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let $ \ kappa $ be an infinite cardinal. a topological space $ x $ is $ \ kappa $ - bounded if the closure of any subset of cardinality $ \ le \ kappa $ in $ x $ is compact. we discuss the problem of embeddability of topological spaces into hausdorff ( urysohn, regular ) $ \ kappa $ - bounded spaces, and present a canonical construction of such an embedding. also we construct a ( consistent ) example of a sequentially compact separable regular space that cannot be embedded into a hausdorff $ \ omega $ - bounded space.
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arxiv:1906.00185
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q - learning is widely employed for optimizing various large - dimensional networks with unknown system dynamics. recent advancements include multi - environment mixed q - learning ( memq ) algorithms, which utilize multiple independent q - learning algorithms across multiple, structurally related but distinct environments and outperform several state - of - the - art q - learning algorithms in terms of accuracy, complexity, and robustness. we herein conduct a comprehensive probabilistic coverage analysis to ensure optimal data coverage conditions for memq algorithms. first, we derive upper and lower bounds on the expectation and variance of different coverage coefficients ( cc ) for memq algorithms. leveraging these bounds, we develop a simple way of comparing the utilities of multiple environments in memq algorithms. this approach appears to be near optimal versus our previously proposed partial ordering approach. we also present a novel cc - based memq algorithm to improve the accuracy and complexity of existing memq algorithms. numerical experiments are conducted using random network graphs with four different graph properties. our algorithm can reduce the average policy error ( ape ) by 65 % compared to partial ordering and is 95 % faster than the exhaustive search. it also achieves 60 % less ape than several state - of - the - art reinforcement learning and prior memq algorithms. additionally, we numerically verify the theoretical results and show their scalability with the action - space size.
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arxiv:2411.08360
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we present a fully - kinetic simulation of the full life cycle of strong langmuir turbulence ( slt ) excited by electron beams that are accelerated under the solar corona conditions. we find that ( 1 ) most packets ( $ \ sim $ 80 % ) are affected by their neighbors during their collapse, as a result, their spatial scale variations present non - standard evolutionary features, i. e., deviating away from what was predicted by the zakharov model ; ( 2 ) the collapsing cavity is too shallow to trap the wave packet due to the growth of the coulomb force, as a result a majority ( $ \ sim $ 70 % ) of the packet energy runs away and a secondary localization may occur. the study indicates that the non - standard langmuir collapse may play an important role in coronal plasmas interacting with an intense electron beam, that may be eventually confirmed by humanity ' s first mission to fly through the corona.
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arxiv:2406.05467
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let omega be a domain in c ^ 2. we prove the following theorem. if the envelope of holomorphy of omega is schlicht over omega, then the envelope is in fact schlicht. we provide examples showing that the theorem is not true in c ^ n, n > 2. additionally, we show that the theorem cannot be generalized to provide information about domains in c ^ 2 whose envelopes are multiply sheeted.
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arxiv:math/0404497
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semiconductor compounds are widely used for water splitting applications, where photo - generated electron - hole pairs are exploited to induce catalysis. recently, powders of a metallic oxide ( sr $ _ { 1 - x } $ nbo $ _ 3 $, 0. 03 < x < 0. 20 ) have shown competitive photocatalytic efficiency, opening up the material space available for finding optimizing performance in water - splitting applications. the origin of the visible light absorption in these powders was reported to be due to an interband transition and the charge carrier separation was proposed to be due to the high carrier mobility of this material. in the current work we have prepared epitaxial thin films of sr $ _ { 0. 94 } $ nbo $ _ { 3 + { \ delta } } $ and found that the bandgap of this material is ~ 4. 1 ev, which is very large. surprisingly the carrier density of the conducting phase reaches 10 $ ^ { 22 } $ cm $ ^ { - 3 } $, which is only one order smaller than that of elemental metals and the carrier mobility is only 2. 47 cm $ ^ 2 $ / ( v $ \ cdot $ s ). contrary to earlier reports, the visible light absorption at 1. 8 ev ( ~ 688 nm ) is due to the bulk plasmon resonance, arising from the large carrier density, instead of an interband transition. excitation of the plasmonic resonance results in a multifold enhancement of the lifetime of charge carriers. thus we propose that the hot charge carriers generated from decay of plasmons produced by optical absorption is responsible for the water splitting efficiency of this material under visible light irradiation.
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arxiv:1608.00194
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hu, kriz and may recently reexamined ideas implicit in priddy ' s elegant homotopy theoretic construction of the brown - peterson spectrum at a prime p. they discussed may ' s notions of nuclear complexes and of cores of spaces, spectra, and commutative s - algebras. their most striking conclusions, due to hu and kriz, were negative : cores are not unique up to equivalence, and bp is not a core of mu considered as a commutative s - algebra, although it is a core of mu considered as a p - local spectrum. we investigate these ideas further, obtaining much more positive conclusions. we show that nuclear complexes have several non - obviously equivalent characterizations. up to equivalence, they are precisely the irreducible complexes, the minimal atomic complexes, and the hurewicz complexes with trivial mod p hurewicz homomorphism above the hurewicz dimension, which we call complexes with no mod p detectable homotopy. unlike the notion of a nuclear complex, these other notions are all invariant under equivalence. this simple and conceptual criterion for a complex to be minimal atomic allows us to prove that many familiar spectra, such as ko, eo _ 2, and bop at the prime 2, all bp < n > at any prime p, and the indecomposable wedge summands of the suspension spectra of $ cp ^ \ infty $ and $ hp ^ \ infty $ at any prime p are minimal atomic.
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arxiv:math/0206067
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accurate recognition of specific categories, such as persons ' names, dates or other identifiers is critical in many automatic speech recognition ( asr ) applications. as these categories represent personal information, ethical use of this data including collection, transcription, training and evaluation demands special care. one way of ensuring the security and privacy of individuals is to redact or eliminate personally identifiable information ( pii ) from collection altogether. however, this results in asr models that tend to have lower recognition accuracy of these categories. we use text - injection to improve the recognition of pii categories by including fake textual substitutes of pii categories in the training data using a text injection method. we demonstrate substantial improvement to recall of names and dates in medical notes while improving overall wer. for alphanumeric digit sequences we show improvements to character error rate and sentence accuracy.
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arxiv:2308.07393
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in the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristic ( attribute ) of nodes ( or edges ) of networks. each isospectral compression ( when a certain characteristic is fixed ) defines a dynamical system on the space of all networks. it is shown that any orbit of such dynamical system which starts at any finite network ( as the initial point of this orbit ) converges to an attractor. such attractor is a smaller network where a chosen characteristic has the same value for all nodes ( or edges ). we demonstrate that isospectral contractions of one and the same network defined by different characteristics of nodes ( or edges ) may converge to the same as well as to different attractors. it is also shown that spectrally equivalent with respect to some characteristic networks could be non - spectrally equivalent for another characteristic of nodes ( edges ). these results suggest a new constructive approach to analysis of networks structures and to comparison of topologies of different networks.
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arxiv:1804.00976
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the high altitude platform station ( haps ) technology is garnering significant interest as a viable technology for serving as base stations in communication networks. however, haps faces the challenge of high spatial correlation among adjacent users ' channel gains which is due to the dominant line - of - sight ( los ) path between haps and terrestrial users. furthermore, there is a spatial correlation among antenna elements of haps that depends on the propagation environment and the distance between elements of the antenna array. this paper presents an antenna architecture for haps and considers the mentioned issues by characterizing the channel gain and the spatial correlation matrix of the haps. we propose a cylindrical antenna for haps that utilizes vertical uniform linear array ( ula ) sectors. moreover, to address the issue of high spatial correlation among users, the non - orthogonal multiple access ( noma ) clustering method is proposed. an algorithm is also developed to allocate power among users to maximize both spectral efficiency and energy efficiency while meeting quality of service ( qos ) and successive interference cancellation ( sic ) conditions. finally, simulation results indicate that the spatial correlation has a significant impact on spectral efficiency and energy efficiency in multiple antenna haps systems.
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arxiv:2407.00549
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pattern plays a vital role in software architecture and it is a general reusable solution to commonly occurring problem. software architecture of a system is the set of structures needed to reason about the system, which comprise software elements, relations among them, and properties of both. patterns can be implemented at run - time ; they identify key resource constraints and best practices. architecture pattern expresses a fundamental structural organization or schema for software systems. patterns in software architecture, offer the promise of helping the architect to identify combinations of architecture or solution building blocks that have been proven to deliver effective solutions. in internet banking, we analyzed some attributes such as reliability, security, availability, load balancing and so on. the use of patterns, which is of a reusable component, is a good tool to help designers build load balancing systems. in this paper we are going to propose pattern based adaptive architecture for internet banking system and so the above attributes can be improved by the usage of patterns.
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arxiv:1312.2325
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we show that the fritzsch texture of lepton mass matrices can naturally lead to the bi - large flavor mixing pattern, if three neutrinos have a normal but weak mass hierarchy ( typically, $ m _ 1 : m _ 2 : m _ 3 \ sim 1 : 3 : 10 $ ). the effective mass of the tritium beta decay and that of the neutrinoless double beta decay are too small to be observable in this ansatz, but cp violation at the percent level is allowed and could be measured in long - baseline neutrino oscillations.
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arxiv:hep-ph/0210276
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collisions of gas particles with a drifting grain give rise to a mechanical torque on the grain. recent work by lazarian & hoang showed that mechanical torques might play a significant role in aligning helical grains along the interstellar magnetic field direction, even in the case of subsonic drift. we compute the mechanical torques on 13 different irregular grains and examine their resulting rotational dynamics, assuming steady rotation about the principal axis of greatest moment of inertia. we find that the alignment efficiency in the subsonic drift regime depends sensitively on the grain shape, with more efficient alignment for shapes with a substantial mechanical torque even in the case of no drift. the alignment is typically more efficient for supersonic drift. a more rigorous analysis of the dynamics is required to definitively appraise the role of mechanical torques in grain alignment.
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arxiv:1602.04775
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in this paper we will study the asymptotic behaviour of the energy decay of a transmission plate equation with locally distributed kelvin - voigt feedback. precisly, we shall prove that the energy decay at least logarithmically over the time. the originality of this method comes from the fact that using a carleman estimate for a transmission second order system which will be derived from the plate equation to establish a resolvent estimate which provide, by the famous burq ' s result [ bur98 ], the kind of decay mentionned above.
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arxiv:1403.0356
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we report our study of the evolution of superconductivity and the phase diagram of the ternary fe ( se1 - xtex ) 0. 82 ( 0 < = x < = 1. 0 ) system. we discovered a new superconducting phase with tc, max = 14 k in the 0. 3 < x < 1. 0 range. this superconducting phase is suppressed when the sample composition approaches the end member fete0. 82, which exhibits an incommensurate antiferromagnetic order. we discuss the relationship between the superconductivity and magnetism of this material system in terms of recent results from neutron scattering measurements. our results and analyses suggest that superconductivity in this new class of fe - based compounds is associated with magnetic fluctuations, and therefore may be unconventional in nature.
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arxiv:0807.4775
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self - supervised learning ( ssl ) as an effective paradigm of representation learning has achieved tremendous success on various curated datasets in diverse scenarios. nevertheless, when facing the long - tailed distribution in real - world applications, it is still hard for existing methods to capture transferable and robust representation. conventional ssl methods, pursuing sample - level uniformity, easily leads to representation learning disparity where head classes dominate the feature regime but tail classes passively collapse. to address this problem, we propose a novel geometric harmonization ( gh ) method to encourage category - level uniformity in representation learning, which is more benign to the minority and almost does not hurt the majority under long - tailed distribution. specially, gh measures the population statistics of the embedding space on top of self - supervised learning, and then infer an fine - grained instance - wise calibration to constrain the space expansion of head classes and avoid the passive collapse of tail classes. our proposal does not alter the setting of ssl and can be easily integrated into existing methods in a low - cost manner. extensive results on a range of benchmark datasets show the effectiveness of gh with high tolerance to the distribution skewness. our code is available at https : / / github. com / mediabrain - sjtu / geometric - harmonization.
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arxiv:2310.17622
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we present initial results from monte carlo simulations of nrqcd - light, static - light, and nrqcd - nrqcd mesons, using a variational technique ( most ), as part of our ongoing calculation of the $ f _ { b } $ decay constant. the basis states for the variational calculation are quark - antiquark operators separated by all possible relative distances not equivalent under the cubic group ( for example, for a $ 20 ^ { 3 } $ lattice there are 286 operators ). the efficacy of the method is demonstrated by the good plateaus obtained for the ground state and the clean extraction of the wave functions of the ground and first radially excited state.
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arxiv:hep-lat/9411087
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influence of associative delusions ( ad ) onto development of physics and mathematics is investigated. the associative delusion ( ad ) means a mistake, appearing from incorrect associations, when a property of one object is attributed to another one. examples of most ancient delusions are : ( 1 ) connection of the gravitation field direction with a preferred direction in space ( instead of the direction towards the earth centre ), that had lead to the antipode paradox, ( 2 ) statement that the earth ( not the sun ) is the centre of the planetary system, that had lead to the ptolemaic doctrine. now these ads have been overcame. in the paper one considers four modern and not yet got over ads, whose corollaries are false space - time geometry in the micro world and most of problems and difficulties of the quantum field theory ( qft ). one shows that ads have a series of interesting properties : ( 1 ) ads appear to be long - living delusions, because they are compensated partly by means of introduction of compensating ( ptolemaic ) conceptions, ( 2 ) ads influence on scientific investigations, generating a special pragmatic style ( p - style ) of investigations resembling experimental trial and error method, ( 3 ) acting on investigations directly and via p - style, ads direct the science development into a blind alley. one considers concrete properties of modern ads and the methods of their overcoming. from viewpoint of application the paper is an analysis of mistakes, made in the quantum theory development. one analyses reasons of these mistakes and suggests methods of their correction.
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arxiv:physics/0201065
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phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization - group theory is one of the greatest achievements of theoretical physics. however, the predictions of the theory above an upper critical dimension $ d _ c $ seriously disagree with reality. in addition to its fundamental significance, the problem is also of practical importance because both complex systems with spatial or temporal long - range interactions and quantum phase transitions can substantially lower $ d _ c $. the extant scenarios built on a dangerous irrelevant variable ( div ) to resolve the problem introduce two sets of critical exponents and even two sets of scaling laws whose origin is obscure. here, we consider the div from a different perspective and clearly unveil the origin of the two sets of exponents and hence the intrinsic inconsistency in those scenarios. we then develop an effective - dimension theory in which critical fluctuations and system volume are fixed at an effective dimension by the div. this enables us to account for all the extant results consistently. a novel asymptotic finite - size scaling behavior for a correlation function together with a new anomalous dimension and its associated scaling law is also derived.
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arxiv:2203.16245
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we give an example of an infinitesimally nonrigid polyhedron in the lobachevsky 3 - space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn ' t stationary under the flex.
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arxiv:1002.3884
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it is shown that passive gravitational mass operator of a hydrogen atom in the post - newtonian approximation of the general relativity does not commute with its energy operator, taken in the absence of gravitational field. nevertheless, the equivalence between the expectation values of passive gravitational mass and energy is shown to survive at a macroscopic level for stationary quantum states. breakdown of the equivalence between passive gravitational mass and energy at a microscopic level for stationary quantum states can be experimentally detected by studying unusual electromagnetic radiation, emitted by the atoms, supported and moved in the earth gravitational field with constant velocity using spacecraft or satellite.
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arxiv:1208.5756
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we consider inclusions $ \ mathcal { s } \ leq \ mathcal { r } $ of discrete, probability measure - preserving orbit equivalence relations. in previous work with ab \ ' { e } rt - fra \ c { c } zyk, we established the pointwise almost sure existence of the cospectral radius of a random walk on the $ \ mathcal { r } $ - classes. in this paper, we investigate the connections of this cospectral radius to the coamenability of the inclusion $ \ mathcal { s } \ leq \ mathcal { r } $. we also undertake a systematic study of coamenability for inclusions of relations, establishing several equivalence formulations of this notion.
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arxiv:2410.16480
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2. 54 $ mev and $ 18. 4 $ mev, respectively. we have established a new recommended $ ^ { 38 } \ mathrm { k } ( p, \ gamma ) { } ^ { 39 } \ mathrm { ca } $ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of $ { \ sim } 250 $. using the rate obtained in this work in model calculations of the hottest oxygen - neon novae reduces overall uncertainties on $ \ mathrm { ar } $, $ \ mathrm { k } $, and $ \ mathrm { ca } $ synthesis to factors of $ 15 $ or less in all cases.
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arxiv:1801.00845
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motivated by original equipment manufacturer ( oem ) service and maintenance practices we consider a single component subject to replacements at failure instances and two types of preventive maintenance opportunities : scheduled, which occur due to periodic system reviews of the equipment, and unscheduled, which occur due to failures of other components in the system. modelling the state of the component appropriately and incorporating a realistic cost structure for corrective maintenance as well as condition - based maintenance ( cbm ), we derive the optimal cbm policy. in particular, we show that the optimal long - run average cost policy for the model at hand is a control - limit policy, where the control limit depends on the time until the next scheduled opportunity. furthermore, we explicitly calculate the long - run average cost for any given control - limit time dependent policy and compare various policies numerically.
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arxiv:1607.02299
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we show that space - time evolution of one - dimensional fermionic systems is described by nonlinear equations of soliton theory. we identify a space - time dependence of a matrix element of fermionic systems related to the { \ it orthogonality catastrophe } or { boundary states } with the $ \ tau $ - function of the modified kp - hierarchy. the established relation allows to apply the apparatus of soliton theory to the study of non - linear aspects of quantum dynamics. we also describe a { \ it bosonization in momentum space } - a representation of a fermion operator by a bose field in the presence of a boundary state.
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arxiv:nlin/0605006
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lanthanum hydride lah $ _ { 10 } $ with a sodalitelike clathrate structure was experimentally realized to exhibit a room - temperature superconductivity under megabar pressures. based on first - principles calculations, we reveal that the metal framework of la atoms has the excess electrons at interstitial regions. such anionic electrons are easily captured to form a stable clathrate structure of h cages. we thus propose that the charge transfer from la to h atoms is mostly driven by the electride property of the la framework. further, the interaction between la atoms and h cages induces a delocalization of la - 5 $ p $ semicore states to hybridize with h - 1 $ s $ state. consequently, the bonding nature between la atoms and h cages is characterized as a mixture of ionic and covalent. our findings demonstrate that anionic and semicore electrons play important roles in stabilizing clathrate h cages in lah $ _ { 10 } $, which can be broadly applicable to other high - pressure rare - earth hydrides with clathrate structures.
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arxiv:2007.01531
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this paper offers an insightful examination of how currently top - trending ai technologies, i. e., generative artificial intelligence ( generative ai ) and large language models ( llms ), are reshaping the field of video technology, including video generation, understanding, and streaming. it highlights the innovative use of these technologies in producing highly realistic videos, a significant leap in bridging the gap between real - world dynamics and digital creation. the study also delves into the advanced capabilities of llms in video understanding, demonstrating their effectiveness in extracting meaningful information from visual content, thereby enhancing our interaction with videos. in the realm of video streaming, the paper discusses how llms contribute to more efficient and user - centric streaming experiences, adapting content delivery to individual viewer preferences. this comprehensive review navigates through the current achievements, ongoing challenges, and future possibilities of applying generative ai and llms to video - related tasks, underscoring the immense potential these technologies hold for advancing the field of video technology related to multimedia, networking, and ai communities.
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arxiv:2404.16038
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in physically realistic scalar - field based dynamical dark energy models ( including, e. g., quintessence ) one naturally expects the scalar field to couple to the rest of the model ' s degrees of freedom. in particular, a coupling to the electromagnetic sector leads to a time ( redshift ) dependence of the fine - structure constant and a violation of the weak equivalence principle. here we extend the previous euclid forecast constraints on dark energy models to this enlarged ( but physically more realistic ) parameter space, and forecast how well euclid, together with high - resolution spectroscopic data and local experiments, can constrain these models. our analysis combines simulated euclid data products with astrophysical measurements of the fine - structure constant, $ \ alpha $, and local experimental constraints, and includes both parametric and non - parametric methods. for the astrophysical measurements of $ \ alpha $ we consider both the currently available data and a simulated dataset representative of extremely large telescope measurements and expected to be available in the 2030s. our parametric analysis shows that in the latter case the inclusion of astrophysical and local data improves the euclid dark energy figure of merit by between $ 8 \ % $ and $ 26 \ % $, depending on the correct fiducial model, with the improvements being larger in the null case where the fiducial coupling to the electromagnetic sector is vanishing. these improvements would be smaller with the current astrophysical data. moreover, we illustrate how a genetic algorithms based reconstruction provides a null test for the presence of the coupling. our results highlight the importance of complementing surveys like euclid with external data products, in order to accurately test the wider parameter spaces of physically motivated paradigms.
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arxiv:2105.09746
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high - temperature alloy design requires a concurrent consideration of multiple mechanisms at different length scales. we propose a workflow that couples highly relevant physics into machine learning ( ml ) to predict properties of complex high - temperature alloys with an example of the 9 - 12 wt. % cr steels yield strength. we have incorporated synthetic alloy features that capture microstructure and phase transformations into the dataset. identified high impact features that affect yield strength of 9cr from correlation analysis agree well with the generally accepted strengthening mechanism. as part of the verification process, the consistency of sub - datasets has been extensively evaluated with respect to temperature and then refined for the boundary conditions of trained ml models. the predicted yield strength of 9cr steels using the ml models is in excellent agreement with experiments. the current approach introduces physically meaningful constraints in interrogating the trained ml models to predict properties of hypothetical alloys when applied to data - driven materials.
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arxiv:2004.05424
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q - balls formed from the affleck - dine field have rich cosmological implications and have been extensively studied from both theoretical and simulational approaches. from the theoretical point of view, the exact solution of the q - ball was obtained and it shows a circular orbit in the complex plane of the field value. in practice, however, it is reported that the q - ball that appears after the affleck - dine mechanism has an $ elliptical $ orbit, which carries larger energy per unit $ u ( 1 ) $ charge than the well - known solution with a circular orbit. we call them " elliptical " q - balls. in this paper, we report the first detailed investigation of the properties of the elliptical q - balls by $ 3 $ d lattice simulation. the simulation results indicate that the elliptical q - ball has an almost spherical spatial profile with no nodes, and we observed a highly elliptic orbit that cannot be described through small perturbations around the ground state q - ball. higher ellipticity leads to more excitation of the energy, whose relation is also derived as a dispersion relation. finally, we derive two types of approximate solutions by extending the gaussian approximation and considering the time - averaged equation of motion and we also show the consistency with the simulation results.
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arxiv:1903.07281
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spatiotemporal point processes ( stpps ) are probabilistic models for events occurring in continuous space and time. real - world event data often exhibit intricate dependencies and heterogeneous dynamics. by incorporating modern deep learning techniques, stpps can model these complexities more effectively than traditional approaches. consequently, the fusion of neural methods with stpps has become an active and rapidly evolving research area. in this review, we categorize existing approaches, unify key design choices, and explain the challenges of working with this data modality. we further highlight emerging trends and diverse application domains. finally, we identify open challenges and gaps in the literature.
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arxiv:2502.09341
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we present karl g jansky very large array molecular line observations of the nearby starburst galaxy ngc 253, from swan : " survey of water and ammonia in nearby galaxies ". swan is a molecular line survey at centimeter wavelengths designed to reveal the physical conditions of star forming gas over a range of star forming galaxies. ngc 253 has been observed in four 1ghz bands from 21 to 36 ghz at 6 " ( $ \ sim100 $ pc ) spatial and 3. 5 km s $ ^ { - 1 } $ spectral resolution. in total we detect 19 transitions from seven molecular and atomic species. we have targeted the metastable inversion transitions of ammonia ( nh $ _ { 3 } $ ) from ( 1, 1 ) to ( 5, 5 ) and the ( 9, 9 ) line, the 22. 2 ghz water ( h $ _ 2 $ o ) ( $ 6 _ { 16 } - 5 _ { 23 } $ ) maser, and the 36. 1 ghz methanol ( ch $ _ 3 $ oh ) ( $ 4 _ { - 1 } - 3 _ { 0 } $ ) maser. utilizing nh $ _ { 3 } $ as a thermometer, we present evidence for uniform heating over the central kpc of ngc 253. the molecular gas is best described by a two kinetic temperature model with a warm 130k and a cooler 57k component. a comparison of these observations with previous alma results suggests that the molecular gas is not heated in photon dominated regions or shocks. it is possible that the gas is heated by turbulence or cosmic rays. in the galaxy center we find evidence for nh $ _ { 3 } $ ( 3, 3 ) masers. furthermore we present velocities and luminosities of three water maser features related to the nuclear starburst. we partially resolve ch $ _ 3 $ oh masers seen at the edges of the bright molecular emission, which coincides with expanding molecular superbubbles. this suggests that the masers are pumped by weak shocks in the bubble surfaces.
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arxiv:1705.07103
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short - period comet p / 2010 v1 ( ikeya - murakami, hereafter v1 ) was discovered visually by two amateur astronomers. the appearance of the comet was peculiar, consisting of an envelope, a spherical coma near the nucleus and a tail extending in the anti - solar direction. we investigated the brightness and the morphological development of the comet by taking optical images with ground - based telescopes. our observations show that v1 experienced a large - scale explosion between ut 2010 october 31 and november 3. the color of the comet was consistent with the sun ( g ' - rc = 0. 61 + - 0. 20, rc - ic = 0. 20 + - 0. 20, and b - rc = 0. 93 + - 0. 25 ), suggesting that dust particles were responsible for the brightening. we used a dynamical model to understand the peculiar morphology, and found that the envelope consisted of small grains ( 0. 3 - 1 micron ) expanding at a maximum speed of 500 + - 40 m / s, while the tail and coma were composed of a wider range of dust particle sizes ( 0. 4 - 570 micron ) and expansion speeds 7 - 390 m / s. the total mass of ejecta is ~ 5x10 ^ 8 kg and kinetic energy ~ 5x10 ^ 12 j. these values are much smaller than in the historic outburst of 17p / holmes in 2007, but the energy per unit mass ( 1x10 ^ 4 j / kg ) is comparable. the energy per unit mass is about 10 % of the energy released during the crystallization of amorphous water ice suggesting that crystallization of buried amorphous ice can supply the mass and energy of the outburst ejecta.
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arxiv:1404.1630
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in this paper, we will construct a pre - normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. we will also give a sufficient condition, in the quasi - homogeneous, three - dimensional case, for these foliations to be of generalized surface type.
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arxiv:1306.4695
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we perform numerical and experimental studies on the melting process of thin films initiated by a small hole. the presence of a non - trivial capillary surface, namely the liquid / air interface, leads to a few counter - intuitive results : ( 1 ) the melting point is elevated if the film surface is partially wettable, even with a small contact angle. ( 2 ) for a film that is finite in size, melting may prefer to start from the outer boundary, rather than a hole inside. ( 3 ) more complex melting scenario may arise, including morphology transitions, and the " de facto " melting point being a range instead of a single value. these are verified by experiments on melting alkane films between silica and air. this work continues a series of investigations on the capillary aspects on melting. both our model and analysis approach can be easily generalized to other systems.
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arxiv:2204.10895
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this text aims to provide a self - contained, comprehensive, and reasonably detailed presentation of the theory of stallings automata and some of its main applications.
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arxiv:2403.10757
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precise control of hyperfine matterwaves via raman excitations is instrumental to a class of atom - based quantum technology. we investigate the raman spinor control technique for alkaline atoms in an intermediate regime of single - photon detuning where a choice can be made to balance the raman excitation power efficiency with the control speed, excited - state adiabatic elimination, and spontaneous emission suppression requirements. within the regime, rotations of atomic spinors by the raman coupling are biased by substantial light shifts. taking advantage of the fixed bias angle, we show that composite biased rotations can be optimized to enable precise ensemble spinor matterwave control within nanoseconds, even for multiple zeeman pseudo - spins defined on the hyperfine ground states and when the laser illumination is strongly inhomogeneous. our scheme fills a technical gap in light pulse atom interferometry, for achieving high speed raman spinor matterwave control with moderate laser power.
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arxiv:2305.17610
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this chapter reflects on about 10 years of research in ai - assisted music composition, in particular during the flow machines project. we reflect on the motivations for such a project, its background, its main results and impact, both technological and musical, several years after its completion. we conclude with a proposal for new categories of new, created by the many uses of ai techniques to generate novel material.
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arxiv:2006.09232
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most existing trackers are based on using a classifier and multi - scale estimation to estimate the target state. consequently, and as expected, trackers have become more stable while tracking accuracy has stagnated. while trackers adopt a maximum overlap method based on an intersection - over - union ( iou ) loss to mitigate this problem, there are defects in the iou loss itself, that make it impossible to continue to optimize the objective function when a given bounding box is completely contained within / without another bounding box ; this makes it very challenging to accurately estimate the target state. accordingly, in this paper, we address the above - mentioned problem by proposing a novel tracking method based on a distance - iou ( diou ) loss, such that the proposed tracker consists of target estimation and target classification. the target estimation part is trained to predict the diou score between the target ground - truth bounding - box and the estimated bounding - box. the diou loss can maintain the advantage provided by the iou loss while minimizing the distance between the center points of two bounding boxes, thereby making the target estimation more accurate. moreover, we introduce a classification part that is trained online and optimized with a conjugate - gradient - based strategy to guarantee real - time tracking speed. comprehensive experimental results demonstrate that the proposed method achieves competitive tracking accuracy when compared to state - of - the - art trackers while with a real - time tracking speed.
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arxiv:2007.01864
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we provide evidence that the sunward - propagating half of the solar wind electron halo distribution evolves without scattering in the inner heliosphere. we assume the particles conserve their total energy and magnetic moment, and perform a " liouville mapping " on electron pitch angle distributions measured by the parker solar probe span - e instrument. namely, we show that the distributions are consistent with liouville ' s theorem if an appropriate interplanetary potential is chosen. this potential, an outcome of our fitting method, is compared against the radial profiles of proton bulk flow energy. we find that the inferred potential is responsible for nearly 100 % of the proton acceleration in the solar wind at heliocentric distances 0. 18 - 0. 79 au. these observations combine to form a coherent physical picture : the same interplanetary potential accounts for the acceleration of the solar wind protons as well as the evolution of the electron halo. in this picture the halo is formed from a sunward - propagating population that originates somewhere in the outer heliosphere by a yet - unknown mechanism.
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arxiv:2204.06532
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the growth of the dimension of the homogeneous components of algebra is an essential topic in algebraic geometry and commutative algebra. in this context, the homogeneous components of an algebra are the pieces of the algebra that have the same degree. the study of the growth of the dimension of these components can shed light on the structure of the algebra and its behavior as the degree of the components increases. this concept is particularly important in the study of polynomial rings, which are a fundamental object in algebraic geometry and commutative algebra. understanding the growth of the dimension of their homogeneous components can provide insight into the geometry of the corresponding algebraic varieties. this topic is also particularly important in the study of projective varieties, where the homogeneous components correspond to the spaces of sections of line bundles of increasing degree. understanding the growth of these spaces is crucial for understanding the geometry of the variety. in this abstract, we provide an overview of the growth of the dimension of homogeneous components of an algebra, including its applications, results, and future research directions.
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arxiv:2306.01542
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radiology report generation ( rrg ) draws attention as a vision - and - language interaction of biomedical fields. previous works inherited the ideology of traditional language generation tasks, aiming to generate paragraphs with high readability as reports. despite significant progress, the independence between diseases - a specific property of rrg - was neglected, yielding the models being confused by the co - occurrence of diseases brought on by the biased data distribution, thus generating inaccurate reports. in this paper, to rethink this issue, we first model the causal effects between the variables from a causal perspective, through which we prove that the co - occurrence relationships between diseases on the biased distribution function as confounders, confusing the accuracy through two backdoor paths, i. e. the joint vision coupling and the conditional sequential coupling. then, we proposed a novel model - agnostic counterfactual augmentation method that contains two strategies, i. e. the prototype - based counterfactual sample synthesis ( p - css ) and the magic - cube - like counterfactual report reconstruction ( cube ), to intervene the backdoor paths, thus enhancing the accuracy and generalization of rrg models. experimental results on the widely used mimic - cxr dataset demonstrate the effectiveness of our proposed method. additionally, a generalization performance is evaluated on iu x - ray dataset, which verifies our work can effectively reduce the impact of co - occurrences caused by different distributions on the results.
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arxiv:2311.13307
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for a prime power $ q $, we study the distribution of determinent of matrices with restricted entries over a finite field $ \ mathbbm { f } _ q $ of $ q $ elements. more precisely, let $ n _ d ( \ mathcal { a } ; t ) $ be the number of $ d \ times d $ matrices with entries in $ \ mathcal { a } $ having determinant $ t $. we show that \ [ n _ d ( \ mathcal { a } ; t ) = ( 1 + o ( 1 ) ) \ frac { | \ mathcal { a } | ^ { d ^ 2 } } { q }, \ ] if $ | \ mathcal { a } | = \ omega ( q ^ { \ frac { d } { 2d - 1 } } ) $, $ d \ geqslant 4 $. when $ q $ is a prime and $ \ mathcal { a } $ is a symmetric interval $ [ - h, h ] $, we get the same result for $ d \ geqslant 3 $. this improves a result of ahmadi and shparlinski ( 2007 ).
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arxiv:0903.2508
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in this note we address the question of the $ \ theta $ dependence in non abelian gauge theories from a pure quantum information point of view. the main result is that the topological susceptibility is the quantum fisher information of the ground state and that the maximally efficient quantum estimator of $ \ theta $ can be identified with the physical axion. in this setup the low energy dynamics of the axion is fully determined by quantum estimation theory.
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arxiv:2007.03566
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in two - dimensional topological insulators, such as inverted hgte / cdte quantum wells, helical quantum spin hall ( qsh ) states persist even at finite magnetic fields below a critical magnetic field $ b _ \ mathrm { c } $, above which only quantum hall ( qh ) states can be found. using linear - response theory, we theoretically investigate the magneto - optical properties of inverted hgte / cdte quantum wells, both for infinite two - dimensional and finite - strip geometries, and possible signatures of the transition between the qsh and qh regimes. in the absorption spectrum, several peaks arise due to non - equidistant landau levels in both regimes. however, in the qsh regime, we find an additional absorption peak at low energies in the finite - strip geometry. this peak arises due to the presence of edge states in this geometry and persists for any fermi level in the qsh regime, while in the qh regime the peak vanishes if the fermi level is situated in the bulk gap. thus, by sweeping the gate voltage, it is possible to experimentally distinguish between the qsh and qh regimes due to this signature. moreover, we investigate the effect of spin - orbit coupling and finite temperature on this measurement scheme.
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arxiv:1502.05605
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when considering recurrent tasks in real - time systems, concurrent accesses to shared resources, can cause race conditions or data corruptions. such a problem has been extensively studied since the 1990s, and numerous resource synchronization protocols have been developed for both uni - processor and multiprocessor real - time systems, with the assumption that the implementation overheads are negligible. however, in practice, the implementation overheads may impact the performance of different protocols depending upon the practiced scenarios, e. g., resources are accessed locally or remotely, and tasks spin or suspend themselves when the requested resources are not available. in this paper, to show the applicability of different protocols in real - world systems, we detail the implementation of several state - of - the - art multiprocessor resource synchronization protocols in rtems. to study the impact of the implementation overheads, we deploy these implemented protocols on a real platform with synthetic task set. the measured results illustrate that the developed resource synchronization protocols in rtems are comparable to the existed protocol, i. e., mrsp.
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arxiv:2104.06366
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we apply wildeshaus ' s theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by deninger - murre and corti - hanamura. we first obtain a general motivic decomposition for the chow motive of an arbitrary smooth projective family $ f : x \ rightarrow s $ whose geometric fibers are tate. using voevodsky ' s motives with rational coefficients, the formula is valid for an arbitrary regular base $ s $, without assuming the existence of a base field or even of a prime integer $ \ ell $ invertible on $ s $. this result, and some of bondarko ' ideas, lead us to a generalized formulation of corti - hanamura ' s conjecture. secondly we establish the existence of the motivic decomposition when $ f : x \ rightarrow s $ is a projective quadric bundle over a characteristic $ 0 $ base, which is either sufficiently general or whose discriminant locus is a normal crossing divisor. this provides a motivic lift of the bernstein - beilinson - deligne decomposition in this setting.
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arxiv:2007.11447
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we report on landauer - b \ " uttiker studies of anomalous hall transport in a two - dimensional electron gas with rashba spin - orbit coupling and a magnetization provided by localized magnetic moments. our system is described by a discretized tight - binding model in a four - terminal geometry. we consider both the case of magnetically disordered systems as well as ballistic transport in disorder - free systems with spatially homoge - neous magnetization. in the latter case we investigate both out - of - plane and in - plane magnetizations. we numerically establish a close connection between singularities in the density of states and peaks in the hall conductance close to the lower band edge. consistent with previous theoretical studies based on diagrammatic perturbation expansions, these peaks occur at fermi energies where only the lower dispersion branch is occupied. moreover, for large magnetization the hall conductance is, along with the density of states, sup - pressed. this numerical finding can be understood from analytical properties of the underlying model in the limit of an infinite system.
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arxiv:0907.0110
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b. it is denoted by f − 1 ( b ) { \ displaystyle f ^ { - 1 } ( b ) } and is given by the equation f − 1 ( b ) = { x ∈ x f ( x ) ∈ b }. { \ displaystyle f ^ { - 1 } ( b ) = \ { x \ in x \ mid f ( x ) \ in b \ }. } for example, the preimage of { 4, 9 } { \ displaystyle \ { 4, 9 \ } } under the square function is the set { − 3, − 2, 2, 3 } { \ displaystyle \ { - 3, - 2, 2, 3 \ } }. by definition of a function, the image of an element x of the domain is always a single element of the codomain. however, the preimage f − 1 ( y ) { \ displaystyle f ^ { - 1 } ( y ) } of an element y of the codomain may be empty or contain any number of elements. for example, if f is the function from the integers to themselves that maps every integer to 0, then f − 1 ( 0 ) = z { \ displaystyle f ^ { - 1 } ( 0 ) = \ mathbb { z } }. if f : x → y { \ displaystyle f : x \ to y } is a function, a and b are subsets of x, and c and d are subsets of y, then one has the following properties : a ⊆ b f ( a ) ⊆ f ( b ) { \ displaystyle a \ subseteq b \ longrightarrow f ( a ) \ subseteq f ( b ) } c ⊆ d f − 1 ( c ) ⊆ f − 1 ( d ) { \ displaystyle c \ subseteq d \ longrightarrow f ^ { - 1 } ( c ) \ subseteq f ^ { - 1 } ( d ) } a ⊆ f − 1 ( f ( a ) ) { \ displaystyle a \ subseteq f ^ { - 1 } ( f ( a ) ) } c f ( f − 1 ( c ) ) { \ displaystyle c \ supseteq f ( f ^ { - 1 } ( c ) ) } f ( f − 1 ( f ( a ) ) ) = f ( a ) { \ displaystyle f ( f ^ { - 1 } ( f ( a
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https://en.wikipedia.org/wiki/Function_(mathematics)
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physical process version of the first law of black hole thermodynamics in einstein - maxwell dark matter gravity was derived. the dark matter sector is mimicked by the additional u ( 1 ) - gauge field coupled to the ordinary maxwell one. by considering any cross section of the black hole event horizon to the future of the bifurcation surface, the equilibrium state version of the first law of black hole mechanics was achieved. the considerations were generalized to the case of einstein - yang - mills dark matter gravity theory. the main conclusion is that the influence of dark matter is crucial in the formation process of black objects. this fact may constitute the explanation of the recent observations of the enormous mass of the super luminous quasars formed in a relatively short time after big bang. we also pay attention to the compact binaries thermodynamics, when dark matter sector enters the game.
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arxiv:1704.01370
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the threshold pump power for modelocking decreased by 18 % when the temperature was increased from 25 to 100 degrees c, where a swcnt / pdms coated tapered fiber was used as the saturable absorber in a fiber laser. further, the pump power at which multi - pulse operation began decreased by 24 %, and the pump power range over which fundamental modelocking could be maintained decreased by 59 % over the same temperature range. this decrease in stability is attributed to the large thermo - optic coefficient of the pdms polymer, which results in a 40 % reduction of the overlap between the evanescent field and swcnt coating of the taper fiber over a temperature range of 75 degrees c.
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arxiv:2404.18449
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fingerprints feature a ridge pattern with moderately varying ridge frequency ( rf ), following an orientation field ( of ), which usually features some singularities. additionally at some points, called minutiae, ridge lines end or fork and this point pattern is usually used for fingerprint identification and authentication. whenever the of features divergent ridge lines ( e. g. near singularities ), a nearly constant rf necessitates the generation of more ridge lines, originating at minutiae. we call these the necessary minutiae. it turns out that fingerprints feature additional minutiae which occur at rather arbitrary locations. we call these the random minutiae or, since they may convey fingerprint individuality beyond the of, the characteristic minutiae. in consequence, the minutiae point pattern is assumed to be a realization of the superposition of two stochastic point processes : a strauss point process ( whose activity function is given by the divergence field ) with an additional hard core, and a homogeneous poisson point process, modelling the necessary and the characteristic minutiae, respectively. we perform bayesian inference using an mcmc - based minutiae separating algorithm ( miseal ). in simulations, it provides good mixing and good estimation of underlying parameters. in application to fingerprints, we can separate the two minutiae patterns and verify by example of two different prints with similar of that characteristic minutiae convey fingerprint individuality.
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arxiv:2009.07910
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the n component scalar tricritical theory is considered in a non - perturbative setting. we derive non - perturbative beta functions for the relevant couplings in $ d \ leq 3 $. the beta functions are obtained through the use of an exact evolution equation for the so called effective average action. in d = 3 it is established the existence of an ultraviolet stable fixed point for n > 4. this confirms earlier results obtained using the 1 / n expansion where such a fixed point is believed to exist at least for $ n \ gtrsim 1000 $.
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arxiv:hep-th/9612227
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a second - order block coordinate descent method is proposed for the unconstrained minimization of an objective function with lipschitz continuous hessian. at each iteration, a block of variables is selected by means of a greedy ( gauss - southwell ) rule which considers the amount of first - order stationarity violation, then an approximate minimizer of a cubic model is computed for the block update. in the proposed scheme, blocks are not required to have a prefixed structure and their size is allowed to change during the iterations. for non - convex objective functions, global convergence to stationary points is proved and a worst - case iteration complexity analysis is provided. in particular, given a tolerance $ \ epsilon $, we show that at most $ { \ cal o ( \ epsilon ^ { - 3 / 2 } ) } $ iterations are needed to drive the stationarity violation with respect to the selected block of variables below $ \ epsilon $, while at most $ { \ cal o ( \ epsilon ^ { - 2 } ) } $ iterations are needed to drive the stationarity violation with respect to all variables below $ \ epsilon $. numerical results are finally given.
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arxiv:2407.18150
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we proposed to use polarized neutrons scattering from a hyperpolarized 131xe gaseous target in order to measure time - reversal violation effect in baryon processes with nucleons. this article provides a brief introduction, historical review, and possible methods to construct a hyperpolarized 131xe gaseous target.
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arxiv:1403.1584
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we investigate the thermodynamic curvature resulting from a riemannian geometry approach to thermodynamics for the pauli paramagnetic gas which is a system of identical fermions each with spin 1 / 2. we observe that the absolute value of thermodynamic curvature can be interpreted as a measure of the stability of the considered system only in the classical and semiclassical regime. but in quantum regime some exceptions are observed.
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arxiv:cond-mat/9812054
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in this paper we present a hierarchical multi - rate control architecture for nonlinear autonomous systems operating in partially observable environments. control objectives are expressed using syntactically co - safe linear temporal logic ( ltl ) specifications and the nonlinear system is subject to state and input constraints. at the highest level of abstraction, we model the system - environment interaction using a discrete mixed observable markov decision problem ( momdp ), where the environment states are partially observed. the high level control policy is used to update the constraint sets and cost function of a model predictive controller ( mpc ) which plans a reference trajectory. afterwards, the mpc planned trajectory is fed to a low - level high - frequency tracking controller, which leverages control barrier functions ( cbfs ) to guarantee bounded tracking errors. our strategy is based on model abstractions of increasing complexity and layers running at different frequencies. we show that the proposed hierarchical multi - rate control architecture maximizes the probability of satisfying the high - level specifications while guaranteeing state and input constraint satisfaction. finally, we tested the proposed strategy in simulations and experiments on examples inspired by the mars exploration mission, where only partial environment observations are available.
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arxiv:2012.06558
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in this paper we consider fractional higher - order stochastic differential equations of the form \ begin { align * } \ left ( \ mu + c _ \ alpha \ frac { d ^ \ alpha } { d ( - t ) ^ \ alpha } \ right ) ^ \ beta x ( t ) = \ mathcal { e } ( t ), \ quad t \ geq 0, \ ; \ mu > 0, \ ; \ beta > 0, \ ; \ alpha \ in ( 0, 1 ) \ cup \ mathbb { n } \ end { align * } where $ \ mathcal { e } ( t ) $ is a gaussian white noise. we derive stochastic processes satisfying the above equations of which we obtain explicitly the covariance functions and the spectral functions.
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arxiv:1507.01712
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we derive some consequences of the liouville theorem for plurisubharmonic functions of l. - f. tam and the author. the first result provides a nonlinear version of the complex splitting theorem ( which splits off a factor of $ \ mathbb { c } $ isometrically from the simply - connected k \ " ahler manifold with nonnegative bisectional curvature and a linear growth holomorphic function ) of l. - f. tam and the author. the second set of results concerns the so - called $ k $ - hyperbolicity and its connection with the negativity of the $ k $ - scalar curvature ( when $ k = 1 $ they are the negativity of holomorphic sectional curvature and kobayashi hyperbolicity ) introduced recently by f. zheng and the author. we lastly prove a new schwarz lemma type estimate in terms of { \ it only the holomorphic sectional curvatures of both domain and target manifolds }.
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arxiv:1807.02674
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we develop new tools leading, for each integer $ n \ ge 4 $, to a significantly improved upper bound for the uniform exponent of rational approximation $ \ widehat { \ lambda } _ n ( \ xi ) $ to successive powers $ 1, \ xi, \ dots, \ xi ^ n $ of a given real transcendental number $ \ xi $. as an application, we obtain a refined lower bound for the exponent of approximation to $ \ xi $ by algebraic integers of degree at most $ n + 1 $. the new lower bound is $ n / 2 + a \ sqrt { n } + 4 / 3 $ with $ a = ( 1 - \ log ( 2 ) ) / 2 \ simeq 0. 153 $, instead of the current $ n / 2 + \ mathcal { o } ( 1 ) $.
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arxiv:2109.14141
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we develop a parametrised model to describe the formation and evolution of massive black holes, designed for comparisons with both electromagnetic and gravitational wave observations. using an extended press - schechter formalism, we generate dark matter halo merger trees. we then seed and evolve massive black holes through parameterised prescriptions. this approach, which avoids solving differential equations, is computationally efficient, enabling us to analyse observational data and infer the parameters of our model in a fully bayesian framework. we find that observations of the black hole luminosity function are compatible with the nhz gravitational wave signal ( likely ) measured by ptas, provided we allow for an increased luminosity function at high redshift ( $ 4 - 7 $ ), as recently suggested by jwst observations. our model can simultaneously reproduce the bulk of the $ m _ * - m _ { \ rm bh } $ relation at $ z - 0 $, as well as its outliers, something cosmological simulations struggle to do. the inferred model parameters are consistent with expectations from observations and more complex simulations : they favour heavier black hole seeds and short delays between halo and black hole mergers, while requiring supper - edington accretion episodes lasting a few tens of million years, which in our model are linked to galaxy mergers. we find accretion to be suppressed in the most massive black holes below $ z \ simeq 2. 5 $, consistently with the anti - hierarchical growth hypothesis. finally, our predictions for lisa, although fairly broad, are in agreement with previous models. our model offers a new perspective on the apparent tensions between the black hole luminosity function and the latest jwst and pta results. its flexibility makes it ideal to fully exploit the potential of future gravitational wave observations of massive black hole binaries with lisa.
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arxiv:2410.17916
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the second $ \ mathbb { z } _ { 3 } $ parafermionic conformal theories are associated with the coset construction $ \ frac { su ( 2 ) _ { k } \ times su ( 2 ) _ { 4 } } { su ( 2 ) _ { k + 4 } } $. solid - on - solid integrable lattice models obtained by fusion of the model based on level - 1 representation of the affine algebra $ b _ 1 ^ { ( 1 ) } $ have a critical point described by these conformal theories. explicit values for the boltzmann weights are derived for these models, and it is shown that the boltzmann weights can be made positive for a particular value of the spectral parameter, opening a way to eventual numerical simulations of these conformal field theories. away from criticality, these lattice models describe an integrable, massive perturbation of the parafermionic conformal theory by the relevant field $ \ psi _ { - 2 / 3 } ^ { \ dagger } d _ { 1, 3 } $.
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arxiv:0812.3473
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we consider artinian algebras $ a = \ mathbb { c } [ x _ 0, \ ldots, x _ m ] / i $, with $ i $ generated by a regular sequence of homogeneous forms of the same degree $ d \ geq 2 $. we show that the multiplication by a general linear form from $ a _ { d - 1 } $ to $ a _ d $ is injective. we prove that the weak lefschetz property holds for artinian complete intersection algebras as above, with $ d = 2 $ and $ m \ leq 4 $. apparently, this was previously known only for $ m \ leq 3 $. although we are proposing only very limited progress towards the wlp conjecture for complete intersections, we hope that the methods of the present article can illustrate some geometrical aspects of the general problem.
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arxiv:1802.06253
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we consider the effect of time - periodic forcing on a one - dimensional schr { \ " o } dinger equation with a topologically protected defect ( edge ) mode. the unforced system models a domain - wall or dislocation defect in a periodic structure, and it supports a defect mode which bifurcates from the dirac point ( linear band crossing ) of the underlying bulk medium. we study the robustness of this state against time - periodic forcing of the type that arises in the study of floquet topological insulators in condensed matter, photonics, and cold - atoms systems. our numerical simulations demonstrate that under time - periodic forcing of sufficiently high frequency, the defect state undergoes radiative leakage of its energy away from the interface into the bulk ; the time - decay is exponential on a time - scale proportional to the inverse square of the forcing amplitude. the envelope dynamics of our floquet system are approximately governed, on long time scales, by an effective ( homogenized ) periodically - forced dirac equation. multiple scale analysis of the effective envelope dynamics yields an expansion of the radiating solution, which shows excellent agreement with our numerical simulations.
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arxiv:2201.11219
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recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [ s. filatov et al., phys. rev. lett. 116, 054501 ( 2016 ) ]. here we study how a thin ( monomolecular ) film presented at the surface of liquid affects the generated vorticity. we demonstrate that the vorticity becomes parametrically larger than for the case with a clean surface and now it depends on viscosity of the liquid. we also discuss the motion of particles passively advected by the generated surface flow. the results can be used in different applications : from the analysis of pollutants ' diffusion on the ocean surface till the reconstruction of vorticity based on the particle image velocimetry ( piv ) measurements.
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arxiv:1607.04556
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nufact08 is the tenth in a series of workshops started in 1999, whose main goal is to understand options for future neutrino - oscillation experiments to attack the problems of the neutrino mass hierarchy and cp violation in the leptonic sector. i present a very brief review of what we know and what we would like to know about neutrino mass, mixing, and flavor change. i consider the interplay between neutrino physics and forthcoming information from the large hadron collider. i comment on a decade ' s progress and offer some context for work that lies ahead.
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arxiv:0810.1530
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we report on the discovery of a type 1 quasar, sdss 0956 + 5128, with a surprising combination of extreme velocity offsets. sdss 0956 + 5128 is a broad - lined quasar exhibiting emission lines at three substantially different redshifts : a systemic redshift of z ~ 0. 714 based on narrow emission lines, a broad mgii emission line centered 1200 km / s bluer than the systemic velocity, at z ~ 0. 707, and broad h \ alpha and h \ beta emission lines centered at z ~ 0. 690. the balmer line peaks are 4100 km / s bluer than the systemic redshift. there are no previously known objects with such an extreme difference between broad mgii and broad balmer emission. the two most promising explanations are either an extreme disk emitter or a high - velocity black hole recoil. however, neither explanation appears able to explain all of the observed features of sdss 0956 + 5128, so the object may provide a challenge to our general understanding of quasar physics.
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arxiv:1209.1635
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let $ { \ mathfrak g } $ be a finite dimensional complex simple lie algebra, and let $ r, s \ in \ mathbb { c } ^ { \ ast } $ be transcendental over $ \ mathbb { q } $ such that $ r ^ { m } s ^ { n } = 1 $ implies $ m = n = 0 $. we will obtain some basic properties of the two - parameter quantized enveloping algebra $ u _ { r, s } ^ { + } ( \ mathfrak g ) $. in particular, we will verify that the algebra $ u _ { r, s } ^ { + } ( \ mathfrak g ) $ satisfies many nice properties such as having normal separation, catenarity and dixmier - moeglin equivalence. we shall study a concrete example, the algebra $ u _ { r, s } ^ { + } ( b _ { 2 } ) $ in detail. we will first determine the normal elements, prime ideals and primitive ideals for the algebra $ u _ { r, s } ^ { + } ( b _ { 2 } ) $, and study their stratifications. then we will prove that the algebra automorphism group of the algebra $ u _ { r, s } ^ { + } ( b _ { 2 } ) $ is isomorphic to $ ( \ mathbb { c } ^ { \ ast } ) ^ { 2 } $.
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arxiv:1109.2640
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we studied switchable photovoltaic and photo - diode characteristics of pt ( bi0. 9sm0. 1 ) ( fe0. 97hf0. 03 ) o3 lanio3 ( pt bsfho lno ) heterostructures integrated on si ( 100 ). the directions of photocurrent ( jsc ) and rectification are found to be reversibly switchable after applying external poling voltages. in pristine state, metal - ferroelectric - metal capacitor pt bsfho lno shows jsc 32 microamp cm2 and voc 0. 04 v, which increase to maximum value of jsc 303 ( 206 ) microamp cm2 and voc 0. 32 ( 0. 26 ) v after upward ( downward ) poling at 8 v. we believe that schottky barrier modulation by polarization flipping at pt bsfho interface could be a main driving force behind switchable photovoltaic and rectifying diode characteristics of pt bsfho lno heterostructures.
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arxiv:1510.03132
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in this brief note we point out that in the case of two dimensional crystals like graaphene, there is an interesting anomalous behaviour of fermions. this could potentially be useful.
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arxiv:1611.05323
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we present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak - value amplification. the shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. this is done by an amplification of both the real and imaginary parts of the weak - value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin - orbit coupling. our experiment demonstrates the first realization of weak - value amplification in the azimuthal degree of freedom. we have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.
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arxiv:1312.2981
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we briefly survey some concepts related to empirical entropy - - normal numbers, de bruijn sequences and markov processes - - and investigate how well it approximates kolmogorov complexity. our results suggest $ \ ell $ th - order empirical entropy stops being a reasonable complexity metric for almost all strings of length $ m $ over alphabets of size $ n $ about when $ n ^ \ ell $ surpasses $ m $.
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arxiv:cs/0506056
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transactions involving multiple blockchains are implemented by cross - chain protocols. these protocols are based on smart contracts, programs that run on blockchains, executed by a network of computers. because smart contracts can automatically transfer ownership of cryptocurrencies, electronic securities, and other valuable assets among untrusting parties, verifying the runtime correctness of smart contracts is a problem of compelling practical interest. such verification is challenging since smart contract execution is time - sensitive, and the clocks on different blockchains may not be perfectly synchronized. this paper describes a method for runtime monitoring of blockchain executions. first, we propose a generalized runtime verification technique for verifying partially synchronous distributed computations for the metric temporal logic ( mtl ) by exploiting bounded - skew clock synchronization. second, we introduce a progression - based formula rewriting scheme for monitoring \ mtl specifications which employ smt solving techniques and report experimental results.
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arxiv:2204.09796
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a system of particles is studied in which the stochastic processes are one - particle type - change ( or one - particle diffusion ) and multi - particle annihilation. it is shown that, if the annihilation rate tends to zero but the initial values of the average number of the particles tends to infinity, so that the annihilation rate times a certain power of the initial values of the average number of the particles remain constant ( the double scaling ) then if the initial state of the system is a multi - poisson distribution, the system always remains in a state of multi - poisson distribution, but with evolving parameters. the large time behavior of the system is also investigated. the system exhibits a dynamical phase transition. it is seen that for a k - particle annihilation, if k is larger than a critical value k _ c, which is determined by the type - change rates, then annihilation does not enter the relaxation exponent of the system ; while for k < k _ c, it is the annihilation ( in fact k itself ) which determines the relaxation exponent.
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arxiv:cond-mat/0612405
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we provide an open - source c + + library for real - time metric - semantic visual - inertial simultaneous localization and mapping ( slam ). the library goes beyond existing visual and visual - inertial slam libraries ( e. g., orb - slam, vins - mono, okvis, rovio ) by enabling mesh reconstruction and semantic labeling in 3d. kimera is designed with modularity in mind and has four key components : a visual - inertial odometry ( vio ) module for fast and accurate state estimation, a robust pose graph optimizer for global trajectory estimation, a lightweight 3d mesher module for fast mesh reconstruction, and a dense 3d metric - semantic reconstruction module. the modules can be run in isolation or in combination, hence kimera can easily fall back to a state - of - the - art vio or a full slam system. kimera runs in real - time on a cpu and produces a 3d metric - semantic mesh from semantically labeled images, which can be obtained by modern deep learning methods. we hope that the flexibility, computational efficiency, robustness, and accuracy afforded by kimera will build a solid basis for future metric - semantic slam and perception research, and will allow researchers across multiple areas ( e. g., vio, slam, 3d reconstruction, segmentation ) to benchmark and prototype their own efforts without having to start from scratch.
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arxiv:1910.02490
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we give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative lie algebra cohomology. applications include both reductive and nonreductive cases. for example, we prove that there does not exist a compact manifold locally modelled on a positive dimensional coadjoint orbit of a real linear solvable algebraic group.
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arxiv:1508.04862
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a summary of the on - going preparations from the atlas and cms collaborations to perform top quark physics in run ii of the lhc and at the hl - lhc is given. to maintain the current level of precision and profit from the high - luminosity scenario expected in the next runs of the lhc, several new reconstruction techniques and detector upgrades are foreseen. the prospects for precise measurements and possible discovery stories for new physics with top quarks are summarized.
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arxiv:1411.7053
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in this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity laplacian, which opens the door for numerical approximation of eigenfunctions. a rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. subsequently, we present consistent monotone schemes to approximate infinity ground states and higher eigenfunctions on grids. we prove that our method converges ( up to a subsequence ) to a viscosity solution of the eigenvalue problem, and perform numerical experiments which investigate theoretical conjectures and compute eigenfunctions on a variety of different domains.
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arxiv:2004.08127
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this paper proposes a mixed variational formulation for the problem of two coupled plates with a rigid { junction }. the proposed mixed { formulation } introduces { the union of } stresses and moments as { an auxiliary variable }, which { are } commonly of great interest in practical applications. the primary challenge lies in determining a suitable { space involving } both boundary and junction conditions of the auxiliary variable. the { theory } of densely defined operators in hilbert spaces is employed to define { a nonstandard sobolev space } without the use of trace operators. the well - posedness is established for the mixed formulation. based on these conditions, this paper provides a framework { of } conforming { mixed } finite element methods. numerical experiments are given to validate the theoretical results.
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arxiv:2403.18217
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prediction tasks in digital pathology are challenging due to the massive size of whole - slide images ( wsis ) and the weak nature of training signals. advances in computing, data availability, and self - supervised learning ( ssl ) have paved the way for slide - level foundation models ( slfms ) that can improve prediction tasks in low - data regimes. however, working with these models is challenging, with issues such as catastrophic forgetting during fine - tuning and under - utilization of shared information between tasks and modalities. to overcome these two challenges, we propose modaltune, a novel fine - tuning framework which introduces the modal adapter to integrate new modalities without modifying slfm weights. additionally, we use large - language models ( llms ) to encode labels as text, capturing semantic relationships and enhancing generalization across multiple tasks and cancer types in a single training recipe. modaltune achieves state - of - the - art ( sota ) results against both uni - modal and multi - modal models across four cancer types, jointly improving survival and cancer subtype prediction while remaining competitive in pan - cancer settings. additionally, we show modaltune is highly generalizable to two out - of - distribution ( ood ) datasets. to our knowledge, this is the first unified fine - tuning framework for multi - modal, multi - task, and pan - cancer modeling in digital pathology.
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arxiv:2503.17564
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we present a phase - space analysis of a mathematical model of tumor growth with an immune responses. we consider mathematical analysis of the model equations with multipoint initial condition regarding to dissipativity, boundedness of solutions, invariance of non - negativity, local and global stability and the basins of attractions. we derive some features of behavior of one of three - dimensional tumor growth models with dynamics described in terms of densities of three cells populations : tumor cells, healthy host cells and effector immune cells. we found sufficient conditions, under which trajectories from the positive domain of feasible multipoint initial conditions tend to one of equilibrium points. here, cases of the small tumor mass equilibrium points - the healthy equilibrium point, the " death " equilibrium point have been examined. biological implications of our results are discussed.
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arxiv:1902.10203
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due to its constrained support, the dirichlet distribution is uniquely suited to many applications. the constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing markov chain monte carlo ( mcmc ) techniques such as hamiltonian monte carlo. i demonstrate a series of transformations that reshape the canonical dirichlet distribution into a form much more amenable to mcmc algorithms.
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arxiv:1010.3436
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we construct the basic representation of the double affine hecke algebra at critical level $ q = 1 $ associated to an irreducible reduced affine root system $ r $ with a reduced gradient root system. for $ r $ of untwisted type such a representation was studied by oblomkov [ o04 ] and further detailed by gehles [ g06 ] in the presence of minuscule weights.
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arxiv:2412.09397
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in this paper connections between different gauge - theoretical problems in high and low dimensions are established. in particular it is shown that higher dimensional asd equations on total spaces of spinor bundles over low dimensional manifolds can be interpreted as taubes - pidstrygach ' s generalization of the seiberg - witten equations. by collapsing each fibre of the spinor bundle to a point, solutions of the taubes - pidstrygach equations are related to generalized harmonic spinors. this approach is also generalized for arbitrary fibrations ( without singular fibres ) compatible with an appropriate calibration.
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arxiv:0902.3738
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a number of ways are reviewed in which the study of charmed particles can answer corresponding questions about particles containing $ b $ quarks. topics include the properties of resonances, the magnitude of decay constants, the size of spin - dependent effects, and the hierarchy of lifetime differences.
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arxiv:hep-ph/9407256
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extending the qubit coherence times is a crucial task in building quantum information processing devices. in the three - dimensional cavity implementations of circuit qed, the coherence of superconducting qubits was improved dramatically due to cutting the losses associated with the photon emission. next frontier in improving the coherence includes the mitigation of the adverse effects of superconducting quasiparticles. in these lectures, we review the basics of the quasiparticles dynamics, their interaction with the qubit degree of freedom, their contribution to the qubit relaxation rates, and approaches to control their effect.
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arxiv:2003.04366
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ai technologies have become more widely adopted in wireless communications. as an emerging type of ai technologies, the generative artificial intelligence ( gai ) gains lots of attention in communication security. due to its powerful learning ability, gai models have demonstrated superiority over conventional ai methods. however, gai still has several limitations, including high computational complexity and limited adaptability. mixture of experts ( moe ), which uses multiple expert models for prediction through a gate mechanism, proposes possible solutions. firstly, we review gai model ' s applications in physical layer communication security, discuss limitations, and explore how moe can help gai overcome these limitations. furthermore, we propose an moe - enabled gai framework for network optimization problems for communication security. to demonstrate the framework ' s effectiveness, we provide a case study in a cooperative friendly jamming scenario. the experimental results show that the moe - enabled framework effectively assists the gai algorithm, solves its limitations, and enhances communication security.
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arxiv:2405.04198
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within - basket recommendation ( wbr ) refers to the task of recommending items to the end of completing a non - empty shopping basket during a shopping session. while the latest innovations in this space demonstrate remarkable performance improvement on benchmark datasets, they often overlook the complexity of user behaviors in practice, such as 1 ) co - existence of multiple shopping intentions, 2 ) multi - granularity of such intentions, and 3 ) interleaving behavior ( switching intentions ) in a shopping session. this paper presents neural pattern associator ( npa ), a deep item - association - mining model that explicitly models the aforementioned factors. specifically, inspired by vector quantization, the npa model learns to encode common user intentions ( or item - combination patterns ) as quantized representations ( a. k. a. codebook ), which permits identification of users ' s shopping intentions via attention - driven lookup during the reasoning phase. this yields coherent and self - interpretable recommendations. we evaluated the proposed npa model across multiple extensive datasets, encompassing the domains of grocery e - commerce ( shopping basket completion ) and music ( playlist extension ), where our quantitative evaluations show that the npa model significantly outperforms a wide range of existing wbr solutions, reflecting the benefit of explicitly modeling complex user intentions.
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arxiv:2401.16433
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we study the low temperature conductivity of the electron accumulation layer induced by the very strong electric field at the surface of $ \ text { srtio } _ 3 $ sample. due to the strongly nonlinear lattice dielectric response, the three - dimensional density of electrons $ n ( x ) $ in such a layer decays with the distance from the surface $ x $ very slowly as $ n ( x ) \ propto 1 / x ^ { 12 / 7 } $. we show that when the mobility is limited by the surface scattering the contribution of such a tail to the conductivity diverges at large $ x $ because of growing time electrons need to reach the surface. we explore truncation of this divergence by the finite sample width, by the bulk scattering rate, or by the crossover to the bulk linear dielectric response with the dielectric constant $ \ kappa $. as a result we arrive at the anomalously large mobility, which depends not only on the rate of the surface scattering, but also on the physics of truncation. similar anomalous behavior is found for the hall factor, the magnetoresistance, and the thermopower.
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arxiv:1604.08509
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motivated by reported claims of the measurements of a variation of the fine structure constant $ \ alpha $ we consider a theory where the electric charge, and consequently $ \ alpha $, is not a constant but depends on the ricci scalar $ r $. % we then show how this can be considered a particular case of the bekenstein theory in which there is no need to % introduce an additional kinetic term for the scalar field associated to the electric charge, since the einstein ' s % % equations are sufficient to determine the geometry and, consequently the ricci scalar. we then study the cosmological implications of this theory, considering in particular the effects of dark energy and of a cosmological constant on the evolution of $ \ alpha $. some low - red shift expressions for the variation of $ \ alpha ( z ) $ are derived, showing the effects of the equation of state of dark energy on $ \ alpha $ and observing how future measurements of the variation of the fine structure constant could be used to determine indirectly the equation of state of dark energy and test this theory. in the case of a $ \ lambda cdm $ universe, according to the current estimations of the cosmological parameters, the present value of the ricci scalar is $ \ approx 10 % $ smaller than its future asymptotic value determined by the value of the cosmological constant, setting also a bound on the future asymptotic value of $ \ alpha $.
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arxiv:1403.2044
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we calculate the amplitudes of j ^ { pc } = 3 ^ { - - } meson production in diffractive dis within the k _ t - factorization approach, with a particular attention paid to the rho _ 3 ( 1690 ) meson. we find that at all q ^ 2 the rho _ 3 ( 1690 ) production cross section is 2 - 5 times smaller than the rho ( 1700 ) production cross section, which is assumed to be a pure d - wave state. studying sigma _ l and sigma _ t separately, we observe domination of rho _ 3 in sigma _ l and domination of rho ( 1700 ) in sigma _ t and offer an explanation of this behavior in simple terms. we also find very strong contributions - - sometimes even domination - - of the s - channel helicity violating amplitudes. the typical color dipole sizes probed in rho _ 3 production are shown to be larger than those in the ground state rho production, and the energy dependence of rho _ 3 cross section turns out to be much flatter than the rho production cross section. all the conclusions about the relative behavior of rho _ 3 ( 1690 ) and rho ( 1700 ) mesons are numerically stable against variations of input parameters.
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arxiv:hep-ph/0504139
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the atlas and cms experiments at the cern lhc have collected about 25 inverse femtobarns ( fb ) of data each at the end of their 8 tev run, and ruled out a huge swath of parameter space in the context of minimally supersymmetric standard model ( mssm ). limits on masses of the gluino have been pushed to above 1 tev. these limits are however extremely model dependent and do not always reflect the level of exclusion. so far the limits on the gluino mass using the simplified model approach only constrained its value using its three - body decays. we show in this work that already existing atlas and cms analysis can also constrain the radiative gluino decay mode and we derived improved mass limits in particular when the mass difference between the lsp and the gluino is small.
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arxiv:1509.03639
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with only bounding - box annotations in the spatial domain, existing video scene text detection ( vstd ) benchmarks lack temporal relation of text instances among video frames, which hinders the development of video text - related applications. in this paper, we systematically introduce a new large - scale benchmark, named as stvtext4, a well - designed spatial - temporal detection metric ( stdm ), and a novel clustering - based baseline method, referred to as temporal clustering ( tc ). stvtext4 opens a challenging yet promising direction of vstd, termed as st - vstd, which targets at simultaneously detecting video scene texts in both spatial and temporal domains. stvtext4 contains more than 1. 4 million text instances from 161, 347 video frames of 106 videos, where each instance is annotated with not only spatial bounding box and temporal range but also four intrinsic attributes, including legibility, density, scale, and lifecycle, to facilitate the community. with continuous propagation of identical texts in the video sequence, tc can accurately output the spatial quadrilateral and temporal range of the texts, which sets a strong baseline for st - vstd. experiments demonstrate the efficacy of our method and the great academic and practical value of the stvtext4. the dataset and code will be available soon.
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arxiv:2011.09781
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radiologists can classify a mammogram as normal or abnormal at better than chance levels after less than a second ' s exposure to the images. in this work, we combine these radiologists ' gist inputs into pre - trained machine learning models to validate that integrating gist with a cnn model can achieve an auc ( area under the curve ) statistically significantly higher than either the gist perception of radiologists or the model without gist input.
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arxiv:1912.05470
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key refinements to the number system, such as the introduction of decimal point notation. mathematicians such as muhammad ibn musa al - khwarizmi ( c. 780 – 850 ) gave his name to the concept of the algorithm, while the term algebra is derived from al - jabr, the beginning of the title of one of his publications. islamic trigonometry continued from the works of ptolemy ' s almagest and indian siddhanta, from which they added trigonometric functions, drew up tables, and applied trignometry to spheres and planes. many of their engineers, instruments makers, and surveyors contributed books in applied mathematics. it was in astronomy where islamic mathematicians made their greatest contributions. al - battani ( c. 858 – 929 ) improved the measurements of hipparchus, preserved in the translation of ptolemy ' s he megale syntaxis ( the great treatise ) translated as almagest. al - battani also improved the precision of the measurement of the precession of the earth ' s axis. corrections were made to ptolemy ' s geocentric model by al - battani, ibn al - haytham, averroes and the maragha astronomers such as nasir al - din al - tusi, mu ' ayyad al - din al - urdi and ibn al - shatir. scholars with geometric skills made significant improvements to the earlier classical texts on light and sight by euclid, aristotle, and ptolemy. the earliest surviving arabic treatises were written in the 9th century by abu ishaq al - kindi, qusta ibn luqa, and ( in fragmentary form ) ahmad ibn isa. later in the 11th century, ibn al - haytham ( known as alhazen in the west ), a mathematician and astronomer, synthesized a new theory of vision based on the works of his predecessors. his new theory included a complete system of geometrical optics, which was set in great detail in his book of optics. his book was translated into latin and was relied upon as a principal source on the science of optics in europe until the 17th century. = = = = institutionalization of medicine = = = = the medical sciences were prominently cultivated in the islamic world. the works of greek medical theories, especially those of galen, were translated into arabic and there was an outpouring of medical texts by islamic physicians, which were aimed at organizing, elaborating, and disseminating classical medical knowledge. medical specialties started to emerge, such as
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https://en.wikipedia.org/wiki/History_of_science
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a critical assessment is given of the theoretical uncertainty in the predicted cross - sections for large - angle bhabha scattering at lep 1, with or without t - channel subtraction. to this end a detailed comparison is presented of the results obtained with the programs alibaba and topaz0. differences in the implementation of the radiative corrections and the effect of missing higher - order terms are critically discussed.
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arxiv:hep-ph/9710376
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recent lattice qcd calculations from the hal and nplqcd collaborations have reported evidence for the existence of a bound state with strangeness - 2 and baryon number 2 at quark masses somewhat higher than the physical values. a controlled chiral extrapolation of these lattice results to the physical point suggested that the state, identified with the famed h dibaryon, is most likely slightly unbound ( by 13 $ \ pm $ 14 mev ) with respect to the $ \ lambda - - \ lambda $ threshold. we report the results of an updated analysis which finds the h unbound by 26 $ \ pm $ 11 mev. apart from the insight it would give us into how qcd is realized in nature, the h is of great interest because of its potential implications for the equation of state of dense matter and studies of neutron stars. it may also explain the enhancement above the $ \ lambda - - \ lambda $ threshold already reported experimentally. it is clearly of great importance that the latter be pursued in experiments at the new j - parc facility.
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arxiv:1308.1748
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we discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. the latter is modelled as a porous medium which gives rise to permeation forces. in the simplest model, the brinkman equation, the porous medium is characterised by a single length scale $ \ ell $ - - the square root of the permeability. we compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of $ \ ell $. we furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. in the limit $ \ ell \ to \ infty $, corresponding to a very dilute gel, we recover stokes flow. the opposite limit, $ \ ell \ to 0 $, corresponding to a space filling gel, is singular and not equivalent to darcy ' s equation, which cannot account for self - propulsion.
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arxiv:1803.08695
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accurate estimates of subnational health and demographic indicators are critical for informing health policy decisions. many countries collect relevant data using complex household surveys, but when data are limited, direct survey weighted estimates of small area proportions may be unreliable. area level models treating these direct estimates as response data can improve precision but often require known sampling variances of the direct estimators for all areas. in practice, the sampling variances are typically estimated, so standard approaches do not account for a key source of uncertainty. in order to account for variability in the estimated sampling variances, we propose a hierarchical bayesian spatial area level model that smooths both the estimated means and sampling variances to produce point and interval estimates of small area proportions. our model explicitly targets estimation of small area proportions rather than means of continuous variables and we consider examples of both moderate and low prevalence events. we demonstrate the performance of our approach via simulation and application to vaccination coverage and hiv prevalence data from the demographic and health surveys.
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arxiv:2209.02602
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_ { i _ 2 } | \ cdots | t _ { i _ m } $, then $ p $ is serializable.
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arxiv:1807.03144
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the problem of counting unicellular hypermonopoles by the number of their hyperedges is equivalent to describing the cycle length distribution of a product of two circular permutations, first solved by zagier. the solution of this problem has also been used in the study of the cycle graph model of bafna and pevzner and of related models in mathematical biology. in this paper we develop a method to compute the finite number of reduced unicellular hypermonopoles of a given genus. the problem of representing any hypermap as a drawing is known to be simplifiable to solving the same problem for reduced unicellular hypermonopoles. we also outline a correspondence between our hypermap model, the cycle graph model of bafna and pevzner, and the polygon gluing model of alexeev and zograf. reduced unicellular hypermonopoles correspond to reduced objects in the other models as well, and the notion of genus is the same.
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arxiv:2403.19569
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