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bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be estimated. the uncertainty of classification is determined by a trade - off between the amount of data available for training, the diversity of a classifier ensemble and the required performance. the interpretability of classification models can also give useful information for experts responsible for making reliable classifications. for this reason decision trees ( dts ) seem to be attractive classification models. the required diversity of the dt ensemble can be achieved by using the bayesian model averaging all possible dts. in practice, the bayesian approach can be implemented on the base of a markov chain monte carlo ( mcmc ) technique of random sampling from the posterior distribution. for sampling large dts, the mcmc method is extended by reversible jump technique which allows inducing dts under given priors. for the case when the prior information on the dt size is unavailable, the sweeping technique defining the prior implicitly reveals a better performance. within this chapter we explore the classification uncertainty of the bayesian mcmc techniques on some datasets from the statlog repository and real financial data. the classification uncertainty is compared within an uncertainty envelope technique dealing with the class posterior distribution and a given confidence probability. this technique provides realistic estimates of the classification uncertainty which can be easily interpreted in statistical terms with the aim of risk evaluation. | arxiv:cs/0504065 |
recently, a state of the art experiment shows evidence for lorentz violation in the gravitational sector. to explain this experiment, we investigate a spontaneous lorentz violation scenario with a generalized scalar field. we find that when the scalar field is nonminimally coupled to gravity, the lorentz violation induces a deformation in the newtonian potential along the direction of lorentz violation. | arxiv:0903.0227 |
$ ^ 7 $ li and $ ^ 7 $ be play an important role in big bang nucleosynthesis and nuclear astrophysics. the $ ^ 3 $ h ( $ ^ 4 $ he, $ \ gamma $ ) $ ^ 7 $ li radiative capture reaction is crucial for the determination of the primordial $ ^ 7 $ li abundance. in nuclear astrophysics, lithium isotopes have attracted a great interest because of the puzzled abundance of $ ^ 6 $ li and $ ^ 7 $ li. purpose : in this work we study spectra of $ ^ 7 $ be, $ ^ 7 $ li and elastic scattering cross sections $ ^ 4 $ he ( $ ^ 3 $ he, $ ^ 3 $ he ), $ ^ 4 $ he ( $ ^ 3 $ h, $ ^ 3 $ h ) within the gamow shell model ( gsm ) in the coupled - channel formulation ( gsm - cc ). the evolution of channel amplitudes and spectroscopic factors in the vicinity of the channel threshold is studied for selected states. methods : gsm provides the open quantum system formulation of nuclear shell model. in the representation of gsm - cc, gsm provides the unified theory of nuclear structure and reactions which is suited for the study of resonances in $ ^ 7 $ be, $ ^ 7 $ li and elastic scattering cross - sections involving $ ^ 3 $ h and $ ^ 3 $ he projectiles. results : the gsm - cc in multi - mass partition formulation applied to a translationally invariant hamiltonian with an effective finite - range two - body interaction reproduce well the spectra of $ ^ 7 $ be, $ ^ 7 $ li and elastic scattering reactions : $ ^ 4 $ he ( $ ^ 3 $ he, $ ^ 3 $ he ), $ ^ 4 $ he ( $ ^ 3 $ h, $ ^ 3 $ h ). detailed analysis of the dependence of reaction channel amplitudes and spectroscopic factors on the distance from the particle decay threshold allowed to demonstrate the alignment of the wave function in the vicinity of the decay threshold. this analysis also demonstrates the appearance of clustering in the gsm - cc wave function in the vicinity of the cluster decay threshold. | arxiv:2306.05215 |
among the various generative adversarial network ( gan ) - based image inpainting methods, a coarse - to - fine network with a contextual attention module ( cam ) has shown remarkable performance. however, owing to two stacked generative networks, the coarse - to - fine network needs numerous computational resources such as convolution operations and network parameters, which result in low speed. to address this problem, we propose a novel network architecture called pepsi : parallel extended - decoder path for semantic inpainting network, which aims at reducing the hardware costs and improving the inpainting performance. pepsi consists of a single shared encoding network and parallel decoding networks called coarse and inpainting paths. the coarse path produces a preliminary inpainting result to train the encoding network for the prediction of features for the cam. simultaneously, the inpainting path generates higher inpainting quality using the refined features reconstructed via the cam. in addition, we propose diet - pepsi that significantly reduces the network parameters while maintaining the performance. in diet - pepsi, to capture the global contextual information with low hardware costs, we propose novel rate - adaptive dilated convolutional layers, which employ the common weights but produce dynamic features depending on the given dilation rates. extensive experiments comparing the performance with state - of - the - art image inpainting methods demonstrate that both pepsi and diet - pepsi improve the qualitative scores, i. e. the peak signal - to - noise ratio ( psnr ) and structural similarity ( ssim ), as well as significantly reduce hardware costs such as computational time and the number of network parameters. | arxiv:1905.09010 |
background : immortal time is a period of follow - up during which death or the study outcome cannot occur by design. bias from immortal time has been increasingly recognized in epidemiologic studies. however, the fundamental causes and structures of bias from immortal time have not been explained systematically using a structural approach. methods : we use an example " do nobel prize winners live longer than less recognized scientists? " for illustration. we illustrate how immortal time arises and present the structures of bias from immortal time using time - varying directed acyclic graphs ( dags ). we further explore the structures of bias with the exclusion of immortal time and with the presence of competing risks. we discuss how these structures are shared by different study designs in pharmacoepidemiology and provide solutions, where possible, to address the bias. results : we illustrate that immortal time arises from using postbaseline information to define exposure or eligibility. we use time - varying dags to explain the structures of bias from immortal time are confounding by survival until exposure allocation or selection bias from selecting on survival until eligibility. we explain that excluding immortal time from the follow - up does not fully address this confounding or selection bias, and that the presence of competing risks can worsen the bias. bias from immortal time may be avoided by aligning time zero, exposure allocation and eligibility, and by excluding individuals with prior exposure. conclusions : understanding bias from immortal time in terms of confounding or selection bias helps researchers identify and thereby avoid or ameliorate this bias. | arxiv:2312.06155 |
a metropolis monte carlo simulation is used in this paper to investigate the temperature dependency of the hysteresis loops of a spin - 1 bilayer with square monolayers. in this system, the atoms interact ferromagnetically in - plane, with either ferromagnetic or antiferromagnetic interplane interactions. the effects of four distinct combinations of the hamiltonian parameters on the hysteresis behaviours are discussed in detail. the geometry of the hysteresis loops changes depending on how the exchange couplings are combined. with ferromagnetic interlayer coupling, only the central hysteresis loop opens while for the antiferromagnetic case, the hysteresis loop becomes a double loop for the specific combination of coupling strengths. additionally, in all these cases, the area of the hysteresis loops grows with the gradual lowering of the temperature. | arxiv:2205.03349 |
human falls rarely occur ; however, detecting falls is very important from the health and safety perspective. due to the rarity of falls, it is difficult to employ supervised classification techniques to detect them. moreover, in these highly skewed situations it is also difficult to extract domain specific features to identify falls. in this paper, we present a novel framework, \ textit { deepfall }, which formulates the fall detection problem as an anomaly detection problem. the \ textit { deepfall } framework presents the novel use of deep spatio - temporal convolutional autoencoders to learn spatial and temporal features from normal activities using non - invasive sensing modalities. we also present a new anomaly scoring method that combines the reconstruction score of frames across a temporal window to detect unseen falls. we tested the \ textit { deepfall } framework on three publicly available datasets collected through non - invasive sensing modalities, thermal camera and depth cameras and show superior results in comparison to traditional autoencoder methods to identify unseen falls. | arxiv:1809.00977 |
the closed form solution is found for the fully nonlinear dynamics of the gyroscope with a fixed point at the tip. the solution is found by using cardano ' s formulae to factor a cubic, in the case where all roots are known to be real. from this, the nutation angle is solved first in terms of jacobi ' s elliptic integral of the first kind. a simple change of variables then transforms the dependent variable of the remaining equations from time to the projection of the nutation angle onto the vertical axis. after this transformation, the remaining equations can be integrated exactly, giving solutions expressed in jacobi ' s elliptic integrals of the third kind. reduced energy, angular momentum, moment of inertia and cardano ' s discriminant are defined. the thresholds are found, separating looping, cuspidial, and unidirectional domains of nutation. | arxiv:2310.01223 |
did not derive from any scientific fact or theory catastrophism, including its identification of the worldwide flood, failed as a science " relatively recent inception " was the product of religious readings and had no scientific meaning, and was neither the product of, nor explainable by, natural law ; nor is it tentative the court further noted that no recognized scientific journal had published any article espousing the creation science theory as described in the arkansas law, and stated that the testimony presented by defense attributing the absence to censorship was not credible. in its ruling, the court wrote that for any theory to qualify as scientific, the theory must be tentative, and open to revision or abandonment as new facts come to light. it wrote that any methodology which begins with an immutable conclusion that cannot be revised or rejected, regardless of the evidence, is not a scientific theory. the court found that creation science does not culminate in conclusions formed from scientific inquiry, but instead begins with the conclusion, one taken from a literal wording of the book of genesis, and seeks only scientific evidence to support it. the law in arkansas adopted the same two - model approach as that put forward by the institute for creation research, one allowing only two possible explanations for the origins of life and existence of man, plants and animals : it was either the work of a creator or it was not. scientific evidence that failed to support the theory of evolution was posed as necessarily scientific evidence in support of creationism, but in its judgment the court ruled this approach to be no more than a " contrived dualism which has not scientific factual basis or legitimate educational purpose. " the judge concluded that " act 590 is a religious crusade, coupled with a desire to conceal this fact, " and that it violated the first amendment ' s establishment clause. the decision was not appealed to a higher court, but had a powerful influence on subsequent rulings. louisiana ' s 1982 balanced treatment for creation - science and evolution - science act, authored by state senator bill p. keith, judged in the 1987 united states supreme court case edwards v. aguillard, and was handed a similar ruling. it found the law to require the balanced teaching of creation science with evolution had a particular religious purpose and was therefore unconstitutional. = = = intelligent design splits off = = = in 1984, the mystery of life ' s origin was first published. it was co - authored by chemist and creationist charles b. thaxton with walter l. bradley and roger l. olsen, the foreword written by | https://en.wikipedia.org/wiki/Creation_science |
discovery of a higgs boson and precise measurements of its properties open a new window to test physics beyond the standard model. models with universal extra dimensions are not exception. kaluza - klein excitations of the standard model particles contribute to the production and decay of the higgs boson. in particular, the parameters associated with third generation quarks are constrained by higgs data, which are relatively insensitive to other searches often involving light quarks and leptons. we investigate implications of the 126 gev higgs in next - to - minimal universal extra dimensions, and show that boundary terms and bulk masses allow a lower compactification scale as compared to in minimal universal extra dimensions. | arxiv:1309.7077 |
in this paper, an efficient numerical technique for the time - fractional telegraph equation is proposed. the aim of this paper is to use a relatively new type of b - spline called the cubic trigonometric b - splines for the proposed scheme. this technique is based on finite difference formulation for the caputo time - fractional derivative and cubic trigonometric b - splines based technique for the derivatives in space. a stability analysis of the scheme is set up to affirm that the errors do not amplify. computational experiments are carried out in addition to verify the theoretical analysis. numerical results are compared with some existing techniques and it is concluded that the present scheme is more accurate and effective. | arxiv:1808.01158 |
publication patterns of 79 forest scientists awarded major international forestry prizes during 1990 - 2010 were compared with the journal classification and ranking promoted as part of the ' excellence in research for australia ' ( era ) by the australian research council. the data revealed that these scientists exhibited an elite publication performance during the decade before and two decades following their first major award. an analysis of their 1703 articles in 431 journals revealed substantial differences between the journal choices of these elite scientists and the era classification and ranking of journals. implications from these findings are that additional cross - classifications should be added for many journals, and there should be an adjustment to the ranking of several journals relevant to the era field of research classified as 0705 forestry sciences. | arxiv:1108.4828 |
the upcoming karlsruhe tritium neutrino ( katrin ) experiment will put unprecedented constraints on the absolute mass of the electron neutrino, $ \ mnue $. in this paper we investigate how this information on $ \ mnue $ will affect our constraints on cosmological parameters. we consider two scenarios ; one where $ \ mnue = 0 $ ( i. e., no detection by katrin ), and one where $ \ mnue = 0. 3 $ ev. we find that the constraints on $ \ mnue $ from katrin will affect estimates of some important cosmological parameters significantly. for example, the significance of $ n _ s < 1 $ and the inferred value of $ \ omega _ \ lambda $ depend on the results from the katrin experiment. | arxiv:0709.4152 |
graphs have emerged as an important foundation for a variety of applications, including capturing and reasoning over factual knowledge, semantic data integration, social networks, and providing factual knowledge for machine learning algorithms. to formalise certain properties of the data and to ensure data quality, there is a need to describe the schema of such graphs. because of the breadth of applications and availability of different data models, such as rdf and property graphs, both the semantic web and the database community have independently developed graph schema languages : shacl, shex, and pg - schema. each language has its unique approach to defining constraints and validating graph data, leaving potential users in the dark about their commonalities and differences. in this paper, we provide formal, concise definitions of the core components of each of these schema languages. we employ a uniform framework to facilitate a comprehensive comparison between the languages and identify a common set of functionalities, shedding light on both overlapping and distinctive features of the three languages. | arxiv:2502.01295 |
a true place - value system, where digits written in the left column represented larger values ( much as, in our base ten system, 734 = 7×100 + 3×10 + 4×1 ). = = old babylonian mathematics ( 2000 – 1600 bc ) = = = = = arithmetic = = = the babylonians used pre - calculated tables to assist with arithmetic, including multiplication tables, tables of reciprocals, and tables of squares ( or, by using the same table in the opposite way, tables of square roots ). their multiplication tables were not the 60 × 60 { \ displaystyle 60 \ times 60 } tables that one might expect by analogy to decimal multiplication tables. instead, they kept only tables for multiplication by certain " principal numbers " ( the regular numbers and 7 ). to calculate other products, they would split one of the numbers to be multiplied into a sum of principal numbers. although many babylonian tablets record exercises in multi - digit multiplication, these typically jump directly from the numbers being multiplied to their product, without showing intermediate values. based on this, and on certain patterns of mistakes in some of these tablets, jens høyrup has suggested that long multiplication was performed in such a way that each step of the calculation erased the record of previous steps, as would happen using an abacus or counting board and would not happen with written long multiplication. a rare exception, " the only one of its kind known ", is the late babylonian / seleucid tablet bm 34601, which has been reconstructed as computing the square of a 13 - digit sexagesimal number ( the number 5 ⋅ 3 25 { \ displaystyle 5 \ cdot 3 ^ { 25 } } ) using a " slanting column of partial products " resembling modern long multiplication. the babylonians did not have an algorithm for long division. instead they based their method on the fact that : a b = a × 1 b { \ displaystyle { \ frac { a } { b } } = a \ times { \ frac { 1 } { b } } } together with a table of reciprocals. numbers whose only prime factors are 2, 3 or 5 ( known as 5 - smooth or regular numbers ) have finite reciprocals in sexagesimal notation, and tables with extensive lists of these reciprocals have been found. reciprocals such as 1 / 7, 1 / 11, 1 / 13, etc. do not have finite representations in sexagesimal notation. to compute 1 / 13 or to divide a | https://en.wikipedia.org/wiki/Babylonian_mathematics |
for fixed $ l, m \ ge 1 $, let $ \ mathbf { x } _ n ^ { ( 0 ) }, \ mathbf { x } _ n ^ { ( 1 ) }, \ dots, \ mathbf { x } _ n ^ { ( l ) } $ be independent random $ n \ times n $ matrices with independent entries, let $ \ mathbf { f } _ n ^ { ( 0 ) } : = \ mathbf { x } _ n ^ { ( 0 ) } ( \ mathbf { x } _ n ^ { ( 1 ) } ) ^ { - 1 } \ cdots ( \ mathbf { x } _ n ^ { ( l ) } ) ^ { - 1 } $, and let $ \ mathbf { f } _ n ^ { ( 1 ) }, \ dots, \ mathbf { f } _ n ^ { ( m ) } $ be independent random matrices of the same form as $ \ mathbf { f } _ n ^ { ( 0 ) } $. we investigate the limiting spectral distributions of the matrices $ \ mathbf { f } _ n ^ { ( 0 ) } $ and $ \ mathbf { f } _ n ^ { ( 1 ) } + \ dots + \ mathbf { f } _ n ^ { ( m ) } $ as $ n \ to \ infty $. our main result shows that the sum $ \ mathbf { f } _ n ^ { ( 1 ) } + \ dots + \ mathbf { f } _ n ^ { ( m ) } $ has the same limiting eigenvalue distribution as $ \ mathbf { f } _ n ^ { ( 0 ) } $ after appropriate rescaling. this extends recent findings by tikhomirov and timushev ( 2014 ). to obtain our results, we apply the general framework recently introduced in g \ " otze, k \ " osters and tikhomirov ( 2014 ) to sums of products of independent random matrices and their inverses. we establish the universality of the limiting singular value and eigenvalue distributions, and we provide a closer description of the limiting distributions in terms of free probability theory. | arxiv:1506.04436 |
the cycling performance of lithium - ion batteries is closely related to the expansion effect of anode materials during charge and discharge processes. studying the mechanical field evolution of anode materials is crucial for evaluating battery per - formance. here, we propose a phase - sensitive ultra - high spatial resolution optical frequency domain reflectometry tech - nique, in which the test fiber is embedded into the anode of a lithium - ion battery to monitor the mechanical evolution of the anode material during cycling. we investigated the strain evolution of the anode material under different loading levels and used this method to infer the morphological changes of the material. furthermore, combining this with battery capacity in - formation provides a new approach for assessing the performance of lithium - ion batteries. | arxiv:2407.02817 |
we present cryptflow, a system that converts tensorflow inference code into secure multi - party computation ( mpc ) protocols at the push of a button. to do this, we build two components. our first component is an end - to - end compiler from tensorflow to a variety of mpc protocols. the second component is an improved semi - honest 3 - party protocol that provides significant speedups for inference. we empirically demonstrate the power of our system by showing the secure inference of real - world neural networks such as densenet121 for detection of lung diseases from chest x - ray images and 3d - unet for segmentation in radiotherapy planning using ct images. in particular, this paper provides the first evaluation of secure segmentation of 3d images, a task that requires much more powerful models than classification and is the largest secure inference task run till date. | arxiv:2012.05064 |
this work proposes a dual - functional blockchain framework named bagchain for bagging - based decentralized learning. bagchain integrates blockchain with distributed machine learning by replacing the computationally costly hash operations in proof - of - work with machine - learning model training. bagchain utilizes individual miners ' private data samples and limited computing resources to train potentially weak base models, which may be very weak, and further aggregates them into strong ensemble models. specifically, we design a three - layer blockchain structure associated with the corresponding generation and validation mechanisms to enable distributed machine learning among uncoordinated miners in a permissionless and open setting. to reduce computational waste due to blockchain forking, we further propose the cross fork sharing mechanism for practical networks with lengthy delays. extensive experiments illustrate the superiority and efficacy of bagchain when handling various machine learning tasks on both independently and identically distributed ( iid ) and non - iid datasets. bagchain remains robust and effective even when facing constrained local computing capability, heterogeneous private user data, and sparse network connectivity. | arxiv:2502.11464 |
we show how to extend the standard functional approach to bosonisation, based on a decoupling change of path - integral variables, to the case in which a finite temperature is considered. as examples, in order to both illustrate and check the procedure, we derive the thermodynamical partition functions for the thirring and schwinger models. | arxiv:hep-th/9701160 |
we review the random first order transition theory of the glass transition, emphasizing the experimental tests of the theory. many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature $ t _ g $. these include : the viscosity catastrophe and heat capacity jump at $ t _ g $, and their connection ; the non - exponentiality of relaxations and their correlation with the fragility ; dynamic heterogeneity in supercooled liquids owing to the mosaic structure ; deviations from the vogel - fulcher law, connected with strings or fractral cooperative rearrangements ; deviations from the stokes - einstein relation close to $ t _ g $ ; aging, and its correlation with fragility ; the excess density of states at cryogenic temperatures due to two level tunneling systems and the boson peak. | arxiv:cond-mat/0607349 |
interacting fluids, endowed with bulk viscous stresses, are discussed in a unified perspective with the aim of generalizing the treatment of cosmological perturbation theory to the case where both fluctuating decay rates and fluctuating bulk viscosity coefficients are simultaneously present in the relativistic plasma. a gauge - invariant treatment of the qualitatively new phenomena arising in this context is provided. in a complementary approach, faithful gauge - fixed descriptions of the gravitational and hydrodynamical fluctuations are developed and exploited. to deepen the interplay between bulk viscous stresses and fluctuating decay rates, illustrative examples are proposed and discussed both analytically and numerically. particular attention is paid to the coupled evolution of curvature and entropy fluctuations when, in the relativistic plasma, at least one of the interacting fluids possesses a fluctuating bulk viscosity coefficient. it is argued that this class of models may be usefully employed as an effective description of the decay of the inflaton as well as of other phenomena involving imperfect relativistic fluids. | arxiv:astro-ph/0504655 |
we study some properties of the askey - wilson polynomials ( awp ) when q is a primitive n - th root of unity. for general four - parameter awp, zeros of the n - th polynomial and the orthogonality measure are found explicitly. special subclasses of the awp, e. g., the continuous q - jacobi and big q - jacobi polynomials, are considered in detail. a set of discrete weight functions positive on a real interval is described. some new trigonometric identities related to the awp are obtained. normalization conditions of some polynomials are expressed in terms of the gauss sums. | arxiv:q-alg/9605034 |
michel proved that for a one - parameter family of elliptic curves over q ( t ) with non - constant j ( t ) that the second moment of the number of solutions modulo p is p ^ 2 + o ( p ^ { 3 / 2 } ). we show this bound is sharp by studying y ^ 2 = x ^ 3 + tx ^ 2 + 1. lower order terms for such moments in a family are related to lower order terms in the n - level densities of katz and sarnak, which describe the behavior of the zeros near the central point of the associated l - functions. we conclude by investigating similar families and show how the lower order terms in the second moment may affect the expected bounds for the average rank of families in numerical investigations. | arxiv:math/0506461 |
this paper examines an optimal investment problem in a continuous - time ( essentially ) complete financial market with a finite horizon. we deal with an investor who behaves consistently with principles of cumulative prospect theory, and whose utility function on gains is bounded above. the well - posedness of the optimisation problem is trivial, and a necessary condition for the existence of an optimal trading strategy is derived. this condition requires that the investor ' s probability distortion function on losses does not tend to 0 near 0 faster than a given rate, which is determined by the utility function. under additional assumptions, we show that this condition is indeed the borderline for attainability, in the sense that for slower convergence of the distortion function there does exist an optimal portfolio. | arxiv:1309.0362 |
the planetary differentiation models of mars are proposed that take into account core - mantle and core - mantle - crust differentiation. the numerical simulations are presented for the early thermal evolution of mars spanning up to the initial 25 million years ( ma ) of the early solar system, probably for the first time, by taking into account the radiogenic heating due to the short - lived nuclides, 26al and 60fe. the influence of impact heating during the accretion of mars is also incorporated in the simulations. the early accretion of mars would necessitate a substantial role played by the short - lived nuclides in its heating. 26al along with impact heating could have provided sufficient thermal energy to the entire body to substantially melt and trigger planetary scale differentiation. this is contrary to the thermal models based exclusively on the impact heating that could not produce widespread melting and planetary differentiation. the early onset of the accretion of mars perhaps within the initial ~ 1. 5 ma in the early solar system could have resulted in substantial differentiation of mars provide it accreted over the timescale of ~ 1 ma. this seems to be consistent with the chronological records of the martian meteorites. | arxiv:1408.3341 |
recently there have been efforts to introduce new benchmark tasks for spoken language understanding ( slu ), like semantic parsing. in this paper, we describe our proposed spoken semantic parsing system for the quality track ( track 1 ) in spoken language understanding grand challenge which is part of icassp signal processing grand challenge 2023. we experiment with both end - to - end and pipeline systems for this task. strong automatic speech recognition ( asr ) models like whisper and pretrained language models ( lm ) like bart are utilized inside our slu framework to boost performance. we also investigate the output level combination of various models to get an exact match accuracy of 80. 8, which won the 1st place at the challenge. | arxiv:2305.01620 |
motivated by fluorescence lifetime measurements this paper considers the problem of nonparametric density estimation in the pile - up model. adaptive nonparametric estimators are proposed for the pile - up model in its simple form as well as in the case of additional measurement errors. furthermore, oracle type risk bounds for the mean integrated squared error ( mise ) are provided. finally, the estimation methods are assessed by a simulation study and the application to real fluorescence lifetime data. | arxiv:1011.0592 |
a non - markovian stochastic model shows the emergence of structures in the medium, a self - organization characterized by a relationship between particle ' s energy, driven frequency $ \ omega $ and a frequency of interaction with the medium $ \ nu $. the interaction determines its mass and this fine tuning results in an effective force given by $ f _ l = \ hbar \ omega ^ 2 n ( \ lambda ) / c $, similar to the interaction force between photons and atoms. condition for the particle - medium resonance is determined, with relevance to detect dark matter axion - like particles and the parametric resonance as a pop - up mechanism to turn fields into particles. | arxiv:1507.07810 |
the energy spectra and wavefunctions of up to 14 interacting quasielectrons ( qe ' s ) in the laughlin nu = 1 / 3 fractional quantum hall ( fqh ) state are investigated using exact numerical diagonalization. it is shown that at sufficiently high density the qe ' s form pairs or larger clusters. this behavior, opposite to laughlin correlations, invalidates the ( sometimes invoked ) reapplication of the composite fermion picture to the individual qe ' s. the series of finite - size incompressible ground states are identified at the qe filling factors nu _ qe = 1 / 2, 1 / 3, 2 / 3, corresponding to the electron fillings nu = 3 / 8, 4 / 11, 5 / 13. the equivalent quasihole ( qh ) states occur at nu _ qh = 1 / 4, 1 / 5, 2 / 7, corresponding to nu = 3 / 10, 4 / 13, 5 / 17. all these six novel fqh states were recently discovered experimentally. detailed analysis indicates that qe or qh correlations in these states are different from those of well - known fqh electron states ( e. g., laughlin or moore - read states ), leaving the origin of their incompressibility uncertain. halperin ' s idea of laughlin states of qp pairs is also explored, but is does not seem adequate. | arxiv:cond-mat/0312290 |
recently, the belle collaboration has updated the analysis of the cross sections for the processes $ e ^ + e ^ - \ to \ upsilon ( ns ) \, \ pi ^ + \ pi ^ - $ ( $ n = 1, \, 2, \, 3 $ ) in the $ e ^ + e ^ - $ center - of - mass energy range from 10. 52 to 11. 02 ~ gev. a new structure, called $ y _ b ( 10750 ) $, with the mass $ m ( y _ b ) = ( 10752. 7 \ pm 5. 9 ^ { + 0. 7 } _ { - 1. 1 } ) $ ~ mev and the breit - wigner width $ \ gamma ( y _ b ) = ( 35. 5 ^ { + 17. 6 + 3. 9 } _ { - 11. 3 - 3. 3 } ) $ ~ mev was observed. we interpret $ y _ b ( 10750 ) $ as a compact $ j ^ { pc } = 1 ^ { - - } $ state with a dominant tetraquark component. the mass eigenstate $ y _ b ( 10750 ) $ is treated as a linear combination of the diquark - antidiquark and $ b \ bar b $ components due to the mixing via gluonic exchanges shown recently to arise in the limit of large number of quark colors. the mixing angle between $ y _ b $ and $ \ upsilon ( 5s ) $ can be estimated from the electronic width, recently determined to be $ \ gamma _ { ee } ( y _ b ) = ( 13. 7 \ pm 1. 8 ) $ ~ ev. the mixing provides a plausible mechanism for $ y _ b ( 10750 ) $ production in high energy collisions from its $ b \ bar b $ component and we work out the drell - yan and prompt production cross sections for $ p p \ to y _ b ( 10750 ) \ to \ upsilon ( ns ) \, \ pi ^ + \ pi ^ - $ at the lhc. the resonant part of the dipion invariant mass spectrum in $ y _ b ( 10750 ) \ to \ upsilon ( 1s ) \, \ pi ^ + \ pi ^ - $ and the corresponding angular distribution of $ \ pi ^ + $ - meson in the dipion rest frame are presented. | arxiv:2012.07761 |
we consider the problem of generalization in reinforcement learning where visual aspects of the observations might differ, e. g. when there are different backgrounds or change in contrast, brightness, etc. we assume that our agent has access to only a few of the mdps from the mdp distribution during training. the performance of the agent is then reported on new unknown test domains drawn from the distribution ( e. g. unseen backgrounds ). for this " zero - shot rl " task, we enforce invariance of the learned representations to visual domains via a domain adversarial optimization process. we empirically show that this approach allows achieving a significant generalization improvement to new unseen domains. | arxiv:2102.07097 |
we have used modern supercomputer facilities to carry out extensive numerical simulations of statistical properties of 1d and 2d arrays of single - electron islands with random background charges, in the limit of small island self - capacitance. in particular, the spectrum of single - electron addition energies shows a clear coulomb gap that, in 2d arrays, obeys the efros - shklovskii theory modified for the specific electron - electron interaction law. the coulomb blockade threshold voltage statistics for 1d arrays is very broad, with r. m. s. width $ \ delta v _ t $ growing as $ < v _ t > \ propto n ^ { 1 / 2 } $ with the array size $ n $. on the contrary, in square 2d arrays of large size the distribution around $ < v _ t > \ propto n $ becomes relatively narrow $ ( \ delta v _ t / < v _ t > \ propto 1 / n ) $, and the dc $ i $ - $ v $ curves are virtually universal. at low voltages, the slope $ g _ 0 ( t ) $ of $ i $ - $ v $ curves obeys the arrhenius law. the corresponding activation energy $ u _ 0 $ grows only slowly with $ n $ and is considerably lower than the formally calculated " lowest pass " energy $ e _ { max } $ of the potential profile, thus indicating the profile " softness ". | arxiv:cond-mat/0303439 |
the physical world is marked by the phenomenon of spontaneous broken symmetry ( sbs ) i. e. where the state of a system is assymmetric with respect to the symmetry principles that govern its dynamics. for material systems this is not surprising since more often than not energetic considerations dictate that the ground state or low lying excited states of many body system become ordered i. e. a collective variable, such as magnetization or the fourier transform of the density of a solid, picks up expectation values which otherwise would vanish by virtue of the dynamical symmetry ( isotropy or translational symmetry in the aforementioned examples ). more surprising was the discovery of the role of sbs in describing the vacuum or low lyng excitations of a quantum field theory. first came spontaneously broken chiral symmetry which was then applied to soft pion physics. when combined with current algebra, this field dominated particle physics in the 60 ' s. then came the application of the notion of sbs to situations where the symmetry is locally implemented by gauge fields. in that case the concept of order becomes more subtle. this development lead the way to electroweak unification and it remains one of the principal tools of the theorist in the quest for physics beyond the standard model. this brief review is intended to span the history of sbs with emphasis on conceptual rather than quantitative content. it is a written version of lectures of r. brout on the ` ` paleolithic age ' ' and on ` ` modern times ' ' by f. englert, i. e. respectively without and with gauge fields. | arxiv:hep-th/0203096 |
unpinned dirac points ( dps ) are nodal point degeneracies that occur at generic momentum points lacking high symmetry, often exhibiting characteristics typically forbidden by symmetry. while this phenomenon has been observed in solid - state materials, the formation of unpinned dps in photonic crystals has not been extensively studied. this study presents a novel approach to achieving unpinned dps in two - dimensional ` ` defected photonic crystals " - photonic superlattices created by modifying the size or refractive index of dielectric disks at specific sites. the defected photonic crystal hosts multiple unpinned dps through accidental band crossings induced by rotational symmetry breaking across the nodal line degeneracies prevalent in the superlattice. furthermore, the number of unpinned dps, along with their positions and anisotropic dispersions, can be manipulated by adjusting the size or refractive index of the dielectric disks. this study pioneers the exploration of defected photonic crystals, proposing them as effective means of achieving unpinned dps and facilitating the investigation of novel relativistic photonic wave phenomena with significant flexibility and control. | arxiv:2502.10753 |
the standard model of particle physics predicts the existence of quantum tunnelling processes across topological inequivalent vacua, known as instantons. in the electroweak sector, instantons provide a source of baryon asymmetry within the standard model. in quantum chromodynamics they are linked to chiral symmetry breaking and confinement. the direct experimental observation of instanton - induced processes would therefore be a breakthrough in modern particle physics. recently, new calculations for qcd instanton processes in proton - proton collisions became public, suggesting sizable cross sections as well as promising experimental signatures at the lhc. in this work, we study possible analysis strategies to discover qcd instanton induced processes at the lhc and derive a first limit based on existing minimum bias data. | arxiv:2012.09120 |
we report the local magnetic response of an electron - doped cuprate superconductor, pr $ _ { 0. 89 } $ lace $ _ { 0. 11 } $ cuo $ _ { 4 } $ ( $ t _ c \ simeq26 $ k ), studied by muon spin rotation ( \ msr ) over a field range from 200 oe to 50 koe. in the paramagnetic state, the muon knight shift along the crystal c - axis ( $ k _ \ mu ^ z $ ) is proportional to the in - plane susceptibility $ \ chi _ { ab } $. more surprisingly, $ k _ \ mu ^ z $ is strongly enhanced by the occurrence of superconductivity ( below $ \ sim $ 40 koe ), changing its sign from positive to negative around $ \ sim1 $ koe with increasing field. this finding can be understood by considering the weak polarization of pr ions due to superexchange interaction with the antiferromagnetic cu sublattice, which coexists with superconductivity. | arxiv:cond-mat/0407228 |
we present lightcurves of the afterglow of grb050502a, including very early data at t - t _ { grb } < 60s. the lightcurve is composed of unfiltered rotse - iiib optical observations from 44s to 6h post - burst, r - band mdm observations from 1. 6 to 8. 4h post - burst, and pairitel j h k _ s observations from 0. 6 to 2. 6h post - burst. the optical lightcurve is fit by a broken power law, where t ^ { alpha } steepens from alpha = - 1. 13 + - 0. 02 to alpha = - 1. 44 + - 0. 02 at \ ~ 5700s. this steepening is consistent with the evolution expected for the passage of the cooling frequency nu _ c through the optical band. even in our earliest observation at 44s post - burst, there is no evidence that the optical flux is brighter than a backward extrapolation of the later power law would suggest. the observed decay indices and spectral index are consistent with either an ism or a wind fireball model, but slightly favor the ism interpretation. the expected spectral index in the ism interpretation is consistent within 1 sigma with the observed spectral index beta = - 0. 8 + - 0. 1 ; the wind interpretation would imply a slightly ( ~ 2 sigma ) shallower spectral index than observed. a small amount of dust extinction at the source redshift could steepen an intrinsic spectrum sufficiently to account for the observed value of beta. in this picture, the early optical decay, with the peak at or below 4. 7e14 hz at 44s, requires very small electron and magnetic energy partitions from the fireball. | arxiv:astro-ph/0509594 |
the goal of the eudet project is the development and construction of infrastructure to permit detector r & d for the international linear collider ( ilc ) with larger scale prototypes. it encompasses major detector components : the vertex detector, the tracker and the calorimeters. we describe here the status and plans of the project with emphasis on issues related to data acquisition for future test beam experiments. | arxiv:physics/0608090 |
left ( ^ { a, \ frac { b } { 4 }, \ frac { b + 1 } { 4 }, \ frac { b + 2 } { 4 }, \ frac { b + 3 } { 4 } } _ { \ frac { c } { 4 }, \ frac { c + 1 } { 4 }, \ frac { c + 2 } { 4 }, \ frac { c + 3 } { 4 } } ; z \ right ) $ is in the each of the classes $ \ mathcal { s } ^ { * } _ { \ lambda } $, $ \ mathcal { c } _ { \ lambda } $, $ ucv $ and $ \ mathcal { s } _ p $. subsequently, conditions on $ a, \, b, \, c, \, \ lambda, $ and $ \ beta $ are determined using the integral operator such that functions belonging to $ \ mathcal { r } ( \ beta ) $ and $ \ mathcal { s } $ are mapped onto each of the classes $ \ mathcal { s } ^ * _ \ lambda $, $ \ mathcal { c } _ { \ lambda } $, $ ucv $, and $ \ mathcal { s } _ p $. | arxiv:2211.04950 |
we analytically identify sufficient conditions for manifesting thermal rectification in two - terminal hybrid structures within the quantum master equation formalism. we recognize two classes of rectifiers. in type a rectifiers the contacts are dissimilar. in type b rectifiers the contacts are equivalent, but the system and baths have different particle statistics, and the system is ( parametrically ) asymmetrically coupled to the baths. our study applies to various hybrid junctions including metals, dielectrics, and spins. | arxiv:0810.4347 |
we know extensions of first order logic by quantifiers of the kind " there are uncountable many... ", " most... " with new axioms and appropriate semantics. related are operations such as " set of x, such that... ", hilbert ' s $ \ epsilon $ - operator, churche ' s $ \ lambda $ - notation, minimization and similar ones, which also bind a variable within some expression, the meaning of which is however partly defined by a translation into the language of first order logic. in this paper a generalization is presented that comprises arbitrary variable - binding symbols as non - logical operations. the axiomatic extension is determined by new equality - axioms ; models assign functionals to variable - binding symbols. the completeness of this system of the so called " functional logic of 1st order " will be proved. | arxiv:math/9503206 |
topological insulators ( tis ) exhibit exciting optical properties, which opens up a new pathway to generate ultrashort pulses from fiber lasers. layered tis display distinct saturable absorption property due to excited state absorption, as compared to their bulk structures. moreover, the electronic structures of the films of tis depend on the thickness of the films due to the quantum confinement of the electrons. by virtue of this, the nanoparticles of tis play a key role in all - fiber modelocked laser. by tweaking the crystal structures of tis, it is possible to generate ultrashort pulses across the visible, near - infrared and mid - infrared wavelengths. starting from the crystal structures and density of states calculations, how different topological insulators can be fabricated and integrated as an efficient passive saturable absorber in all - fiber modelocked lasers with the capability of producing fundamental to high - harmonic pulse generation are described clearly in this review report. moreover, this report reviews the current state - of - art of ti - based saturable absorbers and their applications in different regimes of modelocked fiber lasers. | arxiv:2105.09195 |
the recently proposed hard - pion chiral perturbation theory predicts that the leading chiral logarithms factorize with respect to the energy dependence in the chiral limit. this claim has been successfully tested in the pion form factors up to two loops in chiral perturbation theory. in the present paper we explain this factorization property at two loops and even show that it is valid to all orders for a subclass of diagrams. we also demonstrate that factorization is violated starting at three loops. | arxiv:1208.0498 |
we determined perturbatively the low - energy universal thermodynamics of dilute one - dimensional bosons with the three - body repulsive forces. the final results are presented for the limit of vanishing potential range in terms of three - particle scattering length. an analogue of tan ` s energy theorem for considered system is derived in generic case without assuming weakness of the interparticle interaction. we also obtained an exact identity relating the three - body contact to the energy density. | arxiv:1807.07106 |
public attention towards explainability of artificial intelligence ( ai ) systems has been rising in recent years to offer methodologies for human oversight. this has translated into the proliferation of research outputs, such as from explainable ai, to enhance transparency and control for system debugging and monitoring, and intelligibility of system process and output for user services. yet, such outputs are difficult to adopt on a practical level due to a lack of a common regulatory baseline, and the contextual nature of explanations. governmental policies are now attempting to tackle such exigence, however it remains unclear to what extent published communications, regulations, and standards adopt an informed perspective to support research, industry, and civil interests. in this study, we perform the first thematic and gap analysis of this plethora of policies and standards on explainability in the eu, us, and uk. through a rigorous survey of policy documents, we first contribute an overview of governmental regulatory trajectories within ai explainability and its sociotechnical impacts. we find that policies are often informed by coarse notions and requirements for explanations. this might be due to the willingness to conciliate explanations foremost as a risk management tool for ai oversight, but also due to the lack of a consensus on what constitutes a valid algorithmic explanation, and how feasible the implementation and deployment of such explanations are across stakeholders of an organization. informed by ai explainability research, we conduct a gap analysis of existing policies, leading us to formulate a set of recommendations on how to address explainability in regulations for ai systems, especially discussing the definition, feasibility, and usability of explanations, as well as allocating accountability to explanation providers. | arxiv:2304.11218 |
the quantum chemical version of the density matrix renormalization group ( dmrg ) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. in this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which dmrg is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection ( ac ) technique, which requires only up to two - body active space reduced density matrices. we report encouraging results of this approach on typical candidates for dmrg computations, namely the $ n $ - acenes ( $ n = 2 \ rightarrow 7 $ ), fe ( ii ) - porphyrin, and fe $ _ 3 $ s $ _ 4 $ cluster. | arxiv:2108.12803 |
we have studied the effect of local coulomb interactions on the electronic structure of the molecular magnet mn12 - acetate within the lda + u approach. the account of the on - site repulsion results in a finite energy gap and an integer value of the molecule ' s magnetic moment, both quantities being in a good agreement with the experimental results. the resulting magnetic moments and charge states of non - equivalent manganese ions agree very well with experiments. the calculated values of the intramolecular exchange parameters depend on the molecule ' s spin configuration, differing by 25 - 30 % between the ferrimagnetic ground state and the completely ferromagnetic configurations. the values of the ground - state exchange coupling parameters are in reasonable agreement with the recent data on the magnetization jumps in megagauss magnetic fields. simple estimates show that the obtained exchange parameters can be applied, at least qualitatively, to the description of the spin excitations in mn12 - acetate. | arxiv:cond-mat/0110488 |
we present hydrodynamical simulations of the formation, structure and evolution of photoionized columns, with parameters based on those observed in the eagle nebula. on the basis of these simulations we argue that there is no unequivocal evidence that the dense neutral clumps at heads of the columns were cores in the pre - existing molecular cloud. in our simulations, a variety of initial conditions leads to the formation and maintenance of near - equilibrium columns. therefore, it is likely that narrow columns will often occur in regions with large - scale inhomogeneities, but that observations of such columns can tell us little about the processes by which they formed. the manner in which the columns in our simulations develop suggests that their evolution may result in extended sequences of radiation - induced star formation. | arxiv:astro-ph/0107272 |
the universe is filled with a diffuse background of mev gamma - rays and pev neutrinos, whose origins are unknown. here, we propose a scenario that can account for both backgrounds simultaneously. low - luminosity active galactic nuclei have hot accretion flows where thermal electrons naturally emit soft gamma rays via comptonization of their synchrotron photons. protons there can be accelerated via turbulence or reconnection, producing high - energy neutrinos via hadronic interactions. we demonstrate that our model can reproduce the gamma - ray and neutrino data. combined with a contribution by hot coronae in luminous active galactic nuclei, these accretion flows can explain the kev - - mev photon and tev - - pev neutrino backgrounds. this scenario can account for the mev background without non - thermal electrons, suggesting a higher transition energy from the thermal to non - thermal universe than expected. our model is consistent with x - ray data of nearby objects, and testable by future mev gamma - ray and high - energy neutrino detectors. | arxiv:2005.01934 |
we describe a study in which introductory physics students engage in reflection with peers about problem solving. the recitations for an introductory physics course with 200 students were broken into the " peer reflection " ( pr ) group and the traditional group. each week in recitation, students in the pr group reflected in small teams on selected problems from the homework and discussed why solutions of some students employed better problem solving strategies than others. the graduate and undergraduate teaching assistants ( tas ) in the pr group recitations provided guidance and coaching to help students learn effective problem solving heuristics. in the recitations for the traditional group, students had the opportunity to ask the graduate ta questions about the homework before they took a weekly quiz. the traditional group recitation quiz questions were similar to the homework questions selected for " peer reflection " in the pr group recitations. as one measure of the impact of this intervention, we investigated how likely students were to draw diagrams to help with problem solving. on the final exam with only multiple - choice questions, the pr group drew diagrams on more problems than the traditional group, even when there was no external reward for doing so. since there was no partial credit for drawing the diagrams on the scratch books, students did not draw diagrams simply to get credit for the effort shown and must value the use of diagrams for solving problems if they drew them. we also find that, regardless of whether the students belonged to the traditional or pr groups, those who drew more diagrams for the multiple - choice questions outperformed those who did not draw them. | arxiv:1602.05628 |
ch $ _ { 3 } $ oh peak by a factor of $ \ sim 19 $ in oph - emb9, while the difference in this column density ratio between these two positions is a factor of $ \ sim2. 6 $ in oph - emb5. these differences are attributed to the efficiency of the photon - dominated region ( pdr ) chemistry in oph - emb9. the higher dco $ ^ { + } $ column density and the detection of dcn in oph - emb9 are also discussed in the context of uv irradiation flux. | arxiv:2108.10993 |
the ground state of alkali metals when the particle size decreases from bulk to nanometric atomic clusters is inevitably accompanied by quantum effects that can suppress their pristine metallic state. we demonstrate that the metallic nature of rubidium clusters confined and arrayed in the framework of insulating low - silica x zeolite is preserved. the $ ^ { 87 } $ rb nmr spin - lattice relaxation assigned to rubidium clusters in supercages shows a korringa behavior from 190 ~ k down to 10 ~ k, which is compatible with a macroscopic observation of low electrical resistivity. the density of states at the fermi level is found to be enhanced compared to the analogous sodium case, consistent with a holstein - hubbard model of alkali - loaded zeolites. | arxiv:1912.01913 |
we review several algebraic, combinatorial and geometric interpretations of motivic donaldson - thomas invariants of symmetric quivers. | arxiv:2410.03219 |
we discuss the origin of the finite size error of the energy in many - body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. the correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. results are presented for the electron gas and silicon. | arxiv:cond-mat/0605004 |
we call a semigroup $ s $ f - noetherian if every right congruence of finite index on $ s $ is finitely generated. we prove that every finitely generated semigroup is f - noetherian, and investigate whether the properties of being f - noetherian and being finitely generated coincide for various semigroup classes. | arxiv:2002.04910 |
nonparametric two - stage procedures to construct fixed - width confidence intervals are studied to quantify uncertainty. it is shown that the validity of the random central limit theorem ( rclt ) accompanied by a consistent and asymptotically unbiased estimator of the asymptotic variance already guarantees consistency and first as well as second order efficiency of the two - stage procedures. this holds under the common asymptotics where the length of the confidence interval tends to $ 0 $ as well as under the novel proposed high - confident asymptotics where the confidence level tends to $ 1 $. the approach is motivated by and applicable to data analysis from distributed big data with non - negligible costs of data queries. the following problems are discussed : fixed - width intervals for a the mean, for a projection when observing high - dimensional data and for the common mean when using nonlinear common mean estimators under order constraints. the procedures are investigated by simulations and illustrated by a real data analysis. | arxiv:1910.02829 |
we report the discovery of the first hot subdwarf b ( sdb ) star with a massive compact companion in a wide ( $ p = 892. 5 \ pm60. 2 \, { \ rm d } $ ) binary system. it was discovered based on an astrometric binary solution provided by the gaia mission data release 3. we performed detailed analyses of the spectral energy distribution ( sed ) as well as spectroscopic follow - up observations and confirm the nature of the visible component as a sdb star. the companion is invisible despite of its high mass of $ m _ { \ rm comp } = 1. 50 _ { - 0. 45 } ^ { + 0. 37 } \, m _ { \ rm \ odot } $. a main sequence star of this mass would significantly contribute to the sed and can be excluded. the companion must be a compact object, either a massive white dwarf or a neutron star. stable roche lobe overflow to the companion likely led to the stripping of a red giant and the formation of the sdb, the hot and exposed helium core of the giant. based on very preliminary data, we estimate that $ \ sim9 \ % $ of the sdbs might be formed through this new channel. this binary might also be the prototype for a new progenitor class of supernovae type ia, which has been predicted by theory. | arxiv:2305.03475 |
advances in understanding of the white light faculae measured at the royal greenwich observatory from 1874 to 1976 suggest that they offer a more direct measure of solar brightening by small diameter photospheric magnetic flux tubes than do chromospheric proxies. proxies such as the area of ca k plages, the mg index or the microwave flux include many dark photospheric structures as well as pores and sunspots. our reconstruction of variation in total solar irradiance, tsi, based on the faculae indicates that the sun dimmed by almost 0. 1 percent in the mid - twentieth century rather than brightening as represented in previous reconstructions. this dimmimg at the sun ' s highest activity level since the seventeenth century is consistent with the photometric behavior observed in somewhat younger sun like stars. the prolonged tsi decrease may have contributed more to the cooling of climate between about 1940 and 1970 than present models indicate. | arxiv:1505.01040 |
the machinery of braided geometry introduced previously is used now to construct the $ \ epsilon $ ` totally antisymmetric tensor ' on a general braided vector space determined by r - matrices. this includes natural $ q $ - euclidean and $ q $ - minkowski spaces. the formalism is completely covariant under the corresponding quantum group such as $ \ widetilde { so _ q ( 4 ) } $ or $ \ widetilde { so _ q ( 1, 3 ) } $. the hodge $ * $ operator and differentials are also constructed in this approach. | arxiv:hep-th/9406157 |
we present a semi - analytical approach to the interaction of two ( originally ) kerr black holes through a head - on collision process. an expression for the rate of emission of gravitational radiation is derived from an exact solution to the einstein ' s field equations. the total amount of gravitational radiation emitted in the process is calculated and compared to current numerical investigations. we find that the spin - spin interaction increases the emission of gravitational wave energy up to 0. 2 % of the total rest mass. we discuss also the possibility of spin - exchange between the holes. | arxiv:gr-qc/9711005 |
thin pbte films ( thickness 500 - 600 angstrom ), deposited on srtio3, have been investigated by electric field effect ( efe ). the high resistivity of such thin films warrants a high sensitivity of the efe method. the srtio3 substrate serves as the dielectric layer in the gate - dielectric - pbte structure. due to the large dielectric constant of srtio3, particularly at low temperatures, the electric displacement d in the film reaches the high value of about 10 ^ 8 v / cm, and the efe introduced charge into the pbte film amounts to ~ 8 microc / cm2. the high d permits to measure the efe resistance and hall constant over a wide region of d, revealing the characteristic features of their d - dependence. an appropriate theoretical model has been formulated, showing that, for such films, one can measure the dependence of the fermi level on d. in fact, we demonstrate that shifting the fermi level across the gap by varying d, the density - of - states of the in - gape states can be mapped out. our results show, that the pbte layers studied, possess a mobility gap exceeding the gap of bulk pbte. | arxiv:cond-mat/0610107 |
current approaches to designing energy - efficient applications typically rely on measuring individual components using readily available local metrics, like cpu utilization. however, these metrics fall short when applied to cloud - native applications, which operate within the multi - tenant, shared environments of distributed cloud providers. assessing and optimizing the energy efficiency of cloud - native applications requires consideration of the complex, layered nature of modern cloud stacks. to address this need, we present a comprehensive, automated, and extensible experimentation framework that enables developers to measure energy efficiency across all relevant layers of a cloud - based application and evaluate associated quality trade - offs. our framework integrates a suite of service quality and sustainability metrics, providing compatibility with any kubernetes - based application. we demonstrate the feasibility and effectiveness of this approach through initial experimental results, comparing architectural design alternatives for a widely used open - source cloud - native application. | arxiv:2503.08641 |
in the online metric bipartite matching problem, we are given a set $ s $ of server locations in a metric space. requests arrive one at a time, and on its arrival, we need to immediately and irrevocably match it to a server at a cost which is equal to the distance between these locations. a $ \ alpha $ - competitive algorithm will assign requests to servers so that the total cost is at most $ \ alpha $ times the cost of $ m _ { opt } $ where $ m _ { opt } $ is the minimum cost matching between $ s $ and $ r $. we consider this problem in the adversarial model for the case where $ s $ and $ r $ are points on a line and $ | s | = | r | = n $. we improve the analysis of the deterministic robust matching algorithm ( rm - algorithm, nayyar and raghvendra focs ' 17 ) from $ o ( \ log ^ 2 n ) $ to an optimal $ \ theta ( \ log n ) $. previously, only a randomized algorithm under a weaker oblivious adversary achieved a competitive ratio of $ o ( \ log n ) $ ( gupta and lewi, icalp ' 12 ). the well - known work function algorithm ( wfa ) has a competitive ratio of $ o ( n ) $ and $ \ omega ( \ log n ) $ for this problem. therefore, wfa cannot achieve an asymptotically better competitive ratio than the rm - algorithm. | arxiv:1803.07206 |
amphibious ground - aerial vehicles fuse flying and driving modes to enable more flexible air - land mobility and have received growing attention recently. by analyzing the existing amphibious vehicles, we highlight the autonomous fly - driving functionality for the effective uses of amphibious vehicles in complex three - dimensional urban transportation systems. we review and summarize the key enabling technologies for intelligent flying - driving in existing amphibious vehicle designs, identify major technological barriers and propose potential solutions for future research and innovation. this paper aims to serve as a guide for research and development of intelligent amphibious vehicles for urban transportation toward the future. | arxiv:2207.11384 |
based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. the simplest, memoryless model of a deterministic learning rule obeying the axioms is constructed, and shown to be equivalent to the logistic map. the system ' s performance is analysed in an environment in which it is subject to external randomness, weighing learning defectiveness against stability gained. the corresponding random dynamical system with inhomogeneous, additive noise is studied, and shown to exhibit the phenomena of noise induced stability and stochastic bifurcations. the overall results allow for the interpretation that prejudice in uncertain environments entails a considerable portion of stubbornness as a secondary phenomenon. | arxiv:nlin/0306055 |
we consider two $ c _ 0 $ - semigroups on function spaces or, more generally, banach lattices and give necessary and sufficient conditions for the orbits of the first semigroup to dominate the orbits of the second semigroup for large times. as an important special case we consider an $ l ^ 2 $ - space and self - adjoint operators $ a $ and $ b $ which generate $ c _ 0 $ - semigroups ; in this situation we give criteria for the existence of a time $ t _ 1 \ ge 0 $ such that $ e ^ { tb } \ ge e ^ { ta } $ for all subsequent times $ t \ ge t _ 1 $. as a consequence of our abstract theory, we obtain many surprising insights into the behaviour of various second and fourth order differential operators. | arxiv:1912.13057 |
transformer - based models have demonstrated considerable potential for source code modeling tasks in software engineering. however, they are limited by their dependence solely on automatic self - attention weight learning mechanisms. previous studies have shown that these models overemphasize delimiters added by tokenizers ( e. g.,, ), which may lead to overlooking essential information in the original input source code. to address this challenge, we introduce syntaguid, a novel approach that utilizes the observation that attention weights tend to be biased towards specific source code syntax tokens and abstract syntax tree ( ast ) elements in fine - tuned language models when they make correct predictions. syntaguid facilitates the guidance of attention - weight learning, leading to improved model performance on various software engineering tasks. we evaluate the effectiveness of syntaguid on multiple tasks and demonstrate that it outperforms existing state - of - the - art models in overall performance without requiring additional data. experimental result shows that syntaguid can improve overall performance up to 3. 25 % and fix up to 28. 3 % wrong predictions. our work represents the first attempt to guide the attention of transformer - based models towards critical source code tokens during fine - tuning, highlighting the potential for enhancing transformer - based models in software engineering. | arxiv:2402.16790 |
the local enhancement of antiferromagnetic correlations near vacancies observed in a variety of spin systems is analyzed in a single framework. variational calculations suggest that the resonating - valence - bond character of the spin correlations at short distances is responsible for the enhancement. numerical results for uniform spin chains, with and without frustration, dimerized chains, ladders, and two dimensional clusters are in agreement with our conjecture. this short distance phenomenon occurs independently of the long distance behavior of the spin correlations in the undoped system. experimental predictions for a variety of compounds are briefly discussed. | arxiv:cond-mat/9704185 |
the two - point correlation function is computed for galaxies and groups of galaxies selected using 3 - dimensional information from the updated zwicky galaxy catalog - ( uzc ). the redshift space distortion of the correlation function $ \ xi ( \ sigma, \ pi ) $ in the directions parallel and perpendicular to the line of sight, induced by pairwise group peculiar velocities is evaluated. two methods are used to characterize the pairwise velocity field of groups and galaxies. the best fitting parameters are $ \ gamma = - 1. 89 \ pm 0. 17 $ and $ r _ 0 = 9. 7 \ pm 4. 5 $ $ h ^ { - 1 } $ mpc for groups, and $ \ gamma = - 2. 00 \ pm 0. 03 $ and $ r _ 0 = 5. 29 \ pm 0. 21 $ $ h ^ { - 1 } $ mpc for galaxies. we find $ \ beta _ { gx } = 0. 51 \ pm 0. 15 $ for galaxies, while for groups we obtain a noisy estimate $ \ beta < 1. 5 $. | arxiv:astro-ph/0102372 |
large language models achieve high performance on many but not all downstream tasks. the interaction between pretraining data and task data is commonly assumed to determine this variance : a task with data that is more similar to a model ' s pretraining data is assumed to be easier for that model. we test whether distributional and example - specific similarity measures ( embedding -, token - and model - based ) correlate with language model performance through a large - scale comparison of the pile and c4 pretraining datasets with downstream benchmarks. similarity correlates with performance for multilingual datasets, but in other benchmarks, we surprisingly find that similarity metrics are not correlated with accuracy or even each other. this suggests that the relationship between pretraining data and downstream tasks is more complex than often assumed. | arxiv:2311.09006 |
we prove asymptotic stability of shear flows close to the planar couette flow in the 2d inviscid euler equations on $ \ torus \ times \ real $. that is, given an initial perturbation of the couette flow small in a suitable regularity class, specifically gevrey space of class smaller than 2, the velocity converges strongly in l ^ 2 to a shear flow which is also close to the couette flow. the vorticity is asymptotically driven to small scales by a linear evolution and weakly converges as $ t \ rightarrow \ pm \ infty $. the strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with landau damping in the vlasov equations. this convergence was formally derived at the linear level by kelvin in 1887 and it occurs at an algebraic rate first computed by orr in 1907 ; our work appears to be the first rigorous confirmation of this behavior on the nonlinear level. | arxiv:1306.5028 |
we introduce a machine learning approach to determine the transition dynamics of silicon atoms on a single layer of carbon atoms, when stimulated by the electron beam of a scanning transmission electron microscope ( stem ). our method is data - centric, leveraging data collected on a stem. the data samples are processed and filtered to produce symbolic representations, which we use to train a neural network to predict transition probabilities. these learned transition dynamics are then leveraged to guide a single silicon atom throughout the lattice to pre - determined target destinations. we present empirical analyses that demonstrate the efficacy and generality of our approach. | arxiv:2311.17894 |
the complexified gauging of the de sitter group gives a unified theory for the electroweak and gravitational interactions. the standard spectrum for the electroweak gauge bosons is recovered with the correct mass assignments, following a spontaneous breaking of the gauge symmetry imposed by the geometry. there is no conventional higgs sector. new physics is predicted with gravity - induced electroweak processes ( at the electroweak and at an intermediate scale of about $ 10 ^ { 10 } gev $ ) as well as with novel - type of effects ( such as gravitational aharonov - bohm and violations of the principle of equivalence to 1 part in $ 10 ^ { 17 } $ ). the new theoretical perspectives emerging from this geometric unification are briefly discussed. | arxiv:hep-th/9605217 |
in this note, we present an existence result of a nash equilibrium between electricity producers selling their production on an electricity market and buying co2 emission allowances on an auction carbon market. the producers ' strategies integrate the coupling of the two markets via the cost functions of the electricity production. we set out a clear nash equilibrium that can be used to compute equilibrium prices on both markets as well as the related electricity produced and co2 emissions covered. | arxiv:1311.1535 |
to illustrate the conceptual problems for the low - energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, galileo symmetries are investigated in the polymer particle representation of a non - relativistic particle as a simple toy model. the complete galileo transformations ( translation, rotation and galileo boost ) are naturally defined in the polymer particle hilbert space and galileo symmetries are recovered with highly suppressed deviations in the low - energy regime from the underlying polymer particle description. | arxiv:gr-qc/0612155 |
as we increase the number of personal computing devices that we carry ( mobile devices, tablets, e - readers, and laptops ) and these come equipped with increasing resources, there is a vast potential computation power that can be utilized from those devices. edge computing promises to exploit these underlying computation resources closer to users to help run latency - sensitive applications such as augmented reality and video analytics. however, one key missing piece has been how to incorporate personally owned unmanaged devices into a usable edge computing system. the primary challenges arise due to the heterogeneity, lack of interference management, and unpredictable availability of such devices. in this paper we propose an orchestration framework ibdash, which orchestrates application tasks on an edge system that comprises a mix of commercial and personal edge devices. ibdash targets reducing both end - to - end latency of execution and probability of failure for applications that have dependency among tasks, captured by directed acyclic graphs ( dags ). ibdash takes memory constraints of each edge device and network bandwidth into consideration. to assess the effectiveness of ibdash, we run real application tasks on real edge devices with widely varying capabilities. we feed these measurements into a simulator that runs ibdash at scale. compared to three state - of - the - art edge orchestration schemes, lavea, petrel, and lats, and two intuitive baselines, ibdash reduces the end - to - end latency and probability of failure, by 14 % and 41 % on average respectively. the main takeaway from our work is that it is feasible to combine personal and commercial devices into a usable edge computing platform, one that delivers low latency and predictable and high availability. | arxiv:2301.09278 |
we calculate exactly the two point mass - mass correlations in arbitrary spatial dimensions in the aggregation model of takayasu. in this model, masses diffuse on a lattice, coalesce upon contact and adsorb unit mass from outside at a constant rate. our exact calculation of the variance of mass at a given site proves explicitly, without making any assumption of scaling, that the upper critical dimension of the model is 2. we also extend our method to calculate the spatio - temporal correlations in a generalized class of models with aggregation, fragmentation and injection which include, in particular, the $ q $ - model of force fluctuations in bead packs. we present explicit expressions for the spatio - temporal force - force correlation function in the $ q $ - model. these can be used to test the applicability of the $ q $ - model in experiments. | arxiv:cond-mat/0004442 |
we consider the statistical properties of eigenstates of the time - evolution operator in chaotic many - body quantum systems. our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterise entanglement dynamics and operator spreading. in order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider floquet systems in which there are no conserved densities. the correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis ( eth ). in particular, eth provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations amongst sets of four or more eigenstates. we establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies. we also propose a maximum - entropy ansatz for the joint distribution of a small number $ n $ of eigenstates. in the case $ n = 2 $ this ansatz reproduces eth. for $ n = 4 $ it captures both the growth with time of entanglement between subsystems, as characterised by the purity of the time - evolution operator, and also operator spreading, as characterised by the behaviour of the out - of - time - order correlator. we test these ideas by comparing results from monte carlo sampling of our ansatz with exact diagonalisation studies of floquet quantum circuits. | arxiv:2309.12982 |
we analyze the peculiar case where the free carrier absorption arising from lo phonon absorption - assisted transitions becomes negative and therefore turns into a gain source for quantum cascade lasers. such an additional source of gain exists when the ratio between the electronic and the lattice temperatures is larger than one, a condition that is usually fulfilled in quantum cascade lasers. we find a gain of few cm $ ^ { - 1 } $ ' s at 200k. we report the development of a terahertz quantum cascade laser operating in the negative free carrier absorption regime. | arxiv:1611.09269 |
we derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [ driscoll et al. nature physics, 2016 ]. our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamics interactions, and reproduces the lengthscale selection observed in large scale particle simulations and in experiments. by adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations and qualitative agreement with experimental measurements. our linear stability analysis indicate that this instability is caused by the combination of the advective and transverse flows generated by the microrollers near a no - slip surface. our simple model offers an interesting formalism to characterize other hydrodynamic instabilities that have not been yet well understood, such as size scale selection in suspensions of particles sedimenting adjacent to a wall, or the recently observed formations of traveling phonons in systems of confined driven particles. | arxiv:1706.07330 |
we show that assuming a conjecture in non - archimedean geometry, then a metric formulation of the syz conjecture can be proved in large generality. | arxiv:2007.01384 |
many simulations of relativistic heavy ion collisions involve the switching from relativistic hydrodynamics to kinetic particle transport. this switching entails the sampling of particles from the distribution of energy, momentum and conserved currents provided by hydrodynamics. usually this sampling ensures the conservation of these quantities only on the average, i. e. the conserved quantities may actually fluctuate among the sampled particle configurations and only their averages over many such configurations agree with their values from hydrodynamics. here we apply a recently invented method [ oliinychenko, koch ; prl 123, 18, 182302 ( 2019 ) ] to ensure conservation laws for each sampled configuration in spatially compact regions ( patches ) and study their effects : from the well - known ( micro - ) canonical suppression of means and variances to little studied ( micro - ) canonical correlations and higher order fluctuations. most of these effects are sensitive to the patch size. many of them do not disappear even in the thermodynamic limit, when the patch size goes to infinity. the developed method is essential for particlization of stochastic hydrodynamics. it is useful for studying the chiral magnetic effect, small systems, and in general for fluctuation and correlation observables. | arxiv:2001.08176 |
in this paper, we consider a six parameter family of affine segre surfaces embedded in $ \ mathbb c ^ 6 $. for generic values of the parameters, this family is associated to the $ q $ - difference sixth painlev \ ' e equation. we show that different limiting forms of this family give segre surfaces that are isomorphic as affine varieties to the the monodromy manifolds of each painlev \ ' e differential equation. | arxiv:2405.10541 |
in this paper, we study a birth and death process $ \ { n _ t \ } _ { t \ ge0 } $ on positive half lattice, which at each discontinuity jumps at most a distance $ r \ ge 1 $ to the right or exactly a distance $ 1 $ to the left. the transitional probabilities at each site are nonhomogeneous. firstly, sufficient conditions for the recurrence and positive recurrence are presented. then by the branching structure within random walk with one - side bounded jumps set up in hong and wang ( 2013 ), the explicit form of the stationary distribution of the process $ \ { n _ t \ } _ { t \ ge0 } $ is formulated. | arxiv:1407.4007 |
in this paper, we first provide an explicit description of { \ it all } holomorphic discs ( ` ` disc instantons ' ' ) attached to lagrangian torus fibers of arbitrary compact toric manifolds, and prove their fredholm regularity. using this, we compute fukaya - oh - ohta - ono ' s ( fooo ' s ) obstruction ( co ) chains and the floer cohomology of lagrangian torus fibers of fano toric manifolds. in particular specializing to the formal parameter $ t ^ { 2 \ pi } = e ^ { - 1 } $, our computation verifies the folklore that fooo ' s obstruction ( co ) chains correspond to the landau - ginzburg superpotentials under the mirror symmetry correspondence, and also proves the prediction made by k. hori about the floer cohomology of lagrangian torus fibers of fano toric manifolds. the latter states that the floer cohomology ( for the parameter value $ t ^ { 2 \ pi } = e ^ { - 1 } $ ) of all the fibers vanish except at a finite number, the euler characteristic of the toric manifold, of base points in the momentum polytope that are critical points of the superpotential of the landau - ginzburg mirror to the toric manifold. in the latter cases, we also prove that the floer cohomology of the corresponding fiber is isomorphic to its singular cohomology. we also introduce a restricted version of the floer cohomology of lagrangian submanifolds, which is a priori more flexible to define in general, and which we call the { \ it adapted floer cohomology }. we then prove that the adapted floer cohomology of any non - singular torus fiber of fano toric manifolds is well - defined, invariant under the hamiltonian isotopy and isomorphic to the bott - morse floer cohomology of the fiber. | arxiv:math/0308225 |
the notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many - body background. we discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. in particular, we exemplify the modifications of the medium in the presence of either fermi or bose polarons. regarding fermi polarons we present a corresponding many - body diagrammatic approach operating at finite temperatures and discuss how mediated two - and three - body interactions are implemented within this framework. utilizing this approach, we analyze the behavior of the spectral function of fermi polarons at finite temperature by varying impurity - medium interactions as well as spatial dimensions from three to one. interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition / crossover from attractive polarons to molecules in three - dimensions. as for the bose polaron, we showcase the depletion of the background bose - einstein condensate in the vicinity of the impurity atom. such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in bose polaron problems. | arxiv:2101.07643 |
the purpose of this paper is to introduce and study new extension of rako \ v { c } evi \ ' { c } ' s property $ ( w ) $ and property $ ( b ) $ introduced by berkani - - zariouh in \ cite { berkani - zariouh1 }, in connection with other weyl type theorems and recent properties. we prove in particular, the two following results : 1. a bounded linear operator $ t $ satisfies property $ ( w _ { \ pi _ { 00 } } ) $ if and only if $ t $ satisfies property $ ( w ) $ and $ \ sigma _ { uf } ( t ) = \ sigma _ { uw } ( t ). $ 2. $ t $ satisfies property $ ( gw _ { \ pi _ { 00 } } ) $ if and only if $ t $ satisfies property $ ( w _ { \ pi _ { 00 } } ) $ and $ \ pi _ { 0 } ( t ) = p _ { 0 } ^ a ( t ). $ classes of operators are considered as illustrating examples. | arxiv:2007.11710 |
a compilation of new results on the asymptotic behaviour of the humbert functions $ \ psi _ 1 $ and $ \ psi _ 2 $, and also on the appell function $ f _ 2 $, is presented. as a by - product, we confirm a conjectured limit which appeared recently in the study of the $ 1d $ glauber - ising model. we also propose two elementary asymptotic methods and confirm through some illustrative examples that both methods have great potential and can be applied to a large class of problems of asymptotic analysis. finally, some directions of future research are pointed out in order to suggest ideas for further study. | arxiv:2501.07281 |
during the past two decades, chiral effective field theory has evolved into a powerful tool to derive nuclear forces from first principles. nearly all two - nucleon interactions have been worked out up to sixth order of chiral perturbation theory, while, with few exceptions, three - nucleon forces, which play a subtle, but crucial role in microscopic nuclear structure calculations, have been derived up to fifth order. we review the current status of these forces as well as their applications in nuclear many - body systems. while the ab initio description of light nuclei is generally very successful, we point out and analyze problems encountered with medium - mass nuclei. we also survey the construction of equations of state for symmetric nuclear matter and neutron - rich matter based on chiral forces. a focal point is the symmetry energy and its impact on neutron skins and systems of astrophysical relevance. the physics of neutron - rich systems, from nuclei to compact stars, is essentially determined by the density dependence of the symmetry energy. we review the status of predictions in comparison with latest empirical constraints, with particular attention to those extracted from parity violating electron scattering. | arxiv:2402.14032 |
starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. the first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects : more precisely, we prove that two symmetric edge polytopes are unimodularly equivalent precisely when they share the same graphical matroid. the second goal is to show that one can construct a generalized symmetric edge polytope starting from every regular matroid. just like in the usual case, we are able to find combinatorial ways to describe the facets and an explicit regular unimodular triangulation of any such polytope. finally, we show that the ehrhart theory of the polar of a given generalized symmetric edge polytope is tightly linked to the structure of the lattice of flows of the dual regular matroid. | arxiv:2307.04933 |
consider a locally compact group $ g $ and a locally compact space $ x $. a local right action of $ g $ on $ x $ is a continuous map $ ( x, p ) \ mapsto x \ cdot p $ from an open subset $ \ gamma $ of the cartesian product $ x \ times g $ to $ x $ satisfying certain obvious properties. a global right action of $ g $ on $ x $ gives rise to a global left action of $ g $ on the space $ c _ c ( x ) $ of continuous complex functions with compact support in $ x $ by the formula $ p \, \ cdot f : x \ mapsto f ( x \ cdot p ) $. in the case of a local action, one still can define $ p \, \ cdot f $ in $ c _ c ( x ) $ by this formula for $ f \ in c _ c ( x ) $ and $ p $ in a neighborhood $ v _ f $ of the identity in $ g $. this yields a local left action of $ g $ on $ c _ c ( x ) $. given a local right action of $ g $ on $ x $, a function $ f \ in c _ c ( x ) $ is called polynomial if there is a neighborhood $ v $ of the identity, contained in $ v _ f $, and a finite - dimensional subspace $ f $ of $ c _ c ( x ) $ containing all the functions $ v \ cdot f $ for $ v \ in v $. in this paper we study such polynomial functions. if $ g $ acts on itself by multiplication, we are also interested in the local actions obtained by restricting it to an open subset of $ g $. this is the typical situation that is encountered in our paper on bicrossproducts of groups with a compact open subgroup. in fact, the need for a better understanding of polynomial functions for that case has led us to develop the theory in general here. | arxiv:2309.08319 |
context. large thermal variations have been observed in neutron stars that typically are not aligned with density gradients. such terms may activate the biermann battery effect, leading to thermoelectric interactions and to the generation of electromotive force. aims. we aim to identify the possible impact of a temperature anisotropy on the crust of a neutron star can have in the evolution of its magnetic field, through the thermoelectric terms. methods. we consider a neutron star crust with large temperature gradients, associated with long - lived hot spots, described by a localized gaussian - type function. we simulate the interplay between the battery term and the hall and ohmic evolution numerically for axisymmetric systems. results. the results indicate that for crust temperatures of $ \ sim $ $ 10 ^ 9 $ k the toroidal field can be amplified up to $ \ sim $ $ 10 ^ { 14 } - 10 ^ { 15 } $ g near the points of maximum temperature gradients, and it locally changes the architecture of the poloidal field lines. for internal crustal temperatures of $ \ sim $ $ 10 ^ 8 $ k, the temperature gradient generates fields that are lower by about two orders of magnitude. in these cases, saturation is achieved after some hundred thousand years, after which the battery and ohmic dissipation balance each other, whereas the hall drift contributes comparatively little to the final field strength, but it can affect its structure. conclusions. we conclude that the thermoelectric effect can impact the overall magnetic field evolution, provided that the thermal gradient is maintained for a sufficiently long time. neutron stars endowned with moderate - strength magnetic fields may be affected by the thermoelectric effect if the hotspots survive for timescales of a few kiloyears. | arxiv:2402.14911 |
the spherical proportional counter is a novel type of radiation detector, with a low energy threshold ( typically below 100 ev ) and good energy resolution. this detector is being developed by the network news, which includes several applications. we can name between many others dark matter searches, low level radon and neutron counting or low energy neutrino detection from supernovas or nuclear reactors via neutrino - nucleus elastic scattering. in this context, this works will present the characterization of a spherical detector of 1 meter diameter using two argon - based mixtures ( with methane and isobutane ) and for gas pressures between 50 and 1250 mbar. in each case, the energy resolution shows its best value in a wide range of gains, limited by the ballistic effect at low gains and by ion - backflow at high gains. moreover, the best energy resolution shows a degradation with pressure. these effects will be discussed in terms of gas avalanche properties. finally, the effect of an electrical field corrector in the homogenity of the gain and the energy threshold measured in our setup will be also discussed. | arxiv:1501.01626 |
we consider the k \ " ahler - ricci flow on a fano manifold. we show that if the curvature remains uniformly bounded along the flow, the mabuchi energy is bounded below, and the manifold is k - polystable, then the manifold admits a k \ " ahler - einstein metric. the main ingredient is a result that says that a sufficiently small perturbation of a csck manifold admits a csck metric if it is k - polystable. | arxiv:0803.1613 |
we study the relationship between microscopic structure and viscosity in non - brownian suspensions. we argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. we show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. in particular, we predict that ( i ) the viscosity { \ eta } diverges with the coordination z as { \ eta } ~ ( z _ c - z ) ^ { - ( 3 + { \ theta } ) / ( 1 + { \ theta } ) }, ( ii ) the operator that governs flow displays a low - frequency mode that controls the divergence of viscosity, at a frequency { \ omega } _ min \ sim ( z _ c - z ) ^ { ( 3 + { \ theta } ) / ( 2 + 2 { \ theta } ) }, and ( iii ) the distribution of forces displays a scale f * that vanishes near jamming as f * / < f > \ sim ( z _ c - z ) ^ { 1 / ( 1 + { \ theta } ) } where { \ theta } characterizes the distribution of contact forces p ( f ) \ simf ^ { \ theta } at jamming, and where z _ c is the maxwell threshold for rigidity. | arxiv:1201.3650 |
it is shown that majorana fermions trapped in three vortices in a p - wave superfluid form a qubit in a topological quantum computing ( tqc ). several similar ideas have already been proposed : ivanov [ phys. rev. lett. { \ bf 86 }, 268 ( 2001 ) ] and zhang { \ it et al. } [ phys. rev. lett. { \ bf 99 }, 220502 ( 2007 ) ] have proposed schemes in which a qubit is implemented with two and four majorana fermions, respectively, where a qubit operation is performed by exchanging the positions of majorana fermions. the set of gates thus obtained is a discrete subset of the relevant unitary group. we propose, in this paper, a new scheme, where three majorana fermions form a qubit. we show that continuous 1 - qubit gate operations are possible by exchanging the positions of majorana fermions complemented with dynamical phase change. 2 - qubit gates are realized through the use of the coupling between majorana fermions of different qubits. | arxiv:0906.4444 |
our theme is that not every interesting question in set theory is independent of $ zfc $. we give an example of a first order theory $ t $ with countable $ d ( t ) $ which cannot have a universal model at $ \ aleph _ 1 $ without ch ; we prove in $ zfc $ a covering theorem from the hypothesis of the existence of a universal model for some theory ; and we prove - - - again in zfc - - - that for a large class of cardinals there is no universal linear order ( e. g. in every $ \ aleph _ 1 < \ l < 2 ^ { \ aleph _ 0 } $ ). in fact, what we show is that if there is a universal linear order at a regular $ \ l $ and its existence is not a result of a trivial cardinal arithmetical reason, then $ \ l $ ` ` resembles ' ' $ \ aleph _ 1 $ - - - a cardinal for which the consistency of having a universal order is known. as for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. as a result of the non existence of a universal linear order, we show the non - existence of universal models for all theories possessing the strict order property ( for example, ordered fields and groups, boolean algebras, p - adic rings and fields, partial orders, models of pa and so on ). | arxiv:math/9209201 |
many recent efforts augment language models with retrieval, by adding retrieved data to the input context. for this approach to succeed, the retrieved data must be added at both training and test time. moreover, as input length grows linearly with the size of retrieved data, cost in computation and memory grows quadratically for modern transformers. to avoid these complications, we simply fine - tune the model on retrieved data at test time, using its standard training setup. we build a large - scale distributed index based on text embeddings of the pile dataset. for each test input, our system retrieves its neighbors and fine - tunes the model on their text. surprisingly, retrieving and training on as few as 20 neighbors, each for only one gradient iteration, drastically improves performance across more than 20 language modeling tasks in the pile. for example, test - time training with nearest neighbors significantly narrows the performance gap between a small gpt - 2 and a gpt - neo model more than 10 times larger. sufficient index quality and size, however, are necessary. our work establishes a first baseline of test - time training for language modeling. | arxiv:2305.18466 |
inspired by recent work of i. baoulina, we give a simultaneous generalization of the theorems of chevalley - warning and morlaye. | arxiv:1707.04391 |
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