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the turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. in this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the turing machines. a deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human ( the researcher ) starts to describe a turing machine ( the object of the study ) by different mathematical languages ( the instruments of investigation ). together with traditional mathematical languages using such concepts as ' enumerable sets ' and ' continuum ' a new computational methodology allowing one to measure the number of elements of different infinite sets is used in this paper. it is shown how mathematical languages used to describe the machines limit our possibilities to observe them. in particular, notions of observable deterministic and non - deterministic turing machines are introduced and conditions ensuring that the latter can be simulated by the former are established.
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arxiv:1203.3298
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we present a result of p. ara which establishes that the unbounded generating number property is a morita invariant for unital rings. using this, we give necessary and sufficient conditions on a graph $ e $ so that the leavitt path algebra associated to $ e $ has ugn. we conclude by identifying the graphs for which the leavitt path algebra is ( equivalently ) directly finite ; stably finite ; hermite ; and has cancellation of projectives.
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arxiv:1603.09695
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matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. this scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a np - complete problem. errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. the property of finding the right solution for an instance and the expected value of the energy are found to be remarkably robust against these errors. as a symbolic example, we simulate the algorithm solving a 100 - qubit hard instance, that is, finding the correct product state out of ~ 10 ^ 30 possibilities. accumulated statistics for up to 60 qubits point at a slow growth of the average minimum time to solve hard instances with highly - truncated simulations of adiabatic quantum evolution.
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arxiv:quant-ph/0503174
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we investigate split supersymmetry ( susy ) within a supergravity framework, where local susy is broken by the f - term of a hidden sector chiral superfield x. with reasonably general assumptions, we show that the fermionic component of x will always have mass within a tev. though its coupling to the observable sector superfields is highly suppressed in tev scale susy, we show that it can be enhanced by many orders in split susy, leading to its likely participation in accelerator phenomenology. we conclude with a specific example of such a scenario in a string based supergravity model.
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arxiv:hep-ph/0503167
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let $ f \ in w ^ { 1, n } _ { \ text { loc } } ( \ omega ; \ bbb r ^ n ) $ be a mapping with nonnegative jacobian $ j _ f ( x ) = \ det df ( x ) \ ge 0 $ for a. e. $ x $ in a domain $ \ omega \ subset \ bbb r ^ n $. the { \ it dilatation } of $ f $ is defined ( almost everywhere in $ \ omega $ ) by the formula $ $ k ( x ) = \ frac { | df ( x ) | ^ n } { j _ f ( x ) } \ cdot $ $ iwaniec and \ v sver \ ' ak \ ncite { is } have conjectured that if $ p \ ge n - 1 $ and $ k \ in l ^ { p } _ { \ text { loc } } ( \ omega ) $ then $ f $ must be continuous, discrete and open. moreover, they have confirmed this conjecture in the two - dimensional case $ n = 2 $. in this article, we verify it in the higher - dimensional case $ n \ ge 2 $ whenever $ p > n - 1 $.
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arxiv:math/9504225
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in this paper we generalize the notion of a $ k $ - graph into ( countable ) infinite rank. we then define our $ c ^ * $ - algebra in a similar way as in $ k $ - graph $ c ^ * $ - algebras. with this construction we are able to find analogues to the gauge invariant uniqueness and cuntz - krieger uniqueness theorems. we also show that the $ \ mathbb { n } $ - graph $ c ^ * $ - algebras can be viewed as the inductive limit of $ k $ - graph $ c ^ * $ - algebras. this gives a nice way to describe the gauge - invariant ideal structure. additionally, we describe the vertex - set for regular gauge - invariant ideals of our $ n $ - graph $ c ^ * $ - algebras. we then take our construction of the $ \ mathbb { n } $ - graph into the algebraic setting and receive many similarities to the $ c ^ * $ - algebra construction.
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arxiv:2202.08327
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we show that the painlev { \ ' e } vi equation has an equivalent form of the non - autonomous zhukovsky - volterra gyrostat. this system is a generalization of the euler top in $ c ^ 3 $ and include the additional constant gyrostat momentum. the quantization of its autonomous version is achieved by the reflection equation. the corresponding quadratic algebra generalizes the sklyanin algebra. as by product we define integrable xyz spin chain on a finite lattice with new boundary conditions.
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arxiv:math/0508058
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translating natural language utterances to executable queries is a helpful technique in making the vast amount of data stored in relational databases accessible to a wider range of non - tech - savvy end users. prior work in this area has largely focused on textual input that is linguistically correct and semantically unambiguous. however, real - world user queries are often succinct, colloquial, and noisy, resembling the input of a search engine. in this work, we introduce data augmentation techniques and a sampling - based content - aware bert model ( colloql ) to achieve robust text - to - sql modeling over natural language search ( nls ) questions. due to the lack of evaluation data, we curate a new dataset of nls questions and demonstrate the efficacy of our approach. colloql ' s superior performance extends to well - formed text, achieving 84. 9 % ( logical ) and 90. 7 % ( execution ) accuracy on the wikisql dataset, making it, to the best of our knowledge, the highest performing model that does not use execution guided decoding.
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arxiv:2010.09927
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we propose the generative adversarial neural operator ( gano ), a generative model paradigm for learning probabilities on infinite - dimensional function spaces. the natural sciences and engineering are known to have many types of data that are sampled from infinite - dimensional function spaces, where classical finite - dimensional deep generative adversarial networks ( gans ) may not be directly applicable. gano generalizes the gan framework and allows for the sampling of functions by learning push - forward operator maps in infinite - dimensional spaces. gano consists of two main components, a generator neural operator and a discriminator neural functional. the inputs to the generator are samples of functions from a user - specified probability measure, e. g., gaussian random field ( grf ), and the generator outputs are synthetic data functions. the input to the discriminator is either a real or synthetic data function. in this work, we instantiate gano using the wasserstein criterion and show how the wasserstein loss can be computed in infinite - dimensional spaces. we empirically study gano in controlled cases where both input and output functions are samples from grfs and compare its performance to the finite - dimensional counterpart gan. we empirically study the efficacy of gano on real - world function data of volcanic activities and show its superior performance over gan.
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arxiv:2205.03017
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multi - source translation is an approach to exploit multiple inputs ( e. g. in two different languages ) to increase translation accuracy. in this paper, we examine approaches for multi - source neural machine translation ( nmt ) using an incomplete multilingual corpus in which some translations are missing. in practice, many multilingual corpora are not complete due to the difficulty to provide translations in all of the relevant languages ( for example, in ted talks, most english talks only have subtitles for a small portion of the languages that ted supports ). existing studies on multi - source translation did not explicitly handle such situations. this study focuses on the use of incomplete multilingual corpora in multi - encoder nmt and mixture of nmt experts and examines a very simple implementation where missing source translations are replaced by a special symbol < null >. these methods allow us to use incomplete corpora both at training time and test time. in experiments with real incomplete multilingual corpora of ted talks, the multi - source nmt with the < null > tokens achieved higher translation accuracies measured by bleu than those by any one - to - one nmt systems.
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arxiv:1806.02525
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multi - wavelength observations indicate that some starburst galaxies show a dominant non - thermal contribution from their central region. these active galactic nuclei ( agn ) - starburst composites are of special interest, as both phenomena on their own are potential sources of highly - energetic cosmic rays and associated gamma - ray and neutrino emission. in this work, a homogeneous, steady - state two - zone multi - messenger model of the non - thermal emission from the agn corona as well as the circumnuclear starburst region is developed and subsequently applied to the case of ngc 1068, which has recently shown some first indications of high - energy neutrino emission. here, we show that the entire spectrum of multi - messenger data - from radio to gamma - rays including the neutrino constraint - can be described very well if both, starburst and agn corona, are taken into account. using only a single emission region is not sufficient.
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arxiv:2207.00102
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we discuss high - resolution, time - resolved spectra of the caustic exit of the binary microlensing event ogle 2002 - bul - 69 obtained with uves on the vlt. the source star is a g5iii giant in the galactic bulge. during such events, the source star is highly magnified, and a strong differential magnification around the caustic resolves its surface. using an appropriate model stellar atmosphere generated by the nextgen code we obtained a model light curve for the caustic exit and compared it with a dense set of photometric observations obtained by the planet microlensing follow up network. we further compared predicted variations in the h alpha equivalent width with those measured from our spectra. while the model and observations agree in the gross features, there are discrepancies suggesting shortcomings in the model, particularly for the h alpha line core, where we have detected amplified emission from the stellar chromosphere as the source star ' s trailing limb exited the caustic. this achievement became possible by the provision of the ogle - iii early warning system, a network of small telescopes capable of nearly - continuous round - the - clock photometric monitoring, on - line data reduction, daily near - real - time modelling in order to predict caustic crossing parameters, and a fast and efficient response of a 8m - class telescope to a ` ` target - of - opportunity ' ' observation request.
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arxiv:astro-ph/0401071
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we carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the universe. these three set - ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely accepted $ \ lambda $ cdm model. in addition, each of the models under study induce different future singularities or abrupt events known as ( i ) big rip, ( ii ) little rip and ( iii ) little sibling of the big rip. only the first one is regarded as a true singularity since it occurs at a finite cosmic time. for this reason, we refer to the others as abrupt events. with the aim to find possible footprints of this scenario in the universe matter distribution, we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model. we have carried the perturbations in the absence of any anisotropic stress and within a phenomenological approach for the speed of sound. we constrain observationally these models using several measurements of the growth rate function, more precisely $ f \ sigma _ 8 $, and compare our results with the observational ones.
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arxiv:1611.00392
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we extend the well known phenomenon of magnetoresistance ( extra resistivity of materials in transverse magnetic field ) to a new and unexplored regime where in addition to a transverse magnetic field, a transverse ac field of resonant frequency is also applied. in a magnetic field, electron spin levels are zeeman split. in a resonant ac field, we uncover a new channel of momentum relaxation in which electrons in upper zeeman level can deexcite to lower zeeman level by generating spin fluctuation excitation in the lattice ( similar to what happens in electron spin resonance ( esr ) spectroscopy ). an additional resistivity due to this novel mechanism is predicted in which momentum randomization of zeeman split electrons happen via bosonic excitations ( spin fluctuations ). an order of magnitude of this additional resistivity is calculated. the whole work is based upon an extension of einstein ' s derivation of equilibrium planckian formula to near equilibrium systems.
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arxiv:1712.03062
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we present a microscopic theory of the equilibrium polariton condensate state of a semiconductor quantum well in a planar optical cavity. the theory accounts for the adjustment of matter excitations to the presence of a coherent photon field, predicts effective polariton - polariton interaction strengths that are weaker and condensate exciton fractions that are smaller than in the commonly employed exciton - photon model, and yields effective rabi coupling strengths that depend on the detuning of the cavity photon energy relative to the bare exciton energy. the dressed quasiparticle bands that appear naturally in the theory provide a mechanism for electrical manipulation of polariton condensates.
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arxiv:1608.06916
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/ practical decision. also, unlike the egyptians, greeks, and romans, the babylonians had a place - value system, where digits written in the left column represented larger values, much as in the decimal system. the power of the babylonian notational system lay in that it could be used to represent fractions as easily as whole numbers ; thus multiplying two numbers that contained fractions was no different from multiplying integers, similar to modern notation. the notational system of the babylonians was the best of any civilization until the renaissance, and its power allowed it to achieve remarkable computational accuracy ; for example, the babylonian tablet ybc 7289 gives an approximation of √2 accurate to five decimal places. the babylonians lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context. by the seleucid period, the babylonians had developed a zero symbol as a placeholder for empty positions ; however it was only used for intermediate positions. this zero sign does not appear in terminal positions, thus the babylonians came close but did not develop a true place value system. other topics covered by babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers, and their reciprocal pairs. the tablets also include multiplication tables and methods for solving linear, quadratic equations and cubic equations, a remarkable achievement for the time. tablets from the old babylonian period also contain the earliest known statement of the pythagorean theorem. however, as with egyptian mathematics, babylonian mathematics shows no awareness of the difference between exact and approximate solutions, or the solvability of a problem, and most importantly, no explicit statement of the need for proofs or logical principles. = = egyptian = = egyptian mathematics refers to mathematics written in the egyptian language. from the hellenistic period, greek replaced egyptian as the written language of egyptian scholars. mathematical study in egypt later continued under the arab empire as part of islamic mathematics, when arabic became the written language of egyptian scholars. archaeological evidence has suggested that the ancient egyptian counting system had origins in sub - saharan africa. also, fractal geometry designs which are widespread among sub - saharan african cultures are also found in egyptian architecture and cosmological signs. the most extensive egyptian mathematical text is the rhind papyrus ( sometimes also called the ahmes papyrus after its author ), dated to c. 1650 bc but likely a copy of an older document from the middle kingdom of about 2000 – 1800
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https://en.wikipedia.org/wiki/History_of_mathematics
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gould & depoy proposed a pixel lensing survey towards the galactic bulge using a small aperture ( ~ 65 mm ) camera with a large pixel size ( 10 " ) detector and deliberately degraded optics achieving 30 " psf. in this paper, we estimate the event rate of this pixel lensing survey expected under various detection criteria, which are characterized by the threshold signal - to - noise ratio, ( s / n ) _ { th }, and event duration, t _ { dur, th }, and investigate the characteristics of the detectable events. from this investigation, we find that the event rate varies significantly in the range ~ 6 / yr - 120 / yr depending strongly on the imposed detection criteria, implying that to maximize event detections it will be essential to identify events by diligently inspecting light variations and to promptly conduct followup observations for the identified events. compared to events detectable from classic lensing surveys, the events detectable from the pixel lensing survey will generally involve brighter source stars and have higher amplifications. for the pixel lensing events detectable under the criteria of ( s / n ) _ { th } = 10 and t _ { dur, th } = 6 hr, we find that the baseline brightness of source stars will be in average ~ 2 mag brighter than those of classic lensing events and ~ 90 % will have amplifications a > 20 and ~ 40 % will be extreme emes with a > 200. therefore, followup observations of the pixel lensing events will provide high quality data, which enable one to precisely determine the lensing parameters and obtain extra - information about the lenses and source stars. especially, high amplifications events with a > 20 will be important targets for high - efficiency planet detections and one can uniquely determine the mass, distance, and transverse speed of individual lenses for emes.
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arxiv:astro-ph/0103460
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using the theory of scattering in restricted geometries developed by a. lupu - sax as a starting point, we present a comprehensive multi - channel theory of atom - atom scattering in tight atom waveguides.
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arxiv:cond-mat/0402149
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we determine the shape of all sum - free sets in $ \ { 1, 2, \ ldots, n \ } ^ 2 $ of size close to the maximum $ \ frac { 3 } { 5 } n ^ 2 $, solving a problem of elsholtz and rackham. we show that all such asymptotic maximum sum - free sets lie completely in the stripe $ \ frac { 4 } { 5 } n - o ( n ) \ le x + y \ le \ frac { 8 } { 5 } n + o ( n ) $. we also determine for any positive integer $ p $ the maximum size of a subset $ a \ subseteq \ { 1, 2, \ ldots, n \ } ^ 2 $ which forbids the triple $ ( x, y, z ) $ satisfying $ px + py = z $.
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arxiv:2108.10526
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we present a distributed source - seeking and flocking control method for networked multi - agent systems with non - holonomic constraints. based solely on identical on - board sensor systems, which measure the source local field, the group objective is attained by appointing a leader agent to seek the source while the remaining follower agents form a cohesive flocking with their neighbors using a distributed flocking control law in a connectivity - preserved undirected network. to guarantee the safe separation and group motion for all agents and to solve the conflicts with the " cohesion " flocking rule of reynolds, the distributed control algorithm is solved individually through quadratic - programming optimization problem with constraints, which guarantees the inter - agent collision avoidance and connectivity preservation. stability analysis of the closed - loop system is presented and the efficacy of the methods is shown in simulation results.
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arxiv:2301.04576
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we develop a model of how information flows into a market, and derive algorithms for automatically detecting and explaining relevant events. we analyze data from twenty - two " political stock markets " ( i. e., betting markets on political outcomes ) on the iowa electronic market ( iem ). we prove that, under certain efficiency assumptions, prices in such betting markets will on average approach the correct outcomes over time, and show that iem data conforms closely to the theory. we present a simple model of a betting market where information is revealed over time, and show a qualitative correspondence between the model and real market data. we also present an algorithm for automatically detecting significant events and generating semantic explanations of their origin. the algorithm operates by discovering significant changes in vocabulary on online news sources ( using expected entropy loss ) that align with major price spikes in related betting markets.
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arxiv:1301.0594
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we study the two - body decay of a mother particle into a massless daughter. we further assume that the mother particle is unpolarized and has a generic boost distribution in the laboratory frame. in this case, we show analytically that the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the ( fixed ) energy of that particle in the rest frame of the corresponding mother particle. given its simplicity and " invariance " under variations of the boost distribution of the mother particle, our finding should be useful for the determination of masses of mother particles. in particular, we anticipate that such a procedure will then not require a full reconstruction of this two - body decay chain ( or for that matter, information about the rest of the event ). with this eventual goal in mind, we make a proposal for extracting the peak position by fitting the data to a well - motivated analytic function describing the shape of such energy distribution. this fitting function is then tested on the theoretical prediction for top quark pair production and its decay and it is found to be quite successful in this regard. as a proof of principle of the usefulness of our observation, we apply it for measuring the mass of the top quark at the lhc, using simulated data and including experimental effects.
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arxiv:1209.0772
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we present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. the method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. in the paper we consider, as an example, a garch model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. in particular the method is applied to the problem of model calibration. the method is easily generalizable to be used with other models or problems.
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arxiv:1701.01429
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most recent semantic segmentation methods adopt a u - net framework with an encoder - decoder architecture. it is still challenging for u - net with a simple skip connection scheme to model the global multi - scale context : 1 ) not each skip connection setting is effective due to the issue of incompatible feature sets of encoder and decoder stage, even some skip connection negatively influence the segmentation performance ; 2 ) the original u - net is worse than the one without any skip connection on some datasets. based on our findings, we propose a new segmentation framework, named uctransnet ( with a proposed ctrans module in u - net ), from the channel perspective with attention mechanism. specifically, the ctrans module is an alternate of the u - net skip connections, which consists of a sub - module to conduct the multi - scale channel cross fusion with transformer ( named cct ) and a sub - module channel - wise cross - attention ( named cca ) to guide the fused multi - scale channel - wise information to effectively connect to the decoder features for eliminating the ambiguity. hence, the proposed connection consisting of the cct and cca is able to replace the original skip connection to solve the semantic gaps for an accurate automatic medical image segmentation. the experimental results suggest that our uctransnet produces more precise segmentation performance and achieves consistent improvements over the state - of - the - art for semantic segmentation across different datasets and conventional architectures involving transformer or u - shaped framework. code : https : / / github. com / mcgregorwwww / uctransnet.
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arxiv:2109.04335
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here we demonstrate a new monoclinic iron oxide phase ( { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ ), epitaxially stabilized by growth on ( 010 ) { \ beta } - ga $ _ { 2 } $ o $ _ { 3 } $. density functional theory ( dft ) calculations find that the lattice parameters of freestanding { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ are within ~ 1 % of those of { \ beta } - ga $ _ { 2 } $ o $ _ { 3 } $ and that its energy of formation is comparable to that of naturally abundant fe $ _ { 2 } $ o $ _ { 3 } $ polytypes. a superlattice of { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ / { \ beta } - ga $ _ { 2 } $ o $ _ { 3 } $ is grown by plasma assisted molecular beam epitaxy, with resulting high - resolution x - ray diffraction ( xrd ) measurements indicating that the { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ layers are lattice - matched to the substrate. the measured out - of - plane ( b ) lattice parameter of 3. 12 $ \ pm $ 0. 4 { \ aa } is in agreement with the predicted lattice constants and atomic - resolution scanning transmission electron microscopy ( stem ) images confirm complete registry of the { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ layers with { \ beta } - ga $ _ { 2 } $ o $ _ { 3 } $. finally, dft modeling predicts that bulk { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ is antiferromagnetic, while the interface region between { \ mu } - fe $ _ { 2 } $ o $ _ { 3 } $ and { \ beta } - ga $ _ { 2 } $ o $ _ { 3 } $ leads to ferromagnetic coupling between interface fe $ ^ { 3 + } $ cations selectively occupying tetrahedral positions. magnetic hysteresis persisting to room temperature is observed via squid measurements, consistent with the computationally predicted interface magnetism.
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arxiv:1901.04844
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in theories of gravity where the cosmological constant defines a thermodynamic variable, the pressure, it has been shown that solutions of einstein ' s equations have a corresponding thermodynamic volume. in general, the expression for the volume is not the same as the one arising from naive geometrical considerations. both rotation and nut charge are properties known in the literature to give non - geometric thermodynamic volumes, and so we combine the two in a single example and compute the volume for the kerr - bolt - ads spacetime, presenting a new expression that generalizes the previously known non - geometric cases.
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arxiv:1406.1257
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we prove that the quotient space of a variationally complete group action is a good riemannian orbifold. the result is generalized to singular riemannian foliations without horizontal conjugate points.
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arxiv:0709.2607
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by means of the diffusion entropy approach, we detect the scale - invariance characteristics embedded in the 4737 human promoter sequences. the exponent for the scale - invariance is in a wide range of $ [ { 0. 3, 0. 9 } ] $, which centered at $ \ delta _ c = 0. 66 $. the distribution of the exponent can be separated into left and right branches with respect to the maximum. the left and right branches are asymmetric and can be fitted exactly with gaussian form with different widths, respectively.
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arxiv:0704.0158
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hybrid quantum photonics combines classical photonics with quantum emitters in a postprocessing step. it facilitates to link ideal quantum light sources to optimized photonic platforms. optical cavities enable to harness the purcell - effect boosting the device efficiency. here, we postprocess a free - standing, crossed - waveguide photonic crystal cavity based on si $ _ 3 $ n $ _ 4 $ with siv $ ^ - $ center in nanodiamonds. we develop a routine that holds the capability to optimize all degrees of freedom of the evanescent coupling term utilizing afm nanomanipulation. after a few optimization cycles we resolve the fine - structure of individual siv $ ^ - $ centers and achieve a purcell enhancement of more than 4 on individual optical transitions, meaning that four out of five spontaneously emitted photons are channeled into the photonic device. our work opens up new avenues to construct efficient quantum photonic devices.
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arxiv:1910.06114
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we establish some relations between the spectra of simple and non - backtracking random walks on non - regular graphs, generalizing some well - known facts for regular graphs. our two main results are 1 ) a quantitative relation between the mixing rates of the simple random walk and of the non - backtracking random walk 2 ) a variant of the " ihara determinant formula " which expresses the characteristic polynomial of the adjacency matrix, or of the laplacian, as the determinant of a certain non - backtracking random walk with holomorphic weights.
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arxiv:1703.03852
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in this paper, we present a simple yet effective boolean map based representation that exploits connectivity cues for visual tracking. we describe a target object with histogram of oriented gradients and raw color features, of which each one is characterized by a set of boolean maps generated by uniformly thresholding their values. the boolean maps effectively encode multi - scale connectivity cues of the target with different granularities. the fine - grained boolean maps capture spatially structural details that are effective for precise target localization while the coarse - grained ones encode global shape information that are robust to large target appearance variations. finally, all the boolean maps form together a robust representation that can be approximated by an explicit feature map of the intersection kernel, which is fed into a logistic regression classifier with online update, and the target location is estimated within a particle filter framework. the proposed representation scheme is computationally efficient and facilitates achieving favorable performance in terms of accuracy and robustness against the state - of - the - art tracking methods on a large benchmark dataset of 50 image sequences.
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arxiv:1610.09652
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using the framework of random walks in random scenery, cohen and samorodnitsky ( 2006 ) introduced a family of symmetric $ \ alpha $ - stable motions called local time fractional stable motions. when $ \ alpha = 2 $, these processes are precisely fractional brownian motions with $ 1 / 2 < h < 1 $. motivated by random walks in alternating scenery, we find a " complementary " family of symmetric $ \ alpha $ - stable motions which we call indicator fractional stable motions. these processes are complementary to local time fractional stable motions in that when $ \ alpha = 2 $, one gets fractional brownian motions with $ 0 < h < 1 / 2 $.
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arxiv:1010.3136
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we present new complete calabi - yau metrics defined on the complement of a smooth anticanonical divisor with ample normal bundle, approaching the calabi model space at a polynomial rate. moreover, we establish the uniqueness of this type of calabi - yau metric within a fixed cohomology class.
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arxiv:2404.18070
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we probe the u ( n ) chiral gross - neveu model with a source - term $ j \ l { \ psi } \ psi $. we find an expression for the renormalization scheme and scale invariant source $ \ hat { j } $, as a function of the generated mass gap. the expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter $ d $. we obtain a non - perturbative mass gap as the solution of $ \ hat { j } = 0 $. a physical choice for $ d $ gives good results for $ n > 2 $. the self - consistent minimal sensitivity condition gives a slight improvement.
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arxiv:hep-th/0202194
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addressing the question of how to achieve optimal decision - making under risk and uncertainty is crucial for enhancing the capabilities of artificial agents that collaborate with or support humans. in this work, we address this question in the context of public goods games. we study learning in a novel multi - objective version of the public goods game where agents have different risk preferences, by means of multi - objective reinforcement learning. we introduce a parametric non - linear utility function to model risk preferences at the level of individual agents, over the collective and individual reward components of the game. we study the interplay between such preference modelling and environmental uncertainty on the incentive alignment level in the game. we demonstrate how different combinations of individual preferences and environmental uncertainties sustain the emergence of cooperative patterns in non - cooperative environments ( i. e., where competitive strategies are dominant ), while others sustain competitive patterns in cooperative environments ( i. e., where cooperative strategies are dominant ).
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arxiv:2408.00682
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$ ^ { 195 } $ pt - nmr measurements of pt nanoparticles with a mean diameter of 4. 0 nm were performed in a high magnetic field of approximately $ \ mu _ 0 h = 23. 3 $ t to investigate the low - temperature electronic state of the nanoparticles. the characteristic temperature $ t ^ * $, below which the nuclear spin - lattice relaxation rate $ 1 / t _ 1 $ deviates from the relaxation rate of the bulk, shows a magnetic - field dependence. this dependence supports the theoretical prediction of the appearance of discrete energy levels.
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arxiv:2007.07688
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we present the general conditions to realize a fourth order exceptional point of degeneracy ( epd ) in two uniform ( i. e., invariant along z ) lossless and gainless coupled transmission lines ( ctls ), namely, a degenerate band edge ( dbe ). until now the dbe has been shown only in periodic structures. in contrast, the ctls considered here are uniform and subdivided into four cases where the two tls support combinations of forward propagation, backward propagation and evanescent modes ( when neglecting the mutual coupling ). we demonstrate for the first time that a dbe is supported in uniform ctls when there is proper coupling between : ( i ) propagating modes and evanescent modes, ( ii ) forward and backward propagating modes, or ( iii ) four evanescent modes ( two in each direction ). we also show that the loaded quality factor of uniform ctls exhibiting a fourth order epd at k = 0 is robust to series losses due to the fact that the degenerate modes do not advance in phase. we also provide a microstrip possible implementation of a uniform ctl exhibiting a dbe using periodic series capacitors with very sub - wavelength unit - cell length. finally, we show an experimental verification of the existence dbe for a microstrip implementation of a ctl supporting coupled propagating and evanescent modes.
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arxiv:2003.04215
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for any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. yet, its full distribution often carries extremely interesting information and can be invoked to put any surprising properties of the individual moments into perspective. as an example, we consider a problem concerning simple random walks which was posed in a recent text. when a drunk is observed over l nights, taking n steps per night, and the number of steps to the right is recorded for each night, an average and a variance based on these data can be computed. when the variance is used to estimate p, the probability for the drunk to step right, complex values for p are frequently found. to put such obviously nonsensical results into context, we study the full probability distribution for the variance of the data string. we discuss the connection of our results to the problem of data binning and provide two other brief examples to demonstrate the importance of full distributions.
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arxiv:cond-mat/0209044
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this paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. a novel approach to modeling imitation is presented, based on range - dependent processes that describe how firms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. using a particularly tractable approach, we are able to analyze how drastically different economic growth scenarios emerge from different imitation strategies. these emerging scenarios range from diffusive growth where the variance of productivity grows indefinitely, to balanced growth described by a traveling wave with fixed variance. the latter scenario is sustained only when imitation strength among firms exceeds a critical bifurcation threshold.
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arxiv:1312.4321
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probably, the long - term monitoring of the solar atmosphere started in italy with the first telescopic observations of the sun made by galileo galilei in the early $ 17 ^ { \ mathrm { th } } $ century. his recorded observations and science results, as well as the work carried out by other following outstanding italian astronomers inspired the start of institutional programs of regular solar observations at the arcetri, catania, and rome observatories. these programs have accumulated daily images of the solar photosphere and chromosphere taken at various spectral bands over a time span greater than 80 years. in the last two decades, regular solar observations were continued with digital cameras only at the catania and rome observatories, which are now part of the inaf national institute for astrophysics. at the two sites, daily solar images are taken at the photospheric g - band, blue ( $ \ lambda = 409. 4 $ nm ), and red ( $ \ lambda = 606. 9 $ nm ) continua spectral ranges and at the chromospheric ca ii k and h $ \ alpha $ lines, with a $ 2 ^ { \ prime \ prime } $ spatial resolution. solar observation in italy, which benefits from over 2500 hours of yearly sunshine, currently aims at the operational monitoring of solar activity and long - term variability and at the continuation of the historical series as well. existing instruments will be soon enriched by the samm double channel telescope equipped with magneto - optical filters that will enable the tomography of the solar atmosphere with simultaneous observations at the k i 769. 9 nm and na i d 589. 0 nm lines. in this contribution, we present the available observations and outline their scientific relevance.
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arxiv:1901.01050
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we analyze jwst miri / mrs ifu observations of three seyferts and showcase the intriguing polycyclic aromatic hydrocarbon ( pah ) emission characteristics in regions of $ \ sim 500 \, \ rm pc $ scales over or around their active galactic nuclei ( agn ). combining the model predictions and the measurements of pah features and other infrared emission lines, we find that the central regions containing a high fraction of neutral pahs with small sizes, e. g., those in eso137 - g034, are in highly heated environments, due to collisional shock heating, with hard and moderately intense radiation fields. such environments are proposed to be associated with inhibited growth or preferential erosion of pahs, decreasing the average pah size and the overall abundance of pahs. we additionally find that the central regions containing a high fraction of ionized pahs with large sizes, e. g., those in mcg - 05 - 23 - 016, are likely experiencing severe photo - ionization because of the radiative effects from the radiative shock precursor besides the agn. the severe photo - ionization can contribute to the ionization of all pahs and further destruction of small pahs. overall, different seyferts, even different regions in the same galaxy, e. g., those in ngc \, 3081, can contain pah populations of different properties. specifically, seyferts that exhibit similar pah characteristics to eso137 - g034 and mcg - 05 - 23 - 016 also tend to have similar emission line properties to them, suggesting that the explanations for pah characteristics of eso137 - g034 and mcg - 05 - 23 - 016 may also apply generally. these results have promising application in the era of jwst, especially in diagnosing different ( i. e., radiative, and kinetic ) agn feedback modes.
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arxiv:2409.09772
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building on work by kasparov, we study the notion of spanier - whitehead k - duality for a discrete group. it is defined as duality in the kk - category between two c * - algebras which are naturally attached to the group, namely the reduced group c * - algebra and the crossed product for the group action on the universal example for proper actions. we compare this notion to the baum - connes conjecture by constructing duality classes based on two methods : the standard " gamma element " technique, and the more recent approach via cycles with property gamma. as a result of our analysis, we prove spanier - whitehead duality for a large class of groups, including bieberbach ' s space groups, groups acting on trees, and lattices in lorentz groups.
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arxiv:1908.03749
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the reply to g. w. bruhn is added.
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arxiv:physics/9801024
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graphene / hexagonal boron nitride ( g / $ h $ - bn ) heterostructures offer an excellent platform for developing nanoelectronic devices and for exploring correlated states in graphene under modulation by a periodic superlattice potential. here, we report on transport measurements of nearly $ 0 ^ { \ circ } $ - twisted g / $ h $ - bn heterostructures. the heterostructures investigated are prepared by dry transfer and thermally annealing processes and are in the low mobility regime ( approximately $ 3000 ~ \ mathrm { cm } ^ { 2 } \ mathrm { v } ^ { - 1 } \ mathrm { s } ^ { - 1 } $ at 1. 9 k ). the replica dirac spectra and hofstadter butterfly spectra are observed on the hole transport side, but not on the electron transport side, of the heterostructures. we associate the observed electron - hole asymmetry to the presences of a large difference between the opened gaps in the conduction and valence bands and a strong enhancement in the interband contribution to the conductivity on the electron transport side in the low - mobility g / $ h $ - bn heterostructures. we also show that the gaps opened at the central dirac point and the hole - branch secondary dirac point are large, suggesting the presence of strong graphene - substrate interaction and electron - electron interaction in our g / $ h $ - bn heterostructures. our results provide additional helpful insight into the transport mechanism in g / $ h $ - bn heterostructures.
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arxiv:1802.03307
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in mathematics, an identity is an equality relating one mathematical expression a to another mathematical expression b, such that a and b ( which might contain some variables ) produce the same value for all values of the variables within a certain domain of discourse. in other words, a = b is an identity if a and b define the same functions, and an identity is an equality between functions that are differently defined. for example, ( a + b ) 2 = a 2 + 2 a b + b 2 { \ displaystyle ( a + b ) ^ { 2 } = a ^ { 2 } + 2ab + b ^ { 2 } } and cos 2 θ + sin 2 θ = 1 { \ displaystyle \ cos ^ { 2 } \ theta + \ sin ^ { 2 } \ theta = 1 } are identities. identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign. formally, an identity is a universally quantified equality. = = common identities = = = = = algebraic identities = = = certain identities, such as a + 0 = a { \ displaystyle a + 0 = a } and a + ( − a ) = 0 { \ displaystyle a + ( - a ) = 0 }, form the basis of algebra, while other identities, such as ( a + b ) 2 = a 2 + 2 a b + b 2 { \ displaystyle ( a + b ) ^ { 2 } = a ^ { 2 } + 2ab + b ^ { 2 } } and a 2 − b 2 = ( a + b ) ( a − b ) { \ displaystyle a ^ { 2 } - b ^ { 2 } = ( a + b ) ( a - b ) }, can be useful in simplifying algebraic expressions and expanding them. = = = trigonometric identities = = = geometrically, trigonometric identities are identities involving certain functions of one or more angles. they are distinct from triangle identities, which are identities involving both angles and side lengths of a triangle. only the former are covered in this article. these identities are useful whenever expressions involving trigonometric functions need to be simplified. another important application is the integration of non - trigonometric functions : a common technique which involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. one of the most prominent examples of trigonometric identities involves the equation sin 2 θ + cos 2 θ = 1
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https://en.wikipedia.org/wiki/Identity_(mathematics)
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accurate and safety - quantifiable localization is of great significance for safety - critical autonomous systems, such as unmanned ground vehicles ( ugv ) and unmanned aerial vehicles ( uav ). the visual odometry - based method can provide accurate positioning in a short period but is subjected to drift over time. moreover, the quantification of the safety of the localization solution ( the error is bounded by a certain value ) is still a challenge. to fill the gaps, this paper proposes a safety - quantifiable line feature - based visual localization method with a prior map. the visual - inertial odometry provides a high - frequency local pose estimation which serves as the initial guess for the visual localization. by obtaining a visual line feature pair association, a foot point - based constraint is proposed to construct the cost function between the 2d lines extracted from the real - time image and the 3d lines extracted from the high - precision prior 3d point cloud map. moreover, a global navigation satellite systems ( gnss ) receiver autonomous integrity monitoring ( raim ) inspired method is employed to quantify the safety of the derived localization solution. among that, an outlier rejection ( also well - known as fault detection and exclusion ) strategy is employed via the weighted sum of squares residual with a chi - squared probability distribution. a protection level ( pl ) scheme considering multiple outliers is derived and utilized to quantify the potential error bound of the localization solution in both position and rotation domains. the effectiveness of the proposed safety - quantifiable localization system is verified using the datasets collected in the uav indoor and ugv outdoor environments.
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arxiv:2211.15127
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we propose a novel hematoxylin and eosin ( h & e ) stain normalization method based on a modified u - net neural network architecture. unlike previous deep - learning methods that were often based on generative adversarial networks ( gans ), we take a teacher - student approach and use paired datasets generated by a trained cyclegan to train a u - net to perform the stain normalization task. through experiments, we compared our method to two recent competing methods, cyclegan and stainnet, a lightweight approach also based on the teacher - student model. we found that our method is faster and can process larger images with better quality compared to cyclegan. we also compared to stainnet and found that our method delivered quantitatively and qualitatively better results.
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arxiv:2211.05420
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this paper deals with unbounded solutions to a class of chemotaxis systems. in particular, for a rather general attraction - repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect lebesgue spaces where given unbounded solutions blow - up also in the corresponding norms of those spaces ; subsequently, estimates for the blow - up time are established. finally, for a simplified version of the model, some blow - up criteria are proved.
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arxiv:2303.15039
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it is constructed a normal form for a class of real - smooth surfaces m \ subset \ mathbb { c } ^ { 2 } defined near a degenerate cr singularity.
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arxiv:1408.6882
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cross validation is a central tool in evaluating the performance of machine learning and statistical models. however, despite its ubiquitous role, its theoretical properties are still not well understood. we study the asymptotic properties of the cross validated - risk for a large class of models. under stability conditions, we establish a central limit theorem and berry - esseen bounds, which enable us to compute asymptotically accurate confidence intervals. using our results, we paint a big picture for the statistical speed - up of cross validation compared to a train - test split procedure. a corollary of our results is that parametric m - estimators ( or empirical risk minimizers ) benefit from the " full " speed - up when performing cross - validation under the training loss. in other common cases, such as when the training is done using a surrogate loss or a regularizer, we show that the behavior of the cross - validated risk is complex with a variance reduction which may be smaller or larger than the " full " speed - up, depending on the model and the underlying distribution. we allow the number of folds to grow with the number of observations at any rate.
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arxiv:2001.11111
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the famous pentagon identity for quantum dilogarithms has a generalization for every dynkin quiver, due to reineke. a more advanced generalization is associated with a pair of alternating dynkin quivers, due to keller. the description and proof of keller ' s identities involves cluster algebras and cluster categories, and the statement of the identity is implicit. in this paper we describe keller ' s identities explicitly, and prove them by a dimension counting argument. namely, we consider quiver representations $ \ boldsymbol { \ mathrm { rep } } _ \ gamma $ together with a superpotential function $ w _ \ gamma $, and calculate the betti numbers of the equivariant $ w _ \ gamma $ rapid decay cohomology algebra of $ \ boldsymbol { \ mathrm { rep } } _ \ gamma $ in two different ways corresponding to two natural stratifications of $ \ boldsymbol { \ mathrm { rep } } _ \ gamma $. this approach is suggested by kontsevich and soibelman in relation with the cohomological hall algebra of quivers, and the associated donaldson - thomas invariants.
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arxiv:1702.04766
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the time evolution of wavepackets in crystals in the presence of a homogeneous electric field is formulated in k - space in a numerically tractable form. the dynamics is governed by separate equations for the motion of the waveform in k - space and for the evolution of the underlying bloch - like states. a one - dimensional tight - binding model is studied numerically, and both bloch oscillations and zener tunneling are observed. the long - lived bloch oscillations of the wavepacket center under weak fields are accompanied by oscillations in its spatial spread. these are analyzed in terms of a k - space expression for the spread having contributions from both the quantum metric and the berry connection of the bloch states. we find that when sizeable spread oscillations do occur, they are mostly due to the latter term.
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arxiv:0810.2057
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a distributed algorithm performs local computations on pieces of input and communicates the results through given communication links. when processing a massive graph in a distributed algorithm, local outputs must be configured as a solution to a graph problem without shared memory and with few rounds of communication. in this paper we consider the problem of computing a local cluster in a massive graph in the distributed setting. computing local clusters are of certain application - specific interests, such as detecting communities in social networks or groups of interacting proteins in biological networks. when the graph models the computer network itself, detecting local clusters can help to prevent communication bottlenecks. we give a distributed algorithm that computes a local cluster in time that depends only logarithmically on the size of the graph in the congest model. in particular, when the value of the optimal local cluster is known, the algorithm runs in time entirely independent of the size of the graph and depends only on error bounds for approximation. we also show that the local cluster problem can be computed in the k - machine distributed model in sublinear time. the speedup of our local cluster algorithms is mainly due to the use of our distributed algorithm for heat kernel pagerank.
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arxiv:1507.08967
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text summarization is an approach for identifying important information present within text documents. this computational technique aims to generate shorter versions of the source text, by including only the relevant and salient information present within the source text. in this paper, we propose a novel method to summarize a text document by clustering its contents based on latent topics produced using topic modeling techniques and by generating extractive summaries for each of the identified text clusters. all extractive sub - summaries are later combined to generate a summary for any given source document. we utilize the lesser used and challenging wikihow dataset in our approach to text summarization. this dataset is unlike the commonly used news datasets which are available for text summarization. the well - known news datasets present their most important information in the first few lines of their source texts, which make their summarization a lesser challenging task when compared to summarizing the wikihow dataset. contrary to these news datasets, the documents in the wikihow dataset are written using a generalized approach and have lesser abstractedness and higher compression ratio, thus proposing a greater challenge to generate summaries. a lot of the current state - of - the - art text summarization techniques tend to eliminate important information present in source documents in the favor of brevity. our proposed technique aims to capture all the varied information present in source documents. although the dataset proved challenging, after performing extensive tests within our experimental setup, we have discovered that our model produces encouraging rouge results and summaries when compared to the other published extractive and abstractive text summarization models.
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arxiv:2106.15313
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in smart healthcare, human activity recognition ( har ) is considered to be an efficient model in pervasive computation from sensor readings. the ambient assisted living ( aal ) in the home or community helps the people in providing independent care and enhanced living quality. however, many aal models were restricted using many factors that include computational cost and system complexity. moreover, the har concept has more relevance because of its applications. hence, this paper tempts to implement the har system using deep learning with the data collected from smart sensors that are publicly available in the uc irvine machine learning repository ( uci ). the proposed model involves three processes : ( 1 ) data collection, ( b ) optimal feature selection, ( c ) recognition. the data gathered from the benchmark repository is initially subjected to optimal feature selection that helps to select the most significant features. the proposed optimal feature selection is based on a new meta - heuristic algorithm called colliding bodies optimization ( cbo ). an objective function derived by the recognition accuracy is used for accomplishing the optimal feature selection. here, the deep learning model called recurrent neural network ( rnn ) is used for activity recognition. the proposed model on the concerned benchmark dataset outperforms existing learning methods, providing high performance compared to the conventional models.
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arxiv:2010.03324
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we prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. we construct blowdowns. we define chen - ruan cohomology ring for any omnioriented quasitoric orbifold. we prove that the euler characteristic of this cohomology is preserved by a crepant blowdown. we prove that the betti numbers are also preserved if dimension is less or equal to six. in particular, our work reveals a new form of mckay correspondence for orbifold toric varieties that are not gorenstein. we illustrate with an example.
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arxiv:1202.5578
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$ k $ - core decomposition is widely used to identify the center of a large network, it is a pruning process in which the nodes with degrees less than $ k $ are recursively removed. although the simplicity and effectiveness of this method facilitate its implementation on broad applications across many scientific fields, it produces few analytical results. we here simplify the existing theoretical framework to a simple iterative relationship and obtain the exact analytical solutions of the $ k $ - core pruning process on large uncorrelated networks. from these solutions we obtain such statistical properties as the degree distribution and the size of the remaining subgraph in each of the pruning steps. our theoretical results resolve the long - lasting puzzle of the $ k $ - core pruning dynamics and provide an intuitive description of the dynamic process.
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arxiv:1810.08936
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we consider the recent relativistic bit commitment protocol introduced by lunghi et al. [ phys. rev. lett. 2015 ] and present a new security analysis against classical attacks. in particular, while the initial complexity of the protocol scaled double - exponentially with the commitment time, our analysis shows that the correct dependence is only linear. this has dramatic implications in terms of implementation : in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation.
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arxiv:1507.00239
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brueckner - hartree - fock calculations are performed for nuclear matter with an exact treatment of the pauli exclusion operator in the bethe - goldstone equation. the differences in the calculated binding energy, compared to the angle - average approximation, which is commonly used, are non - negligible. these difference exhibits a specific density dependence, which shifts the calculated saturation point towards smaller densities. this effect is observed for various versions of modern models for the nn interaction.
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arxiv:nucl-th/9812011
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we study the prospect of determining the decay properties of the gluino in the supersymmetric ( susy ) standard model at a 100 tev future hadron collider. we consider the case where the neutral wino is the lightest superparticle. in this case, the long - lived charged wino can be used to eliminate standard model backgrounds, which enables us to study the details of superparticles. we show that, based on the analysis of the numbers of high $ p _ t $ leptons, boosted $ w $ - jets, and $ b $ - tagged jets, we may determine the gaugino species and the quark flavors in the gluino decay. with such determinations, we can obtain information about the mass spectrum of squarks even if squarks are out of the kinematical reach.
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arxiv:2102.07910
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the investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. here we consider diffusion of charged particles in fully three - dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. we identify different ranges of particle energy depending upon the ratio of the larmor radius of the charged particle to the characteristic outer length scale of the turbulence. two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. the theoretical results are compared with those from computer simulations, showing good agreement.
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arxiv:1612.09507
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it has long been noticed that the efficacy observed in small early phase studies is generally better than that observed in later larger studies. historically, the inflation of the efficacy results from early proof - of - concept studies is either ignored, or adjusted empirically using a frequentist or bayesian approach. in this article, we systematically explained the underlying reason for the inflation of efficacy results in small early phase studies from the perspectives of measurement error models and selection bias. a systematic method was built to adjust the early phase study results from both frequentist and bayesian perspectives. a hierarchical model was proposed to estimate the distribution of the efficacy for a portfolio of compounds, which can serve as the prior distribution for the bayesian approach. we showed through theory that the systematic adjustment provides an unbiased estimator for the true mean efficacy for a portfolio of compounds. the adjustment was applied to paired data for the efficacy in early small and later larger studies for a set of compounds in diabetes and immunology. after the adjustment, the bias in the early phase small studies seems to be diminished.
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arxiv:2006.05795
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item - item collaborative filtering ( cf ) models are a well known and studied family of recommender systems, however current literature does not provide any theoretical explanation of the conditions under which item - based recommendations will succeed or fail. we investigate the existence of an ideal item - based cf method able to make perfect recommendations. this cf model is formalized as an eigenvalue problem, where estimated ratings are equivalent to the true ( unknown ) ratings multiplied by a user - specific eigenvalue of the similarity matrix. preliminary experiments show that the magnitude of the eigenvalue is proportional to the accuracy of recommendations for that user and therefore it can provide reliable measure of confidence.
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arxiv:1809.02052
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an obstacle for spin - based quantum sensors is magnetic noise due to proximal spins. however, such a spin cluster surrounding the sensor can become an asset, if it can be controlled. here, we polarize and readout a cluster of three nitrogen ( n ) electron spins coupled to a single nitrogen - vacancy ( nv ) spin in diamond. we further achieve sub - nm localization of the cluster spins. finally, we demonstrate coherent spin exchange between the species by simultaneous dressing of the nv and the n states. these results establish the feasibility of environment - assisted sensing and quantum simulations with diamond spins.
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arxiv:1605.07552
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in the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. despite the growing body of impressive results, the performance of most posted price mechanisms however, rely crucially on price discrimination when multiple copies of a good are available. for the more general case with non - linear production costs on each good, hardly anything is known for general multi - good markets. with this in mind, we study a bayesian setting where the seller can produce any number of copies of a good but faces convex production costs for the same, and buyers arrive sequentially. our main contribution is a framework for non - discriminatory pricing in the presence of production costs : the framework yields posted price mechanisms with o ( 1 ) - approximation factors for fractionally subadditive ( xos ) buyers, logarithmic approximations for subadditive buyers, and also extends to settings where the seller is oblivious to buyer valuations. our work presents the first known results for bayesian settings with production costs and is among the few posted price mechanisms that do not charge buyers differently for the same good.
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arxiv:1609.06844
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this investigation is aimed at clarifying the nature of the interstellar gas seen in absorption against bright o and b stars. towards this end we have obtained for the first time hi absorption spectra towards radio sources very close to the lines of sight towards 25 bright stars previously studied. in this paper we describe the selection criteria, the details regarding our observations, and finally present the absorption spectra. in the accompanying paper we analyse the results and draw conclusions.
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arxiv:astro-ph/9904240
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we present the realization of mid - infrared waveguide by ultrafast laser inscription technique in a chalcogenide glass. our approach is based on multicore waveguide that consists in an alignment on a mesh of positive refractive index channels placed parallel to each other. two different meshes are investigated with different refractive index contrasts between the channel and the glass matrix. a detailed analysis of the performances at a wavelength of 4. 5 $ \ mu $ m shows propagation losses of 0. 20 $ \ pm $ 0. 05 db / cm and coupling efficiencies higher than 60 %.
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arxiv:1908.03452
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question answering over knowledge bases ( kbqa ) has become a popular approach to help users extract information from knowledge bases. although several systems exist, choosing one suitable for a particular application scenario is difficult. in this article, we provide a comparative study of six representative kbqa systems on eight benchmark datasets. in that, we study various question types, properties, languages, and domains to provide insights on where existing systems struggle. on top of that, we propose an advanced mapping algorithm to aid existing models in achieving superior results. moreover, we also develop a multilingual corpus covid - kgqa, which encourages covid - 19 research and multilingualism for the diversity of future ai. finally, we discuss the key findings and their implications as well as performance guidelines and some future improvements. our source code is available at \ url { https : / / github. com / tamlhp / kbqa }.
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arxiv:2211.08170
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iris recognition systems are vulnerable to the presentation attacks, such as textured contact lenses or printed images. in this paper, we propose a lightweight framework to detect iris presentation attacks by extracting multiple micro - stripes of expanded normalized iris textures. in this procedure, a standard iris segmentation is modified. for our presentation attack detection network to better model the classification problem, the segmented area is processed to provide lower dimensional input segments and a higher number of learning samples. our proposed micro stripes analyses ( msa ) solution samples the segmented areas as individual stripes. then, the majority vote makes the final classification decision of those micro - stripes. experiments are demonstrated on five databases, where two databases ( iiitd - wvu and notre dame ) are from the livdet - 2017 iris competition. an in - depth experimental evaluation of this framework reveals a superior performance compared with state - of - the - art algorithms. moreover, our solution minimizes the confusion between textured ( attack ) and soft ( bona fide ) contact lens presentations.
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arxiv:2010.14850
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we study recovering fluid density and velocity from sparse multiview videos. existing neural dynamic reconstruction methods predominantly rely on optical flows ; therefore, they cannot accurately estimate the density and uncover the underlying velocity due to the inherent visual ambiguities of fluid velocity, as fluids are often shapeless and lack stable visual features. the challenge is further pronounced by the turbulent nature of fluid flows, which calls for properly designed fluid velocity representations. to address these challenges, we propose hybrid neural fluid fields ( hyfluid ), a neural approach to jointly infer fluid density and velocity fields. specifically, to deal with visual ambiguities of fluid velocity, we introduce a set of physics - based losses that enforce inferring a physically plausible velocity field, which is divergence - free and drives the transport of density. to deal with the turbulent nature of fluid velocity, we design a hybrid neural velocity representation that includes a base neural velocity field that captures most irrotational energy and a vortex particle - based velocity that models residual turbulent velocity. we show that our method enables recovering vortical flow details. our approach opens up possibilities for various learning and reconstruction applications centered around 3d incompressible flow, including fluid re - simulation and editing, future prediction, and neural dynamic scene composition. project website : https : / / kovenyu. com / hyfluid /
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arxiv:2312.06561
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we model the electrons / positrons produced by dark matter annihilations in the colliding galaxy cluster system 1e0657 - 56 ( the bullet cluster ). these charged particles, confined by the magnetic field, clearly trace the path of the bullet, which passes through the main cluster with a speed of 3000 - 5000 km / s. adding the effect of dark matter substructure ( subhalos ) in each cluster we find the annihilation rate is enhancedgreatly and the density of positrons in the trail is similar to that within the bullet cluster. this opens the door to unambiguous detection of the annihilation signal through the sz effect, at significant separation from the thermal electrons.
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arxiv:0708.1891
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according to recent studies, the vulnerability of state - of - the - art neural networks to adversarial input samples has increased drastically. a neural network is an intermediate path or technique by which a computer learns to perform tasks using machine learning algorithms. machine learning and artificial intelligence model has become a fundamental aspect of life, such as self - driving cars [ 1 ], smart home devices, so any vulnerability is a significant concern. the smallest input deviations can fool these extremely literal systems and deceive their users as well as administrator into precarious situations. this article proposes a defense algorithm that utilizes the combination of an auto - encoder [ 3 ] and block - switching architecture. auto - coder is intended to remove any perturbations found in input images whereas the block switching method is used to make it more robust against white - box attacks. the attack is planned using fgsm [ 9 ] model, and the subsequent counter - attack by the proposed architecture will take place thereby demonstrating the feasibility and security delivered by the algorithm.
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arxiv:2203.10930
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ultralight scalar fields such as axions can form clouds around rotating black holes ( bhs ) by the superradiant instability. it is important to consider the evolution of clouds associated with bh binaries for the detectability of the presence of clouds through gravitational wave signals and observations of the mass and spin parameters of bhs. we re - examine the impact on the axion cloud due to the tidal perturbation from the companion in a binary system taking into account the following points. first, we study the influence of higher - multipole moments. second, we consider the backreaction due to the angular momentum transfer between the cloud and the orbital motion. this angular momentum transfer further causes the backreaction to the hyperfine split through the change in geometry. finally, we calculate the particle number flux to the infinity induced by the tidal interaction. as a result, we found that the scalar field is not reabsorbed by the bh. instead, the scalar particles are radiated away to evaporate during the inspiral, irrespectively of the direction of the orbital motion, for almost equal mass binaries.
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arxiv:2112.05774
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a one - dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries. the particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the boundaries. we will show that on a special manifold in the parameters space multiple shocks evolve in the system for both species of particles which perform continuous time random walks on the lattice.
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arxiv:cond-mat/0504093
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this work contains two papers : the first published in 2022 and entitled " on the nature of some euler ' s double equations equivalent to fermat ' s last theorem " provides a marvellous proof through the so - called discordant forms of appropriate euler ' s double equations, which could have entered in a not very narrow margin and the second instead published in 2024 and entitled " some diophantus - fermat double equations equivalent to frey ' s elliptic curve " provides the possible proof, which fermat has not published in detail, but which uses the characteristic of all right - angled triangles with sides equal to whole numbers, or the famous pythagorean identity. some explanations in session ( iii ) are provided : the first makes evident the nature of the " proof a ' la fermat " and the subsequent sessions clarify the direct and interesting connection of the two elementary proofs and it is necessary if you want to understand how two different elementary proofs of fermat ' s last theorem are possible. it must be observed that those proofs must in no way be interpreted as a sort of absurd revenge of elementary number theory over more modern analytic and algebraic treatments. the author himself has added a section in which he connects his concepts with some of those used by wiles in his complex demonstration. this implies that, to a certain extent, wiles ' demonstration inspired the author of those works. ultimately in this paper we will illustrate how only thanks to some of euler ' s discoveries was it possible to shed light on the so - called too narrow margin never written by fermat. for this reason we will also provide some details on an article that was the real inspiration for achieving these results ( see last conclusions ).
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arxiv:1704.06335
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recently, the problem of bounding the sup norms of $ l ^ 2 $ - normalized cuspidal automorphic newforms $ \ phi $ on $ \ text { gl } _ 2 $ in the level aspect has received much attention. however at the moment strong upper bounds are only available if the central character $ \ chi $ of $ \ phi $ is not too highly ramified. in this paper, we establish a uniform upper bound in the level aspect for general $ \ chi $. if the level $ n $ is a square, our result reduces to $ $ \ | \ phi \ | _ \ infty \ ll n ^ { \ frac14 + \ epsilon }, $ $ at least under the ramanujan conjecture. in particular, when $ \ chi $ has conductor $ n $, this improves upon the previous best known bound $ \ | \ phi \ | _ \ infty \ ll n ^ { \ frac12 + \ epsilon } $ in this setup ( due to saha [ 14 ] ) and matches a lower bound due to templier [ 17 ], thus our result is essentially optimal in this case.
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arxiv:1905.03661
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understanding the decoherence of electron spins in semiconductors due to their interaction with nuclear spins is of fundamental interest as they realize the central spin model and of practical importance for using electron spins as qubits. interesting effects arise from the quadrupolar interaction of nuclear spins with electric field gradients, which have been shown to suppress diffusive nuclear spin dynamics. one might thus expect them to enhance electron spin coherence. here we show experimentally that for gate - defined gaas quantum dots, quadrupolar broadening of the nuclear larmor precession can also reduce electron spin coherence due to faster decorrelation of transverse nuclear fields. however, this effect can be eliminated for appropriate field directions. furthermore, we observe an additional modulation of spin coherence that can be attributed to an anisotropic electronic $ g $ - tensor. these results complete our understanding of dephasing in gated quantum dots and point to mitigation strategies. they may also help to unravel unexplained behaviour in related systems such as self - assembled quantum dots and iii - v nanowires.
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arxiv:1508.05136
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discussion of " bayesian models and methods in public policy and government settings " by s. e. fienberg [ arxiv : 1108. 2177 ]
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arxiv:1108.3912
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the e1 transitions of $ \ psi ( 3686 ) $ and $ \ psi ( 3770 ) \ to \ gamma \ chi _ { cj } $ are investigated in a non - relativistic effective field theory ( nreft ) where the open charm effects are included systematically as the leading corrections. it also allows a self - consistent inclusion of the $ s $ - $ d $ mixing in the same framework. we are able to show that the open charm contributions are essential for understanding the significant discrepancies between the non - relativistic leading order calculations and the experimental data.
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arxiv:1608.07947
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we have investigated the temperature dependence of the electrical conductivity sigma ( n, b, t ) of nominally uncompensated, neutron - transmutation - doped ^ { 70 } ge : ga samples in magnetic fields up to b = 8 t at low temperatures ( t = 0. 05 - 0. 5 k ). in our earlier studies at b = 0, the critical exponent mu = 0. 5 defined by sigma ( n, 0, 0 ) \ propto ( n - n _ c ) ^ { mu } has been determined for the same series of ^ { 70 } ge : ga samples with the doping concentration n ranging from 1. 861 \ times 10 ^ { 17 } cm ^ { - 3 } to 2. 434 \ times 10 ^ { 17 } cm ^ { - 3 }. in magnetic fields, the motion of carriers loses time - reversal symmetry, the universality class may change and with it the value of mu. in this work, we show that magnetic fields indeed affect the value of mu ( mu changes from 0. 5 at b = 0 to 1. 1 at b \ geq 4 t ). the same exponent mu ' = 1. 1 is also found in the magnetic - field - induced mit for three different ^ { 70 } ge : ga samples, i. e., sigma ( n, b, 0 ) \ propto [ b _ c ( n ) - b ] ^ { mu ' } where b _ c ( n ) is the concentration - dependent critical magnetic induction. we show that sigma ( n, b, 0 ) obeys a simple scaling rule on the ( n, b ) plane. based on this finding, we derive from a simple mathematical argument that mu = mu ' as has been observed in our experiment.
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arxiv:cond-mat/9910112
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capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects. micromorphic theories are often applied in this context to model the inelastic deformation behavior of foam - like structures, in particular to incorporate such size effect into the investigation of structure - property correlations. this raises the problems of formulating appropriate constitutive relations for the numerous non - classical stress measures and determining the corresponding material parameters, which are usually difficult to assess experimentally. the present contribution therefore alternatively employs a concurrent micromorphic multi - scale approach within the direct fe $ ^ 2 $ framework to simulate the complex irreversible behavior of foam - like porous solids. the predictions of cosserat ( micropolar ) and a fully - micromorphic theory are compared with conventional fe $ ^ 2 $ results and direct numerical simulations ( dns ) for complex loading scenarios with elastic, elastic - plastic, and creep deformations.
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arxiv:2403.10532
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the fast execution speed and energy efficiency of analog hardware has made them a strong contender for deployment of deep learning model at the edge. however, there are concerns about the presence of analog noise which causes changes to the weight of the models, leading to performance degradation of deep learning model, despite their inherent noise resistant characteristics. the effect of the popular batch normalization layer on the noise resistant ability of deep learning model is investigated in this work. this systematic study has been carried out by first training different models with and without batch normalization layer on cifar10 and cifar100 dataset. the weights of the resulting models are then injected with analog noise and the performance of the models on the test dataset is obtained and compared. the results show that the presence of batch normalization layer negatively impacts noise resistant property of deep learning model and the impact grows with the increase of the number of batch normalization layers.
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arxiv:2205.07372
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td - delaunay graphs, where td stands for triangular distance, is a variation of the classical delaunay triangulations obtained from a specific convex distance function. bonichon et. al. noticed that every triangulation is the td - delaunay graph of a set of points in $ \ mathbb { r } ^ 2 $, and conversely every td - delaunay graph is planar. it seems natural to study the generalization of this property in higher dimensions. such a generalization is obtained by defining an analogue of the triangular distance for $ \ mathbb { r } ^ d $. it is easy to see that td - delaunay complexes of $ \ mathbb { r } ^ { d - 1 } $ are of dushnik - miller dimension $ d $. the converse holds for $ d = 2 $ or $ 3 $ and it was conjectured independently by mary and evans et. al. to hold for larger $ d $. here we disprove the conjecture already for $ d = 4 $.
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arxiv:1803.09576
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its right cosets. if they are ( that is, if all g { \ displaystyle g } in g { \ displaystyle g } satisfy g h = h g { \ displaystyle gh = hg } ), then h { \ displaystyle h } is said to be a normal subgroup. in d 4 { \ displaystyle \ mathrm { d } _ { 4 } }, the group of symmetries of a square, with its subgroup r { \ displaystyle r } of rotations, the left cosets g r { \ displaystyle gr } are either equal to r { \ displaystyle r }, if g { \ displaystyle g } is an element of r { \ displaystyle r } itself, or otherwise equal to u = f c r = { f c, f d, f v, f h } { \ displaystyle u = f _ { \ mathrm { c } } r = \ { f _ { \ mathrm { c } }, f _ { \ mathrm { d } }, f _ { \ mathrm { v } }, f _ { \ mathrm { h } } \ } } ( highlighted in green in the cayley table of d 4 { \ displaystyle \ mathrm { d } _ { 4 } } ). the subgroup r { \ displaystyle r } is normal, because f c r = u = r f c { \ displaystyle f _ { \ mathrm { c } } r = u = rf _ { \ mathrm { c } } } and similarly for the other elements of the group. ( in fact, in the case of d 4 { \ displaystyle \ mathrm { d } _ { 4 } }, the cosets generated by reflections are all equal : f h r = f v r = f d r = f c r { \ displaystyle f _ { \ mathrm { h } } r = f _ { \ mathrm { v } } r = f _ { \ mathrm { d } } r = f _ { \ mathrm { c } } r }. ) = = = quotient groups = = = suppose that n { \ displaystyle n } is a normal subgroup of a group g { \ displaystyle g }, and g / n = { g n g ∈ g } { \ displaystyle g / n = \ { gn \ mid g \ in g \ } } denotes its set of co
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https://en.wikipedia.org/wiki/Group_(mathematics)
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a model of an organism as an autonomous intelligent system has been proposed. this model was used to analyze learning of an organism in various environmental conditions. processes of learning were divided into two types : strong and weak processes taking place in the absence and the presence of aprioristic information about an object respectively. weak learning is synonymous to adaptation when aprioristic programs already available in a system ( an organism ) are started. it was shown that strong learning is impossible for both an organism and any autonomous intelligent system. it was shown also that the knowledge base of an organism cannot be updated. therefore, all behavior programs of an organism are congenital. a model of a conditioned reflex as a series of consecutive measurements of environmental parameters has been advanced. repeated measurements are necessary in this case to reduce the error during decision making.
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arxiv:cs/0604009
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we show some examples of calculations of massless and massive feynman integrals.
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arxiv:2107.08003
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this paper is concerned with the investigation of the bistatic mimo radar for estimating various multitarget parameters of interest in the presence of clutter and noise. the parameters of interest include direction of departure ( dod ), direction of arrival ( doa ), range and velocity and a novel algorithm is proposed for estimating these target parameters based on the concepts of the " array manifold " and " manifold extenders ". the performance of the proposed algorithm is evaluated using monte carlo simulation studies.
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arxiv:2411.02072
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a system consisting of a point particle coupled to gravity is investigated. the set of constraints is derived. it was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time coordinate $ t \ equiv x ^ 0 $ and serves as the hamiltonian which gives the correct equations of motion. besides that, the system satisfies the mass shell constraint, $ p ^ \ mu p _ \ mu - m ^ 2 = 0 $, which is the generator of the worldsheet reparametrizations, where the momenta $ p _ \ mu $, $ \ mu = 0, 1, 2, 3 $, generate infinitesimal changes of the particle ' s position $ x ^ \ mu $ in spacetime. consequently, the hamiltonian contains $ p _ 0 $, which upon quantization becomes the operator $ - i \ partial / \ partial t $, occurring on the r. h. s. of the wheeler - dewitt euqtion. here the role of time has the particle coordinate $ x ^ 0 \ equiv t $, which is a distinct concept than the spacetime coordinate $ x ^ 0 \ equiv t $. it is also shown how the ordering ambiguities can be avoided if a quadratic form of the momenta is cast into the form that instead of the metric contains the basis vectors.
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arxiv:2105.08430
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this note generalizes the celebrated bogomolov - gieseker inequality for smooth projective surfaces over an algebraically closed field of characteristic zero to projective surfaces in arbitrary characteristic with canonical singularities. we also generalize to this context some classical applications of the bogomolov - gieseker inequality.
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arxiv:2308.03307
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measurement of the d + d - > 4he + eta reaction using vector and tensor polarised beam has been performed at cosy using big karl magnetic spectrograph. the beam polarisation necessary for obtaining the vector and tensor analysing power for this reaction was measured. the method and the results of the tensor polarisation measurement of the deuteron beam are presented.
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arxiv:hep-ex/0512033
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in this paper, we address the enhancement of classification accuracy for 3d point cloud lidar data, an optical remote sensing technique that estimates the three - dimensional coordinates of a given terrain. our approach introduces product coefficients, theoretical quantities derived from measure theory, as additional features in the classification process. we define and present the formulation of these product coefficients and conduct a comparative study, using them alongside principal component analysis ( pca ) as feature inputs. results demonstrate that incorporating product coefficients into the feature set significantly improves classification accuracy within this new framework.
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arxiv:2503.11943
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high - redshift blazars are one of the most powerful monsters in the universe and $ \ gamma $ - ray variability carries crucial information of their relativistic jets. in this work we present results of the first systematical temporal analysis of { \ it fermi } - lat data of all known seven $ \ gamma $ - ray blazars beyond redshift 3. significant long - term $ \ gamma $ - ray variability is found from five sources in monthly $ \ gamma $ - ray light curves, in which three of them are reported for the first time. furthermore, intraday $ \ gamma $ - ray variations are detected from nvss j053954 $ - $ 283956 and nvss j080518 $ + $ 614423. doubling variability timescale of the former source is limited as short as $ \ lesssim $ 1 hour ( at the source frame ). together with variability amplitude over one order of magnitude, nvss j053954 $ - $ 283956 is the most distant $ \ gamma $ - ray flaring blazar so far. meanwhile, intraday optical variability of nvss j163547 $ + $ 362930 is found based on archival ptf / iptf light curve. benefited from multiwavelength activity of these sources, constraints of their doppler factors as well as locations of $ \ gamma $ - ray radiation region and indications for the sdss high redshift jetted active galactic nuclei deficit are discussed.
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arxiv:1710.02904
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based on a path integral prescription for anomaly calculation, we analyze an effective theory of the two - dimensional $ n = 2 $ supergravity, i. e., $ n = 2 $ super - liouville theory. we calculate the anomalies associated with the brst supercurrent and the ghost number supercurrent. from those expressions of anomalies, we construct covariant brst and ghost number supercurrents in the effective theory. we then show that the ( super - ) coordinate brst current algebra forms a superfield extension of the topological conformal algebra for an { \ it arbitrary \ / } type of conformal matter or, in terms of the string theory, for an arbitrary number of space - time dimensions. this fact is very contrast with $ n = 0 $ and $ n = 1 $ ( super - ) liouville theory, where the topological algebra singles out a particular value of dimensions. our observation suggests a topological nature of the two - dimensional $ n = 2 $ supergravity as a quantum theory.
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arxiv:hep-th/9203021
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recursion relations are succinctly obtained for $ ( + +... + ) $ and $ ( - + +... + ) $ amplitudes in the context of the space - cone gauge in qcd. we rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. of great importance is the power of gauge lorentz invariance, which is enough to determine the soft factors in the latter cases.
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arxiv:0805.2645
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using the example of the jaynes - cummings model, we present a comparison between time - delayed coherent feedback mediated by reservoirs with continuous and discrete mode structures and work out their qualitative differences. in contrast to the discrete - mode case, the continuous - mode case results in the well - known single - delay dynamics which can, e. g., stabilize rabi oscillations. the discrete - mode case, however, shows population trapping, not present in the continuous - mode model. given these differences, we discuss the cavity output spectra and show how these characteristic properties are spectrally identifiable. this work demonstrates the fundamental difference between the continuous - mode case, which represents a truly dissipative mechanism, and the discrete - mode case that is in principle based on a coherent excitation exchange process.
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arxiv:1902.08328
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how do humans respond to indirect social influence when making decisions? we analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. while the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. we found that the adjustment of individual guesses depends linearly on the distance to the mean of all guesses. this is a remarkable, and yet surprisingly simple, statistical regularity. it holds across all questions analysed, even though the correct answers differ in several orders of magnitude. our finding supports the assumption that individual diversity does not affect the response to indirect social influence. it also complements previous results on the nonlinear response in information - rich scenarios. we argue that the nature of the response to social influence crucially changes with the level of information aggregation. this insight contributes to the empirical foundation of models for collective decisions under social influence.
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arxiv:1302.2472
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this work investigates a potential time dependence of the absolute magnitude of type ia supernovae ( sn ia ). employing the gaussian process approach, we obtain the sn ia absolute magnitude and its derivative as a function of redshift. the data set considered in the analysis comprises measurements of apparent magnitude from sn ia, hubble rate from cosmic chronometers, and the ratio between angular and radial distances from large - scale structure data ( bao and voids ). our findings reveal good compatibility between the reconstructed sn ia absolute magnitudes and a constant value. however, the mean value obtained from the gaussian process reconstruction is $ m = - 19. 456 \ pm 0. 059 $, which is $ 3. 2 \ sigma $ apart from local measurements by pantheon + sh0es. this incompatibility may be directly associated to the $ \ lambda $ cdm model and local data, as it does not appear in either model - dependent or model - independent estimates of the absolute magnitude based on early universe data. furthermore, we assess the implications of a variable $ m $ within the context of modified gravity theories. considering the local estimate of the absolute magnitude, we find $ \ sim3 \ sigma $ tension supporting departures from general relativity in analyzing scenarios involving modified gravity theories with variations in planck mass through newton ' s constant.
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arxiv:2504.15127
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fine - grained sentiment analysis involves extracting and organizing sentiment elements from textual data. however, existing approaches often overlook issues of category semantic inclusion and overlap, as well as inherent structural patterns within the target sequence. this study introduces a generative sentiment analysis model. to address the challenges related to category semantic inclusion and overlap, a latent category distribution variable is introduced. by reconstructing the input of a variational autoencoder, the model learns the intensity of the relationship between categories and text, thereby improving sequence generation. additionally, a trie data structure and constrained decoding strategy are utilized to exploit structural patterns, which in turn reduces the search space and regularizes the generation process. experimental results on the restaurant - acos and laptop - acos datasets demonstrate a significant performance improvement compared to baseline models. ablation experiments further confirm the effectiveness of latent category distribution and constrained decoding strategy.
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arxiv:2407.21560
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let $ ( m, g, j ) $ be a riemannian manifold with a compatible integrable complex structure $ j \ in \ mathrm { end } ( t _ \ mathbb { r } m ) $ and $ \ mathcal { a } _ { g, j } $ be the space of real connections on $ t _ \ mathbb { r } m $ preserving both $ g $ and $ j $. in this paper, we investigate the relationship between the geometry of real connections in $ \ mathcal { a } _ { g, j } $ and that of hermitian connections on $ t ^ { 1, 0 } m $. in particular, we study the geometry of the real chern connection $ \ nabla ^ { \ mathrm { ch, \ mathrm { r } } } $ on $ ( m, g, j ) $, and obtain k \ " ahler - einstein metrics by using real chern - einstein metrics.
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arxiv:1912.12024
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we classify the solutions of the planar weighted allen - cahn equation arising from the critical equivariant $ so ( 4 ) $ yang - mills problem. we first give a complete classification for radially symmetric solutions, and then without symmetry assumptions, we show bounded classical solutions are radially symmetric and also classify them.
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arxiv:2407.13034
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