0.37512831628704685, -0.05728205332156787, -0.19531345668469724, 0.1905658078403809, -0.19956967479382187, -0.028116751483116202, 0.19459102094883862, 0.14621018388798127, 0.11459880923846355, -0.16909941483456165, 0.04192084256479015, -0.02400752356147561, 0.12452136789339327, 0.12289360530662517, -0.041054454969409376, 0.27737723971203637, 0.18975518014019307, 0.018071973662023455, 0.1239987237264965, -0.12902384319265062, -0.10332078846374479, -0.28811227389087435, -0.12547328973559138, -0.13577373404031953, -0.004952736361398517, -0.042060588870252755, -0.2142610372438167, 0.4389773545374807, 0.06398708510077529, 0.18391681200442597, -0.039325795006544255, 0.29787057645332354, 0.13617881200013635, 0.08113628557811563, 0.09131251668963486, 0.20403097653970456, 0.14115804691428843, 0.15502688312867227, -0.2510812605181948, 0.09541682786164948, 0.055022205830587506] |
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