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in this paper we present a framework for the extension of the preferential attachment ( pa ) model to heterogeneous complex networks. we define a class of heterogeneous pa models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. we perform an analytical study of the stationary degree distributions in heterogeneous pa networks. we show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in presence of heterogeneity.
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arxiv:0710.5281
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it is assumed, in general, that the electromagnetic spectrum in the primordial universe was a blackbody spectrum in vacuum. we derive the electromagnetic spectrum, based on the fluctuation - dissipation theorem that describes the electromagnetic fluctuations in a plasma. our description includes thermal and collisional effects in a plasma. the electromagnetic spectrum obtained differs from the blackbody spectrum in vacuum at low frequencies. in particular, concentrating on the primordial nucleosynthesis era, it has more energy for frequencies less than 3 to $ 6 \ omega _ { pe } $, where $ \ omega _ { pe } $ is the electron plasma frequency.
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arxiv:astro-ph/9708246
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in this paper, we perform deep neural networks for learning $ \ psi $ - weakly dependent processes. such weak - dependence property includes a class of weak dependence conditions such as mixing, association, $ \ cdots $ and the setting considered here covers many commonly used situations such as : regression estimation, time series prediction, time series classification, $ \ cdots $ the consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. we achieve the generalization bound and obtain a learning rate, which is less than $ \ mathcal { o } ( n ^ { - 1 / \ alpha } ) $, for all $ \ alpha > 2 $. applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. some simulation results are provided, as well as an application to the us recession data.
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arxiv:2302.00333
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inspired by the lee - wick higher - derivative approach to quantum field theory, grinstein, o ' connell, and wise have illustrated the utility of introducing into the standard model negative - norm states that cancel quadratic divergences in loop diagrams, thus posing a potential resolution of the hierarchy problem. subsequent work has shown that consistency with electroweak precision parameters requires many of the partner states to be too massive to be detected at the lhc. we consider the phenomenology of a yet - higher derivative theory that exhibits three poles in its bare propagators ( hence n = 3 ), whose states alternate in norm. we examine the interference effects of w boson partners on lhc scattering cross sections, and find that the n = 3 lwsm already makes verifiable predictions at 10 fb ^ ( - 1 ) of integrated luminosity.
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arxiv:1205.3213
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the talbot effect, epitomized by periodic revivals of a freely evolving periodic field structure, has been observed with waves of diverse physical nature in space and separately in time, whereby diffraction underlies the former and dispersion the latter. to date, a combined spatio - temporal talbot effect has not been realized in any wave field because diffraction and dispersion are independent physical phenomena, typically unfolding at incommensurable length scales. here we report the observation of an optical ' space - time ' talbot effect, whereby a spatio - temporal optical lattice structure undergoes periodic revivals after suffering the impact of both diffraction and dispersion. the discovered space - time revivals are governed by a single self - imaging length scale, which encompasses both spatial and temporal degrees of freedom. key to this effect is the identification of a unique pulsed optical field structure, which we refer to as a v - wave, that is endowed with intrinsically equal diffraction and dispersion lengths in free space, thereby enabling self - imaging to proceed in lockstep in space and time.
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arxiv:2102.06769
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let $ k $ denote a field and let $ v $ denote a vector space over $ k $ with finite positive dimension. we consider an ordered pair of linear transformations $ a : v \ to v $ and $ a ^ * : v \ to v $ that satisfy conditions ( i ), ( ii ) below. ( i ) there exists a basis for $ v $ with respect to which the matrix representing $ a $ is irreducible tridiagonal and the matrix representing $ a ^ * $ is diagonal. ( ii ) there exists a basis for $ v $ with respect to which the matrix representing $ a $ is diagonal and the matrix representing $ a ^ * $ is irreducible tridiagonal. we call such a pair a { \ it leonard pair } on $ v $. we discuss a correspondence between leonard pairs and a class of orthogonal polynomials consisting of the $ q $ - racah polynomials and some related polynomials of the askey scheme. for the polynomials in this class we obtain the 3 - term recurrence, difference equation, askey - wilson duality, and orthogonality in a uniform manner using the corresponding leonard pair.
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arxiv:math/0306301
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we investigate collective thomson scattering ( cts ) in two - stream non - equilibrium plasmas analytically, numerically and experimentally. in laboratory astrophysics, cts is a unique tool to obtain local plasma diagnostics. while the standard cts theory assumes plasmas to be linear, stationary, isotropic and equilibrium, it is often nonlinear, non - stationary, anisotropic, and non - equilibrium in high energy phenomena relevant to laboratory astrophysics. we theoretically calculate and numerically simulate the cts spectra in two - stream plasmas as a typical example of non - equilibrium system in space and astrophysical plasmas. the simulation results show the feasibility to diagnose two - stream instability directly via cts measurements. in order to confirm the non - equilibrium cts analysis, we have been developing experimental system with high repetition rate table top laser for laboratory astrophysics.
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arxiv:2210.11382
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we experimentally demonstrate a novel nonlinear effect in optical fibers : upconversion luminescence generation excited by multiphoton absorption of femtosecond infrared pulses. we directly estimate the average number of photons involved in the up - conversion process, by varying the wavelength of the pump source. we highlight the role of non - bridging oxygen hole centers and oxygen deficient center defects, and directly compare the intensity of side - scattered luminescence with numerical simulations of pulse propagation.
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arxiv:2009.12459
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courses, and degrees. many mathematicians distinguish between " applied mathematics ", which is concerned with mathematical methods, and the " applications of mathematics " within science and engineering. a biologist using a population model and applying known mathematics would not be doing applied mathematics, but rather using it ; however, mathematical biologists have posed problems that have stimulated the growth of pure mathematics. mathematicians such as poincare and arnold deny the existence of " applied mathematics " and claim that there are only " applications of mathematics. " similarly, non - mathematicians blend applied mathematics and applications of mathematics. the use and development of mathematics to solve industrial problems is also called " industrial mathematics ". the success of modern numerical mathematical methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which use high - performance computing for the simulation of phenomena and the solution of problems in the sciences and engineering. these are often considered interdisciplinary. = = = applicable mathematics = = = sometimes, the term applicable mathematics is used to distinguish between the traditional applied mathematics that developed alongside physics and the many areas of mathematics that are applicable to real - world problems today, although there is no consensus as to a precise definition. mathematicians often distinguish between " applied mathematics " on the one hand, and the " applications of mathematics " or " applicable mathematics " both within and outside of science and engineering, on the other. some mathematicians emphasize the term applicable mathematics to separate or delineate the traditional applied areas from new applications arising from fields that were previously seen as pure mathematics. for example, from this viewpoint, an ecologist or geographer using population models and applying known mathematics would not be doing applied, but rather applicable, mathematics. even fields such as number theory that are part of pure mathematics are now important in applications ( such as cryptography ), though they are not generally considered to be part of the field of applied mathematics per se. such descriptions can lead to applicable mathematics being seen as a collection of mathematical methods such as real analysis, linear algebra, mathematical modelling, optimisation, combinatorics, probability and statistics, which are useful in areas outside traditional mathematics and not specific to mathematical physics. other authors prefer describing applicable mathematics as a union of " new " mathematical applications with the traditional fields of applied mathematics. with this outlook, the terms applied mathematics and applicable mathematics are thus interchangeable. = = utility = = historically, mathematics was most important in the natural sciences and engineering. however, since world war ii, fields outside the physical sciences have spawned the creation of new areas of mathematics
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https://en.wikipedia.org/wiki/Applied_mathematics
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the results of the x - ray, microscopic, magnetic, and dielectric measurements performed for pfn single crystals and ceramic samples are presented. the influence of the technological conditions on selected physical properties of the materials examined is shown.
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arxiv:cond-mat/0209289
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this belongs to a series of papers motivated by ballmann ' s higher rank rigidity conjecture. we prove the following. let $ x $ be a cat ( 0 ) space with a geometric group action. suppose that every geodesic in $ x $ lies in an $ n $ - flat, $ n \ geq 2 $. if $ x $ contains a periodic $ n $ - flat which does not bound a flat $ ( n + 1 ) $ - half - space, then $ x $ is a riemannian symmetric space, a euclidean building or non - trivially splits as a metric product. this generalizes the higher rank rigidity theorem for hadamard manifolds with geometric group actions.
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arxiv:2212.07092
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we study first - passage properties for a particle that diffuses either inside or outside of generalized paraboloids, defined by y = a ( x _ 1 ^ 2 +... + x _ { d - 1 } ^ 2 ) ^ { p / 2 } where p > 1, with absorbing boundaries. when the particle is inside the paraboloid, the survival probability s ( t ) generically decays as a stretched exponential, ln ( s ) ~ - t ^ { ( p - 1 ) / ( p + 1 ) }, independent of the spatial dimensional. for a particle outside the paraboloid, the dimensionality governs the asymptotic decay, while the exponent p specifying the paraboloid is irrelevant. in two and three dimensions, s ~ t ^ { - 1 / 4 } and s ~ ( ln t ) ^ { - 1 }, respectively, while in higher dimensions the particle survives with a finite probability. we also investigate the situation where the interior of a paraboloid is uniformly filled with non - interacting diffusing particles and estimate the distance between the closest surviving particle and the apex of the paraboloid.
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arxiv:1009.2530
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proof, that the area of a cone was 1 / 3 the area of a cylinder with the same base, a result which was later proved by eudoxus of cnidus. = = = = mathematics in the time of plato = = = = while plato was not a mathematician himself, numerous early mathematicians, including archytas, theaetetus, and eudoxus, were associated with plato or with his academy, and plato mentions mathematics in several of his dialogues, including the meno, the theaetetus, the republic, and the timaeus. archytas, a pythagorean philosopher from tarentum, was a friend of plato who made several mathematical discoveries. archytas is often credited with books vii to ix in the elements, which deal with the euclidean algorithm, prime numbers, mean ratios, and perfect numbers. archytas solved the problem of doubling the cube, now known to be impossible with only a compass and a straightedge, with an alternative method, systematized the pythagorean means, and made contributions to optics and mechanics. theaetetus, who figures as a character in the platonic dialogue named after him, where he is working on a problem given to him by theodorus of cyrene to demonstrate that the square roots of several numbers from 3 to 17 are irrational, a construction now known as the spiral of theodorus. theaetetus is traditionally credited with much of the work contained in books x of euclid ' s elements, concerned with incommensurable magnitudes, book xiii, which outlines the construction of the regular polyhedra. although some of the regular polyhedra were certainly known prior to theaetetus, he is credited with the systematic construction of them, and the proof that only five of them exist. another mathematician associated with plato ' s academy is eudoxus of cnidus, developed a theory of proportion in book v of the elements. archimedes also credits eudoxus of cnidus with two propositions in book xii of euclid ' s elements, proving that the volume of a cone is one - third the volume of a cylinder with the same base, which use an early form of calculus known as the method of exhaustion. this method is also used by archimedes himself in order to find an approximation to Ο ( measurement of the circle ) and to prove that the area enclosed by a parabola and a straight line is 4 / 3
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https://en.wikipedia.org/wiki/Ancient_Greek_mathematics
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about conway ' s surreal numbers : a letter to a friend ( written in french ). in memoriam john horton conway.
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arxiv:2101.11790
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for a field $ f $ and a given integer $ n > 1 $, goncharov has given a complex $ \ gamma _ f ( n ) $ which he calls motivic and which he expects to rationally compute the weight $ n $ motivic cohomology of $ \ text { spec } f $, and hence its algebraic $ k $ - groups in adams weight $ n $, and he was also led to - - - conjecturally quasiisomorphic - - - ` thickened ' complexes thereof. these complexes involve tensor products of higher bloch groups, the latter having been linked to the geometry of certain configurations in goncharov ' s proof of zagier ' s polylogarithm conjecture for weight 3, and an analogous picture has long been envisioned by goncharov for higher weight as well. we provide a partial morphism in weight 4 by giving three out of four maps for configurations in general position.
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arxiv:1801.07816
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we revisit the treatment of identical particles in quantum mechanics. two kinds of solutions of schr \ " { o } dinger equation are found and analyzed. first, the known symmetrized and antisymmetrized eigenfunctions. we examine how the very concept of particle is blurred whithin this approach. second, we propose another kind of solution with no symmetries that we identify with maxwell - boltzmann statistics. in it, particles do preserve their individuality, as they are provided with individual energy and momenta. however, these properties cannot be univocally ascribed ; moreover, particles do not possess distinctive positions. finally, we explore how these results affect the calculation of canonical partition function, and we show that extensivity arises as a consequence of identity.
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arxiv:1411.1631
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the challenge of designing an efficient medium access control ( mac ) protocol and analyzing it has been an important research topic for over 30 years. this paper focuses on the performance analysis ( through simulation ) and modification of a well known mac protocol csma / cd. the existing protocol does not consider the wastage of bandwidth due to unutilized periods of the channel. by considering this fact, performance of mac protocol can be enhanced. the purpose of this work is to modify the existing protocol by enabling it to adapt according to state of the network. the modified protocol takes appropriate action whenever unutilized periods detected. in this way, to increase the effective bandwidth utilization and determine how it behaves under increasing load, and varying packet sizes. it will also include effects of attacks i. e. denial of service attacks, replay attack, continuous channel access or exhaustion attack, flooding attack, jamming ( radio interference ) attack, selective forwarding attack which degrade performance of mac protocol. in continuous channel access or exhaustion attack, a malicious node disrupts the mac protocol, by continuously requesting or transmitting over the channel. this eventually leads a starvation for other nodes in the network w. r. t channel access. remedy may be the network ignores excessive requests without sending expensive radio transmissions. this limit however cannot drop below the expected maximum data rate the network has to support. this limit is usually coded into the protocol during the design phase and requires additional logic also. repeated application of these exhaustion or collision based mac layer attacks can lead into unfairness.
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arxiv:0907.0678
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we present an automatic method to identify galaxy mergers using the morphological information contained in the residual images of galaxies after the subtraction of a sersic model. the removal of the bulk signal from the host galaxy light is done with the aim of detecting the fainter minor mergers. the specific morphological parameters that are used in the merger diagnostic suggested here are the residual flux fraction and the asymmetry of the residuals. the new diagnostic has been calibrated and optimized so that the resulting merger sample is very complete. however, the contamination by non - mergers is also high. if the same optimization method is adopted for combinations of other structural parameters such as the cas system, the merger indicator we introduce yields merger samples of equal or higher statistical quality than the samples obtained through the use of other structural parameters. we explore the ability of the method presented here to select minor mergers by identifying a sample of visually classified mergers that would not have been picked up by the use of the cas system, when using its usual limits. given the low prevalence of mergers among the general population of galaxies and the optimization used here, we find that the merger diagnostic introduced in this work is best used as a negative merger test, i. e., it is very effective at selecting non - merging galaxies. as with all the currently available automatic methods, the sample of merger candidates selected is contaminated by non - mergers, and further steps are needed to produce a clean sample. this merger diagnostic has been developed using the hst / acs f606w images of the a901 / 02 cluster ( z = 0. 165 ) obtained by the stages team. in particular, we have focused on a mass and magnitude limited sample ( log m / m _ { o } > 9. 0, r _ { vega } < 23. 5mag ) ) which includes 905 cluster galaxies and 655 field galaxies of all morphological types.
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arxiv:1109.6828
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productive interactions between diverse users and language technologies require outputs from the latter to be culturally relevant and sensitive. prior works have evaluated models ' knowledge of cultural norms, values, and artifacts, without considering how this knowledge manifests in downstream applications. in this work, we focus on extrinsic evaluation of cultural competence in two text generation tasks, open - ended question answering and story generation. we quantitatively and qualitatively evaluate model outputs when an explicit cue of culture, specifically nationality, is perturbed in the prompts. although we find that model outputs do vary when varying nationalities and feature culturally relevant words, we also find weak correlations between text similarity of outputs for different countries and the cultural values of these countries. finally, we discuss important considerations in designing comprehensive evaluation of cultural competence in user - facing tasks.
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arxiv:2406.11565
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in mathematics, a matrix ( pl. : matrices ) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. for example, [ 1 9 β 13 20 5 β 6 ] { \ displaystyle { \ begin { bmatrix } 1 & 9 & - 13 \ \ 20 & 5 & - 6 \ end { bmatrix } } } is a matrix with two rows and three columns. this is often referred to as a " two - by - three matrix ", a " 2 Γ 3 { \ displaystyle 2 \ times 3 } matrix ", or a matrix of dimension 2 Γ 3 { \ displaystyle 2 \ times 3 }. matrices are commonly used in linear algebra, where they represent linear maps. in geometry, matrices are widely used for specifying and representing geometric transformations ( for example rotations ) and coordinate changes. in numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. matrices are used in most areas of mathematics and scientific fields, either directly, or through their use in geometry and numerical analysis. square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. the determinant of a square matrix is a number associated with the matrix, which is fundamental for the study of a square matrix ; for example, a square matrix is invertible if and only if it has a nonzero determinant and the eigenvalues of a square matrix are the roots of a polynomial determinant. matrix theory is the branch of mathematics that focuses on the study of matrices. it was initially a sub - branch of linear algebra, but soon grew to include subjects related to graph theory, algebra, combinatorics and statistics. = = definition = = a matrix is a rectangular array of numbers ( or other mathematical objects ), called the " entries " of the matrix. matrices are subject to standard operations such as addition and multiplication. most commonly, a matrix over a field f { \ displaystyle f } is a rectangular array of elements of f { \ displaystyle f }. a real matrix and a complex matrix are matrices whose entries are respectively real numbers or complex numbers. more general types of entries are
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https://en.wikipedia.org/wiki/Matrix_(mathematics)
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we present a new approach to bayesian inference that entirely avoids markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. existence and uniqueness of a suitable measure - preserving map is established by formulating the problem in the context of optimal transport theory. we discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem, exploiting gradient information from the forward model when possible. the resulting algorithm overcomes many of the computational bottlenecks associated with markov chain monte carlo. advantages of a map - based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves. the optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood. we demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension, involving the inference of parameters appearing in ordinary and partial differential equations.
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arxiv:1109.1516
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we have trapped a gas of long - lifetime, high - mobility excitons in an in - plane harmonic potential. trapping is an important step toward the goal of a controlled bose - einstein condensate of excitons. we show that the repulsive interaction between the excitons plays a dominant role in the behavior of the excitons, in contrast to the weak interactions in atomic gases. we show that under proper conditions the excitons thermalize in the trap to a well - defined equilibrium spatial distribution.
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arxiv:cond-mat/0607163
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we study the scattering of magnon boundstates in the spin - chain description of planar n = 4 susy yang - mills. starting from the conjectured exact s - matrix for magnons in the su ( 2 ) sector, we calculate the corresponding s - matrix for boundstates with an arbitrary number of constituent magnons. the resulting expression has an interesting analytic structure with both simple and double poles. we also calculate the semiclassical s - matrix for the scattering of the corresponding excitations on the string worldsheet known as dyonic giant magnons. we find precise agreement with the magnon boundstate s - matrix in the limit of large ' t hooft coupling.
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arxiv:hep-th/0608047
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in this note, we compute the group of automorphisms of projective, affine and euclidean geometries in the sense of klein. as an application, we give a simple construction of the outer automorphism of s _ 6.
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arxiv:0901.3928
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solar jets are fast - moving, elongated brightenings related to ejections seen in both images and spectra on all scales from barely visible chromospheric jets to coronal jets extending up to a few solar radii. the largest, most powerful jets are the source of type iii radio bursts, energetic electrons and ions with greatly enhanced $ ^ 3 $ he and heavy element abundances. the frequent coronal jets from polar and equatorial coronal holes may contribute to the solar wind. the primary acceleration mechanism for all jets is believed to be release of magnetic stress via reconnection ; however the energy buildup depends on the jets ' source environment. in this review, we discuss how certain features of x - ray and euv jets, such as their repetition rate and association with radio emission, depends on their underlying photospheric field configurations ( active regions, polar and equatorial coronal holes, and quiet sun ).
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arxiv:1603.03258
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we prove that the number of directions contained in a set of the form $ a \ times b \ subset ag ( 2, p ) $, where $ p $ is prime, is at least $ | a | | b | - \ min \ { | a |, | b | \ } + 2 $. here $ a $ and $ b $ are subsets of $ gf ( p ) $ each with at least two elements and $ | a | | b | < p $. this bound is tight for an infinite class of examples. our main tool is the use of the r \ ' edei polynomial with sz \ h { o } nyi ' s extension. as an application of our main result, we obtain an upper bound on the clique number of a paley graph, matching the current best bound obtained recently by hanson and petridis.
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arxiv:2001.06994
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we present a brief description of a model for the broad emission line region ( belr ) in quasars, which is supported by analysis of civ and other emission lines in the spectra of high - z sdss quasars. specifically we consider a two - component belr with a disk and wind where the relative strength of each component is a function of luminosity. the implications of such a model for our understanding of quasar outflows and estimates of their black hole masses and accretion rates are discussed.
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arxiv:1201.2595
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we present a detailed description of the wavelength, astrometric and photometric calibration plan for sitelle, the imaging fourier transform spectrometer attached to the canada - france - hawaii telescope, based on observations of a red ( 647 - 685 nm ) data cube of the central region ( 11 $ ' \ times 11 ' $ ) of the andromeda galaxy. the first application, presented in this paper, is a radial - velocity catalogue ( with uncertainties of $ \ sim 2 - 6 $ km / s ) of nearly 800 emission - line point - like sources, including $ \ sim $ 450 new discoveries. most of the sources are likely planetary nebulae, although we also detect five novae ( having erupted in the first 8 months of 2016 ) and one new supernova remnant candidate.
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arxiv:1707.01366
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in this paper, using the weierstrass - enneper formula and the hodographic coordinate system, we find the relationships between the ramanujan identity and the generalized class of scherk surfaces known as affine scherk surfaces. we find the dirichlet series expansion of the affine scherk surface. we also obtain some of the probability measures of affine scherk surface with respect to its logarithmic distribution. next, we classify the affine minimal translation surfaces in $ \ mathbb { l } ^ 3 $ and remarked the analogous forms in $ \ mathbb { l } ^ 3. $
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arxiv:2003.05277
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a ". the expressions " a includes x " and " a contains x " are also used to mean set membership, although some authors use them to mean instead " x is a subset of a ". logician george boolos strongly urged that " contains " be used for membership only, and " includes " for the subset relation only. for the relation β, the converse relation βt may be written a x { \ displaystyle a \ ni x } meaning " a contains or includes x ". the negation of set membership is denoted by the symbol " β ". writing x β a { \ displaystyle x \ notin a } means that " x is not an element of a ". the symbol β was first used by giuseppe peano, in his 1889 work arithmetices principia, nova methodo exposita. here he wrote on page x : signum β significat est. ita a β b legitur a est quoddam b ; β¦ which means the symbol β means is. so a β b is read as a is a certain b ; β¦ the symbol itself is a stylized lowercase greek letter epsilon ( " " ), the first letter of the word Ξ΅ΟΟΞΉ, which means " is ". = = examples = = using the sets defined above, namely a = { 1, 2, 3, 4 }, b = { 1, 2, { 3, 4 } } and c = { red, green, blue }, the following statements are true : 2 β a 5 β a { 3, 4 } β b 3 β b 4 β b yellow β c = = cardinality of sets = = the number of elements in a particular set is a property known as cardinality ; informally, this is the size of a set. in the above examples, the cardinality of the set a is 4, while the cardinality of set b and set c are both 3. an infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements. the above examples are examples of finite sets. an example of an infinite set is the set of positive integers { 1, 2, 3, 4,... }. = = formal relation = = as a relation, set membership must have a domain and a range. conventionally the domain is called the universe denoted u. the range is the set of subsets of u called the power set of u and denoted p ( u
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https://en.wikipedia.org/wiki/Element_(mathematics)
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we present multi - epoch high - angular resolution observations of 22 ghz h2o masers toward the silicate carbon star eu and to probe the spatio - kinematic distribution of oxygen - rich material. eu and was observed at three epochs ( maximum time interval of 14 months ) with the very long baseline array ( vlba ). our vlba observations of the 22 ghz h2o masers have revealed that the maser spots are distributed along a straight line across ~ 20 mas, with a slight hint of an s - shaped structure. the observed spectra show three prominent velocity components at v _ lsr = - 42, - 38, and - 34 km s ^ - 1, with the masers in sw redshifted and those in ne blueshifted. the maser spots located in the middle of the overall distribution correspond to the component at v _ lsr = - 38 km s ^ - 1, which approximately coincides with the systemic velocity. these observations can be interpreted as either an emerging helical jet or a disk viewed almost edge - on ( a circumbinary or circum - companion disk ). however, the outward motion measured in the vlba images taken 14 months apart is much smaller than that expected from the jet scenario. furthermore, the mid - infrared spectrum obtained with the spitzer space telescope indicates that the 10 micron silicate emission is optically thin and the silicate grains are of sub - micron size. this lends support to the presence of a circum - companion disk, because an optically thin circumbinary disk consisting of such small grains would be blown away by the intense radiation pressure of the primary ( carbon - rich ) star. if we assume keplerian rotation for the circum - companion disk, the mass of the companion is estimated to be 0. 5 - - 0. 8 m _ sun. we also identify co2 emission features at 13 - - 16 micron in the spitzer spectrum of eu and - - the first unambiguous detection of co2 in silicate carbon stars.
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arxiv:0712.2395
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due to the new carbon neutral policies, many district heating operators start operating their combined heat and power ( chp ) plants using different types of biomass instead of fossil fuel. the contracts with the biomass suppliers are negotiated months in advance and involve many uncertainties from the energy producer ' s side. the demand for biomass is uncertain at that time, and heat demand and electricity prices vary drastically during the planning period. furthermore, the optimal operation of combined heat and power plants has to consider the existing synergies between the power and heating systems. we propose a solution method using stochastic optimization to support the biomass supply planning for combined heat and power plants. our two - phase approach determines mid - term decisions about biomass supply contracts as well as short - term decisions regarding the optimal production of the producer to ensure profitability and feasibility. we present results based on two realistic test cases.
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arxiv:1810.10764
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given a graph $ h $, a graph $ g $ is called $ h $ - critical if $ g $ does not admit a homomorphism to $ h $, but any proper subgraph of $ g $ does. observe that $ k _ { k - 1 } $ - critical graphs are the standard $ k $ - ( colour ) - critical graphs. we consider questions of extremal nature previously studied for $ k $ - critical graphs and generalize them to $ h $ - critical graphs. after complete graphs, the next natural case to consider for $ h $ is that of the odd - cycles. thus, given integers $ \ ell $ and $ k $, $ \ ell \ geq k $, we ask : what is the smallest order of a $ c _ { 2 \ ell + 1 } $ - critical graph of odd - girth at least $ 2k + 1 $? denoting this value by $ \ eta ( k, c _ { 2 \ ell + 1 } ) $, we show that $ \ eta ( k, c _ { 2 \ ell + 1 } ) = 4k $ for $ 1 \ leq \ ell \ leq k \ leq \ frac { 3 \ ell + i - 3 } { 2 } $ ( $ 2k = i \ bmod 3 $ ) and that $ \ eta ( 3, c _ 5 ) = 15 $. the latter means that a smallest graph of odd - girth ~ $ 7 $ not admitting a homomorphism to the $ 5 $ - cycle is of order ~ $ 15 $. computational work shows that there are exactly eleven such graphs on $ 15 $ ~ vertices of which only two are $ c _ 5 $ - critical.
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arxiv:1610.03685
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we give a new proof of the completeness of the space $ \ mathcal { o } _ c $ by applying a criterion of compact regularity for the isomorphic sequence space $ \ lim _ { k \ rightarrow } ( s \ hat \ otimes ( \ ell ^ \ infty ) _ { - k } ) $. along the way we show that the strong dual of any quasinormable fr \ ' echet space is a compactly regular $ \ mathcal { lb } $ - space. finally, we prove that $ \ lim _ { k \ rightarrow } ( e _ k \ hat \ otimes _ \ iota f ) = ( \ lim _ { k \ rightarrow } e _ k ) \ hat \ otimes _ \ iota f $ if the inductive limit $ \ lim _ { k \ rightarrow } ( e _ k \ hat \ otimes _ \ iota f ) $ is compactly regular.
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arxiv:2408.11944
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we propose a novel adaptive design for clinical trials with time - to - event outcomes and covariates ( which may consist of or include biomarkers ). our method is based on the expected entropy of the posterior distribution of a proportional hazards model. the expected entropy is evaluated as a function of a patient ' s covariates, and the information gained due to a patient is defined as the decrease in the corresponding entropy. candidate patients are only recruited onto the trial if they are likely to provide sufficient information. patients with covariates that are deemed uninformative are filtered out. a special case is where all patients are recruited, and we determine the optimal treatment arm allocation. this adaptive design has the advantage of potentially elucidating the relationship between covariates, treatments, and survival probabilities using fewer patients, albeit at the cost of rejecting some candidates. we assess the performance of our adaptive design using data from the german breast cancer study group and numerical simulations of a biomarker validation trial.
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arxiv:1502.03813
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the development of robust architectures capable of large - scale fault - tolerant quantum computation should consider both their quantum error - correcting codes, and the underlying physical qubits upon which they are built, in tandem. following this design principle we demonstrate remarkable error correction performance by concatenating the xzzx surface code with kerr - cat qubits. we contrast several variants of fault - tolerant systems undergoing different circuit noise models that reflect the physics of kerr - cat qubits. our simulations show that our system is scalable below a threshold gate infidelity of $ p _ \ mathrm { cx } \ sim 6. 5 \ % $ within a physically reasonable parameter regime, where $ p _ \ mathrm { cx } $ is the infidelity of the noisiest gate of our system ; the controlled - not gate. this threshold can be reached in a superconducting circuit architecture with a kerr - nonlinearity of $ 10 $ mhz, a $ \ sim 6. 25 $ photon cat qubit, single - photon lifetime of $ \ gtrsim 64 \ mu $ s, and thermal photon population $ \ lesssim 8 \ % $. such parameters are routinely achieved in superconducting circuits.
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arxiv:2104.09539
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conditional independence in a multivariate normal ( or gaussian ) distribution is characterized by the vanishing of subdeterminants of the distribution ' s covariance matrix. gaussian conditional independence models thus correspond to algebraic subsets of the cone of positive definite matrices. for statistical inference in such models it is important to know whether or not the model contains singularities. we study this issue in models involving up to four random variables. in particular, we give examples of conditional independence relations which, despite being probabilistically representable, yield models that non - trivially decompose into a finite union of several smooth submodels.
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arxiv:0910.5447
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physicists seeking to understand complex biological systems often find it rewarding to create simple " toy models " that reproduce system behavior. here a toy model is used to understand a puzzling phenomenon from the sport of track and field. races are almost always won, and records set, in 400 m and 800 m running events by people who run the first half of the race faster than the second half, which is not true of shorter races, nor of longer. there is general agreement that performance in the 400 m and 800 m is limited somehow by the amount of anaerobic metabolism that can be tolerated in the working muscles in the legs. a toy model of anaerobic metabolism is presented, from which an optimal pacing strategy is analytically calculated via the euler - lagrange equation. this optimal strategy is then modified to account for the fact that the runner starts the race from rest ; this modification is shown to result in the best possible outcome by use of an elementary variational technique that supplements what is found in undergraduate textbooks. the toy model reproduces the pacing strategies of elite 400 m and 800 m runners better than existing models do. the toy model also gives some insight into training strategies that improve performance.
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arxiv:1204.0313
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safety - critical data, such as crash and near - crash records, are crucial to improving autonomous vehicle ( av ) design and development. sharing such data across av companies, academic researchers, regulators, and the public can help make all avs safer. however, av companies rarely share safety - critical data externally. this paper aims to pinpoint why av companies are reluctant to share safety - critical data, with an eye on how these barriers can inform new approaches to promote sharing. we interviewed twelve av company employees who actively work with such data in their day - to - day work. findings suggest two key, previously unknown barriers to data sharing : ( 1 ) datasets inherently embed salient knowledge that is key to improving av safety and are resource - intensive. therefore, data sharing, even within a company, is fraught with politics. ( 2 ) interviewees believed av safety knowledge is private knowledge that brings competitive edges to their companies, rather than public knowledge for social good. we discuss the implications of these findings for incentivizing and enabling safety - critical av data sharing, specifically, implications for new approaches to ( 1 ) debating and stratifying public and private av safety knowledge, ( 2 ) innovating data tools and data sharing pipelines that enable easier sharing of public av safety data and knowledge ; ( 3 ) offsetting costs of curating safety - critical data and incentivizing data sharing.
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arxiv:2504.17792
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improved in order to achieve a sustainable food supply chain. food engineers must reevaluate current practices and technologies to focus on increasing productivity and efficiency while reducing the consumption of water and energy, and decreasing the amount of waste produced. = = = population growth = = = even though food supply expands yearly, there has also been an increase in the number of hungry people. the world population is expected to reach 9 - 10 billion people by 2050 and the problem of malnutrition remains a priority. to achieve food security, food engineers are required to address land and water scarcity to provide enough growth and food for undernourished people. in addition, food production depends on land and water supply, which are under stress as the population size increases. there is a growing pressure on land resources driven by expanding populations, leading to expansions of croplands ; this usually involves the destruction of forests and exploitation of arable land. food engineers face the challenge of finding sustainable ways to produce to adapt to the growing population. = = = human health = = = food engineers must adapt food technologies and operations to the recent consumer trend toward the consumption of healthy and nutritious food. to supply foods with these qualities, and for the benefit of human health, food engineers must work collaboratively with professionals in other domains such as medicine, biochemistry, chemistry, and consumerism. new technologies and practices must be developed to increase the production of foods that have a positive impact on human health. = = see also = = = = references = =
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https://en.wikipedia.org/wiki/Food_engineering
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examinations using small sample sizes before allowing the manuscripts to be published. nature human behaviour has adopted the registered report format, as it β shift [ s ] the emphasis from the results of research to the questions that guide the research and the methods used to answer them β. european journal of personality defines this format : β in a registered report, authors create a study proposal that includes theoretical and empirical background, research questions / hypotheses, and pilot data ( if available ). upon submission, this proposal will then be reviewed prior to data collection, and if accepted, the paper resulting from this peer - reviewed procedure will be published, regardless of the study outcomes. β note that only a very small proportion of academic journals in psychology and neurosciences explicitly stated that they welcome submissions of replication studies in their aim and scope or instructions to authors. this phenomenon does not encourage the reporting or even attempt on replication studies. overall, the number of participating journals is increasing, as indicated by the center for open science, which maintains a list of journals encouraging the submission of registered reports. = = benefits = = several articles have outlined the rationale for preregistration ( e. g., lakens, 2019 ; nosek et al., 2018 ; wagenmakers et al., 2012 ). the primary goal of preregistration is to improve the transparency of reported hypothesis tests, which allows readers to evaluate the extent to which decisions during the data analysis were pre - planned ( maintaining statistical error control ) or data - driven ( increasing the type 1 or type 2 error rate ). meta - scientific research has revealed additional benefits. researchers indicate preregistering a study leads to a more carefully thought through research hypothesis, experimental design, and statistical analysis. in addition, preregistration has been shown to encourage better learning of open science concepts and students felt that they understood their dissertation and it improved the clarity of the manuscript writing, promoted rigour and were more likely to avoid questionable research practices. in addition, it becomes a tool that can supervisors can use to shape students to combat any questionable research practices. a 2024 study in the journal of political economy : microeconomics preregistration in economics journals found that preregistration did not reduce p - hacking and publication bias, unless the preregistration was accompanied by a preanalysis plan. = = criticisms = = proponents of preregistration have argued that it is " a method to increase the credibility of published results " ( nosek & lakens, 2014 ), that it
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https://en.wikipedia.org/wiki/Preregistration_(science)
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a new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. this thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial coordinates, and does not intrinsically violate the constraints. our new configurational thermostat is closely related to the kinetic temperature nose - hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. we validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n - decane molecules under configurational and kinetic temperature control. practical aspects concerning the implementation of the new thermostat in a molecular dynamics code and the potential applications are discussed.
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arxiv:0709.1575
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the magnitude and phase of the transmission amplitude of a multi - level quantum dot is calculated for the mesoscopic regime of level spacing large compared to level width. the interplay between kondo correlations and the influence by neighboring levels is discussed. as in the single - level case, the kondo plateaus of magnitude and phase disappear with increasing temperature. at certain gate voltages, ` ` stationary ' ' points are found at which the transmission phase is independent of temperature. depending on the mesoscopic parameters of the adjacent levels ( like relative sign and magnitude of tunneling matrix elements ), the stationary points are shifted to or repelled by the neighboring level.
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arxiv:0805.3145
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a model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. this paper presents an extension to the petri nets formalism suitable for describing information systems in which states refer to object instances of predefined types and resources are identified as instances of special object types. several correctness criteria for resource - and object - aware information systems models are proposed, supplemented with discussions on their decidability for interesting classes of systems. these new correctness criteria can be seen as generalizations of the classical soundness property of workflow models concerned with process control flow correctness.
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arxiv:2212.07363
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we present optical measurements of phononic excitations in la $ _ { 2 / 3 } $ ca $ _ { 1 / 3 } $ mno $ _ { 3 } $ ( lcmo ) and la $ _ { 2 / 3 } $ sr $ _ { 1 / 3 } $ mno $ _ { 3 } $ ( lsmo ) thin films covering the full temperature range from the metallic ferromagnetic to the insulating paramagnetic phase. all eight phonons expected for the r $ \ bar { 3 } $ c symmetry in lsmo and 17 out of the expected 25 phonons for the pnma symmetry in lcmo have been determined. close to the ferromagnetic - to - paramagnetic transition both compounds reveal an anomalous behavior but with different characteristics. anomalies in the phononic spectra are a manifestation of the coupling of lattice degrees of freedom ( dof ) to electronic dof. specifically, the low - frequency external group proves to be an indicator for lattice modifications induced by electronic correlations. the enhanced electron - phonon coupling in lcmo is responsible for fano - like interference effects of distinct phonon modes with electronic continuum excitations : we observe asymmetric phonon line shapes, mode splitting and spectral weight transfer between modes.
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arxiv:cond-mat/0404024
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we discuss the form of the chiral anomaly on an s1 / z2 orbifold with chiral boundary conditions. we find that the 4 - divergence of the higher - dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the chiral zero mode there. nevertheless the anomaly, appropriately defined as the five dimensional divergence of the current, lives entirely on the orbifold fixed planes and is independent of the shape of the zero mode. therefore long distance four dimensional anomaly cancellation ensures the consistency of the higher dimensional orbifold theory.
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arxiv:hep-th/0103135
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soft robots promise improved safety and capability over rigid robots when deployed in complex, delicate, and dynamic environments. however, the infinite degrees of freedom and highly nonlinear dynamics of these systems severely complicate their modeling and control. as a step toward addressing this open challenge, we apply the data - driven, hankel dynamic mode decomposition ( hdmd ) with time delay observables to the model identification of a highly inertial, helical soft robotic arm with a high number of underactuated degrees of freedom. the resulting model is linear and hence amenable to control via a linear quadratic regulator ( lqr ). using our test bed device, a dynamic, lightweight pneumatic fabric arm with an inertial mass at the tip, we show that the combination of hdmd and lqr allows us to command our robot to achieve arbitrary poses using only open loop control. we further show that koopman spectral analysis gives us a dimensionally reduced basis of modes which decreases computational complexity without sacrificing predictive power.
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arxiv:2011.07939
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multivariate outcomes are common in pragmatic cluster randomized trials. while sample size calculation procedures for multivariate outcomes exist under parallel assignment, none have been developed for a stepped wedge design. in this article, we present computationally efficient power and sample size procedures for stepped wedge cluster randomized trials ( sw - crts ) with multivariate outcomes that differentiate the within - period and between - period intracluster correlation coefficients ( iccs ). under a multivariate linear mixed model, we derive the joint distribution of the intervention test statistics which can be used for determining power under different hypotheses and provide an example using the commonly utilized intersection - union test for co - primary outcomes. simplifications under a common treatment effect and common iccs across endpoints and an extension to closed cohort designs are also provided. finally, under the common icc across endpoints assumption, we formally prove that the multivariate linear mixed model leads to a more efficient treatment effect estimator compared to the univariate linear mixed model, providing a rigorous justification on the use of the former with multivariate outcomes. we illustrate application of the proposed methods using data from an existing sw - crt and present extensive simulations to validate the methods.
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arxiv:2206.11978
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superagile is the hard x - ray monitor of the agile gamma ray mission, in orbit since 23 $ ^ { rd } $ april 2007. it is an imaging experiment based on a set of four independent silicon strip detectors, equipped with one - dimensional coded masks, operating in the nominal energy range 18 - 60 kev. the main goal of superagile is the observation of cosmic sources simultaneously with the main gamma - ray agile experiment, the gamma ray imaging detector ( grid ). given its $ \ sim $ steradian - wide field of view and its $ \ sim $ 15 mcrab day - sensitivity, superagile is also well suited for the long - term monitoring of galactic compact objects and the detection of bright transients. the superagile detector properties and design allow for a 6 arcmin angular resolution in each of the two independent orthogonal projections of the celestial coordinates. photon by photon data are continuously available by the experiment telemetry, and are used to derive images and fluxes of individual sources, with integration times depending on the source intensity and position in the field of view. in this paper we report on the main scientific results achieved by superagile over its first two years in orbit, until april 2009.
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arxiv:0910.4895
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high - quality layers of the ( ga, mn ) ( bi, as ) quaternary compound semiconductor have been grown by the low - temperature molecular - beam epitaxy technique. an effect of bi incorporation into the ( ga, mn ) as ferromagnetic semiconductor and the post - growth annealing treatment of the layers have been investigated through examination of their magnetic and magneto - transport properties. significant enhancement of the planar hall effect magnitude upon addition of bi into the layers is interpreted as a result of increased spin - orbit coupling in the ( ga, mn ) ( bi, as ) layers.
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arxiv:1406.4992
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outer satellites of the planets have distant, eccentric orbits that can be highly inclined or even retrograde relative to the equatorial planes of their planets. these irregular orbits cannot have formed by circumplanetary accretion and are likely products of early capture from heliocentric orbit. the irregular satellites may be the only small bodies remaining which are still relatively near their formation locations within the giant planet region. the study of the irregular satellites provides a unique window on processes operating in the young solar system and allows us to probe possible planet formation mechanisms and the composition of the solar nebula between the rocky objects in the main asteroid belt and the very volatile rich objects in the kuiper belt. the gas and ice giant planets all appear to have very similar irregular satellite systems irrespective of their mass or formation timescales and mechanisms. water ice has been detected on some of the outer satellites of saturn and neptune whereas none has been observed on jupiter ' s outer satellites.
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arxiv:astro-ph/0605041
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we study distributions of differences of unscaled riemann zeta zeros, $ \ gamma - \ gamma ' $, at large. we show, that independently of the location of the zeros, their differences have similar statistical properties. the distributions of differences are skewed towards the nearest zeta zero, have local maximum of variance and local minimum of kurtosis at or near each zeta zero. furthermore, we show that distributions can be fitted with johnson probability density function, despite the value of skewness or kurtosis of the distribution.
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arxiv:2001.05294
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we calculate the nucleon axial form factor up to the leading one - loop order in a covariant chiral effective field theory with the $ \ delta ( 1232 ) $ resonance as an explicit degree of freedom. we fit the axial form factor to the latest lattice qcd data and pin down the relevant low - energy constants. the lattice qcd data, for various pion masses below $ 400 $ mev, can be well described up to a momentum transfer of $ \ sim 0. 6 $ gev. the $ \ delta ( 1232 ) $ loops contribute significantly to this agreement. furthermore, we extract the axial charge and radius based on the fitted values of the low energy constants. the results are : $ g _ a = 1. 237 ( 74 ) $ and $ \ langle r _ a ^ 2 \ rangle = 0. 263 ( 38 ) ~ { \ rm fm } ^ 2 $. the obtained coupling $ g _ a $ is consistent with the experimental value if the uncertainty is taken into account. the axial radius is below but in agreement with the recent extraction from neutrino quasi - elastic scattering data on deuterium, which has large error bars. up to our current working accuracy, $ r _ a $ is predicted only at leading order, i. e., one - loop level. a more precise determination might need terms of $ \ mathcal { o } ( p ^ 5 ) $.
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arxiv:1708.08776
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these lecture notes accompanied the course time - frequency analysis given at the faculty of mathematics of the university of vienna in the summer term 2021. the material is suitable for an advanced undergraduate course in mathematics or a mathematics class for phd students. besides standard linear algebra and calculus only some basics from functional analysis are needed. a course in fourier analysis may be of advantage, but is not needed. the course contained 4 academic units per week. the appendices and section 11 were not presented in class.
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arxiv:2204.01596
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we consider a planar brownian motion starting from $ o $ at time $ t = 0 $ and stopped at $ t = 1 $ and a set $ f = \ { oi _ i ; i = 1, 2,..., n \ } $ of $ n $ semi - infinite straight lines emanating from $ o $. denoting by $ g $ the last time when $ f $ is reached by the brownian motion, we compute the probability law of $ g $. in particular, we show that, for a symmetric $ f $ and even $ n $ values, this law can be expressed as a sum of $ \ arcsin $ or $ ( \ arcsin ) ^ 2 $ functions. the original result of levy is recovered as the special case $ n = 2 $. a relation with the problem of reaction - diffusion of a set of three particles in one dimension is discussed.
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arxiv:cond-mat/0302269
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robustness is a fundamental pillar of machine learning ( ml ) classifiers, substantially determining their reliability. methods for assessing classifier robustness are therefore essential. in this work, we address the challenge of evaluating corruption robustness in a way that allows comparability and interpretability on a given dataset. we propose a test data augmentation method that uses a robustness distance $ \ epsilon $ derived from the datasets minimal class separation distance. the resulting mscr ( mean statistical corruption robustness ) metric allows a dataset - specific comparison of different classifiers with respect to their corruption robustness. the mscr value is interpretable, as it represents the classifiers avoidable loss of accuracy due to statistical corruptions. on 2d and image data, we show that the metric reflects different levels of classifier robustness. furthermore, we observe unexpected optima in classifiers robust accuracy through training and testing classifiers with different levels of noise. while researchers have frequently reported on a significant tradeoff on accuracy when training robust models, we strengthen the view that a tradeoff between accuracy and corruption robustness is not inherent. our results indicate that robustness training through simple data augmentation can already slightly improve accuracy.
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arxiv:2206.13405
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in analogy with the classical theory of filters, for finitely complete categories, we provide the concepts of filter, g - neighborhood ( short for \ grothendieck - neighborhood " ) and cover - neighborhood of a point, with the aim of studying convergence, cluster point and closure of sieves on objects of that kind of categories.
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arxiv:1910.09423
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global organization of 3 - dimensional ( 3d ) lagrangian chaotic transport is difficult to infer without extensive computation. for 3d time - periodic flows with one invariant we show how constraints on deformation that arise from volume - preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. these points organize all lagrangian transport in such flows through coordination of lower - order and higher - order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant. degenerate points of periodic lines and the extended 3d structures associated with them are easily identified through the trace of the deformation tensor calculated along periodic lines. these results reveal the importance of degenerate points in understanding transport in one - invariant fluid flows.
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arxiv:1911.04607
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making use of self - assembly techniques, we demonstrate the realization of nanoscopic semiconductor quantum rings in which the electronic states are in the true quantum limit. we employ two complementary spectroscopic techniques to investigate both the ground states and the excitations of these rings. applying a magnetic field perpendicular to the plane of the rings, we find that when approximately one flux quantum threads the interior of each ring, a change in the ground state from angular momentum $ \ ell = 0 $ to $ \ ell = - 1 $ takes place. this ground state transition is revealed both by a drastic modification of the excitation spectrum and by a change in the magnetic field dispersion of the single - electron charging energy.
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arxiv:cond-mat/9908263
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aiming at the current problems of theory - oriented, practice - light, and lack of innovation ability in the teaching of postgraduate software engineering courses, a multi - stage feedback teaching mode for software engineering postgraduates based on competition project _ driven is proposed. the model is driven by the competition project, and implementing suggestions are given in terms of stage allocation of software engineering course tasks and ability cultivation, competition case design and process evaluation improvement, etc. through the implementation of this teaching mode, students enthusiasm and initiative are expected to be stimulated, and the overall development of students professional skills and comprehension ability would be improved to meet the demand of society for software engineering technical talents.
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arxiv:2212.09394
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the problem of grounding vqa tasks has seen an increased attention in the research community recently, with most attempts usually focusing on solving this task by using pretrained object detectors. however, pre - trained object detectors require bounding box annotations for detecting relevant objects in the vocabulary, which may not always be feasible for real - life large - scale applications. in this paper, we focus on a more relaxed setting : the grounding of relevant visual entities in a weakly supervised manner by training on the vqa task alone. to address this problem, we propose a visual capsule module with a query - based selection mechanism of capsule features, that allows the model to focus on relevant regions based on the textual cues about visual information in the question. we show that integrating the proposed capsule module in existing vqa systems significantly improves their performance on the weakly supervised grounding task. overall, we demonstrate the effectiveness of our approach on two state - of - the - art vqa systems, stacked nmn and mac, on the clevr - answers benchmark, our new evaluation set based on clevr scenes with ground truth bounding boxes for objects that are relevant for the correct answer, as well as on gqa, a real world vqa dataset with compositional questions. we show that the systems with the proposed capsule module consistently outperform the respective baseline systems in terms of answer grounding, while achieving comparable performance on vqa task.
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arxiv:2105.04836
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hybrid entangled states prove to be necessary for quantum information processing within heterogeneous quantum networks. a method with irreducible number of consumed resources that firmly provides hybrid cv - dv entanglement for any input conditions of the experimental setup is proposed. namely, a family of cv states is introduced. each of such cv states is first superimposed on a beam - splitter with a delocalized photon and then detected by a photo - detector behind the beam - splitter. detection of any photon number heralds generation of a hybrid cv - dv entangled state in the outputs, independent of transmission / reflection coefficients of the beam - splitter and size of the input cv state. nonclassical properties of the generated state are studied and their entanglement degree in terms of negativity is calculated. there are wide domains of values of input parameters of the experimental setup that can be chosen to make the generated state maximally entangled. the proposed method is also applicable to truncated versions of the input cv states. we also propose a simple method to produce even / odd cv states.
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arxiv:2101.02117
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most existing point cloud completion methods are only applicable to partial point clouds without any noises and outliers, which does not always hold in practice. we propose in this paper an end - to - end network, named cs - net, to complete the point clouds contaminated by noises or containing outliers. in our cs - net, the completion and segmentation modules work collaboratively to promote each other, benefited from our specifically designed cascaded structure. with the help of segmentation, more clean point cloud is fed into the completion module. we design a novel completion decoder which harnesses the labels obtained by segmentation together with fps to purify the point cloud and leverages knn - grouping for better generation. the completion and segmentation modules work alternately share the useful information from each other to gradually improve the quality of prediction. to train our network, we build a dataset to simulate the real case where incomplete point clouds contain outliers. our comprehensive experiments and comparisons against state - of - the - art completion methods demonstrate our superiority. we also compare with the scheme of segmentation followed by completion and their end - to - end fusion, which also proves our efficacy.
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arxiv:2203.09772
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the edge - reconstruction number ern $ ( g ) $ of a graph $ g $ is equal to the minimum number of edge - deleted subgraphs $ g - e $ of $ g $ which are sufficient to determine $ g $ up to isomorphsim. building upon the work of molina and using results from computer searches by rivshin and more recent ones which we carried out, we show that, apart from three known exceptions, all bicentroidal trees have edge - reconstruction number equal to 2. we also exhibit the known trees having edge - reconstruction number equal to 3 and we conjecture that the three infinite families of unicentroidal trees which we have found to have edge - reconstruction number equal to 3 are the only ones.
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arxiv:1312.1234
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period - colour ( pc ) and amplitude - colour ( ac ) relations at maximum, mean and minimum light are constructed from a large grid of full amplitude hydrodynamic models of cepheids with a composition appropriate for the smc ( small magellanic cloud ). we compare these theoretical relations with those from observations. the theoretical relations are in general good agreement with their observational counterparts though there exist some discrepancy for short period ( log [ p ] < 1 ) cepheids. we outline a physical mechanism which can, in principle, be one factor to explain the observed pc / ac relations for the long and short period cepheids in the galaxy, lmc and smc. our explanation relies on the hydrogen ionization front - photosphere interaction and the way this interaction changes with pulsation period, pulsation phase and metallicity. since the pc relation is connected with the period - luminosity ( pl ) relation, it is postulated that such a mechanism can also explain the observed properties of the pl relation in these three galaxies.
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arxiv:0706.2629
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we consider the calculation of the master integrals of the three - loop massive banana graph. in the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear differential equations. the solution of the system requires finding a $ 3 \ times 3 $ matrix of homogeneous solutions. we show how the maximal cut can be used to determine all entries of this matrix in terms of products of elliptic integrals of first and second kind of suitable arguments. all independent solutions are found by performing the integration which defines the maximal cut on different contours. once the homogeneous solution is known, the inhomogeneous solution can be obtained by use of euler ' s variation of constants.
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arxiv:1704.05465
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we outline our work ( see [ 1, 2, 3, 4 ] ) on relaxation and 3d - 2d passage with determinant type constraints. some open questions are addressed. this outline - paper comes as a companion to [ 5 ].
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arxiv:0906.5262
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ggr news : we hear that..., by david garfinkle what ' s new in ligo, by david shoemaker news from nsf, by pedro marronetti citation counts and indicies : beware of bad data, by clifford will research briefs : results from planck, by william jones conference reports : gravity - strings and higher dimensions, by simon ross capra 16, by leor barack reduced order modeling in general relativity, by michele vallisneri
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arxiv:1309.6370
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non - intrusive inspection systems based on x - ray radiography techniques are routinely used at transport hubs to ensure the conformity of cargo content with the supplied shipping manifest. as trade volumes increase and regulations become more stringent, manual inspection by trained operators is less and less viable due to low throughput. machine vision techniques can assist operators in their task by automating parts of the inspection workflow. since cars are routinely involved in trafficking, export fraud, and tax evasion schemes, they represent an attractive target for automated detection and flagging for subsequent inspection by operators. in this contribution, we describe a method for the detection of cars in x - ray cargo images based on trained - from - scratch convolutional neural networks. by introducing an oversampling scheme that suitably addresses the low number of car images available for training, we achieved 100 % car image classification rate for a false positive rate of 1 - in - 454. cars that were partially or completely obscured by other goods, a modus operandi frequently adopted by criminals, were correctly detected. we believe that this level of performance suggests that the method is suitable for deployment in the field. it is expected that the generic object detection workflow described can be extended to other object classes given the availability of suitable training data.
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arxiv:1606.08078
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we extend the usual vacuum metric - affine $ f ( r ) $ gravity by supplementing it with all parity even quadratic invariants in torsion and non - metricity. as we show explicitly this supplementation drastically changes the status of the theory which now propagates an additional scalar degree of freedom on top of the graviton. this scalar degree of freedom has a geometric origin as it relates to spacetime torsion and non - metricity. the resulting theory can be written equivalently as a metric and torsionless scalar - tensor theory whose potential and kinetic term coupling depend on the choice of the function $ f ( r ) $ and the dimensionless parameters of the quadratic invariants respectively.
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arxiv:2409.11771
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in this paper, we learn to classify visual object instances, incrementally and via self - supervision ( self - incremental ). our learner observes a single instance at a time, which is then discarded from the dataset. incremental instance learning is challenging, since longer learning sessions exacerbate forgetfulness, and labeling instances is cumbersome. we overcome these challenges via three contributions : i. we propose vinil, a self - incremental learner that can learn object instances sequentially, ii. we equip vinil with self - supervision to by - pass the need for instance labelling, iii. we compare vinil to label - supervised variants on two large - scale benchmarks, and show that vinil significantly improves accuracy while reducing forgetfulness.
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arxiv:2301.11417
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given the current limited knowledge of meteor plasma micro - physics and its interaction with the surrounding atmosphere and ionosphere, meteors are a highly interesting observational target for high - resolution wide - field astronomical surveys. such surveys are capable of resolving the physical size of meteor plasma heads, but they produce large volumes of images that need to be automatically inspected for possible existence of long linear features produced by meteors. here we show how big aperture sky survey telescopes detect meteors as defocused tracks with a central brightness depression. we derive an analytic expression for a defocused point source meteor track and use it to calculate brightness profiles of meteors modeled as uniform brightness disks. we apply our modeling to meteor images as seen by the sdss and lsst telescopes. the expression is validated by monte carlo ray - tracing simulations of photons traveling through the atmosphere and the lsst telescope optics. we show that estimates of the meteor distance and size can be extracted from the measured fwhm and the strength of the central dip in the observed brightness profile. however, this extraction becomes difficult when the defocused meteor track is distorted by the atmospheric seeing or contaminated by a long lasting glowing meteor trail. the fwhm of satellites tracks is distinctly narrower than meteor values, which enables removal of a possible confusion between satellites and meteors.
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arxiv:1707.07223
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the boundary charge that accumulates at the edge of a one - dimensional single - channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $ 0 $ and $ - 1 $ [ phys. rev. b 101, 165304 ( 2020 ) ]. this quantized contribution is associated with particle - hole duality, ensures charge conservation and fixes the mod ( 1 ) ambiguity appearing in the modern theory of polarization. in the present work we generalize the above - mentioned single - channel results to the multichannel case by employing the technique of boundary green ' s functions. we show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk green ' s functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. we observe that this winding number is restricted to values ranging from $ - n _ c $ to $ 0 $, where $ n _ c $ is the number of channels ( orbitals ) per site. furthermore, we consider translationally invariant one - dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. these invariants are again given in terms of winding numbers of combinations of components of bulk green ' s functions. through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by w. kohn [ phys. rev. lett. 76, 3168 ( 1996 ) ] for noninteracting multichannel lattice models.
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arxiv:2107.10787
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we show that failure of local realism can be revealed to observers for whom only extremely coarse - grained measurements are available. in our instances, bell ' s inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. furthermore, we can observe failure of local realism when an inequality enforced by non - local realistic theories is satisfied. this suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. small - scale experimental demonstration of our examples may be possible in the foreseeable future.
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arxiv:0806.3558
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the illinois accelerator research center ( iarc ) hosts a new accelerator development program at fermi national accelerator laboratory. iarc provides access to fermi ' s state - of - the - art facilities and technologies for research, development and industrialization of particle accelerator technology. in addition to facilitating access to available existing fermi infrastructure, the iarc campus has a dedicated 36, 000 ft2 heavy assembly building ( hab ) with all the infrastructure needed to develop, commission and operate new accelerators. connected to the hab is a 47, 000 ft2 office, technology and engineering ( ote ) building, paid for by the state, that has office, meeting, and light technical space. the ote building, which contains the accelerator physics center, and nearby accelerator and technical divisions provide iarc collaborators with unique access to world class expertise in a wide array of accelerator technologies. at iarc scientists and engineers from fermilab and academia work side by side with industrial partners to develop breakthroughs in accelerator science and translate them into applications for the nation ' s health, wealth and security.
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arxiv:1705.00073
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electronic transport and magnetic properties of ge1 - xmnx / ge ( 100 ) films are investigated as a function of mn dilution. depending on x, characteristic temperatures separate different regimes in both properties. resistivity exhibits an insulator - like behavior in the whole temperature range and, below about 80 k, two distinct activation energies are observed. at a higher temperature value, tr, resistivity experiences a sudden reduction. hall coefficient shows a strong contribution from the anomalous hall effect and, at tr, a sign inversion, from positive to negative, is recorded. the magnetic properties, inferred from magneto - optical kerr effect, evidence a progressive decrease of the ferromagnetic long range order as the temperature is raised, with a curie temperature tc not far from tr. the transport and magnetic results are qualitatively consistent with a percolation mechanism due to bound magnetic polarons in a gemn diluted magnetic semiconductor, with localized holes [ a. kaminski and s. das sarma, phys. rev. b 68, 235210 ( 2003 ) ].
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arxiv:cond-mat/0509111
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we report highly tunable control of holes in ge / si core / shell nanowires ( nws ). we demonstrate the ability to create single quantum dots ( qds ) of various sizes, with low hole occupation numbers and clearly observable excited states. for the smallest dot size we observe indications of single - hole occupation. moreover, we create double and triple tunnel - coupled quantum dot arrays. in the double quantum dot configuration we observe pauli spin blockade ( psb ). these results open the way to perform hole spin qubit experiments in these devices.
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arxiv:1805.02532
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the finiteness problem for automaton groups and semigroups has been widely studied, several partial positive results are known. however we prove that, in the most general case, the problem is undecidable. we study the case of automaton semigroups. given a nw - deterministic wang tile set, we construct an mealy automaton, such that the plane admit a valid wang tiling if and only if the mealy automaton generates a finite semigroup. the construction is similar to a construction by kari for proving that the nilpotency problem for cellular automata is unsolvable. moreover kari proves that the tiling of the plane is undecidable for nw - deterministic wang tile set. it follows that the finiteness problem for automaton semigroup is undecidable.
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arxiv:1304.2295
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as a generalization of postnikov ' s construction ( see arxiv : math / 0609764 ), we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the grassmannian. we then show that universal poisson brackets introduced for the space of edge weights in arxiv : 0805. 3541 induce a family of poisson structures on rational - valued matrix functions and on the space of loops in the grassmannian. in the former case, this family includes, for a particular kind of networks, the poisson bracket associated with the trigonometric r - matrix.
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arxiv:0901.0020
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in this note we present some results concerning the unirationality of the algebraic variety $ \ cal { s } _ { f } $ given by the equation \ begin { equation * } n _ { k / k } ( x _ { 1 } + \ alpha x _ { 2 } + \ alpha ^ 2 x _ { 3 } ) = f ( t ), \ end { equation * } where $ k $ is a number field, $ k = k ( \ alpha ) $, $ \ alpha $ is a root of an irreducible polynomial $ h ( x ) = x ^ 3 + ax + b \ in k [ x ] $ and $ f \ in k [ t ] $. we are mainly interested in the case of pure cubic extensions, i. e. $ a = 0 $ and $ b \ in k \ setminus k ^ { 3 } $. we prove that if $ \ op { deg } f = 4 $ and the variety $ \ cal { s } _ { f } $ contains a $ k $ - rational point $ ( x _ { 0 }, y _ { 0 }, z _ { 0 }, t _ { 0 } ) $ with $ f ( t _ { 0 } ) \ neq 0 $, then $ \ cal { s } _ { f } $ is $ k $ - unirational. a similar result is proved for a broad family of quintic polynomials $ f $ satisfying some mild conditions ( for example this family contains all irreducible polynomials ). moreover, the unirationality of $ \ cal { s } _ { f } $ ( with non - trivial $ k $ - rational point ) is proved for any polynomial $ f $ of degree 6 with $ f $ not equivalent to the polynomial $ h $ satisfying the condition $ h ( t ) \ neq h ( \ zeta _ { 3 } t ) $, where $ \ zeta _ { 3 } $ is the primitive third root of unity. we are able to prove the same result for an extension of degree 3 generated by the root of polynomial $ h ( x ) = x ^ 3 + ax + b \ in k [ x ] $, provided that $ f ( t ) = t ^ 6 + a _ { 4 } t ^ 4 + a _ { 1 } t + a _ { 0 } \ in k [ t ] $ with $ a _ { 1 } a _ { 4 } \ neq 0 $.
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arxiv:1305.6242
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a consistent combination of covariant density functional theory ( cdft ) and landau - migdal theory of finite fermi systems ( tffs ) is presented. both methods are in principle exact, but landau - migdal theory cannot describe ground state properties and density functional theory does not take into account the energy dependence of the self - energy and therefore fails to yield proper single - % particle spectra as well as the coupling to complex configurations in the width of giant resonances. starting from an energy functional, phonons and their vertices are calculated without any further parameters. they form the basis of particle - vibrational coupling leading to an energy dependence of the self - energy and an induced energy - dependent interaction in the response equation. a subtraction procedure avoids double counting. applications in doubly magic nuclei and in a chain of superfluid nuclei show excellent agreement with experimental data.
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arxiv:0909.1276
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in this paper we construct an analytical separation ( diagonalization ) of the full ( minimal coupling ) dirac equation into particle and antiparticle components. the diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the foldy - wouthuysen method, and reveals the nonlocal time behavior of the particle - antiparticle relationship. we interpret the zitterbewegung and the result that a velocity measurement ( of a dirac particle ) at any instant in time is, as reflections of the fact that the dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. from this we infer that, although the form of the dirac equation serves to make space and time appear on an equal footing mathematically, it is clear that they are still not on an equal footing from a physical point of view. on the other hand, the foldy - wouthuysen transformation, which connects the dirac and square root operator, is unitary. reflection on these results suggests that a more refined notion ( than that of unitary equivalence ) may be required for physical systems.
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arxiv:quant-ph/0405151
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a simplified derivation of yurtsever ' s result, which states that the entropy of a truncated bosonic fock space is given by a holographic bound when the energy of the fock states is constrained gravitationally, is given for asymptotically flat spacetimes with arbitrary dimension d greater or equal to four. for this purpose, a scalar field confined to a spherical volume in d - dimensional spacetime is considered. imposing an upper bound on the total energy of the corresponding fock states which ensures that the system is in a stable configuration against gravitational collapse and imposing a cutoff on the maximum energy of the field modes of the order of the planck energy leads to an entropy bound of holographic type. a simple derivation of the entropy bound is also given for the fermionic case.
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arxiv:hep-th/0409046
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the nucleosynthesis in the first massive stars may be constrained by observing the surface composition of long - lived very iron - poor stars born around 10 billion years ago from material enriched by their ejecta. many interesting clues on physical processes having occurred in the first stars can be obtained just based on nuclear aspects. two facts are particularly clear, 1 ) in these first massive stars, mixing must have occurred between the h - burning and the he - burning zone during their nuclear lifetimes ; 2 ) only the outer layers of these massive stars have enriched the material from which the very iron - poor stars, observed today in the halo, have formed. these two basic requirements can be obtained by rotating stellar models at very low metallicity. in the present paper, we discuss the arguments supporting this view and illustrates the sensitivity of the results concerning the [ mg / al ] ratio on the rate of the reaction na ( 23 ) ( p, \ gamma ) mg ( 24 ).
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arxiv:1602.04122
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in this paper we discuss the stability of geodesic spheres in $ \ mathbb { s } ^ { n + 1 } $ under constrained curvature flows. we prove that under some standard assumptions on the speed and weight functions, the spheres are stable under perturbations that preserve a volume type quantity. this extends results by escher and simonett, 1998, and the author, 2015, to a riemannian manifold setting.
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arxiv:1601.04986
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. likewise, a negative speed ( rate of change of displacement ) implies a velocity in the opposite direction, i. e., receding instead of advancing ; a special case is the radial speed. in 3d space, notions related to sign can be found in the two normal orientations and orientability in general. = = = signedness in computing = = = in computing, an integer value may be either signed or unsigned, depending on whether the computer is keeping track of a sign for the number. by restricting an integer variable to non - negative values only, one more bit can be used for storing the value of a number. because of the way integer arithmetic is done within computers, signed number representations usually do not store the sign as a single independent bit, instead using e. g. two ' s complement. in contrast, real numbers are stored and manipulated as floating point values. the floating point values are represented using three separate values, mantissa, exponent, and sign. given this separate sign bit, it is possible to represent both positive and negative zero. most programming languages normally treat positive zero and negative zero as equivalent values, albeit, they provide means by which the distinction can be detected. = = = other meanings = = = in addition to the sign of a real number, the word sign is also used in various related ways throughout mathematics and other sciences : words up to sign mean that, for a quantity q, it is known that either q = q or q = βq for certain q. it is often expressed as q = Β±q. for real numbers, it means that only the absolute value | q | of the quantity is known. for complex numbers and vectors, a quantity known up to sign is a stronger condition than a quantity with known magnitude : aside q and βq, there are many other possible values of q such that | q | = | q |. the sign of a permutation is defined to be positive if the permutation is even, and negative if the permutation is odd. in graph theory, a signed graph is a graph in which each edge has been marked with a positive or negative sign. in mathematical analysis, a signed measure is a generalization of the concept of measure in which the measure of a set may have positive or negative values. the concept of signed distance is used to convey side, inside or out. the ideas of signed area and signed volume are sometimes used when it is convenient for certain areas or volumes to count as negative. this is particularly true in
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https://en.wikipedia.org/wiki/Sign_(mathematics)
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we estimate some mixed $ l ^ { p } \ left ( l ^ { 2 } \ right ) $ norms of the discrepancy between the volume and the number of integer points in $ r \ omega - x $, a dilated by a factor $ r $ and translated by a vector $ x $ of a convex body $ \ omega $ in $ \ mathbb { r } ^ { d } $, $ \ left \ { { \ int _ { \ mathbb { t } ^ { d } } } \ left ( \ frac { 1 } { h } { \ int _ { r } ^ { r + h } } \ left \ vert \ sum _ { k \ in \ mathbb { z } ^ { d } } \ chi _ { r \ omega - x } ( k ) - r ^ { d } \ left \ vert \ omega \ right \ vert \ right \ vert ^ { 2 } dr \ right ) ^ { p / 2 } dx \ right \ } ^ { 1 / p }. $ we obtain estimates for fixed values of $ h $ and $ r \ to \ infty $, and also asymptotic estimates when $ h \ to \ infty $.
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arxiv:1706.04419
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style is a significant component of natural language text, reflecting a change in the tone of text while keeping the underlying information the same. even though programming languages have strict syntax rules, they also have style. code can be written with the same functionality but using different language features. however, programming style is difficult to quantify, and thus as part of this work, we define style attributes, specifically for python. to build a definition of style, we utilized hierarchical clustering to capture a style definition without needing to specify transformations. in addition to defining style, we explore the capability of a pre - trained code language model to capture information about code style. to do this, we fine - tuned pre - trained code - language models and evaluated their performance in code style transfer tasks.
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arxiv:2209.06273
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we address the challenging problem of jointly inferring the 3d flow and volumetric densities moving in a fluid from a monocular input video with a deep neural network. despite the complexity of this task, we show that it is possible to train the corresponding networks without requiring any 3d ground truth for training. in the absence of ground truth data we can train our model with observations from real - world capture setups instead of relying on synthetic reconstructions. we make this unsupervised training approach possible by first generating an initial prototype volume which is then moved and transported over time without the need for volumetric supervision. our approach relies purely on image - based losses, an adversarial discriminator network, and regularization. our method can estimate long - term sequences in a stable manner, while achieving closely matching targets for inputs such as rising smoke plumes.
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arxiv:2302.14470
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in this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. we establish a connection between the network coding conjecture ( ncc ) of li and li and several data structure like problems such as non - adaptive function inversion of hellman and the well - studied problem of polynomial evaluation and interpolation. in turn these data structure problems imply super - linear circuit lower bounds for explicit functions such as integer sorting and multi - point polynomial evaluation.
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arxiv:2102.09294
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we investigate holographically the entanglement entropy of a nonconformal medium whose dual geometry is described by an einstein - maxwell - dilaton theory. due to an additional conserved charge corresponding to the number operator, its thermodynamics can be represented in a grandcanonical or canonical ensemble. we study thermodynamics in both ensembles by using the holographic renormalization and the entanglement entropy of a nonconformal medium. after defining the entanglement chemical potential which unlike the entanglement temperature has a nontrivial size dependence, we find that the entanglement entropy of a small subsystem satisfies the relation resembling the first law of thermodynamics in a medium. furthermore, we study the entanglement entropy change in the nonconformal medium caused by the excitation of the ground state and by the global quench corresponding to the insertion of particles.
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arxiv:1501.02908
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a quantum measurement model based upon restricted path - integrals allows us to study measurements of generalized position in various one - dimensional systems of phenomenological interest. after a general overview of the method we discuss the cases of a harmonic oscillator, a bistable potential and two coupled systems, briefly illustrating their applications.
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arxiv:quant-ph/9709004
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inspired by dickson ' s classification of regular ternary quadratic forms, we prove that there are no primitive regular $ m $ - gonal forms when $ m $ is sufficiently large. in order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of the previous primes, a question of independent interest.
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arxiv:1905.01423
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the concept of cross diffusion is applied to some biological systems. the conditions for persistence and turing instability in the presence of cross diffusion are derived. many examples including : predator - prey, epidemics ( with and without delay ), hawk - dove - retaliate and prisoner ' s dilemma games are given.
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arxiv:nlin/0404021
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the r package optimall offers a collection of functions that efficiently streamline the design process of sampling in surveys ranging from simple to complex. the package ' s main functions allow users to interactively define and adjust strata cut points based on values or quantiles of auxiliary covariates, adaptively calculate the optimum number of samples to allocate to each stratum using neyman or wright allocation, and select specific ids to sample based on a stratified sampling design. using real - life epidemiological study examples, we demonstrate how optimall facilitates an efficient workflow for the design and implementation of surveys in r. although tailored towards multi - wave sampling under two - or three - phase designs, the r package optimall may be useful for any sampling survey.
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arxiv:2106.09494
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we explore an optimal partition problem on surfaces using a computational approach. the problem is to minimise the sum of the first dirichlet laplace - - beltrami operator eigenvalues over a given number of partitions of a surface. we consider a method based on eigenfunction segregation and perform calculations using modern high performance computing techniques. we first test the accuracy of the method in the case of three partitions on the sphere then explore the problem for higher numbers of partitions and on other surfaces.
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arxiv:1408.2355
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we address the problem of evaluating the quality of self - supervised learning ( ssl ) models without access to supervised labels, while being agnostic to the architecture, learning algorithm or data manipulation used during training. we argue that representations can be evaluated through the lens of expressiveness and learnability. we propose to use the intrinsic dimension ( id ) to assess expressiveness and introduce cluster learnability ( cl ) to assess learnability. cl is measured in terms of the performance of a knn classifier trained to predict labels obtained by clustering the representations with k - means. we thus combine cl and id into a single predictor - - clid. through a large - scale empirical study with a diverse family of ssl algorithms, we find that clid better correlates with in - distribution model performance than other competing recent evaluation schemes. we also benchmark clid on out - of - domain generalization, where clid serves as a predictor of the transfer performance of ssl models on several visual classification tasks, yielding improvements with respect to the competing baselines.
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arxiv:2206.01251
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we theoretically investigate the origin of the square - type skyrmion crystal in centrosymmetric itinerant magnets, motivated from the recent experimental finding in gdru $ _ 2 $ si $ _ 2 $ [ n. d. khanh $ \ mathit { et } $ $ \ mathit { al. } $, nat. nanotech. $ \ mathbf { 15 } $, 444 ( 2020 ) ]. by simulated annealing for an effective spin model derived from the kondo lattice model on a square lattice, we find that a square skyrmion crystal composed of a superposition of two spin helices is stabilized in a magnetic field by synergy between the positive biquadratic, bond - dependent anisotropic, and easy - axis anisotropic interactions. this is in stark contrast to triangular skyrmion crystals which are stabilized by only one of the three, suggesting that the square skyrmion crystal is characteristic of itinerant magnets with magnetic anisotropy. we also show that a variety of noncollinear and noncoplanar spin textures appear depending on the model parameters as well as the applied magnetic field. the present systematic study will be useful not only for identifying the key ingredients in gdru $ _ 2 $ si $ _ 2 $ but also for exploring further skyrmion - hosting materials in centrosymmetric itinerant magnets.
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arxiv:2010.14671
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in this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive mappings in a real hilbert space. based on parallel computation we can reduce the overall computational effort under widely used conditions on the bifunctions and the nonexpansive mappings. a simple numerical example is given to illustrate the proposed parallel algorithms.
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arxiv:1512.07296
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we investigate the statistical properties of isotropic, stochastic, gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. we discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. we are particularly interested in scale - invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. we determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. we show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. at smaller scales, the scale - invariant spectrum changes with time. it becomes a steeper weak - turbulence spectrum at progressively larger scales. we show numerically that the critical length scale where this happens is the turbulent - diffusive scale, which increases with the square root of time.
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arxiv:1804.01177
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