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cooperative multi - agent reinforcement learning ( marl ) approaches tackle the challenge of finding effective multi - agent cooperation strategies for accomplishing individual or shared objectives in multi - agent teams. in real - world scenarios, however, agents may encounter unforeseen failures due to constraints like battery depletion or mechanical issues. existing state - of - the - art methods in marl often recover slowly - - if at all - - from such malfunctions once agents have already converged on a cooperation strategy. to address this gap, we present the collaborative adaptation ( ca ) framework. ca introduces a mechanism that guides collaboration and accelerates adaptation from unforeseen failures by leveraging inter - agent relationships. our findings demonstrate that ca enables agents to act on the knowledge of inter - agent relations, recovering from unforeseen agent failures and selecting appropriate cooperative strategies.
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arxiv:2310.12909
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topological phenomena in non - hermitian systems have recently become a subject of great interest in the photonics and condensed - matter communities. in particular, the possibility of observing topologically - protected edge states in non - hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. here, we present the first study on the emergence of topological edge states in two - dimensional haldane lattices exhibiting balanced gain and loss. in line with recent studies on other chern insulator models, we show that edge states can be observed in the so - called broken $ \ mathcal { p } \ mathcal { t } $ - symmetric phase, that is, when the spectrum of the gain - loss - balanced system ' s hamiltonian is not entirely real. more importantly, we find that such topologically protected edge states emerge irrespective of the lattice boundaries, namely zigzag, bearded or armchair.
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arxiv:2003.14375
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this article is an essay, both expository and argumentative, on the galton - watson process as a tool in the domain of branching processes. it is at the same time the author ' s ways to honour two distinguished scientists in this domain, both from the russian academy of science, and to congratulate them for their special birthdays coming up very soon. the thread of the article is the role, which the galton - watson process had played in the author ' s own research. we start with an article on a controlled galton - watson process. then we pass to random absorbing processes, and also recall and discuss a problem in medicine. further questions will bring us via the borel - cantelli lemma to $ \ varphi $ - branching processes and extensions. to gain more generality, we then look at bisexual galton - watson processes. finally we briefly discuss relatively complicated resource dependent branching processes to show that, here again, using galton - watson reproduction schemes ( whenever reasonable ) can be a convincing approach to new processes which are then sufficiently tractable to obtain results of interest. keywords : controlled branching process ; $ \ varphi $ - branching process, bisexual reproduction, borel - cantelli lemma ; resource dependence ; society forms, stopping times, theorem of envelopment, brs - inequality.
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arxiv:2112.09683
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mechanical engineering, vol. 4 ( reprint ed. ), cambridge : cambridge university press, isbn 978 - 0 - 521 - 05803 - 2 sleeswyk, andre ( october 1981 ), " vitruvius ' odometer ", scientific american, 252 ( 4 ) : 188 – 200, bibcode : 1981sciam. 245d. 188s, doi : 10. 1038 / scientificamerican1081 - 188. straffin, philip d. ( 1998 ), " liu hui and the first golden age of chinese mathematics ", mathematics magazine, 71 ( 3 ) : 163 – 81, doi : 10. 1080 / 0025570x. 1998. 11996627 tang, birgit ( 2005 ), delos, carthage, ampurias : the housing of three mediterranean trading centres, rome : l ' erma di bretschneider ( accademia di danimarca ), isbn 978 - 88 - 8265 - 305 - 7. volkov, alexei ( 2009 ), " mathematics and mathematics education in traditional vietnam ", in robson, eleanor ; stedall, jacqueline ( eds. ), the oxford handbook of the history of mathematics, oxford : oxford university press, pp. 153 – 76, isbn 978 - 0 - 19 - 921312 - 2 = = further reading = = = = = general = = = aaboe, asger ( 1964 ). episodes from the early history of mathematics. new york : random house. bell, e. t. ( 1937 ). men of mathematics. simon and schuster. burton, david m. ( 1997 ). the history of mathematics : an introduction. mcgraw hill. grattan - guinness, ivor ( 2003 ). companion encyclopedia of the history and philosophy of the mathematical sciences. the johns hopkins university press. isbn 978 - 0 - 8018 - 7397 - 3. kline, morris. mathematical thought from ancient to modern times. struik, d. j. ( 1987 ). a concise history of mathematics, fourth revised edition. dover publications, new york. = = = books on a specific period = = = gillings, richard j. ( 1972 ). mathematics in the time of the pharaohs. cambridge, ma : mit press. heath, thomas little ( 1921 ). a history of greek mathematics. oxford, claredon press. van der waerden, b. l. ( 1983 ). geometry and algebra in ancient
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https://en.wikipedia.org/wiki/History_of_mathematics
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time series motif discovery ( tsmd ) refers to the task of identifying patterns that occur multiple times ( possibly with minor variations ) in a time series. all existing methods for tsmd have one or more of the following limitations : they only look for the two most similar occurrences of a pattern ; they only look for patterns of a pre - specified, fixed length ; they cannot handle variability along the time axis ; and they only handle univariate time series. in this paper, we present a new method, locomotif, that has none of these limitations. the method is motivated by a concrete use case from physiotherapy. we demonstrate the value of the proposed method on this use case. we also introduce a new quantitative evaluation metric for motif discovery, and benchmark data for comparing tsmd methods. locomotif substantially outperforms the existing methods, on top of being more broadly applicable.
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arxiv:2311.17582
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a new concept is proposed for the paramagnetic metal insulator transition in the layer perovskite ca _ { 2 - x } sr _ xruo _ 4. whereas the pure sr compound is metallic up to very large coulomb energies due to strong orbital fluctuations, structural changes induced by doping with ca give rise to a interorbital charge transfer which makes the material extremely sensitive to local correlations. using dynamical mean field theory based on finite temperature multi - band exact diagonalization it is shown that the combination of crystal field splitting and onsite coulomb interactions leads to complete filling of the d _ xy band and to a mott transition in the half - filled d _ xz, yz bands.
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arxiv:cond-mat/0612539
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radio frequency fingerprint identification ( rffi ) is an emerging device authentication technique, which exploits the hardware characteristics of the rf front - end as device identifiers. rffi is implemented in the wireless receiver and acts to extract the transmitter impairments and then perform classification. the receiver hardware impairments will actually interfere with the feature extraction process, but its effect and mitigation have not been comprehensively studied. in this paper, we propose a receiver - agnostic rffi system that is not sensitive to the changes in receiver characteristics ; it is implemented by employing adversarial training to learn the receiver - independent features. moreover, when there are multiple receivers, this functionality can perform collaborative inference to enhance classification accuracy. finally, we show how it is possible to leverage fine - tuning for further improvement with fewer collected signals. to validate the approach, we have conducted extensive experimental evaluation by applying the approach to a lorawan case study involving ten lora devices and 20 software - defined radio ( sdr ) receivers. the results show that receiver - agnostic training enables the trained neural network to become robust to changes in receiver characteristics. the collaborative inference improves classification accuracy by up to 20 % beyond a single - receiver rffi system and fine - tuning can bring a 40 % improvement for under - performing receivers.
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arxiv:2207.02999
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we formulate bang - bang, purification, and minimization principles in dual banach spaces with gelfand integrals and provide a complete characterization of the saturation property of finite measure spaces. we also present a new application of the relaxation technique to large economies with infinite - dimensional commodity spaces, where the space of agents is modeled as a finite measure space. we propose a " relaxation " of large economies, which is regarded as a reasonable convexification of original economies. under the saturation hypothesis, the relaxation and purification techniques enable us to prove the existence of pareto optimal allocations without convexity assumptions.
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arxiv:1604.02514
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let $ x $ be a smooth variety over a finite field $ \ mathbb { f } _ q $. let $ \ ell $ be a rational prime number invertible in $ \ mathbb { f } _ q $. for an $ \ ell $ - adic sheaf $ \ mathcal { f } $ on $ x $, we construct a cycle supported on the singular support of $ \ mathcal { f } $ whose coefficients are $ \ ell $ - adic numbers modulo roots of unity. it is a refinement of the characteristic cycle $ cc ( \ mathcal { f } ) $, in the sense that it satisfies a milnor - type formula for local epsilon factors. after establishing fundamental results on the cycles, we prove a product formula of global epsilon factors modulo roots of unity. we also give a generalization of the results to varieties over general perfect fields.
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arxiv:1911.02269
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phase retardation is a cornerstone of modern optics, yet, at mid - infrared ( mid - ir ) frequencies, it remains a major challenge due to the scarcity of simultaneously transparent and birefringent crystals. most materials resonantly absorb due to lattice vibrations occurring at mid - ir frequencies, and natural birefringence is weak, calling for hundreds of microns to millimeters - thick phase retarders for sufficient polarization rotation. we demonstrate mid - ir phase retardation with flakes of $ \ alpha $ - molybdenum trioxide ( $ \ alpha $ - moo $ _ 3 $ ) that are more than ten times thinner than the operational wavelength, achieving 90 degrees polarization rotation within one micrometer of material. we report conversion ratios above 50 % in reflection and transmission mode, and wavelength tunability by several micrometers. our results showcase that exfoliated flakes of low - dimensional crystals can serve as a platform for mid - ir miniaturized integrated polarization control.
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arxiv:2306.16110
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countering online hate speech is a critical yet challenging task, but one which can be aided by the use of natural language processing ( nlp ) techniques. previous research has primarily focused on the development of nlp methods to automatically and effectively detect online hate speech while disregarding further action needed to calm and discourage individuals from using hate speech in the future. in addition, most existing hate speech datasets treat each post as an isolated instance, ignoring the conversational context. in this paper, we propose a novel task of generative hate speech intervention, where the goal is to automatically generate responses to intervene during online conversations that contain hate speech. as a part of this work, we introduce two fully - labeled large - scale hate speech intervention datasets collected from gab and reddit. these datasets provide conversation segments, hate speech labels, as well as intervention responses written by mechanical turk workers. in this paper, we also analyze the datasets to understand the common intervention strategies and explore the performance of common automatic response generation methods on these new datasets to provide a benchmark for future research.
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arxiv:1909.04251
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for any unramified quadratic extension of $ p $ - adic local fields $ f / f _ 0 $ $ ( p > 2 ) $, we formulate several arithmetic transfer conjectures at any maximal parahoric level, in the context of zhang ' s relative trace formula approach to the arithmetic gan - - gross - - prasad conjecture. the formulation involves a way to resolve the singularity of relevant moduli spaces via natural stratifications and modify derived fixed points. by a local - global method and double induction, we prove these conjectures for $ f _ 0 $ unramified over $ \ mathbb q _ p $, including the arithmetic fundamental lemma for $ p > 2 $. moreover, we prove new modularity results for arithmetic theta series at parahoric levels via a method of modification over $ \ mathbb f _ q $ and $ \ mathbb c $. along the way, we study the complex and mod $ p $ geometry of shimura varieties and special cycles. we introduce the relative cayley map and also establish jacquet - - rallis transfers at maximal parahoric levels.
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arxiv:2112.11994
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fluorescence resonance energy transfer ( fret ) between two dyes acriflavine ( acf ) and rhodamine b ( rhb ) were investigated in solution and layer - by - layer ( lbl ) self assembled films in presence and absence of clay mineral laponite. uv - vis absorption and fluorescence spectroscopy studies suggest both the dyes present mainly as monomer in solution and films. energy transfer occurred from acf to rhb in solution and lbl films. the energy transfer efficiency increases in presence of clay laponite and the maximum efficiency were 78. 17 % and 32. 54 % in clay dispersion and in lbl films respectively. presence of laponite particles onto lbl film was confirmed by atomic force microscopy investigations with a surface coverage of more than 75 %. energy transfer efficiency was ph sensitive and the energy transfer efficiency varies from 4. 5 % to 44. 45 % in mixed dye solution for a change in ph from 3. 0 to 12. 0. with proper calibration it is possible to use the present system under investigation to sense ph over a wide range of ph from 3. 0 to 12. 0.
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arxiv:1409.4307
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we show a geometric rigidity of isometric actions of non compact ( semisimple ) lie groups on lorentz manifolds. namely, we show that the manifold has a warped product structure of a lorentz manifold with constant curvature by a riemannian manifold.
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arxiv:math/0412195
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using molecular dynamics simulations, we investigate the aggregation behavior of neutral stiff ( rod - like ) and flexible polymer chains mediated by attractive crowders. attractive crowders serve as bridging agents, inducing aggregation through effective intra - polymer attractions. the critical monomer - crowder attraction strength ( $ \ epsilon _ { mc } ^ * $ ) required for aggregation differs notably between rigid rods and flexible polymers. interestingly, this aggregation threshold closely matches the critical attraction required for the extended - to - collapsed ( coil - globule ) transition of a single flexible polymer chain, suggesting a fundamental connection between single - chain collapse and multi - chain aggregation. furthermore, we demonstrate that $ \ epsilon _ { mc } ^ * $ decreases with increasing system density and larger crowder sizes, highlighting the synergistic roles of crowding effects and crowder dimensions. aggregate morphologies exhibit strong dependence on polymer flexibility : rigid rods predominantly form elongated cylindrical bundles, whereas flexible polymers aggregate into compact spherical clusters. these findings provide comprehensive insights into how bridging interactions driven by attractive crowders regulate polymer aggregation dynamics and morphologies, emphasizing the importance of polymer rigidity, crowder size, and system density.
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arxiv:2504.00703
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we present moosenet, a trainable speech metric that predicts the listeners ' mean opinion score ( mos ). we propose a novel approach where the probabilistic linear discriminative analysis ( plda ) generative model is used on top of an embedding obtained from a self - supervised learning ( ssl ) neural network ( nn ) model. we show that plda works well with a non - finetuned ssl model when trained only on 136 utterances ( ca. one minute training time ) and that plda consistently improves various neural mos prediction models, even state - of - the - art models with task - specific fine - tuning. our ablation study shows plda training superiority over ssl model fine - tuning in a low - resource scenario. we also improve ssl model fine - tuning using a convenient optimizer choice and additional contrastive and multi - task training objectives. the fine - tuned moosenet nn with the plda module achieves the best results, surpassing the ssl baseline on the voicemos challenge data.
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arxiv:2301.07087
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we introduce the latest progress of qwen - audio, a large - scale audio - language model called qwen2 - audio, which is capable of accepting various audio signal inputs and performing audio analysis or direct textual responses with regard to speech instructions. in contrast to complex hierarchical tags, we have simplified the pre - training process by utilizing natural language prompts for different data and tasks, and have further expanded the data volume. we have boosted the instruction - following capability of qwen2 - audio and implemented two distinct audio interaction modes for voice chat and audio analysis. in the voice chat mode, users can freely engage in voice interactions with qwen2 - audio without text input. in the audio analysis mode, users could provide audio and text instructions for analysis during the interaction. note that we do not use any system prompts to switch between voice chat and audio analysis modes. qwen2 - audio is capable of intelligently comprehending the content within audio and following voice commands to respond appropriately. for instance, in an audio segment that simultaneously contains sounds, multi - speaker conversations, and a voice command, qwen2 - audio can directly understand the command and provide an interpretation and response to the audio. additionally, dpo has optimized the model ' s performance in terms of factuality and adherence to desired behavior. according to the evaluation results from air - bench, qwen2 - audio outperformed previous sotas, such as gemini - 1. 5 - pro, in tests focused on audio - centric instruction - following capabilities. qwen2 - audio is open - sourced with the aim of fostering the advancement of the multi - modal language community.
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arxiv:2407.10759
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we investigate a nonequilibrium coarsening dynamics of a one - dimensional ising spin system with chirality. only spins at domain boundaries are updated so that the model undergoes a coarsening to either of equivalent absorbing states with all spins + or -. chirality is imposed by assigning different transition rates to events at down ( + - ) kinks and up ( - + ) kinks. the coarsening is characterized by power - law scalings of the kink density $ \ rho \ sim t ^ { - \ delta } $ and the characteristic length scale $ \ xi \ sim t ^ { 1 / z } $ with time $ t $. surprisingly the scaling exponents vary continuously with model parameters, which is not the case for systems without chirality. these results are obtained from extensive monte carlo simulations and spectral analyses of the time evolution operator. our study uncovers the novel universality class of the coarsening dynamics with chirality.
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arxiv:1210.1961
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variance - invariance - covariance regularization ( vicreg ) is a self - supervised learning ( ssl ) method that has shown promising results on a variety of tasks. however, the fundamental mechanisms underlying vicreg remain unexplored. in this paper, we present an information - theoretic perspective on the vicreg objective. we begin by deriving information - theoretic quantities for deterministic networks as an alternative to unrealistic stochastic network assumptions. we then relate the optimization of the vicreg objective to mutual information optimization, highlighting underlying assumptions and facilitating a constructive comparison with other ssl algorithms and derive a generalization bound for vicreg, revealing its inherent advantages for downstream tasks. building on these results, we introduce a family of ssl methods derived from information - theoretic principles that outperform existing ssl techniques.
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arxiv:2303.00633
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in this paper, we study geometry of totally real minimal surfaces in the complex hyperquadric $ q _ { n - 2 } $, and obtain some characterizations of the harmonic sequence generated by these minimal immersions. for totally real flat surfaces that are minimal in both $ q _ { n - 2 } $ and $ \ mathbb { c } p ^ { n - 1 } $, we determine them for $ n = 4, 5, 6 $, and give a classification theorem when they are clifford solutions.
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arxiv:2001.02432
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we construct effective hydrodynamics for composite particles in ( 2 + 1 ) dimensions carrying a magnetic flux by employing a holographic approach. the hydrodynamics is obtained by perturbation of the dyonic black brane solutions in the derivative expansion. we introduce a consistent way to avoid mixing of different orders in the expansion. thanks to this method, it is possible to take the strong external magnetic field limit in the dual field theory. to compare our result with those for a composite particle system, we study several cases that correspond to special solutions of einstein ' s equation and maxwell ' s equations.
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arxiv:1307.0428
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the fluid - fluid interface is a complex environment for a floating object where the statics and dynamics may be governed by capillarity, gravity, inertia, and other external body forces. yet, the alignment of these forces in intricate ways might result in beautiful pattern formation and self - assembly of these objects, as in the case of bubble rafts or colloidal particles. while interfacial self - assembly has been explored widely, controlled manipulation of floating objects, e. g. drops, at the fluid - fluid interface still remains a challenge largely unexplored. in this work, we reveal the self - assembly and manipulation of water drops floating at an oil - air interface. we show that the assembly occurs due to electrostatic interactions between the drops and their environment. we highlight the role of the boundary surrounding the system by showing that even drops with a net zero electric charge can self - assemble under certain conditions. using experiments and theory, we show that the depth of the oil bath plays an important role in setting the distance between the self - assembled drops. furthermore, we demonstrate ways to manipulate the drops actively and passively at the interface.
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arxiv:2403.14055
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we calculate the 2 - loop partition function of qcd on the lattice, using the wilson formulation for gluons and the overlap - dirac operator for fermions. direct by - products of our result are the 2 - loop free energy and average plaquette. our calculation serves also as a prototype for further higher loop calculations in the overlap formalism. we present our results as a function of a free parameter $ m _ 0 $ entering the overlap action ; the dependence on the number of colors $ n $ and fermionic flavors $ n _ f $ is shown explicitly.
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arxiv:hep-lat/0408020
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we study markov bases of decomposable graphical models consisting of primitive moves ( i. e., square - free moves of degree two ) by determining the structure of fibers of sample size two. we show that the number of elements of fibers of sample size two are powers of two and we characterize primitive moves in markov bases in terms of connected components of induced subgraphs of the independence graph of a hierarchical model. this allows us to derive a complete description of minimal markov bases and minimal invariant markov bases for decomposable models.
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arxiv:math/0701429
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a private information retrieval ( pir ) protocol guarantees that a user can privately retrieve files stored in a database without revealing any information about the identity of the requested file. existing information - theoretic pir protocols ensure perfect privacy, i. e., zero information leakage to the servers storing the database, but at the cost of high download. in this work, we present weakly - private information retrieval ( wpir ) schemes that trade off perfect privacy to improve the download cost when the database is stored on a single server. we study the tradeoff between the download cost and information leakage in terms of mutual information ( mi ) and maximal leakage ( maxl ) privacy metrics. by relating the wpir problem to rate - distortion theory, the download - leakage function, which is defined as the minimum required download cost of all single - server wpir schemes for a given level of information leakage and a fixed file size, is introduced. by characterizing the download - leakage function for the mi and maxl metrics, the capacity of single - server wpir is fully described.
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arxiv:2001.08727
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the sign problem appears in lattice qcd as soon as a non - zero chemical potential is introduced. this prevents direct simulations to determine the phase structure of the strongly interacting matter. complex langevin methods have been successfully used for various models or approximations of qcd. however, in some scenarios it converges to incorrect results. we present developments of our new method that helps to improve the convergence by keeping the system closer to the su ( 3 ) manifold and discuss preliminary tests and results.
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arxiv:1710.06165
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this study investigates the impact of changes in body composition and follow - up imaging modalities on recurrence and prognosis in patients with head and neck squamous cell carcinoma ( hnscc ). the results indicate that an increase in the adiposity index post - radiotherapy is significantly associated with higher recurrence and mortality rates. additionally, the combined evaluation of muscle and adipose status reveals that patients with muscle loss and adipose gain have the lowest survival probabilities and the highest risk of recurrence. these findings underscore the importance of monitoring adiposity and muscle status, as well as the strategic use of advanced imaging techniques such as pet / ct, mri, and ct. however, this work represents a preliminary analysis, and further detailed studies are necessary to confirm these results and develop more effective strategies.
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arxiv:2411.16264
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we present a novel method to solve the spatially homogeneous and isotropic relativistic boltzmann equation. we employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non - equilibrium. two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature $ t ( t ) $ and phase space occupation factor $ \ upsilon ( t ) $. in this first paper we address ( effectively ) massless fermions and derive dynamical equations for $ t ( t ) $ and $ \ upsilon ( t ) $ such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. we validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical non - equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze - out processes in the early universe, where the essential physical characteristics include reheating from another disappearing particle component ( $ e ^ \ pm $ - annihilation ).
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arxiv:1403.2019
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ground - based high - contrast instruments have yielded reflected light images of protoplanetary disks. quantitative measurements of the reflected radiation provide strong constraints on the scattering dust which can clarify the dust particle evolution in these disks and the composition of the forming planets. this study aimed to derive the wavelength dependence of polarized reflectivity $ ( \ hat { q } _ { \ varphi } / i _ \ star ) _ \ lambda $ for 11 disks, constraining dust properties and identifying systematic differences. using eso archive data from sphere / zimpol and sphere / irdis instruments, we obtained accurate intrinsic polarized reflectivity $ \ hat { q } _ \ varphi / i _ \ star $ values at wavelengths from 0. 62 $ \ mu $ m to 2. 2 $ \ mu $ m. polarized reflectivities ranged from $ q _ \ varphi / i _ \ star \ approx 0. 1 \ % $ to 1. 0 $ \ % $, with psf - corrected values averaging 1. 6 times higher than observed. accurate psf calibrations reduced systematic errors to $ \ delta \ hat { q } _ \ varphi / \ hat { q } _ \ varphi \ approx 10 \ % $ or less. for each disk, we derived a polarized reflectivity color $ \ eta _ { v / ir } $ between a visible band $ \ lambda < 1 ~ \ mu $ m and a near - ir band $ \ lambda > 1 ~ \ mu $ m and other wavelength combinations. wavelength gradients $ \ eta $ varied significantly among objects. disks around herbig stars ( hd 169142, hd 135334b, hd 100453, mwc 758, and hd 142527 ) showed a red color $ \ eta _ { \ rm v / ir } > 0. 5 $, suggesting rather compact dust grains. t - tauri star disks ( pds 70, tw hya, rx j1615, and pds 66 ) were predominantly gray $ - 0. 5 < \ eta _ { \ rm v / ir } < 0. 5 $, with an absence of blue colors incompatible with porous aggregates. exceptional red colors for lkca15 and mwc758 were attributed to potential extra reddening from hot dust near the star. future studies incorporating parameters like fractional polarization $ \ langle p _ \ varphi \ rangle $ hold promise for advancing our understanding of dust properties within protoplanetary disks
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arxiv:2312.14045
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we study states on the universal noncommutative * - algebra generated by the coefficients of a unitary matrix, or equivalently states on the unitary dual group. its structure of dual group in the sense of voiculescu allows to define five natural convolutions. we prove that there exists no haar state for those convolutions. however, we prove that there exists a weaker form of absorbing state, that we call haar trace, for the free and the tensor convolutions. we show that the free haar trace is the limit in distribution of the blocks of a haar unitary matrix when the dimension tends to infinity. finally, we study a particular class of free l \ ' evy processes on the unitary dual group which are also the limit of the blocks of random matrices on the classical unitary group when the dimension tends to infinity.
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arxiv:1505.08083
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this is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. after a short review of group theory, we enumerate the $ 1 + 1 + 16 = 18 $ families of finite simple groups, as an introduction to the sporadic groups. these are described next, in three levels of increasing complexity, plus the six isolated " pariah " groups. the ( old ) five mathieu groups make up the first, smallest order level. the seven groups related to the leech lattice, including the three conway groups, constitute the second level. the third and highest level contains the monster group $ \ mathbb m $, plus seven other related groups. next a brief mention is made of the remaining six pariah groups, thus completing the $ 5 + 7 + 8 + 6 = 26 $ sporadic groups. the review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.
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arxiv:1101.3055
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co is thought to be the main reservoir of volatile carbon in protoplanetary disks, and thus the primary initial source of carbon in the atmospheres of forming giant planets. however, recent observations of protoplanetary disks point towards low volatile carbon abundances in many systems, including at radii interior to the co snowline. one potential explanation is that gas phase carbon is chemically reprocessed into less volatile species, which are frozen on dust grain surfaces as ice. this mechanism has the potential to change the primordial c / h ratio in the gas. however, current observations primarily probe the upper layers of the disk. it is not clear if the low volatile carbon abundances extend to the midplane, where planets form. we have run a grid of 198 chemical models, exploring how the chemical reprocessing of co depends on disk mass, dust grain size distribution, temperature, cosmic ray and x - ray ionization rate, and initial water abundance. building on our previous work focusing on the warm molecular layer, here we analyze the results for our grid of models in the disk midplane at 12 au. we find that either an ism level cosmic ray ionization rate or the presence of uv photons due to a low dust surface density are needed to chemically reduce the midplane co gas abundance by at least an order of magnitude within 1 myr. in the majority of our models co does not undergo substantial reprocessing by in situ chemistry and there is little change in the gas phase c / h and c / o ratios over the lifetime of the typical disk. however, in the small sub - set of disks where the disk midplane is subject to a source of ionization or photolysis, the gas phase c / o ratio increases by up to nearly 9 orders of magnitude due to conversion of co into volatile hydrocarbons.
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arxiv:1904.10422
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we demonstrate that fermion - boson models with nonlocal interactions can be simulated at finite band filling with the continuous - time quantum monte carlo method. we apply this method to explore the influence of the electron - phonon interaction range for a half - filled band in one dimension, covering the full range from the holstein to the fr \ " ohlich regime. the phase diagram contains metallic, peierls, and phase - separated regions, which we characterize in terms of static and dynamical correlation functions. in particular, our results reveal a suppression of $ 2k _ f $ charge correlations with increasing interaction range, allowing for a power - law decay comparable to the pairing correlations.
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arxiv:1205.0612
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we present a quantitative statistical test for the presence of a crossover c0 in the gutenberg - richter distribution of earthquake seismic moments, separating the usual power law regime for seismic moments less than c0 from another faster decaying regime beyond c0. our method is based on the transformation of the ordered sample of seismic moments into a series with uniform distribution under condition of no crossover. the bootstrap method allows us to estimate the statistical significance of the null hypothesis h0 of an absence of crossover ( c0 = infinity ). when h0 is rejected, we estimate the crossover c0 using two different competing models for the second regime beyond c0 and the bootstrap method. for the catalog obtained by aggregating 14 subduction zones of the circum pacific seismic belt, our estimate of the crossover point is log ( c0 ) = 28. 14 + - 0. 40 ( c0 in dyne - cm ), corresponding to a crossover magnitude mw = 8. 1 + - 0. 3. for separate subduction zones, the corresponding estimates are much more uncertain, so that the null hypothesis of an identical crossover for all subduction zones cannot be rejected. such a large value of the crossover magnitude makes it difficult to associate it directly with a seismogenic thickness as proposed by many different authors in the past. our measure of c0 may substantiate the concept that the localization of strong shear deformation could propagate significantly in the lower crust and upper mantle, thus increasing the effective size beyond which one should expect a change of regime.
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arxiv:cond-mat/0201552
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the advent of quantum computing has opened new possibilities in data science, offering unique capabilities for addressing complex, data - intensive problems. traditional machine learning algorithms often face challenges in high - dimensional or limited - quality datasets, which are common in healthcare. quantum machine learning leverages quantum properties, such as superposition and entanglement, to enhance pattern recognition and classification, potentially surpassing classical approaches. this paper explores qml ' s application in healthcare, focusing on quantum kernel methods and hybrid quantum - classical networks for heart disease prediction and covid - 19 detection, assessing their feasibility and performance.
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arxiv:2410.21339
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that the value may vary above and below the nominal. geometric dimensioning and tolerancing is a method of specifying the functional geometry of an object. = = = sizes of drawings = = = sizes of drawings typically comply with either of two different standards, iso ( world standard ) or ansi / asme y14. 1 ( american ). the metric drawing sizes correspond to international paper sizes. these developed further refinements in the second half of the twentieth century, when photocopying became cheap. engineering drawings could be readily doubled ( or halved ) in size and put on the next larger ( or, respectively, smaller ) size of paper with no waste of space. and the metric technical pens were chosen in sizes so that one could add detail or drafting changes with a pen width changing by approximately a factor of the square root of 2. a full set of pens would have the following nib sizes : 0. 13, 0. 18, 0. 25, 0. 35, 0. 5, 0. 7, 1. 0, 1. 5, and 2. 0 mm. however, the international organization for standardization ( iso ) called for four pen widths and set a colour code for each : 0. 25 ( white ), 0. 35 ( yellow ), 0. 5 ( brown ), 0. 7 ( blue ) ; these nibs produced lines that related to various text character heights and the iso paper sizes. all iso paper sizes have the same aspect ratio, one to the square root of 2, meaning that a document designed for any given size can be enlarged or reduced to any other size and will fit perfectly. given this ease of changing sizes, it is of course common to copy or print a given document on different sizes of paper, especially within a series, e. g. a drawing on a3 may be enlarged to a2 or reduced to a4. the us customary " a - size " corresponds to " letter " size, and " b - size " corresponds to " ledger " or " tabloid " size. there were also once british paper sizes, which went by names rather than alphanumeric designations. american society of mechanical engineers ( asme ) ansi / asme y14. 1, y14. 2, y14. 3, and y14. 5 are commonly referenced standards in the us. = = = technical lettering = = = technical lettering is the process of forming letters, numerals, and other characters in technical drawing. it is used to describe
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https://en.wikipedia.org/wiki/Engineering_drawing
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we study evolution of manifolds after their creation at high energies. several kinds of gravitational lagrangians with higher derivatives are considered. it is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. a number of final metrics describing our universe is quite poor if we limit ourselves with a maximally symmetric extra space. we show that the initial conditions can be a reason of nontrivial solutions ( funnels ) and study their properties.
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arxiv:1807.06235
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wireless communication systems to date primarily rely on the orthogonality of resources to facilitate the design and implementation, from user access to data transmission. emerging applications and scenarios in the sixth generation ( 6g ) wireless systems will require massive connectivity and transmission of a deluge of data, which calls for more flexibility in the design concept that goes beyond orthogonality. furthermore, recent advances in signal processing and learning, e. g., deep learning, provide promising approaches to deal with complex and previously intractable problems. this article provides an overview of research efforts to date in the field of signal processing and learning for next - generation multiple access, with an emphasis on massive random access and non - orthogonal multiple access. the promising interplay with new technologies and the challenges in learning - based ngma are discussed.
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arxiv:2309.00559
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we study the multinomial logit ( mnl ) bandit problem, where at each time step, the seller offers an assortment of size at most $ k $ from a pool of $ n $ items, and the buyer purchases an item from the assortment according to a mnl choice model. the objective is to learn the model parameters and maximize the expected revenue. we present ( i ) an algorithm that identifies the optimal assortment $ s ^ * $ within $ \ widetilde { o } ( \ sum _ { i = 1 } ^ n \ delta _ i ^ { - 2 } ) $ time steps with high probability, and ( ii ) an algorithm that incurs $ o ( \ sum _ { i \ notin s ^ * } k \ delta _ i ^ { - 1 } \ log t ) $ regret in $ t $ time steps. to our knowledge, our algorithms are the first to achieve gap - dependent bounds that fully depends on the suboptimality gaps of all items. our technical contributions include an algorithmic framework that relates the mnl - bandit problem to a variant of the top - $ k $ arm identification problem in multi - armed bandits, a generalized epoch - based offering procedure, and a layer - based adaptive estimation procedure.
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arxiv:2011.09998
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we study holographic entanglement entropy in spatially anisotropic field theory. we observe that for the background we consider in this paper, to a good approximation, the holographic entanglement entropy can be decomposed into two terms. one of them is the entanglement entropy of the isotropic field theory at fixed temperature and the other term is only a function of anisotropy parameter. moreover, for large enough values of anisotropy parameter, our numerical results indicate that the entanglement entropy in the perpendicular direction to anisotropic direction is greater than the parallel case.
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arxiv:1803.01754
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langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the ising model field - driven transition, describing the magnetic field - driven transition in ferromagnets and the chemical potential - driven transition of fluids. an immediate further step is to apply it to the study of a transition driven by the temperature, as the one underwent by the two - dimensional potts model. for this model a study based on the analytical continuation of the free energy ( meunier, morel 2000 ) predicts the anomalous vanishing of the metastable temperature range in the limit of large system size, an issue that has been controversial since the eighties. with a parallel - gpu algorithm we compare the monte carlo dynamics with the theory, obtaining agreement and characterizing the anomalous system size dependence. we discuss the microscopic origin of these metastable phenomena, essentially different with respect to the ising case.
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arxiv:1403.4832
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with the recent prevalence of reinforcement learning ( rl ), there have been tremendous interests in utilizing rl for online advertising in recommendation platforms ( e. g., e - commerce and news feed sites ). however, most rl - based advertising algorithms focus on optimizing ads ' revenue while ignoring the possible negative influence of ads on user experience of recommended items ( products, articles and videos ). developing an optimal advertising algorithm in recommendations faces immense challenges because interpolating ads improperly or too frequently may decrease user experience, while interpolating fewer ads will reduce the advertising revenue. thus, in this paper, we propose a novel advertising strategy for the rec / ads trade - off. to be specific, we develop an rl - based framework that can continuously update its advertising strategies and maximize reward in the long run. given a recommendation list, we design a novel deep q - network architecture that can determine three internally related tasks jointly, i. e., ( i ) whether to interpolate an ad or not in the recommendation list, and if yes, ( ii ) the optimal ad and ( iii ) the optimal location to interpolate. the experimental results based on real - world data demonstrate the effectiveness of the proposed framework.
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arxiv:1909.03602
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the detection of scintillation light in noble - liquid detectors is necessary for identifying neutrino interaction candidates from beam, astrophysical, or solar sources. large monolithic detectors typically have highly efficient light sensors, like photomultipliers, mounted outside their electric field. this option is not available for modular detectors that wish to maximize their active volume. the argoncube light readout system detectors ( arclights ) are large - area thin - wavelength - shifting ( wls ) panels that can operate in highly proximate modular detectors and within the electric field. the wls plastic forming the bulk structure of the arclight has tetraphenyl butadiene ( tpb ) and sheets of dichroic mirror layered across its surface. it is coupled to a set of six silicon photomultipliers ( sipms ). this publication compares tpb coating techniques for large surface areas and describes quality control methods for large - scale production.
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arxiv:2409.13613
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a charge order ( co ) with a wavevector $ \ mathbf { q } \ simeq \ left ( \ frac { 1 } { 3 }, 0, 0 \ right ) $ is observed in infinite - layer nickelates. here we use first - principles calculations to demonstrate a charge - transfer - driven co mechanism in infinite - layer nickelates, which leads to a characteristic ni $ ^ { 1 + } $ - ni $ ^ { 2 + } $ - ni $ ^ { 1 + } $ stripe state. for every three ni atoms, due to the presence of near - fermi - level conduction bands, hubbard interaction on ni - $ d $ orbitals transfers electrons on one ni atom to conduction bands and leaves electrons on the other two ni atoms to become more localized. we further derive a low - energy effective model to elucidate that the co state arises from a delicate competition between hubbard interaction on ni - $ d $ orbitals and charge transfer energy between ni - $ d $ orbitals and conduction bands. with physically reasonable parameters, $ \ mathbf { q } = \ left ( \ frac { 1 } { 3 }, 0, 0 \ right ) $ co state is more stable than uniform paramagnetic state and usual checkerboard antiferromagnetic state. our work highlights the multi - band nature of infinite - layer nickelates, which leads to some distinctive correlated properties that are not found in cuprates.
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arxiv:2204.12208
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the well - known erd \ h { o } s - - ko - - rado theorem states that for $ n > 2k $, every intersecting family of $ k $ - sets of $ [ n ] : = \ { 1, \ ldots, n \ } $ has at most $ { n - 1 \ choose k - 1 } $ sets, and the extremal family consists of all $ k $ - sets containing a fixed element ( called a full star ). the hilton - - milner theorem provides a stability result by determining the maximum size of a uniform intersecting family that is not a subfamily of a full star. the further stabilities were studied by han and kohayakawa ( 2017 ) and huang and peng ( 2024 ). two families $ \ mathcal { f } $ and $ \ mathcal { g } $ are called cross - intersecting if for every $ f \ in \ mathcal { f } $ and $ g \ in \ mathcal { g } $, the intersection $ f \ cap g $ is non - empty. let $ k \ geq 1, t \ ge 0 $ and $ n \ geq 2 k + t $ be integers. frankl ( 2016 ) proved that if $ \ mathcal { f } \ subseteq \ binom { [ n ] } { k + t } $ and $ \ mathcal { g } \ subseteq \ binom { [ n ] } { k } $ are cross - intersecting families, and $ \ mathcal { f } $ is non - empty and $ ( t + 1 ) $ - intersecting, then $ | \ mathcal { f } | + | \ mathcal { g } | \ leq \ binom { n } { k } - \ binom { n - k - t } { k } + 1 $. recently, wu ( 2023 ) sharpened frankl ' s result by establishing a stability variant. the aim of this paper is two - fold. inspired by the above results, we first prove a further stability variant that generalizes both frankl ' s result and wu ' s result. secondly, as an interesting application, we illustrate that the aforementioned results on cross - intersecting families could be used to establish the stability results of the erd \ h { o } s - - ko - - rado theorem. more precisely, we present new short proofs of the hilton - - milner theorem, the han - - kohayakawa theorem and
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arxiv:2411.03674
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by computing anomalous dimensions of gauge invariant composite operators $ ( \ bar \ psi \ psi ) ^ n $ and $ ( \ phi ^ * \ phi ) ^ n $ in chern - simons fermion and boson models, we address that chern - simons interactions make these operators more relevant or less irrelevant in the low energy region. we obtain a critical chern - simons fermion coupling, $ { 1 \ over \ kappa _ c ^ 2 } = { 6 \ over 19 } $, for a phase transition at which the leading irrelevant four - fermion operator $ ( \ bar \ psi \ psi ) ^ 2 $ becomes marginal, and a critical chern - simons boson coupling, $ { 1 \ over \ kappa _ c ^ 2 } = { 6 \ over 34 } $, for a similar phase transition for the leading irrelevant operator $ ( \ phi ^ * \ phi ) ^ 4 $. we see this phenomenon also in the $ 1 / n $ expansion.
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arxiv:hep-th/9210149
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the flux of papers from electron positron colliders containing data on the photon structure function ended naturally around 2005. it is thus timely to review the theoretical basis and confront the predictions with a summary of the experimental results. the discussion will focus on the increase of the structure function with x ( for x away from the boundaries ) and its rise with log q * * 2, both characteristics beeing dramatically different from hadronic structure functions. the agreement of the experimental observations with the theoretical calculations of the real and virtual photon structure is a striking success of qcd. it also allows a new determination of the qcd coupling constant which very well agrees with the value quoted in the literature.
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arxiv:1404.3551
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using lanczos exact diagonalization ( ed ), we study the spin - 1 / 2 $ j _ 1 $ - $ j _ 2 $ heisenberg model with the four - spin ring - exchange interaction $ j _ r $ on triangular lattice. we mainly use the level spectroscopic technique of two 36 - site tori to investigate the ground - state phase diagram, and further characterize phases by spin, dimer and chiral correlation functions. the ground state has rich phases including several magnetic ordered phases like zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. however, we do not find direct evidence of a quantum spin liquid phase with spinon fermi surface in this model. our results can give a better understanding of the ground - state properties of the triangular heisenberg model with ring - exchange interaction, and help to understand the relevant triangular materials.
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arxiv:2505.02030
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it was recently proved that for finitely determined germs $ \ phi : ( \ mathbb { c } ^ 2, 0 ) \ to ( \ mathbb { c } ^ 3, 0 ) $ the number $ c ( \ phi ) $ of whitney umbrella points and the number $ t ( \ phi ) $ of triple values of a stable deformation are topological invariants. the proof uses the fact that the combination $ c ( \ phi ) - 3t ( \ phi ) $ is topological since it equals the linking invariant of the associated immersion $ s ^ 3 \ looparrowright s ^ 5 $ introduced by ekholm and sz \ h { u } cs. we provide a new, direct proof for this equality. we also clarify the relation between various definitions of the latter invariant.
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arxiv:2202.05828
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a general framework of constructions of endoscopy correspondences via automorphic integral transforms for classical groups is formulated in terms of the arthur classification of the discrete spectrum of square - integrable automorphic forms. this suggests a principle, which is called the $ ( \ tau, b ) $ - theory of automorphic forms of classical groups, to reorganize and extend the series of work of piatetski - shapiro, rallis, kudla and others on standard $ l $ - functions of classical groups and theta correspondence.
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arxiv:1212.6525
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this paper explores the bottleneck of feature representations of deep neural networks ( dnns ), from the perspective of the complexity of interactions between input variables encoded in dnns. to this end, we focus on the multi - order interaction between input variables, where the order represents the complexity of interactions. we discover that a dnn is more likely to encode both too simple interactions and too complex interactions, but usually fails to learn interactions of intermediate complexity. such a phenomenon is widely shared by different dnns for different tasks. this phenomenon indicates a cognition gap between dnns and human beings, and we call it a representation bottleneck. we theoretically prove the underlying reason for the representation bottleneck. furthermore, we propose a loss to encourage / penalize the learning of interactions of specific complexities, and analyze the representation capacities of interactions of different complexities.
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arxiv:2111.06236
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modelling the temperature of electric vehicle ( ev ) batteries is a fundamental task of ev manufacturing. extreme temperatures in the battery packs can affect their longevity and power output. although theoretical models exist for describing heat transfer in battery packs, they are computationally expensive to simulate. furthermore, it is difficult to acquire data measurements from within the battery cell. in this work, we propose a data - driven surrogate model ( life - net ) that uses readily accessible driving diagnostics for battery temperature estimation to overcome these limitations. this model incorporates neural operators with a traditional numerical integration scheme to estimate the temperature evolution. moreover, we propose two further variations of the baseline model : life - net trained with a regulariser and life - net trained with time stability loss. we compared these models in terms of generalization error on test data. the results showed that life - net trained with time stability loss outperforms the other two models and can estimate the temperature evolution on unseen data with a relative error of 2. 77 % on average.
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arxiv:2212.08403
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multifocal plane microscopy ( mum ) allows three dimensional objects to be imaged in a single camera frame. our approach uses dual orthogonal diffraction phase gratings with a quadratic distortion of the lines to apply defocus to the first diffraction orders which, when paired with a relay lens, allows for 9 focal planes to be imaged on a single camera chip. this approach requires a strong signal level to ensure sufficient intensity in the diffracted light, but has the advantage of being compact and straightforward to implement. as the microscope begins to focus deeper into the sample, aberrations caused by refractive index mismatch and inhomogeneity in the sample ' s media have an adverse effect on the signal ' s quality. in this paper, we investigate the image quality improvement brought by applying adaptive optics ( ao ) to multifocal plane microscopy. a single correction device ( an 8x8 deformable mirror ( dm ) ) is combined with an image - based ao control strategy to perform the correction of optical aberrations. we compare full end - to - end modelling results using an established numerical modelling system adapted for microscopy to laboratory results both on a test sample and on a number of biological samples. finally, we will demonstrate that combining ao and mum, we are able to improve the image quality of biological samples and provide a good correction throughout the volume of the biological sample.
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arxiv:2003.05851
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let p be a rational prime and n a positive integer which is prime to p. let w be the p - adic weight space for gl _ { 2, q }. let c _ n be the p - adic coleman - mazur eigencurve of tame level n. in this paper, we prove that any irreducible component of c _ n which is of finite degree over w is in fact finite over w. combined with an argument of chenevier and a conjecture of coleman - mazur - buzzard - kilford ( which has been proven in special cases, and for general quaternionic eigencurves ) this shows that the only finite degree components of the eigencurve are the ordinary components.
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arxiv:1701.05721
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we use the weak gravity conjecture ( wgc ) to investigate the impact of charge dequantization arising from non - local qed on the scale of non - locality of neutrinos. we find this scale to be < = 87 tev, which could be probed in future colliders. we also investigate the electric force and potential in non - local qed and use them to reformulate the weak gravity conjecture ( wgc ) in non - local qed.
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arxiv:2411.04877
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in recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. a parameter - wise co - clustering model, for data modelled via continuous random variables, is presented. the proposed model, although allowing more flexibility, still maintains the very high degree of parsimony achieved by traditional co - clustering. a stochastic expectation - maximization ( sem ) algorithm along with a gibbs sampler is used for parameter estimation and an integrated complete log - likelihood criterion is used for model selection. simulated and real datasets are used for illustration and comparison with traditional co - clustering.
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arxiv:1808.08366
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we consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in marcinkiewicz spaces. we prove the existence of a solution to the corresponding dirichlet problem. the associated obstacle problem is also solved. finally, we show higher integrability of a solution to the dirichlet problem when the datum is more regular.
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arxiv:2006.14885
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the first experimental evidence is presented of the topological insulator state in pbbi $ _ { 2 } $ te $ _ { 4 } $. a single surface dirac cone is observed by angle - resolved photoemission spectroscopy ( arpes ) with synchrotron radiation. topological invariants $ \ mathbb { z } _ 2 $ are calculated from the { \ it ab initio } band structure to be 1 ; ( 111 ). the observed two - dimensional iso - energy contours in the bulk energy gap are found to be the largest among the known three - dimensional topological insulators. this opens a pathway to achieving a sufficiently large spin current density in future spintronic devices.
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arxiv:1111.5730
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in our analysis, we combine event - by - event hydrodynamics, within the ekrt formulation, with jet quenching - asw quenching weights - to obtain high - $ p _ t $ $ r _ { \ rm aa } $ for charged particles at rhic and lhc energies for different centralities. by defining a $ k $ - factor that quantifies the departure of $ \ hat { q } $ from an ideal estimate, $ k = \ hat { q } / ( 2 \ epsilon ^ { 3 / 4 } ) $, we fit the single - inclusive experimental data for charged particles. this $ k $ - factor is larger at rhic than at the lhc but, surprisingly, it is almost independent of the centrality of the collision.
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arxiv:1705.01493
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the off - diagonal bethe ansatz method is generalized to the integrable model associated with the $ sp ( 4 ) $ ( or $ c _ 2 $ ) lie algebra. by using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. these relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. for the periodic boundary condition case, we recover the same $ t - q $ relations obtained via conventional bethe ansatz methods previously, while for the off - diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneous $ t - q $ relations, which could not be obtained by the conventional bethe ansatz methods. the method developed in this paper can be directly generalized to generic $ sp ( 2n ) $ ( i. e., $ c _ n $ ) integrable model.
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arxiv:1812.03618
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the superconducting order parameter of strontium ruthenate is the center of a lasting puzzle calling for theoretical studies that include the seldom - considered effects of spin - orbit coupling and the frequency - dependence of the order parameters. here we generalize the frequency - dependent theory of superconductivity mediated by spin and charge fluctuations to include spin - orbit coupling in multi - orbital systems and we characterize the superconducting states using the spin - parity - orbital - time $ spot $ quantum numbers, group theory, and phase distributions in the complex plane. we derive a pseudospin formulation that maps the inter - pseudospin sector of the normal state eliashberg equation to a pseudospin - diagonal one. possible superconducting order parameters for strontium ruthenate are obtained starting from a realistic density - functional - theory normal state. we find that spin - orbit coupling leads to ubiquitous entanglement of spin and orbital quantum numbers, along with notable mixing between even - and odd - frequency correlations. we propose a phase diagram obtained from the temperature dependence of the leading and subleading symmetries in the pseudospin - orbital basis. an accidental degeneracy between leading inter - pseudospin symmetries in strontium ruthenate, b $ _ { 1g } ^ + $ and a $ _ { 2g } ^ - $, could resolve apparent experimental contradictions.
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arxiv:2201.08918
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many brain - computer interfaces make use of brain signals that are elicited in response to a visual, auditory or tactile stimulus, so - called event - related potentials ( erps ). in visual erp speller applications, sets of letters shown on a screen are flashed randomly, and the participant attends to the target letter they want to spell. when this letter flashes, the resulting erp is different compared to when any other non - target letter flashes. we propose a new unsupervised approach to detect this attended letter. in each trial, for every available letter our approach makes the hypothesis that it is in fact the attended letter, and calculates the erps based on each of these hypotheses. we leverage the fact that only the true hypothesis produces the largest difference between the class means. note that this unsupervised method does not require any changes to the underlying experimental paradigm and therefore can be employed in almost any erp - based setup. to deal with limited data, we use a block - toeplitz regularized covariance matrix that models the background activity. we implemented the proposed novel unsupervised mean - difference maximization ( umm ) method and evaluated it in offline replays of brain - computer interface visual speller datasets. for a dataset that used 16 flashes per symbol per trial, umm correctly classifies 3651 out of 3654 letters ( $ 99. 92 \, \ % $ ) across 25 participants. in another dataset with fewer and shorter trials, 7344 out of 7383 letters ( $ 99. 47 \, \ % $ ) are classified correctly across 54 participants with two sessions each. even in more challenging datasets obtained from patients with amyotrophic lateral sclerosis ( $ 77. 86 \, \ % $ ) or when using auditory erps ( $ 82. 52 \, \ % $ ), the obtained classification rates obtained by umm are competitive. in addition, umm provides stable confidence measures which can be used to monitor convergence.
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arxiv:2306.11830
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in this talk we will discuss the low energy dynamics of non - bps branes constructed as stable brane / anti - brane pairs at an orbifold. in particular we will determine the effective field theory and compare its predictions with those of the full open string theory. while the position and vector degrees of freedom have the familiar form found in supersymmetric gauge theories, the massless modes orginating in the tachyonic sector display novel non - commuting flat directions. we will show that these flat directions persist to al orders in alpha '. finally we will briefly report on the open string loop corrections.
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arxiv:hep-th/0009155
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we present a new perspective on bulk reconstruction using berry phases in the boundary cft. our parallel transport of modular hamiltonians is associated to a trajectory in the space of states, which we obtain from the insertion of a source in the euclidean path integral. using a modular version of the extrapolate dictionary and the equivalence between modular flow in the boundary and the bulk, we show that the expectation value of the modular berry curvature on the boundary agrees with an appropriately defined bulk symplectic form associated to the entanglement wedge. in addition, we derive a quantum information metric on the space of density matrices from the berry curvature, which is related to the canonical energy in the bulk. we also explore the case where a state change reduces to a shape change, uncovering the coadjoint orbit structure of kinematic space in higher dimensions.
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arxiv:2305.16384
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a class of spinning magnetic string in 4 - dimensional einstein - dilaton gravity with liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. these solutions have no curvature singularity and no horizon, but have a conic geometry. in these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. although the asymptotic behavior of these solutions are neither flat nor ( a ) ds, we calculate the conserved quantities of these solutions by using the counterterm method. we also generalize these four - dimensional solutions to the case of $ ( n + 1 ) $ - dimensional rotating solutions with $ k \ leq [ n / 2 ] $ rotation parameters, and calculate the conserved quantities and electric charge of them.
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arxiv:0710.0120
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pole - swapping algorithms, generalizations of bulge - chasing algorithms, have been shown to be a viable alternative to the bulge - chasing qz algorithm for solving the generalized eigenvalue problem for a matrix pencil a - { \ lambda } b. it is natural to try to devise a pole - swapping algorithm that solves the standard eigenvalue problem for a single matrix a. this paper introduces such an algorithm and shows that it is competitive with francis ' s bulge - chasing qr algorithm.
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arxiv:2411.17671
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we study a kind of new sde that was arisen from the research on optimization in machine learning, we call it power - law dynamic because its stationary distribution cannot have sub - gaussian tail and obeys power - law. we prove that the power - law dynamic is ergodic with unique stationary distribution, provided the learning rate is small enough. we investigate its first exist time. in particular, we compare the exit times of the ( continuous ) power - law dynamic and its discretization. the comparison can help guide machine learning algorithm.
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arxiv:2306.09624
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, the worldwide commercial market activity was estimated at $ 6 billion venture capital over the past five years, : 38 with self - paced learning generating $ 35. 6 billion in 2011. : 4 north american e - learning generated $ 23. 3 billion in revenue in 2013, with a 9 % growth rate in cloud - based authoring tools and learning platforms. : 19 = = see also = = = = references = = = = further reading = = betts, kristen, et al. " historical review of distance and online education from 1700s to 2021 in the united states : instructional design and pivotal pedagogy in higher education. " journal of online learning research and practice 8. 1 ( 2021 ) pp 3 – 55 online. = = external links = = media related to educational technology at wikimedia commons " schools of the future : learning on - line " 1994 documentary from ketc
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https://en.wikipedia.org/wiki/Educational_technology
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using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. we introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. we then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. an exact analytic expression for the decay constant is obtained for the case of uniform interactions on the bethe lattice. our general findings are illustrated using a real biological network of protein - protein interactions in baker ' s yeast with experimentally determined protein concentrations.
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arxiv:q-bio/0611026
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we give a new example of an automata group of intermediate growth. it is generated by an automaton with 4 states on an alphabet with 8 letters. this automata group has exponential activity and its limit space is not simply connected.
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arxiv:1710.10020
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we introduce a framework for comparing the privacy of different mechanisms. a mechanism designer employs a dynamic protocol to elicit agents ' private information. protocols produce a set of contextual privacy violations - - information learned about agents that may be superfluous given the context. a protocol is maximally contextually private if there is no protocol that produces a subset of the violations it produces, while still implementing the choice rule. we show that selecting a maximally contextually private protocol involves a deliberate decision about whose privacy is most important to protect, and these protocols delay questions to those they aim to protect. taking the second - price auction rule as an instructive example, we derive two novel designs that are maximally contextually private : the ascending - join and overdescending - join protocols.
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arxiv:2112.10812
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we discuss how higher - point qcd amplitudes may be constructed from lower point ones by imposing the factorization constraints in the limits as external momenta become collinear. as a particular example, the all - $ n $ gluon one - loop amplitude with maximal helicity violation is presented. we also discuss the necessary collinear behavior of the $ n $ - gluon amplitudes.
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arxiv:hep-ph/9405393
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the fifth generation of cellular technology ( 5g ) delivers faster speeds, lower latency, and improved network service alongside support for a large number of users and a diverse range of verticals. this brings increased complexity to network control and management, making closed - loop automation essential. in response, the 3rd generation partnership project ( 3gpp ) introduced the network data analytics function ( nwdaf ) to streamline network monitoring by collecting, analyzing, and providing insights from network data. while prior research has focused mainly on isolated applications of machine learning within nwdaf, critical aspects such as standardized data collection, analytics integration in closed - loop automation, and end - to - end system evaluation have received limited attention. this work addresses existing gaps by presenting a practical implementation of nwdaf and its integration with leading open - source 5g core network solutions. we develop a 3gpp - compliant user plane function ( upf ) event exposure service for real - time data collection and an ml model provisioning service integrated with mlflow to support end - to - end machine learning lifecycle management. additionally, we enhance the session management function ( smf ) to consume nwdaf analytics and respond accordingly. our evaluation demonstrates the solution ' s scalability, resource efficiency, and effectiveness in enabling closed - loop security management in 5g networks.
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arxiv:2505.06789
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mobile cloud computing has been adopted in many multimedia applications, where the resource - constrained mobile device sends multimedia data ( e. g., images ) to remote cloud servers to request computation - intensive multimedia services ( e. g., image recognition ). while significantly improving the performance of the mobile applications, the cloud - based mechanism often causes privacy concerns as the multimedia data and services are offloaded from the trusted user device to untrusted cloud servers. several recent studies have proposed perturbation - based privacy preserving mechanisms, which obfuscate the offloaded multimedia data to eliminate privacy exposures without affecting the functionality of the remote multimedia services. however, the existing privacy protection approaches require the deployment of computation - intensive perturbation generation on the resource - constrained mobile devices. also, the obfuscated images are typically not compliant with the standard image compression algorithms and suffer from significant bandwidth consumption. in this paper, we develop a novel privacy - preserving multimedia mobile cloud computing framework, namely $ pmc ^ 2 $, to address the resource and bandwidth challenges. $ pmc ^ 2 $ employs secure confidential computing in the cloud to deploy the perturbation generator, which addresses the resource challenge while maintaining the privacy. furthermore, we develop a neural compressor specifically trained to compress the perturbed images in order to address the bandwidth challenge. we implement $ pmc ^ 2 $ in an end - to - end mobile cloud computing system, based on which our evaluations demonstrate superior latency, power efficiency, and bandwidth consumption achieved by $ pmc ^ 2 $ while maintaining high accuracy in the target multimedia service.
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arxiv:2409.01710
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we present a simple one - dimensional trapping model prompted by the problem of ion current across biological membranes. the trap is modeled mimicking the ionic channel membrane behaviour. such voltage - sensitive channels are open or closed depending on the value taken by a potential. here we have assumed that the external potential has two contributions : a determinist periodic and a stochastic one. our model shows a resonant - like maximum when we plot the amplitude of the oscillations in the absorption current vs. noise intensity. the model was solved both numerically and using an analytic approximation and was found to be in good accord with numerical simulations.
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arxiv:cond-mat/0012302
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in this work, we consider the problem of pedestrian detection in natural scenes. intuitively, instances of pedestrians with different spatial scales may exhibit dramatically different features. thus, large variance in instance scales, which results in undesirable large intra - category variance in features, may severely hurt the performance of modern object instance detection methods. we argue that this issue can be substantially alleviated by the divide - and - conquer philosophy. taking pedestrian detection as an example, we illustrate how we can leverage this philosophy to develop a scale - aware fast r - cnn ( saf r - cnn ) framework. the model introduces multiple built - in sub - networks which detect pedestrians with scales from disjoint ranges. outputs from all the sub - networks are then adaptively combined to generate the final detection results that are shown to be robust to large variance in instance scales, via a gate function defined over the sizes of object proposals. extensive evaluations on several challenging pedestrian detection datasets well demonstrate the effectiveness of the proposed saf r - cnn. particularly, our method achieves state - of - the - art performance on caltech, inria, and eth, and obtains competitive results on kitti.
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arxiv:1510.08160
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the increasing demand for the realization of global - scale quantum communication services necessitates critical investigation for a practical quantum secure communication network that relies on full - time all - location coverage. in this direction, the non - terrestrial quantum key distribution is expected to play an important role in providing agility, maneuverability, relay link, on - demand network, and last - mile coverage. in this work, we have summarized the research and development that has happened until now in the domain of quantum communication using non - terrestrial platforms with a specific focus on the associated challenges and the relevant models. further, to extend the analysis beyond the existing know - how, a hybrid model involving the features of vasylyev et al. model and liorni et al. model is introduced here. the hybrid model entails us adapting a spherical beam to an elliptic beam approximation and effectively capturing the characteristics of transmittance in densely humid weather conditions and at low altitudes. further, to understand the potential impact of the weather conditions of a region on atmospheric attenuation, as an example the average monthly visibility of pune city was analyzed for the years 2021 and 2022. in addition, a simulation of a generic model is performed using a software - defined network paradigm where quantum teleportation is simulated between distant parties using a swarm of drones in netsquid.
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arxiv:2309.13417
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the rna world hypothesis predicts that self - replicating rnas evolved before dna genomes and coded proteins. despite widespread support for the rna world, self - replicating rnas have yet to be identified in a natural context, leaving a key ' missing link ' for this explanation of the origin of life. inspired by recent work showing that condensates of charged polymers are capable of catalyzing chemical reactions, we consider a catalytic rna condensate as a candidate for the self - replicating rna. specifically, we propose that short, low - complexity rna polymers formed catalytic condensates capable of templated rna polymerization. because the condensate properties depend on the rna sequences, rnas that formed condensates with improved polymerization and demixing capacity would be amplified, leading to a ' condensate chain reaction ' and evolution by natural selection. many of the needed properties of this self - replicating rna condensate have been realized experimentally in recent studies and our predictions could be tested with current experimental and theoretical tools. our theory addresses central problems in the origins of life : ( i ) the origin of compartmentalization, ( ii ) the error threshold for the accuracy of templated replication, ( iii ) the free energy cost of maintaining an information - rich population of replicating rna polymers. furthermore, we note that the extant nucleolus appears to satisfy many of the requirements of an evolutionary relic for the model we propose. more generally, we suggest that future work on the origin of life would benefit from condensate - centric biophysical models of rna evolution.
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arxiv:2412.05396
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competency questions ( cqs ) are used in many ontology engineering methodologies to collect requirements and track the completeness and correctness of an ontology being constructed. although they are frequently suggested by ontology engineering methodologies, the publicly available datasets of cqs and their formalizations in ontology query languages are very scarce. since first efforts to automate processes utilizing cqs are being made, it is of high importance to provide large and diverse datasets to fuel these solutions. in this paper, we present bigcq, the biggest dataset of cq templates with their formalizations into sparql - owl query templates. bigcq is created automatically from a dataset of frequently used axiom shapes. these pairs of cq templates and query templates can be then materialized as actual cqs and sparql - owl queries if filled with resource labels and iris from a given ontology. we describe the dataset in detail, provide a description of the process leading to the creation of the dataset and analyze how well the dataset covers real - world examples. we also publish the dataset as well as scripts transforming axiom shapes into pairs of cq patterns and sparql - owl templates, to make engineers able to adapt the process to their particular needs.
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arxiv:2105.09574
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we report the first detection of co ( 1 - 0 ) emission from a submillimeter - selected galaxy, using the green bank telescope. we identify the line in the spectrum of smm j13120 + 4242 as a broad emission feature at z = 3. 408, with delta ( v _ fwhm ) = 1040 + / - 190 km / s. if the observed co ( 1 - 0 ) line profile arises from a single object and not several merging objects, then the co ( 4 - 3 ) / co ( 1 - 0 ) brightness temperature ratio of ~ 0. 26 suggests n ( h _ 2 ) > 3 - 10 x 10 ^ 2 cm ^ - 3 and the presence of sub - thermally excited gas. the integrated line flux implies a cold molecular gas mass m ( h _ 2 ) = 1. 6 x 10 ^ 11 m _ sun, comparable to the dynamical mass estimate and 4 times larger than the h _ 2 mass predicted from the co ( 4 - 3 ) line assuming a brightness temperature ratio of 1. 0. while our observations confirm that this submillimeter galaxy is massive and gas - rich, they also suggest that extrapolating gas masses from j _ upper > = 3 transitions of co leads to considerable uncertainties. we also report an upper limit to the mass of cold molecular gas in a second submillimeter galaxy, smm j09431 + 4700, of m ( h _ 2 ) < 4 x 10 ^ 10 m _ sun.
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arxiv:astro-ph/0607089
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de broglie and bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of usual statistical quantum theory. we propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. unlike the wigner distribution the suggested distribution is positive definite and obeys the liouville condition.
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arxiv:hep-ph/9410378
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inspired by work of scheepers and tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. we obtain a partial answer to an old question of bell, ginsburg and woods regarding the cardinality of weakly lindel \ " of first - countable regular spaces and answer a question recently asked by babinkostova, pansera and scheepers. in the second part of the paper we study a game - theoretic version of cellularity, a special case of which has been introduced by aurichi. we obtain a game - theoretic proof of shapirovskii ' s bound for the number of regular open sets in an ( almost ) regular space and give a partial answer to a natural question about the productivity of a game strengthening of the countable chain condition that was introduced by aurichi. as a final application of our results we prove that the hajnal - juh \ ' asz bound for the cardinality of a first - countable ccc hausdorff space is true for almost regular ( non - hausdorff ) spaces.
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arxiv:1212.5724
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when dynamic objects are captured by a camera, motion blur inevitably occurs. such a blur is sometimes considered as just a noise, however, it sometimes gives an important effect to add dynamism in the scene for photographs or videos. unlike the similar effects, such as defocus blur, which is now easily controlled even by smartphones, motion blur is still uncontrollable and makes undesired effects on photographs. in this paper, an unified framework to add motion blur on per - object basis is proposed. in the method, multiple frames are captured without motion blur and they are accumulated to create motion blur on target objects. to capture images without motion blur, shutter speed must be short, however, it makes captured images dark, and thus, a sensor gain should be increased to compensate it. since a sensor gain causes a severe noise on image, we propose a color compensation algorithm based on non - linear filtering technique for solution. another contribution is that our technique can be used to make hdr images for fast moving objects by using multi - exposure images. in the experiments, effectiveness of the method is confirmed by ablation study using several data sets.
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arxiv:2109.10524
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in this paper we give a complete solution to the hamilton - waterloo problem for the case of hamilton cycles and c4k - factors for all positive integers k.
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arxiv:1009.0965
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the problem of discretization of darboux integrable equations is considered. given a darboux integrable continuous equation, one can obtain a darboux integrable differential - discrete equation, using the integrals of the continuous equation. in the present paper, the discretization of the differential - discrete equations is done using the corresponding characteristic algebras. new examples of integrable discrete equations are obtained.
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arxiv:2211.03087
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a reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well - spaced channels in the surrounding rock matrix. although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. in previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non - linear kinetics, and a finite length system.
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arxiv:1204.0917
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we show that in dimensions $ n \ geq 6 $ that one has global regularity for the maxwell - klein - gordon equations in the coulomb gauge provided that the critical sobolev norm $ \ dot h ^ { n / 2 - 1 } \ times \ dot h ^ { n / 2 - 2 } $ of the initial data is sufficiently small. these results are analogous to those recently obtained for the high - dimensional wave map equation but unlike the wave map equation, the coulomb gauge non - linearity cannot be iterated away directly. we shall use a different approach, proving strichartz estimates for the covariant wave equation. this in turn will be achieved by use of littlewood - paley multipliers, and a global parametrix for the covariant wave equation constructed using a truncated, microlocalized cronstrom gauge.
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arxiv:math/0309353
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the activation and subsequent covalent coupling of polycyclic aromatic hydrocarbons ( pahs ) are of great interest in fields like chemistry, energy, biology, or health, among others. however, this is not a trivial process. so far, it is based on the use of catalysts that drive and increase the efficiency of the reaction. here, we report on an unprecedented method in which the dehydrogenation and covalent coupling is thermally activated in the presence of atomic hydrogen and a surface. this mechanism, which requires of the superhydrogenation of the pahs, has been characterized by high - resolution scanning tunnelling microscopy ( stm ) and rationalized by density functional theory ( dft ) calculations. this work opens a door toward the formation of covalent, pah - based, macromolecular nanostructures on low - reactive surfaces, thus facilitating its applicability.
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arxiv:1904.11813
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quantum walks with memory ( qwm ) are a type of modified quantum walks that record the walker ' s latest path. as we know, only two kinds of qwm are presented up to now. it is desired to design more qwm for research, so that we can explore the potential of qwm. in this work, through presenting the one - to - one correspondence between qwm on a regular graph and quantum walks without memory ( qwom ) on line digraph of the regular graph, we construct a generic model of qwm on regular graphs. this construction gives a general scheme for building all possible standard qwm on regular graphs and makes it possible to study properties of different kinds of qwm. here, by taking the simplest example which is qwm with 1 memory on the line, we analyze some properties of qwm, such as variance, occupancy rate and localization.
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arxiv:1508.07674
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we studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. we had raychaudhuri type equation for the expansion. assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. in this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. under some natural conditions we derive the equations of the twist and the shear in terms of the expansion of the universe. in appendix we investigate the geodesic surface congruence of the null strings.
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arxiv:1103.0300
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data forms a key component of any enterprise. the need for high quality and easy access to data is further amplified by organizations wishing to leverage machine learning or artificial intelligence for their operations. to this end, many organizations are building resources for managing heterogenous data, providing end - users with an organization wide view of available data, and acting as a centralized repository for data owned / collected by an organization. very broadly, we refer to these class of techniques as a " data hub. " while there is no clear definition of what constitutes a data hub, some of the key characteristics include : data catalog ; links to data sets or owners of data sets or centralized data repository ; basic ability to serve / visualize data sets ; access control policies that ensure secure data access and respects policies of data owners ; and computing capabilities tied with data hub infrastructure. of course, developing such a data hub entails numerous challenges. this document provides background in databases, data management and outlines best practices and recommendations for developing and deploying a working data hub.
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arxiv:2004.00190
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a highly unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a slab with the mean permittivity that is larger than that of the surrounding media. this pattern is shown to exist in the geometry of grazing - angle scattering ( gas ), that is when the scattered wave ( + 1 diffracted order ) in the slab propagates almost parallel to the slab ( grating ) boundaries. the predicted resonances are demonstrated to be unrelated to resonant generation of the conventional guided modes of the slab. their physical explanation is associated with resonant generation of a completely new type of eigenmodes in a thick slab with a periodic grating. these new slab eigenmodes are generically related to the grating ; they do not exist if the grating amplitude is zero. the field structure of these eigenmodes and their dependence on structural and wave parameters is analysed. the results are extended to the case of gas of guided modes in a slab with a periodic groove array of small corrugation amplitude and small variations in the mean thickness of the slab at the array boundaries.
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arxiv:physics/0509029
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bielliptic surfaces appear as quotient of a product of two elliptic curves and were classified by bagnera - franchis. we give a concrete way of computing their gw - invariants with point insertions using a floor diagram algorithm. using the latter, we are able to prove the quasi - modularity of their generating series by relating them to generating series of graphs for which we also prove quasi - modularity results. we propose a refinement of these invariants by inserting a { \ lambda } - class in the considered gw - invariants.
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arxiv:2401.01627
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when a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. according to a theory this manifests itself as appearance of the fractional quantum hall effect with a quantized conductivity at an unusual half - integer nu = 5 / 2 landau level filling. here we show that similar electron pairing may occur in quantum dots where the gas of electrons is trapped by external electric potentials into small quantum hall droplets. however, we also find theoretical and experimental evidence that, depending on the shape of the external potential, the paired electron state can break down, which leads to a fragmentation of charge and spin densities into incompressible domains. the fragmentation of the quantum hall states could be an issue in the proposed experiments that aim to probe for non - abelian quasi - particle characteristics of the nu = 5 / 2 quantum hall state.
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arxiv:0809.1020
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it is proved that an irreducible quasifinite $ w _ \ infty $ - module is a highest or lowest weight module or a module of the intermediate series ; a uniformly bounded indecomposable weight $ w _ \ infty $ - module is a module of the intermediate series. for a nondegenerate additive subgroup $ g $ of $ f ^ n $, where $ f $ is a field of characteristic zero, there is a simple lie or associative algebra $ w ( g, n ) ^ { ( 1 ) } $ spanned by differential operators $ ud _ 1 ^ { m _ 1 }... d _ n ^ { m _ n } $ for $ u \ in f [ g ] $ ( the group algebra ), and $ m _ i \ ge0 $ with $ \ sum _ { i = 1 } ^ n m _ i \ ge1 $, where $ d _ i $ are degree operators. it is also proved that an indecomposable quasifinite weight $ w ( g, n ) ^ { ( 1 ) } $ - module is a module of the intermediate series if $ g $ is not isomorphic to $ z $.
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arxiv:math/0511523
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the paper studies the relation between a nonlinear time - varying flat discrete - time system and the corresponding linear time - varying systems which are obtained by a linearization along trajectories. it is motivated by the continuous - time case, where it is well - known that the linearization of flat systems along trajectories results in linear time - varying systems which are again flat. since flatness implies controllability, this constitutes an important verifiable necessary condition for flatness. in the present contribution, it is shown that this is also true in the discrete - time case : we prove that the linearized system is again flat, and that a possible flat output is given by the linearization of a flat output of the nonlinear system. analogously, the map that describes the parameterization of the system variables of the linear system by this flat output coincides with the linearization of the corresponding map of the nonlinear system. the results are illustrated by two examples.
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arxiv:2210.09247
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using a one - loop renormalization group improvement for the effective potential in the higgs model of electrodynamics with electrically and magnetically charged scalar fields, we argue for the existence of a triple ( critical ) point in the phase diagram ( $ \ lambda _ { run }, g _ { run } ^ 4 $ ), where $ \ lambda _ { run } $ is the renormalised running selfinteraction constant of the higgs scalar monopoles and $ g _ { run } $ is their running magnetic charge. this triple point is a boundary point of three first - order phase transitions in the dual sector of the higgs scalar electrodynamics : the " coulomb " and two confinement phases meet together at this critical point. considering the arguments for the one - loop approximation validity in the region of parameters around the triple point a we have obtained the following triple point values of the running couplings : $ ( \ lambda _ { ( a ) }, g ^ 2 _ { ( a ) } ) \ approx ( - 13. 4 ; 18. 6 ) $, which are independent of the electric charge influence and two - - loop corrections to $ g ^ 2 _ { run } $ with high accuracy of deviations. at the triple point the mass of monopoles is equal to zero. the corresponding critical value of the electric fine structure constant turns out to be $ \ alpha _ { crit } = \ pi / g ^ 2 _ { ( a ) } \ approx { 0. 17 } $ by the dirac relation. this value is close to the $ \ alpha _ { crit } ^ { lat } \ approx { 0. 20 \ pm 0. 015 } $, which in a u ( 1 ) lattice gauge theory corresponds to the phase transition between the " coulomb " and confinement phases. in our theory for $ \ alpha \ ge \ alpha _ { crit } $ there are two phases for the confinement of the electrically charged particles. the results of the present paper are very encouraging for the anti - - grand unification theory which was developed previously as a realistic alternative to susy guts. the paper is also devoted to the discussion of this problem.
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arxiv:hep-th/0010260
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modern predictive models are often deployed to environments in which computational budgets are dynamic. anytime algorithms are well - suited to such environments as, at any point during computation, they can output a prediction whose quality is a function of computation time. early - exit neural networks have garnered attention in the context of anytime computation due to their capability to provide intermediate predictions at various stages throughout the network. however, we demonstrate that current early - exit networks are not directly applicable to anytime settings, as the quality of predictions for individual data points is not guaranteed to improve with longer computation. to address this shortcoming, we propose an elegant post - hoc modification, based on the product - of - experts, that encourages an early - exit network to become gradually confident. this gives our deep models the property of conditional monotonicity in the prediction quality - - an essential stepping stone towards truly anytime predictive modeling using early - exit architectures. our empirical results on standard image - classification tasks demonstrate that such behaviors can be achieved while preserving competitive accuracy on average.
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arxiv:2306.02652
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in his ph. d. disseration, feldman and his collaborators define the linear programming decoder for binary linear codes, which is a linear programming relaxation of the maximum - likelihood decoding problem. this decoder does not, in general, attain maximum - likelihood performance ; however, the source of this discrepancy is known to be the presence of non - integral extreme points ( vertices ) within the fundamental polytope, vectors which are also called nontrivial linear programming pseudocodewords. restricting to the class of cycle codes, we provide necessary conditions for a vector to be a linear programming pseudocodeword. in particular, the components of any such pseudocodeword can only assume values of zero, one - half, or one.
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arxiv:1212.2953
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periodic approximations of quasicrystals are a powerful tool in analyzing spectra of schr \ " odinger operators arising from quasicrystals, given the known theory for periodic crystals. namely, we seek periodic operators whose spectra approximate the spectrum of the limiting operator ( of the quasicrystal ). this naturally leads to study the convergence of the underlying dynamical systems. we treat dynamical systems which are based on one - dimensional substitutions. we first find natural candidates of dynamical subsystems to approximate the substitution dynamical system. subsequently, we offer a characterization of their convergence and provide estimates for the rate of convergence. we apply the proposed theory to some guiding examples.
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arxiv:2402.19151
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