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ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong - field quantum electrodynamics. our main focus is on the formation of ionization supercontinua. more specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. these supercontinua extend over hundreds of driving photon energies, thus corresponding to high - order nonlinear processes. the corresponding polar - angle distributions show asymmetries which are attributed to the radiation pressure experienced by photoelectrons. moreover, our time analysis shows that the electrons comprising the supercontinuum can form pulses of short duration. while we present the fully numerical results, their interpretation is based on the saddle - point approximation for the ionization probability amplitude. | arxiv:1508.00546 |
the study of time lags between spikes in gamma - ray burst light curves in different energy bands as a function of redshift may lead to the detection of effects due to quantum gravity. we present an analysis of 15 gamma - ray bursts with measured redshift, detected by the hete - 2 mission in order to measure time lags related to astrophysical effects and search for quantum gravity signature in the framework of an extra - dimension string model. the wavelet transform method is used both for de - noising the light curves and for the detection of sharp transitions. the use of photon tagged data allows us to consider various energy ranges and to evaluate systematic effects due to selections and cuts. the analysis of maxima and minima of the light curves leads to no significant quantum gravity effect. a lower limit at 95 % confidence level on the quantum gravity scale parameter of 2x10 * * 15 gev is set. | arxiv:astro-ph/0603725 |
we present an approach for compressing volumetric scalar fields using implicit neural representations. our approach represents a scalar field as a learned function, wherein a neural network maps a point in the domain to an output scalar value. by setting the number of weights of the neural network to be smaller than the input size, we achieve compressed representations of scalar fields, thus framing compression as a type of function approximation. combined with carefully quantizing network weights, we show that this approach yields highly compact representations that outperform state - of - the - art volume compression approaches. the conceptual simplicity of our approach enables a number of benefits, such as support for time - varying scalar fields, optimizing to preserve spatial gradients, and random - access field evaluation. we study the impact of network design choices on compression performance, highlighting how simple network architectures are effective for a broad range of volumes. | arxiv:2104.04523 |
a finitely generated shift invariant space $ v $ is a closed subspace of $ l ^ 2 ( \ r ^ d ) $ that is generated by the integer translates of a finite number of functions. a set of frame generators for $ v $ is a set of functions whose integer translates form a frame for $ v $. in this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. surprisingly the results are very different to the recently studied case when the property to be a frame is not required. | arxiv:1305.2944 |
given a probability measure on a finitely generated group, its martin boundary is a way to compactify the group using the green function of the corresponding random walk. it is known from the work of w. woess that when a finitely supported random walk on a free product of abelian groups is adapted to the free product structure, the martin boundary coincides with the geometric boundary. the main goal of this paper is to deal with non - adapted finitely supported random walks, for which there is no explicit formula for the green function. nevertheless, we show that the martin boundary still coincides with the geometric boundary. we also prove that the martin boundary is minimal. | arxiv:1709.07738 |
finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems. | arxiv:2008.08141 |
in the manufacturing process of heavy industrial equipment, the specific unit in the welding diagram is first manually redrawn and then the corresponding sheet metal parts are cut, which is inefficient. to this end, this paper proposes a u - net - based method for the segmentation and extraction of specific units in welding engineering drawings. this method enables the cutting device to automatically segment specific graphic units according to visual information and automatically cut out sheet metal parts of corresponding shapes according to the segmentation results. this process is more efficient than traditional human - assisted cutting. two weaknesses in the u - net network will lead to a decrease in segmentation performance : first, the focus on global semantic feature information is weak, and second, there is a large dimensional difference between shallow encoder features and deep decoder features. based on the cbam ( convolutional block attention module ) attention mechanism, this paper proposes a u - net jump structure model with an attention mechanism to improve the network ' s global semantic feature extraction ability. in addition, a u - net attention mechanism model with dual pooling convolution fusion is designed, the deep encoder ' s maximum pooling + convolution features and the shallow encoder ' s average pooling + convolution features are fused vertically to reduce the dimension difference between the shallow encoder and deep decoder. the dual - pool convolutional attention jump structure replaces the traditional u - net jump structure, which can effectively improve the specific unit segmentation performance of the welding engineering drawing. using vgg16 as the backbone network, experiments have verified that the iou, map, and accu of our model in the welding engineering drawing dataset segmentation task are 84. 72 %, 86. 84 %, and 99. 42 %, respectively. | arxiv:2209.14102 |
we introduce a bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27 - qubit superconducting qubit devices. we self - consistently estimate up to seven parameters of each qubit ' s state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. on the investigated devices we find non - negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit ' s excited state. we are able to mitigate such errors by applying pre - rotations on the initialized qubits, which we demonstrate with multi - qubit entangled states. our results demonstrate that bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches. | arxiv:2108.10686 |
motivated by the development and deployment of large - scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. in this work we study controllability in the structural system theoretic sense, structural controllability. in other words, instead of focusing on a specific numerical system realization, we provide guarantees for equivalence classes of linear time - invariant systems on the basis of their structural sparsity patterns, i. e., location of zero / nonzero entries in the plant matrices. to this end, we first propose several necessary and / or sufficient conditions to ensure structural controllability of the overall system, on the basis of the structural patterns of the subsystems and their interconnections. the proposed verification criteria are shown to be efficiently implementable ( i. e., with polynomial time complexity in the number of the state variables and inputs ) in two important subclasses of interconnected dynamical systems : similar ( i. e., every subsystem has the same structure ), and serial ( i. e., every subsystem outputs to at most one other subsystem ). secondly, we provide a distributed algorithm to verify structural controllability for interconnected dynamical systems. the proposed distributed algorithm is efficient and implementable at the subsystem level ; the algorithm is iterative, based on communication among ( physically ) interconnected subsystems, and requires only local model and interconnection knowledge at each subsystem. | arxiv:1506.05770 |
experience using hardware knobs as an operator interface for controlling equipment has varied considerably at different facilities. reactions have ranged from " indispensable " at some facilities, to " virtually useless " at others. in this paper, we will attempt to outline some basic principles for successful knob implementation. these principles derive from our own experience with control knobs at the lansce accelerator complex and our recent effort to adapt our control knobs to epics. topics to be covered include what the operator needs the knob to do, what the knob needs to know about the device it is controlling, and knob scaling issues. advanced topics such as closed - loop, pid, and aggregate knobs are left as topics for future papers. | arxiv:physics/0111082 |
flow cytometry is a widespread and powerful technique, whose resolution is determined by its capacity to accurately distinguish fluorescently positive populations from negative ones. however, most informative results are discarded while performing the measurements of conventional flow cytometry, e. g., the cell size, shape, morphology, and distribution or location of labeled exosomes within the unpurified biological samples. we, herein, propose a novel approach using an anti - diffraction light sheet with anisotroic feature to excite fluorescent tags. constituted by an anti - diffraction bessel - gaussian beam array, the light sheet is 12 $ \ mu $ m wide, 12 $ \ mu $ m high, with a thickness of $ ~ 0. 8 \ mu $ m. the intensity profile of the excited fluorescent signal can, therefore, reflect the size and allow samples in the range from o ( 100 nm ) to 10 $ \ mu $ m ( e. g., blood cells ) to be transported via hydrodynamic focusing in a microfluidic chip. the sampling rate is 500 khz provides a capability of high throughput without sacrificing the spatial resolution. consequently, the proposed anti - diffraction light - sheet flow cytometry ( adlsfc ) can obtain more informative results than the conventional methodologies, and is able to provide multiple characteristics ( e. g., the size and distribution of fluorescent signal ) helping to distinguish the target samples from the complex backgrounds. | arxiv:2301.10185 |
this paper, to appear in the ` ` notices of the ams ' ' 2024, is a modified version of a text already appeared in this journal, feb. 2007 after a first publication in french, in ` ` la gazette des math { \ ' e } maticiens ' ' 97 ( 2003 ) on the occasion of sato ' s reception of the 2002 / 2003 wolf prize. | arxiv:2402.15553 |
we consider the effect of electromagnetic coupling between localized surface plasmons in a metallic nanoparticle ( np ) and excitons or weakly interacting electron - hole pairs in a semiconductor matrix where the np is embedded. an expression is derived for the np polarizability renormalized by this coupling and two possible situations are analyzed, both compatable with the conditions for fano - type resonances : ( i ) a narrow bound exciton transition overlapping with the np surface plasmon resonance ( spr ), and ( ii ) spr overlapping with a parabolic absorption band due to electron - hole transitions in the semiconductor. the absorption band lineshape is strongly non - lorentzian in both cases and similar to the typical fano spectrum in the case ( i ). however, it looks differently in the situation ( ii ) that takes place for gold nps embedded in a cuo film and the use of the renormalized polarizability derived in this work permits to obtain a very good fit to the experimentally measured lspr lineshape. | arxiv:1810.02402 |
it was conjectured by \ v { c } ern \ ' y in 1964, that a synchronizing dfa on $ n $ states always has a shortest synchronizing word of length at most $ ( n - 1 ) ^ 2 $, and he gave a sequence of dfas for which this bound is reached. until now a full analysis of all dfas reaching this bound was only given for $ n \ leq 4 $, and with bounds on the number of symbols for $ n \ leq 10 $. here we give the full analysis for $ n \ leq 6 $, without bounds on the number of symbols. for pfas the bound is much higher. for $ n \ leq 6 $ we do a similar analysis as for dfas and find the maximal shortest synchronizing word lengths, exceeding $ ( n - 1 ) ^ 2 $ for $ n = 4, 5, 6 $. for arbitrary n we give a construction of a pfa on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. we give a transformation of this pfa to a pfa on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation. | arxiv:1703.07618 |
in this note we give the formula for the bellman function associated with the problem considered by b. davis in \ cite { davis } in 1976. in this article the estimates of the type $ \ | sf \ | _ p \ le c _ p \ | f \ | _ p $, $ p \ ge 2 $, were considered for the dyadic square function operator $ s $, and davis found the sharp values of constants $ c _ p $. however, along with the sharp constants one can consider a more subtle characteristic of the above estimate. this quantity is called the bellman function of the problem, and it seems to us that it was never proved that the confluent hypergeometric function from davis ' paper ( second page ) basically gives this bellman function. here we fill out this gap by finding the exact bellman function of the unweighted $ l ^ p $ estimate for operator $ s $. we cast the proofs in the language of obstacle problems. for the sake of comparison, we also find the bellman function of weak $ ( 1, 1 ) $ estimate of $ s $. this formula was suggested by bollobas \ cite { bollobas } and proved by osekowski \ cite { os2009 }, so it is not new, but we like to emphasize the common approach to those two bellman functions descriptions. | arxiv:1809.06469 |
most state - of - the - art point trackers are trained on synthetic data due to the difficulty of annotating real videos for this task. however, this can result in suboptimal performance due to the statistical gap between synthetic and real videos. in order to understand these issues better, we introduce cotracker3, comprising a new tracking model and a new semi - supervised training recipe. this allows real videos without annotations to be used during training by generating pseudo - labels using off - the - shelf teachers. the new model eliminates or simplifies components from previous trackers, resulting in a simpler and often smaller architecture. this training scheme is much simpler than prior work and achieves better results using 1, 000 times less data. we further study the scaling behaviour to understand the impact of using more real unsupervised data in point tracking. the model is available in online and offline variants and reliably tracks visible and occluded points. | arxiv:2410.11831 |
a shift - periodic map is a one - dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. it is shown that iterative sequences $ x _ { n + 1 } = f ( x _ n ) $ generated by such maps display rich dynamical behaviour. the integer parts $ \ lfloor x _ n \ rfloor $ give a discrete - time random walk for a suitable initial distribution of $ x _ 0 $ and converge in certain limits to brownian motion or more general l \ ' evy processes. furthermore, for certain shift - periodic maps with small holes on $ [ 0, 1 ] $, convergence of trajectories to a continuous - time random walk is shown in a limit. | arxiv:1811.03070 |
variational auto - encoders ( vae ) are popular deep latent variable models which are trained by maximizing an evidence lower bound ( elbo ). to obtain tighter elbo and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. however, importance sampling is known to perform poorly in high dimensions. while it has been suggested many times in the literature to use more sophisticated algorithms such as annealed importance sampling ( ais ) and its sequential importance sampling ( sis ) extensions, the potential benefits brought by these advanced techniques have never been realized for vae : the ais estimate cannot be easily differentiated, while sis requires the specification of carefully chosen backward markov kernels. in this paper, we address both issues and demonstrate the performance of the resulting monte carlo vaes on a variety of applications. | arxiv:2106.15921 |
cross - modal hashing aims to map heterogeneous multimedia data into a common hamming space, which can realize fast and flexible retrieval across different modalities. supervised cross - modal hashing methods have achieved considerable progress by incorporating semantic side information. however, they mainly have two limitations : ( 1 ) heavily rely on large - scale labeled cross - modal training data which are labor intensive and hard to obtain. ( 2 ) ignore the rich information contained in the large amount of unlabeled data across different modalities, especially the margin examples that are easily to be incorrectly retrieved, which can help to model the correlations. to address these problems, in this paper we propose a novel semi - supervised cross - modal hashing approach by generative adversarial network ( sch - gan ). we aim to take advantage of gan ' s ability for modeling data distributions to promote cross - modal hashing learning in an adversarial way. the main contributions can be summarized as follows : ( 1 ) we propose a novel generative adversarial network for cross - modal hashing. in our proposed sch - gan, the generative model tries to select margin examples of one modality from unlabeled data when giving a query of another modality. while the discriminative model tries to distinguish the selected examples and true positive examples of the query. these two models play a minimax game so that the generative model can promote the hashing performance of discriminative model. ( 2 ) we propose a reinforcement learning based algorithm to drive the training of proposed sch - gan. the generative model takes the correlation score predicted by discriminative model as a reward, and tries to select the examples close to the margin to promote discriminative model by maximizing the margin between positive and negative data. experiments on 3 widely - used datasets verify the effectiveness of our proposed approach. | arxiv:1802.02488 |
evaluating the quality of generated text automatically remains a significant challenge. conventional reference - based metrics have been shown to exhibit relatively weak correlation with human evaluations. recent research advocates the use of large language models ( llms ) as source - based metrics for natural language generation ( nlg ) assessment. while promising, llm - based metrics, particularly those using smaller models, still fall short in aligning with human judgments. in this work, we introduce contrastscore, a contrastive evaluation metric designed to enable higher - quality, less biased, and more efficient assessment of generated text. we evaluate contrastscore on two nlg tasks : machine translation and summarization. experimental results show that contrastscore consistently achieves stronger correlation with human judgments than both single - model and ensemble - based baselines. notably, contrastscore based on qwen 3b and 0. 5b even outperforms qwen 7b, despite having only half as many parameters, demonstrating its efficiency. furthermore, it effectively mitigates common evaluation biases such as length and likelihood preferences, resulting in more robust automatic evaluation. | arxiv:2504.02106 |
let $ \ mathcal { h } $ be a complex hilbert space and $ t : \ mathcal { h } \ to \ mathcal { h } $ be a contraction. let $ $ a _ nf = \ frac { 1 } { n } \ sum _ { j = 1 } ^ nt ^ jf $ $ for $ f \ in \ mathcal { h } $. let $ ( n _ k ) $ be a sequence satisfying $ \ beta \ geq n _ { k + 1 } / n _ k \ geq \ alpha > 1 $ for all $ k \ geq 1 $, then there exists a constant $ c _ 1 > 0 $ such that $ $ \ sum _ { k = 1 } ^ \ infty \ | a _ { n _ { k + 1 } } f - a _ { n _ k } f \ | _ { \ mathcal { h } } \ leq c _ 1 \ | f \ | _ { \ mathcal { h } } $ $ for all $ f \ in \ mathcal { h } $. let $ ( n _ k ) $ be a sequence satisfying $ \ beta \ geq n _ { k + 1 } / n _ k \ geq \ alpha > 1 $ for all $ k \ geq 1 $, and let $ m $ be any sequence. then there exists a constant $ c _ 2 > 0 $ such that $ $ \ sum _ { k = 1 } ^ \ infty \ sup _ { \ substack { n _ k \ leq m < n _ { k + 1 } \ \ m \ in m } } \ | a _ m ( t ) f - a _ { n _ k } ( t ) f \ | _ { h } \ leq c _ 2 \ | f \ | _ { \ mathcal { h } } $ $ for all $ f \ in \ mathcal { h } $. | arxiv:2107.14030 |
a new generation of sensors, hardware random number generators, and quantum and classical signal detectors are exploiting strong responses to external perturbations of system noise. here, we study noise amplification by asymmetric dyads in freely expanding non - hermitian optical systems. we show that modifications of the pumping strengths can counteract bias from natural imperfections of the system ' s hardware, while couplings between dyads lead to systems with non - uniform statistical distributions. our results suggest that asymmetric non - hermitian dyads are promising candidates for efficient sensors and ultra - fast random number generators. we propose that the integrated light emission from such asymmetric dyads can be efficiently used for analog all - optical degenerative diffusion models of machine learning to overcome the digital limitations of such models in processing speed and energy consumption. | arxiv:2206.12200 |
we develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it has a rich structure that is directly related to phase space structures from dynamical systems theory, such as hyperbolic trajectories and their stable and unstable manifolds. we apply our approach to an ocean data set, as well as standard benchmark models from deterministic dynamical systems theory. a significant application of our results, is that they allow a quantitative comparison of the transport performance described from different ocean data sets. this is particularly interesting nowadays when a wide variety of sources are available, since our methodology provides avenues for assessing the effective use of these data sets in a variety of situations. | arxiv:2103.05439 |
su - schrieffer - heeger ( ssh ) model on two - dimensional square lattice exhibits a topological phase transition, which is related to the zak phase determined by bulk band topology. the strong modulation of electron hopping causes nontrivial charge polarization even in the presence of inversion symmetry. the energy band structures and topological edge states have been calculated numerically in previous studies. here, however, full energy spectrum and explicit form of wave functions for two - dimensional bulk and one - dimensional ribbon geometries of ssh model are analytically derived using wave mechanics approach. explicit analytic representations of wave functions provide the information of parity for each subband, localization length and critical point of topological phase transition in ssh ribbon. it is also shown that the dimensional crossover of topological transition point for ssh model from one to two - dimension. | arxiv:1906.06993 |
given a real projective curve with homogeneous coordinate ring r and a nonnegative homogeneous element f in r, we bound the degree of a nonzero homogeneous sum - of - squares g in r such that the product fg is again a sum of squares. better yet, our degree bounds only depend on geometric invariants of the curve and we show that there exist smooth curves and nonnegative elements for which our bounds are sharp. we deduce the existence of a multiplier g from a new bertini theorem in convex algebraic geometry and prove sharpness by deforming rational harnack curves on toric surfaces. our techniques also yield similar bounds for multipliers on surfaces of minimal degree, generalizing hilbert ' s work on ternary forms. | arxiv:1605.08330 |
we develop an analytic framework for lefschetz fixed point theory and morse theory for hilbert complexes on stratified pseudomanifolds. we develop formulas for both global and local lefschetz numbers and morse, poincar \ ' e polynomials as ( polynomial ) supertraces over cohomology groups of hilbert complexes, developing techniques for relating local and global quantities using heat kernel and witten deformation based methods. we focus on the case where the metric is wedge and the hilbert complex is associated to a dirac - type operator and satisfies the witt condition, constructing lefschetz versions of bismut - cheeger $ \ mathcal { j } $ forms for local lefschetz numbers of dirac operators, with specialized formulas for twisted de rham, dolbeault and spin $ ^ { \ mathbb { c } } $ dirac complexes as supertraces of geometric endomorphisms on cohomology groups of local hilbert complexes. we construct geometric endomorphisms to define de rham lefschetz numbers for some self - maps for which the pullback does not induce a bounded operator on $ l ^ 2 $ forms. a de rham witten instanton complex is constructed for witt spaces with stratified morse functions, proving morse inequalities related to other results in the literature including goresky and macpherson ' s in intersection cohomology. we also prove a lefschetz - morse inequality for geometric endomorphisms on the instanton complex that is new even on smooth manifolds. we derive $ l ^ 2 $ lefschetz - riemann - roch formulas, which we compare and contrast with algebraic versions of baum - fulton - quart. in the complex setting, we derive lefschetz formulas for spin dirac complexes and hirzebruch $ \ chi _ y $ genera which we relate to signature, self - dual and anti - self - dual lefschetz numbers, studying their properties and applications including instanton counting. we compute these invariants in various examples with different features, comparing with versions in other cohomology theories. | arxiv:2309.15845 |
this paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate ornstein - uhlenbeck process. information about the drift is obtained by observing stock returns and expert opinions. the latter provide unbiased estimates on the current state of the drift at discrete points in time. the optimal trading strategy of investors maximizing expected logarithmic utility of terminal wealth depends on the filter which is the conditional expectation of the drift given the available information. we state filtering equations to describe its dynamics for different information settings. between expert opinions this is the kalman filter. the conditional covariance matrices of the filter follow ordinary differential equations of riccati type. we rely on basic theory about matrix riccati equations to investigate their properties. firstly, we consider the asymptotic behaviour of the covariance matrices for an increasing number of expert opinions on a finite time horizon. secondly, we state conditions for the convergence of the covariance matrices on an infinite time horizon with regularly arriving expert opinions. finally, we derive the optimal trading strategy of an investor. the optimal expected logarithmic utility of terminal wealth, the value function, is a functional of the conditional covariance matrices. hence, our analysis of the covariance matrices allows us to deduce properties of the value function. | arxiv:1601.08155 |
we provide sufficient conditions for the existence of periodic solutions of the of the lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. the basic assumptions cover relevant models with singularities like coulomb - like electric potentials or the magnetic dipole. | arxiv:2103.09544 |
in this paper is extended the original theorem by fueter - sce ( assigning an $ \ mathbb r _ { 0, m } $ - valued monogenic function to a $ \ mathbb c $ - valued holomorphic function ) to the higher order case. we use this result to prove fueter ' s theorem with an extra monogenic factor $ p _ k ( x _ 0, \ underline x ) $. | arxiv:0912.1635 |
humor generation is a challenging task in natural language processing due to limited resources and the quality of existing datasets. available humor language resources often suffer from toxicity and duplication, limiting their effectiveness for training robust models. this paper proposes cleancomedy, a specialized, partially annotated toxicity - filtered corpus of english and russian jokes collected from various sources. we study the effectiveness of our data filtering approach through a survey on humor and toxicity levels in various joke groups. in addition, we study advances in computer humor generation by comparing jokes written by humans with various groups of generative jokes, including our baseline models trained on the cleancomedy datasets. | arxiv:2412.09203 |
engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over - engineering for unlikely scenarios. assessments such as serviceability limit state ( sls ) involve evaluating weather events, including estimating loads not expected to be exceeded more than a specified number of times ( e. g., 100 ) throughout the structure ' s design lifetime. although physics - based simulations provide robust and detailed insights, they are computationally expensive, making it challenging to generate statistically valid representations of a wide range of weather conditions. to address these challenges, we propose an approach using gaussian process ( gp ) surrogate models trained on a limited set of simulation outputs to directly generate the structural response distribution. we apply this method to an sls assessment for estimating the order statistics \ ( y _ { 100 } \ ), representing the 100th highest response, of a structure exposed to 25 years of historical weather observations. our results indicate that the gp surrogate models provide comparable results to full simulations but at a fraction of the computational cost. | arxiv:2503.01242 |
approximate message passing ( amp ) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals, including those acquired in compressive signal acquisiton systems. the growing prevalence of big data systems has increased interest in large - scale problems, which may involve huge measurement matrices that are unsuitable for conventional computing systems. to address the challenge of large - scale processing, multiprocessor ( mp ) versions of amp have been developed. we provide an overview of two such mp - amp variants. in row - mp - amp, each computing node stores a subset of the rows of the matrix and processes corresponding measurements. in column - mp - amp, each node stores a subset of columns, and is solely responsible for reconstructing a portion of the signal. we will discuss pros and cons of both approaches, summarize recent research results for each, and explain when each one may be a viable approach. aspects that are highlighted include some recent results on state evolution for both mp - amp algorithms, and the use of data compression to reduce communication in the mp network. | arxiv:1702.03049 |
the primary goal of this paper is to systematically exploit the method of deligne - illusie to obtain kodaira type vanishing theorems for vector bundles and more generally coherent sheaves on algebraic varieties. the key idea is to introduce a number which provides a cohomological measure of the positivity of a coherent sheaf called the frobenius or f - amplitude. as the terminology indicates, the definition is most natural over a field of positive characteristic, however it can be forced into characteristic 0 by standard tricks. the f - amplitude enters into the statement of the basic vanishing theorem, and this leads to the problem of calculating, or at least estimating, this number. most of the work in this paper is devoted to doing this various situations. the key result in this direction is a bound on the f - amplitude of an ample vector bundle. when combined with the vanishing theorem, this has some reasonably down to earth corollaries ( both old and new ). | arxiv:math/0202129 |
tetrad based equation for dirac - k \ " { a } hler particle is solved in spherical coordinates in the flat minkocski space - time. spherical solutions of boson type ( j = 0, 1, 2,... ) are constructed. after performing a special transformation over spherical boson solutions of the dirac - k \ " { a } hler equation, 4 \ times 4 - matrices u ( x ) \ longrightarrow v ( x ), simple linear expansions of the four rows of new representativeof the dirac - - k \ " { a } hler field v ( x ) in terms of spherical fermion solutions \ psi _ { i } ( x ) of the four ordinary dirac equations have been derived. however, this fact cannot be interpreted as the possibility not to distinguish between the dirac - k \ " { a } hler field and the system four dirac fermions. the main formal argument is that the special transformation ( i \ otimes s ( x ) ) involved does not belong to the group of tetrad local gauge transformation for dirac - k \ " { a } hler field, 2 - rank bispinor under the lorentz group. therefore, the linear expansions between boson and fermion functions are not gauge invariant under the group of local tetrad rotations. | arxiv:1109.3298 |
we study the fermion pair production from a strong electric field in boost - invariant coordinates in ( 3 + 1 ) dimensions and exploit the cylindrical symmetry of the problem. this problem has been used previously as a toy model for populating the central - rapidity region of a heavy - ion collision ( when we can replace the electric by a chromoelectric field ). we derive and solve the renormalized equations for the dynamics of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $ \ tau = \ sqrt { t ^ 2 - z ^ 2 } $. we determine the proper - time evolution of the comoving energy density and pressure of the ensuing plasma and the time evolution of suitable interpolating number operators. we find that unlike in ( 1 + 1 ) dimensions, the energy density closely follows the longitudinal pressure. the transverse momentum distribution of fermion pairs at large momentum is quite different and larger than that expected from the constant field result. | arxiv:0905.1360 |
we consider an initial - boundary value problem for the chemotaxis - navier - - stokes system \ begin { align * } \ left \ { \ begin { array } { c @ { \ quad } l @ { \ quad } l @ { \, } c } n _ { t } + u \ cdot \ nabla n = \ nabla \ cdot \ big ( d ( n ) \ nabla n - ns ( x, n, c ) \ cdot \ nabla c \ big ), \ & x \ in \ omega, & t > 0, \ \ c _ { t } + u \ cdot \ nabla c = \ delta c - cn, \ & x \ in \ omega, & t > 0, \ \ u _ { t } + ( u \ cdot \ nabla ) u = \ delta u + \ nabla p + n \ nabla \ phi, \ quad \ nabla \ cdot u = 0, \ & x \ in \ omega, & t > 0, \ \ \ big ( d ( n ) \ nabla n - ns ( x, n, c ) \ cdot \ nabla c ) \ cdot \ nu = \ nabla c \ cdot \ nu = 0, \ u = 0, \ & x \ in \ partial \ omega, & t > 0, \ \ n ( \ cdot, 0 ) = n _ 0, \ c ( \ cdot, 0 ) = c _ 0, \ u ( \ cdot, 0 ) = u _ 0, \ & x \ in \ omega. \ end { array } \ right. \ end { align * } in a smoothly bounded domain $ \ omega \ subset \ mathbb { r } ^ 2 $. assuming $ s : \ overline { \ omega } \ times [ 0, \ infty ) \ times ( 0, \ infty ) \ rightarrow \ mathbb { r } ^ { 2 \ times 2 } $ to be sufficiently regular and such that with $ \ gamma \ in [ 0, \ frac56 ] $ and some non - decreasing $ s _ 0 : ( 0, \ infty ) \ to ( 0, \ infty ) $, we have \ begin { align * } \ big | s ( x, n, c ) \ big | \ leq \ frac { s _ 0 ( c ) } { c ^ \ | arxiv:2411.18336 |
these are the lecture notes for a course on exceptional polynomials taught at the \ textit { aims - volkswagen stiftung workshop on introduction to orthogonal polynomials and applications } that took place in douala ( cameroon ) from october 5 - 12, 2018. they summarize the basic results and construction of exceptional poynomials, developed over the past ten years. in addition, some new results are presented on the construction of rational solutions to painlev \ ' e equation piv and its higher order generalizations that belong to the $ a _ { 2n } ^ { ( 1 ) } $ - painlev \ ' e hierarchy. the construction is based on dressing chains of schr \ " odinger operators with potentials that are rational extensions of the harmonic oscillator. some of the material presented here ( sturm - liouville operators, classical orthogonal polynomials, darboux - crum transformations, etc. ) are classical and can be found in many textbooks, while some results ( genus, interlacing and cyclic maya diagrams ) are new and presented for the first time in this set of lecture notes. | arxiv:1912.07597 |
in this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. in particular, we developed two momentum - based algorithms for optimizing this kind of problem and established the convergence rate of our two algorithms, providing the sample and communication complexities. importantly, to the best of our knowledge, our convergence rate is the first one achieving the linear speedup with respect to the number of devices for federated bilevel optimization algorithms. at last, our extensive experimental results confirm the effectiveness of our two algorithms. | arxiv:2204.13299 |
a soft x - ray excess above the 2 - 10 kev power law extrapolation is generally observed in agn x - ray spectra. presently there are two competitive models to explain it : blurred ionized reflection and warm comptonisation. in the latter case, observations suggest a corona temperature $ \ sim $ 1 kev and a corona optical depth $ \ sim $ 10. moreover, radiative constraints from spectral fits with comptonisation models suggest that most of the accretion power should be released in the warm corona. the disk below is basically non - dissipative, radiating only the reprocessed emission from the corona. the true radiative properties of such a warm and optically thick plasma are not well - known, however. for instance, the importance of the comptonisation process, the potential presence of strong absorption / emission features or the spectral shape of the output spectrum have been studied only very recently. we present in this paper simulations of warm and optically thick coronae using the titan radiative transfer code coupled with the noar monte - carlo code, the latter fully accounting for compton scattering of continuum and lines. illumination from above by a hard x - ray emission and from below by an optically thick accretion disk is taken into account as well as ( uniform ) internal heating. our simulations show that for a large part of the parameter space, the warm corona with sufficient internal mechanical heating is dominated by compton cooling and neither strong absorption nor emission lines are present in the outgoing spectra. in a smaller part of the parameter space, the calculated emission agrees with the spectral shape of the observed soft x - ray excess. remarkably, this also corresponds to the conditions of radiative equilibrium of an extended warm corona covering almost entirely a non - dissipative accretion disk. these results confirm the warm comptonisation as a valuable model for the soft x - ray excess. | arxiv:2001.02026 |
we measure the superconducting transition of yin $ _ 3 $ by resistivity, susceptibility, and specific heat. despite using high - quality single - crystal samples, the transitions detected by the three techniques are shifted from each other in temperature, suggesting a region of filamentary superconductivity. we discuss the possible implications for filamentary superconductivity in unconventional superconductors. | arxiv:1112.3083 |
we study the scattering of monochromatic bosonic plane waves impinging upon a rotating black hole, in the special case that the direction of incidence is aligned with the spin axis. we present accurate numerical results for electromagnetic kerr scattering cross sections for the first time, and give a unified picture of the kerr scattering for all massless bosonic fields. | arxiv:1910.07666 |
in this study, we develop a hybrid operational typhoon forecasting model that integrates the fuxi machine - learning ( ml ) model with the physics - based shanghai typhoon model ( shtm ) into a dual physics - data - driven framework. by employing spectral nudging, the hybrid model named fuxi - shtm leverages fuxi ' s robust large - scale forecasting capabilities alongside shtm ' s mesoscale strengths, significantly enhancing track, intensity, and precipitation predictions for super typhoons yagi ( 2024 ) and krathon ( 2024 ). besides, this study aims to identify the sensitive regions for the hybrid model by using conditional nonlinear optimal perturbation ( cnop ) method. despite being constrained by fuxi ' s large - scale forecast fields, the dense assimilation of satellite observations within these sensitive regions can further enhance typhoon forecasts. besides, this study offers key insights into the emerging paradigms that are set to shape the future development of both machine learning and physics - based modeling approaches. | arxiv:2503.00424 |
we perform a three dimensional radiation hydrodynamics simulation to investigate the formation of first stars from initial collapse of a primordial gas cloud to formation and growth of protostars. the simulation is integrated until 0. 1 myrs after the formation of the primary protostar by which the protostars have already settled onto main sequence stars. this is the first attempt of simulating first star formation to take into account the ultraviolet radiative feedback effect by the multiple protostars as well as the three dimensional effects such as fragmentation of the accretion disk. we find that the mass accretions onto the population iii protostars are significantly suppressed by the radiative feedback from themselves. as a result, we find five stars formed in this particular simulation, and that the final mass of the stars are < 60msun, including a star of 4. 4msun. formation of such a star hints at the existence of even lower - mass stars that would live today. | arxiv:1304.6794 |
we present optical photometry and spectroscopy of the peculiar type iin / ibn supernova sn2011hw. its light curve exhibits a slower decline rate than normal sneibc, with a peak absolute magnitude of - 19. 5 ( unfiltered ) and a secondary peak of - 18. 3 mag ( r ). spectra of sn2011hw are unusual compared to normal sn types, most closely resembling the spectra of sneibn. we center our analysis on comparing sn 2011hw to the well - studied typeibn sn2006jc. while the two sne have many important similarities, the differences are quite telling : compared to sn2006jc, sn2011hw has weaker hei and caii lines and relatively stronger h lines, its light curve has a higher luminosity and slower decline rate, and emission lines associated with the progenitor ' s csm are narrower. one can reproduce the unusual continuum shape of sn2011hw with equal contributions of a 6000k blackbody and a spectrum of sn2006jc. we attribute this emission component and many other differences between the two sne to extra opacity from a small amount of additional h in sn2011hw, analogous to the small h mass that makes sneiib differ from sneib. slower speeds in the csm and elevated h content suggest a connection between the progenitor of sn2011hw and the class of ofpe / wn9 stars, which have been associated with lbvs in their hot quiescent phases between outbursts, and are h - poor - but not h - free like classical wolf - rayet ( wr ) stars. we conclude that the similarities and differences between sn2011hw and sn2006jc can be largely understood if their progenitors exploded at different points in the transitional evolution from an lbv to a wr star. | arxiv:1204.0043 |
we stress the importance of wolf - rayet stars for the understanding of the agn phenomenon in galaxies. wr stars provide an unique opportunity to explore from the ground whether non - thermal nuclear activity and circumnuclear starbursts are connected. we review the known reported wr signatures observed so far in agns and point out some intrincacies related to the analysis of the spectra, linked to reddening correction, the origin of the hbeta line, etc. finally, we advocate that integral field spectroscopy is a very promising tool to study this problem and present preliminary results of a long - term project that have been obtained at the cfht in 1998. | arxiv:astro-ph/9901170 |
point cloud based retrieval for place recognition is still a challenging problem due to drastic appearance and illumination changes of scenes in changing environments. existing deep learning based global descriptors for the retrieval task usually consume a large amount of computation resources ( e. g., memory ), which may not be suitable for the cases of limited hardware resources. in this paper, we develop an efficient point cloud learning network ( epc - net ) to form a global descriptor for visual place recognition, which can obtain good performance and reduce computation memory and inference time. first, we propose a lightweight but effective neural network module, called proxyconv, to aggregate the local geometric features of point clouds. we leverage the spatial adjacent matrix and proxy points to simplify the original edge convolution for lower memory consumption. then, we design a lightweight grouped vlad network ( g - vlad ) to form global descriptors for retrieval. compared with the original vlad network, we propose a grouped fully connected ( gfc ) layer to decompose the high - dimensional vectors into a group of low - dimensional vectors, which can reduce the number of parameters of the network and maintain the discrimination of the feature vector. finally, to further reduce the inference time, we develop a simple version of epc - net, called epc - net - l, which consists of two proxyconv modules and one max pooling layer to aggregate global descriptors. by distilling the knowledge from epc - net, epc - net - l can obtain discriminative global descriptors for retrieval. extensive experiments on the oxford dataset and three in - house datasets demonstrate that our proposed method can achieve state - of - the - art performance with lower parameters, flops, and runtime per frame. | arxiv:2101.02374 |
we have conducted a multiwavelength study of several radio sources within or near the error boxes of egret unidentified sources at mid to high galactic latitude, under the hypothesis that the radio sources are blazars and are thus the best identification candidates for the egret objects. we show that one of these radio sources, pmn 0850 - 12, has a flux of 1. 5 jy at 22 ghz and a nearly flat spectrum up to 230 ghz and is thus very likely to be the correct identification for for the egret source 2eg j0852 - 1237. | arxiv:astro-ph/9709279 |
current simulations of air showers produced by ultra - high energy cosmic rays ( uhecrs ) do not satisfactorily describe recent experimental data, particularly when looking at the muonic shower component relative to the electromagnetic one. discrepancies can be seen in both average values and on an individual shower - by - shower basis. it is thought that the muonic part of the air showers isn ' t accurately represented in simulations, despite various attempts to boost the number of muons within standard hadronic interaction physics. in this study, we investigate whether modifying the final state of events created with sibyll ~ 2. 3d in air shower simulations can achieve a more consistent description of the muon content observed in experimental data. we create several scenarios where we separately increase the production of baryons, $ \ rho ^ 0 $, and strange particles to examine their impact on realistic air shower simulations. our results suggest that these ad - hoc modifications can improve the simulations, providing a closer match to the observed muon content in air showers. one side - effect of the increased muon production in the considered model versions is a smaller difference in the predicted total muon numbers for proton and iron showers. however, more research is needed to find out whether any of these adjustments offers a realistic solution to the mismatches seen in data, and to identify the precise physical process causing these changes in the model. we hope that these modified model versions will also help to develop improved machine - learning analyses of air shower data and to estimate sys. { } uncertainties related to shortcomings of hadronic interaction models. | arxiv:2309.05390 |
in this paper, we investigate optimal boundary control problems for cahn - hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the laplace - beltrami operator. the cost functional is of standard tracking type, and box constraints for the controls are prescribed. we prove existence of optimal controls and derive first - order necessary conditions of optimality. the general strategy, which follows the lines of the recent approach by colli, farshbaf - shaker, sprekels ( see the preprint arxiv : 1308. 5617 ) to the ( simpler ) allen - cahn case, is the following : we use the results that were recently established by colli, gilardi, sprekels in the preprint arxiv : 1407. 3916 [ math. ap ] for the case of ( differentiable ) logarithmic potentials and perform a so - called " deep quench limit ". using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first - order necessary optimality conditions for the case of ( non - differentiable ) double obstacle potentials. | arxiv:1408.6146 |
the hamamatsu uv - light enhanced 64 - channel sipm array of the newest generation ( s13361 - 3050as - 08 ) has been examined for the purpose of being used for the silicon elementary cell add - on ( sieca ) of the euso - spb balloon experiment. characterization measurements have been performed with the newly installed single photon calibration stand at kit ( spock ). the results of the characterization measurements including the breakdown voltage, the gain, the pde, the dark - count rate and the crosstalk probability of all 64 sipm channels are presented. additional measurements of the sipm sensitivity to photons with wavelengths lower than 400nm show an improved pde for small wavelengths compared to the sipm array s12642 - 0808pa - 50, which was also investigated for comparison. the response dynamics have been investigated for low numbers of incoming photons. temperature dependent measurements of the gain, the pde, the dark - count rate and the crosstalk probability have been performed for one channel of the sipm array. | arxiv:1804.00897 |
let $ g $ be a group and assume that $ ( a _ p ) _ { p \ in g } $ is a family of algebras with identity. we have a { \ it hopf $ g $ - coalgebra } ( in the sense of turaev ) if, for each pair $ p, q \ in g $, there is given a unital homomorphism $ \ co _ { p, q } : a _ { pq } \ to a _ p \ ot a _ q $ satisfying certain properties. consider now the direct sum $ a $ of these algebras. it is an algebra, without identity, except when $ g $ is a finite group, but the product is non - degenerate. the maps $ \ co _ { p, q } $ can be used to define a coproduct $ \ co $ on $ a $ and the conditions imposed on these maps give that $ ( a, \ co ) $ is a multiplier hopf algebra. it is $ g $ - cograded as explained in this paper. we study these so - called { \ it group - cograded multiplier hopf algebras }. they are, as explained above, more general than the hopf group - coalgebras as introduced by turaev. moreover, our point of view makes it possible to use results and techniques from the theory of multiplier hopf algebras in the study of hopf group - coalgebras ( and generalizations ). in a separate paper, we treat the quantum double in this context and we recover, in a simple and natural way ( and generalize ) results obtained by zunino. in this paper, we study integrals, in general and in the case where the components are finite - dimensional. using these ideas, we obtain most of the results of virelizier on this subject and consider them in the framework of multiplier hopf algebras. | arxiv:math/0404026 |
we study the possibly existing anisotropy in the accelerating expansion universe with the union2 type ia supernovae data and gamma - ray burst data. we construct a direction - dependent dark energy model and constrain the anisotropy direction and strength of modulation. we find that the maximum anisotropic deviation direction is $ ( l, \, b ) = ( 126 ^ { \ circ }, \, 13 ^ { \ circ } ) $ ( or equivalently $ ( l, \, b ) = ( 306 ^ { \ circ }, \, - 13 ^ { \ circ } ) $ ), and the current anisotropy level is $ g _ 0 = 0. 030 _ { + 0. 010 } ^ { - 0. 030 } $ ( $ 1 \ sigma $ confidence level with union2 data ). our results do not show strong evidence for the anisotropic dark energy model. we also discuss potential methods that may distinguish the peculiar velocity field from the anisotropic dark energy model. | arxiv:1303.0961 |
in this work, we study various properties of embedded hypersurfaces in $ 1 + 1 + 2 $ decomposed spacetimes with a preferred spatial direction, denoted $ e ^ { \ mu } $, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper conformal transformation. to ensure a non - vanishing positivity scalar curvature of the induced metric, we impose that the scalar curvature of the conformal metric is non - negative and that the associated conformal factor satisfies $ \ hat { \ varphi } ^ 2 + 2 \ hat { \ hat { \ varphi } } > 0 $, where $ \ hat { \ ast } $ denotes derivative along $ e ^ { \ mu } $. firstly, it is demonstrated that such hypersurface is either einstein or the twist vanishes on it, and that the scalar curvature of the induced metric is constant. it is then proved that if the hypersurface is compact and of einstein, and admits a proper conformal transformation, then the hypersurface must be isomorphic to the $ 3 $ - sphere, where we make use of well known results on riemannian manifolds admitting conformal transformations. if the hypersurface is not einstein and has nowhere vanishing sheet expansion, we show that this conclusion fails. however, with the additional conditions that the scalar curvatures of the induced metric and the conformal metric coincide, the associated conformal factor is strictly negative and the third and higher order derivatives of the conformal factor vanish, the conclusion follows. furthermore, additional results are obtained under the conditions that the scalar curvature of a metric conformal to the induced metric is also constant. finally, we consider some of our results in context of locally rotationally symmetric spacetimes and show that, if the hypersurfaces are compact and not of einstein type, then under specified conditions the hypersurface is isomorphic to the $ 3 $ - sphere, where we constructed explicit examples of proper conformal killing vector fields along $ e ^ { \ mu } $. | arxiv:2112.08753 |
morse and ingard give a coupled system of time - harmonic equations for the temperature and pressure of an excited gas. these equations form a critical aspect of modeling trace gas sensors. like other wave propagation problems, the computational problem must be closed with suitable far - field boundary conditions. working in a scattered - field formulation, we adapt a nonlocal boundary condition proposed earlier for the helmholtz equation to this coupled system. this boundary condition uses a green ' s formula for the true solution on the boundary, giving rise to a nonlocal perturbation of standard transmission boundary conditions. however, the boundary condition is exact and so galerkin discretization of the resulting problem converges to the restriction of the exact solution to the computational domain. numerical results demonstrate that accuracy can be obtained on relatively coarse meshes on small computational domains, and the resulting algebraic systems may be solved by gmres using the local part of the operator as an effective preconditioner. | arxiv:2210.13765 |
although most fingerprint matching methods utilize minutia points and / or texture of fingerprint images as fingerprint features, the frequency spectrum is also a useful feature since a fingerprint is composed of ridge patterns with its inherent frequency band. we propose a novel cnn - based method for extracting fingerprint features from texture, minutiae, and frequency spectrum. in order to extract effective texture features from local regions around the minutiae, the minutia attention module is introduced to the proposed method. we also propose new data augmentation methods, which takes into account the characteristics of fingerprint images to increase the number of images during training since we use only a public dataset in training, which includes a few fingerprint classes. through a set of experiments using fvc2004 db1 and db2, we demonstrated that the proposed method exhibits the efficient performance on fingerprint verification compared with a commercial fingerprint matching software and the conventional method. | arxiv:2008.11917 |
we prove that the minimum - time controlled kepler problem is not liouville integrable in the class of meromorphic functions, via the moral \ ` es - ramis theory. | arxiv:1801.04198 |
in this article we use the technique of luttinger surgery to produce small examples of simply connected and non - simply connected minimal symplectic 4 - manifolds. in particular, we construct : ( 1 ) an example of a minimal symplectic 4 - manifold that is homeomorphic but not diffeomorphic to cp ^ 2 # 3 ( - cp ^ 2 ) which contains a symplectic surface of genus 2, trivial normal bundle, and simply connected complement and a disjoint nullhomologous lagrangian torus with the fundamental group of the complement generated by one of the loops on the torus. ( 2 ) a minimal symplectic 4 - manifold that is homeomorphic but not diffeomorphic to 3cp ^ 2 # 5 ( - cp ^ 2 ) which has two essential lagrangian tori with simply connected complement. these manifolds can be used to replace e ( 1 ) in many known theorems and constructions. examples in this article include the smallest known minimal symplectic manifolds with abelian fundamental groups including symplectic manifolds with finite and infinite cyclic fundamental group and euler characteristic 6. | arxiv:math/0703065 |
we discuss the perspectives of measuring direct cp violation parameters in hyperon decays by measurements with proton and / or antiproton beams, to be carried out at various facilities, and in particular we propose new experiments at the tevatron and at the lhc. | arxiv:hep-ph/9810518 |
spectroscopic observations of quasar outflows at rest - frame 500 - 1000 angstrom have immense diagnostic power. we present analyses of such data, where absorption troughs from three important ions are measured : first, o iv and o iv * that allow us to obtain the distance of high ionization outflows from the agn ; second, ne viii and mg x that are sensitive to the very high ionization phase of the outflow. their inferred column densities, combined with those of troughs from o vi, n iv, and h i, yield two important results : 1 ) the outflow shows two ionization phases, where the high ionization phase carries the bulk of the material. this is similar to the situation seen in x - ray warm absorber studies. furthermore, the low ionization phase is inferred to have a volume filling factor of 10 ^ ( - 5 ) - 10 ^ ( - 6 ). 2 ) from the o iv to o iv * column density ratio, and the knowledge of the ionization parameter, we determine a distance of 3000 pc. from the outflow to the central source. since this is a typical high ionization outflow, we can determine robust values for the mass flux and kinetic luminosity of the outflow : 40 solar masses per year and 10 ^ 45 ergs / s, respectively, where the latter is roughly equal to 1 % of the bolometric luminosity. such a large kinetic luminosity and mass flow rate measured in a typical high ionization wind suggests that quasar outflows are a major contributor to agn feedback mechanisms. | arxiv:1305.2181 |
addprod } ( a _ 1, \ dots, a _ c ) ) $. this last fact is proven by generalizing godsil ' s notion of treelike walks on a graph $ g $ to a notion of freelike walks on a collection of atoms $ a _ 1, \ dots, a _ c $. | arxiv:1904.03500 |
. august borsig ( 1804 – 1854 ), businessman carl bosch ( 1874 – 1940 ), chemist, nobel prize winner 1931 franz breisig ( 1868 – 1934 ), mathematician, inventor of the calibration wire and father of the term quadripole network in electrical engineering. wilhelm cauer ( 1900 – 1945 ), mathematician, essential contributions to the design of filters. henri marie coanda ( 1886 – 1972 ), romanian aircraft designer ; discovered the coanda effect. lotte cohn ( 1893 - 1983 ), german - israeli architect jan czochralski ( 1885 – 1953 ), polish chemist carl dahlhaus ( 1928 – 1989 ), musicologist. kurt daluege ( 1897 – 1946 ), ss official, chief of ordnungspolizei ( order police ) of nazi germany from 1936 to 1943, hanged as a war criminal walter dornberger ( 1895 – 1980 ), major - general, developer of the air force - nasa x - 20 dyna - soar project. ottmar edenhofer ( born 1961 ), economist krafft arnold ehricke ( 1917 – 1984 ), rocket - propulsion engineer, worked for the nasa, chief designer of the centaur gerhard ertl ( born 10 october 1936 in stuttgart ) physicist and surface chemist, hon. prof. and nobel prize winner 2007 ladislaus farkas ( 1904 – 1948 ), austro - hungarian / israeli chemist gottfried feder ( 1883 – 1941 ), economist and key member of the national socialist party wigbert fehse ( born 1937 ) german engineer and researcher in the area of automatic space navigation, guidance, control and docking / berthing. ursula franklin ( 1921 – 2016 ), canadian physicist ( archaeometry ) and theorist on the political and social effects of technology, pearson medal of peace winner 2001 dennis gabor ( 1900 – 1971 ), hungarian - british physicist ( holography ), nobel prize winner 1971 hans geiger ( 1882 – 1945 ), physicist, co - inventor of the detector component of the geiger counter elsa gidoni ( 1901 – 1978 ), german - american architect and interior designer. thomas gil ( born 1954 ), professor of practical philosophy. fritz gosslau ( 1898 – 1965 ), german engineer, known for his work at the v - 1 flying bomb. fritz haber ( 1868 – 1934 ), chemist who received the nobel prize in chemistry in 1918 gustav ludwig hertz ( 1887 – 1975 ), physicist, nobel prize winner 1925 ernst herzfeld ( | https://en.wikipedia.org/wiki/Technische_Universität_Berlin |
in this paper we study real hypersurfaces in the complex quadric space $ q ^ m $ whose structure jacobi operator commutes with their structure tensor field. we show that the reeb curvature $ \ alpha $ of such hypersurfaces is constant and if $ \ alpha $ is non - zero then the hypersurface is a tube around a totally geodesic submanifold $ \ mathbb { c } p ^ k \ subset q ^ m $, where $ m = 2k $. we also consider reeb flat hypersurfaces, namely, when the reeb curvature is zero. we show that the tube around $ \ mathbb { c } p ^ k \ subset q ^ m $ ( $ m = 2k $ ), with radius $ \ frac { \ pi } { 4 } $ is the only reeb flat hopf hypersurface with commuting ricci tensor and also the only one with commuting shape operator. finally, we prove that there does not exist any reeb flat hopf hypersurfaces with non - parallel killing ricci tensor or with killing shape operator. | arxiv:1807.11021 |
we consider a class of well motivated string - inspired flipped $ su ( 5 ) $ supergravity models which include four supersymmetry breaking scenarios : no - scale, strict no - scale, dilaton, and special dilaton, such that only three parameters are needed to describe all new phenomena $ ( m _ t, \ tan \ beta, m _ { \ tilde g } ) $. we show that the lep precise measurements of the electroweak parameters in the form of the $ \ epsilon _ 1 $ variable, and the cleoii allowed range for $ \ bsg $ are at present the most important experimental constraints on this class of models. for $ m _ t \ gsim155 \, ( 165 ) \ gev $, the $ \ epsilon _ 1 $ constraint ( at 90 ( 95 ) \ % cl ) requires the presence of light charginos ( $ m _ { \ chi ^ \ pm _ 1 } \ lsim50 - 100 \ gev $ depending on $ m _ t $ ). since all sparticle masses are proportional to $ m _ { \ tilde g } $, $ m _ { \ chi ^ \ pm _ 1 } \ lsim100 \ gev $ implies : $ m _ { \ chi ^ 0 _ 1 } \ lsim55 \ gev $, $ m _ { \ chi ^ 0 _ 2 } \ lsim100 \ gev $, $ m _ { \ tilde g } \ lsim360 \ gev $, $ m _ { \ tilde q } \ lsim350 \, ( 365 ) \ gev $, $ m _ { \ tilde e _ r } \ lsim80 \, ( 125 ) \ gev $, $ m _ { \ tilde e _ l } \ lsim120 \, ( 155 ) \ gev $, and $ m _ { \ tilde \ nu } \ lsim100 \, ( 140 ) \ gev $ in the no - scale ( dilaton ) flipped $ su ( 5 ) $ supergravity model. the $ \ bsg $ constraint excludes a significant fraction of the otherwise allowed region in the $ ( m _ { \ chi ^ \ pm _ 1 }, \ tan \ beta ) $ plane ( irrespective of the magnitude of the chargino mass ), while future experimental improvements will result in decisive tests of these models | arxiv:hep-ph/9308266 |
we consider $ e _ 8 \ times e _ 8 $ heterotic compactifications on $ k3 $ and $ k3 \ times t ^ 2 $. the idea of heterotic / heterotic duality in $ d = 6 $ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. recently duff, minasian and witten ( dmw ) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $ e _ 8 $ ' s. we consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. upon further toroidal compactification to $ d = 4 $, we find that the duals in the dmw case correspond to $ n = 2 $ models in which the $ \ beta $ - function of the different group factors verify $ { \ beta } _ \ alpha = 12 $, whereas the asymmetric solutions that we propose have $ { \ beta } _ \ alpha = 24 $. we check the consistency of these dualities by studying the different large $ t, s $ limits of the gauge kinetic function. dual $ n = 1 $, $ d = 4 $ models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples. | arxiv:hep-th/9602097 |
which all protostars start forming at the same time. | arxiv:2310.13125 |
we consider a diatomic infinite fermi - pasta - ulam ( fpu ) system with light and heavy particles. for a small mass ratio, we prove error estimates for the approximation of the dynamics of this system by the dynamics of the monoatomic fpu system. the light particles are squeezed by the heavy particles at the mean value of their displacements. the error estimates are derived by means of the energy method and hold for sufficiently long times, for which the dynamics of the monoatomic fpu system is observed. the approximation result is restricted to sufficiently small displacements of the heavy particles relatively to each other. | arxiv:2003.00046 |
we are currently exploiting the deep radio / optical / ir information available for the extra - galactic component of the spitzer first look survey ( fls ) to investigate the physical properties of faint radio - selected agns, with the aim of studying the agn component of sub - mjy radio fields. one of the key unresolved issues is whether, as a function of cosmic epoch, low - power agns are more related to efficiently accreting systems ( mostly radio - quiet ) or to systems with very low accretion rates ( mostly radio - loud ). here we present a sample of optically identified radio - emitting agns extracted from the fls. preliminary results show that at the flux densities probed by the fls ( s ( 1. 4 ghz ) > 100 microjy ) we still have a significant number of radio - loud agns, similarly to what found in ' brighter ' sub - mjy radio samples. very interestingly, however, we have also a clear and direct evidence of a population of radio - emitting agns in the fls, whose properties are consistent with those expected from existing radio - quiet agn modeling. such agns could be recognised as such thanks to the availability of ir colors which proved to be especially useful to efficiently separate radio sources triggered by agns, from sources triggered by star - formation. this latter result supports the idea that radio - quiet agns are not necessarily radio silent, and very promisingly may indicate that the bulk of the radio - quiet agn population could emerge from studies of deeper radio samples. | arxiv:0909.3761 |
simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. discerning the presence of direct links between neuron from data is still a not completely solved problem. to enlarge the number of tools for detecting the underlying network structure, we propose here the use of copulas, pursuing on a research direction we started in [ 1 ]. here, we adapt their use to distinguish different types of connections on a very simple network. our proposal consists in choosing suitable random intervals in pairs of spike trains determining the shapes of their copulas. we show that this approach allows to detect different types of dependencies. we illustrate the features of the proposed method on synthetic data from suitably connected networks of two or three formal neurons directly connected or influenced by the surrounding network. we show how a smart choice of pairs of random times together with the use of empirical copulas allows to discern between direct and un - direct interactions. | arxiv:1903.08460 |
currently, the technique of numerical model - based atmospheric environment forecasting has becoming mature, yet traditional numerical prediction methods struggle to balance computational costs and forecast accuracy, facing developmental bottlenecks. recent advancements in artificial intelligence ( ai ) offer new solutions for weather prediction. however, most existing ai models do not have atmospheric environmental forecasting capabilities, while those with related functionalities remain constrained by grid - dependent data requirements, thus unable to deliver operationally feasible city - scale atmospheric environment forecasts. here we introduce ' bixiao ', a novel discontinuous - grid ai model for atmospheric environment forecasting. ' bixiao ' couples meteorological and environmental sub - models to generate predictions using site - specific observational data, completing 72 - hour forecasts for six major pollutants across all key cities in the beijing - tianjin - hebei region within 30 seconds. in the comparative experiments, the ' bixiao ' model outperforms mainstream numerical models in both computational efficiency and forecast accuracy. it surpasses cams with respect of operational 72 - hour forecasting and exceeds wrf - chem ' s performance in heavy pollution case predictions. the ' bixiao ' shows potential for nationwide application, providing innovative technical support and new perspectives for china ' s atmospheric environment forecasting operations. | arxiv:2504.19764 |
in this paper, we explore how transfer learning, coupled with intel xeon, specifically 4th gen intel xeon scalable processor, defies the conventional belief that training is primarily gpu - dependent. we present a case study where we achieved near state - of - the - art accuracy for image classification on a publicly available image classification tensorflow dataset using intel advanced matrix extensions ( amx ) and distributed training with horovod. | arxiv:2310.06916 |
multi - state capture - recapture data comprise individual - specific sighting histories together with information on individuals ' states related, for example, to breeding status, infection level, or geographical location. such data are often analysed using the arnason - schwarz model, where transitions between states are modelled using a discrete - time markov chain, making the model most easily applicable to regular time series. when time intervals between capture occasions are not of equal length, more complex time - dependent constructions may be required, increasing the number of parameters to estimate, decreasing interpretability, and potentially leading to reduced precision. here we develop a novel continuous - time multi - state model that can be regarded as an analogue of the arnason - schwarz model for irregularly sampled data. statistical inference is carried out by regarding the capture - recapture data as realisations from a continuous - time hidden markov model, which allows the associated efficient algorithms to be used for maximum likelihood estimation and state decoding. to illustrate the feasibility of the modelling framework, we use a long - term survey of bottlenose dolphins where capture occasion are not regularly spaced through time. here we are particularly interested in seasonal effects on the movement rates of the dolphins along the scottish east coast. the results reveal seasonal movement patterns between two core areas of their range, providing information that will inform conservation management. | arxiv:2002.10997 |
a boson sampler implements a restricted model of quantum computing. it is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non - interacting dynamics. here, we demonstrate a new combination of tools for implementing boson sampling using ultracold atoms in a two - dimensional, tunnel - coupled optical lattice. these tools include fast and programmable preparation of large ensembles of nearly identical bosonic atoms ( $ 99. 5 ^ { + 0. 5 } _ { - 1. 6 } \ ; \ % $ indistinguishability ) by means of rearrangement with optical tweezers and high - fidelity optical cooling, propagation for variable evolution time in the lattice with low loss ( $ 5. 0 ( 2 ) \ ; \ % $, independent of evolution time ), and high fidelity detection of the atom positions after their evolution ( typically $ 99. 8 ( 1 ) \ ; \ % $ ). with this system, we study specific instances of boson sampling involving up to $ 180 $ atoms distributed among $ \ sim 1000 $ sites in the lattice. direct verification of a given boson sampling distribution is not feasible in this regime. instead, we introduce and perform targeted tests to determine the indistinguishability of the prepared atoms, to characterize the applied family of single particle unitaries, and to observe expected bunching features due to interference for a large range of atom numbers. when extended to interacting systems, our work demonstrates the core capabilities required to directly assemble ground and excited states in simulations of various hubbard models. | arxiv:2307.06936 |
the study of universal approximation of arbitrary functions $ f : \ mathcal { x } \ to \ mathcal { y } $ by neural networks has a rich and thorough history dating back to kolmogorov ( 1957 ). in the case of learning finite dimensional maps, many authors have shown various forms of the universality of both fixed depth and fixed width neural networks. however, in many cases, these classical results fail to extend to the recent use of approximations of neural networks with infinitely many units for functional data analysis, dynamical systems identification, and other applications where either $ \ mathcal { x } $ or $ \ mathcal { y } $ become infinite dimensional. two questions naturally arise : which infinite dimensional analogues of neural networks are sufficient to approximate any map $ f : \ mathcal { x } \ to \ mathcal { y } $, and when do the finite approximations to these analogues used in practice approximate $ f $ uniformly over its infinite dimensional domain $ \ mathcal { x } $? in this paper, we answer the open question of universal approximation of nonlinear operators when $ \ mathcal { x } $ and $ \ mathcal { y } $ are both infinite dimensional. we show that for a large class of different infinite analogues of neural networks, any continuous map can be approximated arbitrarily closely with some mild topological conditions on $ \ mathcal { x } $. additionally, we provide the first lower - bound on the minimal number of input and output units required by a finite approximation to an infinite neural network to guarantee that it can uniformly approximate any nonlinear operator using samples from its inputs and outputs. | arxiv:1910.01545 |
the tunneling conductance between a metal and a multiband s - wave superconductor with a thin layer of single - band s - wave superconductor sandwiched in between is examined in this paper. we show that an in - gap peak in conductance curve is found as a result of the formation of in - gap bound state between the single - band and multiband superconductor junctions if the phases of the superconducting order parameters of the multiband superconductor are frustrated. the implication of this result in determining the gap symmetry of the iron - based superconductors is discussed. | arxiv:0812.1068 |
we present a numerical comparison between two standard finite volume schemes and a discontinuous galerkin method applied to the bgk equation of rarefied gas dynamics. we pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. most of our analysis relies on a 1d problem ( couette flow ), but we also present some results for a 2d aerodynamical flow. | arxiv:2003.05677 |
services computing can offer a high - level abstraction to support diverse applications via encapsulating various computing infrastructures. though services computing has greatly boosted the productivity of developers, it is faced with three main challenges : privacy and security risks, information silo, and pricing mechanisms and incentives. the recent advances of blockchain bring opportunities to address the challenges of services computing due to its build - in encryption as well as digital signature schemes, decentralization feature, and intrinsic incentive mechanisms. in this paper, we present a survey to investigate the integration of blockchain with services computing. the integration of blockchain with services computing mainly exhibits merits in two aspects : i ) blockchain can potentially address key challenges of services computing and ii ) services computing can also promote blockchain development. in particular, we categorize the current literature of services computing based on blockchain into five types : services creation, services discovery, services recommendation, services composition, and services arbitration. moreover, we generalize blockchain as a service ( baas ) architecture and summarize the representative baas platforms. in addition, we also outline open issues of blockchain - based services computing and baas. | arxiv:2012.04172 |
because of their proximity within the transneptunian region, the plutinos ( objects in the 3 : 2 mean - motion resonance with neptune ) are numerous in flux - limited catalogs, and well - studied theoretically. we perform detailed modelling of the on - sky detection biases for plutinos, with special attention to those that are simultaneously in the kozai resonance. in addition to the normal 3 : 2 resonant argument libration, kozai plutinos also show periodic oscillations in eccentricity and inclination, coupled to the argument of perihelion ( omega ) oscillation. due to the mean - motion resonance, plutinos avoid coming to pericenter near neptune ' s current position in the ecliptic plane. because kozai plutinos are restricted to certain values of omega, perihelion always occurs out of the ecliptic plane, biasing ecliptic surveys against finding these objects. the observed kozai plutino fraction ( fkoz ) has been measured by several surveys, finding values between 8 % and 25 %, while the true fkoz has been predicted to be between 10 % and 30 % by different giant planet migration simulations. we show that the observed fkoz varies widely depending on the ecliptic latitude and longitude of the survey, so debiasing to find the true ratio is complex. even a survey that covers most or all of the sky will detect an apparent kozai fraction that is different from the true fkoz. we present a map of the on - sky plutino kozai fraction that would be detected by all - sky flux - limited surveys. this will be especially important for the panoramic survey telescope & rapid response system ( pan - starrs ) and large synoptic survey telescope ( lsst ) projects, which may detect large numbers of plutinos as they sweep the sky. the kozai fraction and the distribution of the orbital elements of kozai plutinos may be a diagnostic of giant planet migration ; future migration simulations should provide details on their resonant kozai populations. | arxiv:1305.1662 |
we study the speed of a biased random walk on a percolation cluster on $ \ z ^ d $ in function of the percolation parameter $ p $. we obtain a first order expansion of the speed at $ p = 1 $ which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice. | arxiv:0812.2532 |
relying on the redefined vacuum state approach, and based on one - particle three - loop feynman diagrams, partial third - order interelectronic corrections to the valence electron energy shift are investigated in li - like ions. the idea is to begin with simple one - particle gauge - invariant subsets composed of feynman diagrams and to keep track of them in the many - electron frame, which is a strong asset of the formalism. an independent derivation is undertaken with the help of perturbation theory to cross - check the expressions. this two - method scheme helps to resolve how the different terms are distributed among three - and four - electron contributions. furthermore, it provides a tool to overcome the difficulties related to the derivation of reducible terms, which are tricky to deal with. these two independent derivations and the comparison of the resulting expressions are fully consistent, except for two expressions. in these cases, the discrepancy can be traced back to a different topology of the poles. | arxiv:2310.12592 |
we show that quasi - projective relation algebras and directed cylindric algebras are equivalent categorialy. we work out a godels second incompleteness theorem for finite varibale fragments of first order logic. we show that distinct set theories ( like one with ch, and another with its negation ) give rise to equationally distinct simple directed cylindric algebras. this correspondance was worked out for quasi projective relation algebras ( with a distinguished element corresponding to membership relation ). the idea of the proof is that the sagi representation of directed cylindric algebras preserve well - foundnes. finally, using that the functor defined preserves order, we show that the class of directed cylindric algebras have the superamalgmation property. | arxiv:1304.0761 |
recent work has demonstrated that finetuning is a promising approach to ' unlearn ' concepts from large language models. however, finetuning can be expensive, as it requires both generating a set of examples and running iterations of finetuning to update the model. in this work, we show that simple guardrail - based approaches such as prompting and filtering can achieve unlearning results comparable to finetuning. we recommend that researchers investigate these lightweight baselines when evaluating the performance of more computationally intensive finetuning methods. while we do not claim that methods such as prompting or filtering are universal solutions to the problem of unlearning, our work suggests the need for evaluation metrics that can better separate the power of guardrails vs. finetuning, and highlights scenarios where guardrails expose possible unintended behavior in existing metrics and benchmarks. | arxiv:2403.03329 |
deepfake detection faces a critical generalization hurdle, with performance deteriorating when there is a mismatch between the distributions of training and testing data. a broadly received explanation is the tendency of these detectors to be overfitted to forgery - specific artifacts, rather than learning features that are widely applicable across various forgeries. to address this issue, we propose a simple yet effective detector called lsda ( \ underline { l } atent \ underline { s } pace \ underline { d } ata \ underline { a } ugmentation ), which is based on a heuristic idea : representations with a wider variety of forgeries should be able to learn a more generalizable decision boundary, thereby mitigating the overfitting of method - specific features ( see fig. ~ \ ref { fig : toy } ). following this idea, we propose to enlarge the forgery space by constructing and simulating variations within and across forgery features in the latent space. this approach encompasses the acquisition of enriched, domain - specific features and the facilitation of smoother transitions between different forgery types, effectively bridging domain gaps. our approach culminates in refining a binary classifier that leverages the distilled knowledge from the enhanced features, striving for a generalizable deepfake detector. comprehensive experiments show that our proposed method is surprisingly effective and transcends state - of - the - art detectors across several widely used benchmarks. | arxiv:2311.11278 |
in this work we present a mobile application we designed and engineered to enable people to log their travels near and far, leave notes behind, and build a community around spaces in between destinations. our design explores new ground for location - based social computing systems, identifying opportunities where these systems can foster the growth of on - line communities rooted at non - places. in our work we develop, explore, and evaluate several innovative features designed around four usage scenarios : daily commuting, long - distance traveling, quantified traveling, and journaling. we present the results of two small - scale user studies, and one large - scale, world - wide deployment, synthesizing the results as potential opportunities and lessons learned in designing social computing for non - places. | arxiv:1605.08548 |
quark confinement is perhaps the most important emergent property of the theory of quantum chromodynamics. herein we review some key aspects of centre vortices in su ( 3 ) lattice gauge theory. starting from the original monte carlo gauge fields, a vortex identification procedure yields vortex - removed and vortex - only backgrounds. the comparison between the original ` untouched ' monte carlo gauge fields and these so called vortex - modified ensembles has provided a variety of results that support the notion that centre vortices are fundamental to confinement in pure gauge theory. for the first time we perform direct numerical tests of the response of centre vortices to the presence of dynamical quarks in su ( 3 ). | arxiv:2204.03816 |
given an abelian category, we introduce a categorical concept of ( strongly ) gorenstein projective ( resp., injective ) objects, by defining a new special class of objects. then we study the transfer of these properties when passing to an abelian category and its n - trivial extension category and also give a characterization of gorenstein object over it. we give, at the end, applications of this study on the category of modules over an associative ring and triangular matrix rings. | arxiv:2005.09038 |
let $ p $ be an odd prime. for any $ p $ - adic integer $ a $ we let $ \ overline { a } $ denote the unique integer $ x $ with $ - p / 2 < x < p / 2 $ and $ x - a $ divisible by $ p $. in this paper we study some permutations involving quadratic residues modulo $ p $. for instance, we consider the following three sequences. \ begin { align * } & a _ 0 : \ overline { 1 ^ 2 }, \ \ overline { 2 ^ 2 }, \ \ cdots, \ \ overline { ( ( p - 1 ) / 2 ) ^ 2 }, \ \ & a _ 1 : \ overline { a _ 1 }, \ \ overline { a _ 2 }, \ \ cdots, \ \ overline { a _ { ( p - 1 ) / 2 } }, \ \ & a _ 2 : \ overline { g ^ 2 }, \ \ overline { g ^ 4 }, \ \ cdots, \ \ overline { g ^ { p - 1 } }, \ end { align * } where $ g \ in \ z $ is a primitive root modulo $ p $ and $ 1 \ le a _ 1 < a _ 2 < \ cdots < a _ { ( p - 1 ) / 2 } \ le p - 1 $ are all quadratic residues modulo $ p $. obviously $ a _ i $ is a permutation of $ a _ j $ and we call this permutation $ \ sigma _ { i, j } $. sun obtained the sign of $ \ sigma _ { 0, 1 } $ when $ p \ equiv 3 \ pmod4 $. in this paper we give the sign of $ \ sigma _ { 0, 1 } $ and determine the sign $ \ sigma _ { 0, 2 } $ when $ p \ equiv 1 \ pmod 4 $. | arxiv:1903.01098 |
we derive the classical kappa - symmetric type iib string action on ads ( 3 ) x s ( 3 ) by employing the su ( 1, 1 | 2 ) ^ 2 algebra. we then gauge fix kappa - symmetry in the background adapted killing spinor gauge and present the action in a very simple form. | arxiv:hep-th/9809164 |
multifragmentation ( mf ) results from 1a gev au on c have been compared with the copenhagen statistical multifragmentation model ( smm ). a large number of observables, including the fragment charge yield distributions, fragment multiplicity distributions, caloric curve, critical exponents, and the critical scaling function are explored in this comparison. the nature of the phase transition in smm is studied as a function of the remnant mass and charge using the microcanonical equation of state. for light remnants $ a \ leq $ 100, backbending is observed indicating negative specific heat, while for $ a \ geq $ 170 the effective latentheat approaches zero. thus for heavier systems this transition can be identified as a continuous thermal phase transition. | arxiv:nucl-ex/0107015 |
we propose a quantum field theory description of beams on a mach - zehnder interferometer and apply the method to describe interaction free measurements ( ifms ), concluding that there is a change of momentum of the fields in ifms. analysing the factors involved in the probability of emission of low - energy photons, we argue that they do not yield meaningful contributions to the probabilities of the ifms. | arxiv:1911.03339 |
we introduce a model of non - unitary quantum dynamics that exhibits infinitely long - lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. ergodicity is evaded by combining a sequence of projective measurements with a local feedback rule that is inspired by toom ' s ` north - east - center ' classical cellular automaton. the measurements in question only partially collapse the wavefunction of the system, allowing some quantum coherence to persist. we demonstrate our claims using numerical simulations of a clifford circuit in two spatial dimensions which allows access to large system sizes, and also present results for more generic dynamics on modest system sizes. we also devise explicit experimental protocols realising this dynamics using one - and two - qubit gates that are available on present - day quantum computing platforms. | arxiv:2111.02499 |
general orbits of a particle of small mass $ \ mu $ around a kerr black hole of mass $ m $ are characterized by three parameters : the energy, the angular momentum and the carter constant. the time - averaged rates of change of the energy and the angular momentum can be obtained by computing the corresponding fluxes of gravitational waves emitted by the particle. by contrast, the time - averaged rate of change of the carter constant cannot be expressed as a flux of gravitational waves. recently a method to compute this rate of change was proposed by mino, and we refined it into a simplified form. in this paper we further extend our previous work to give a new formulation without the aid of expansion in terms of a small inclination angle. | arxiv:gr-qc/0702054 |
starting with arnold ' s pioneering work, the term " arnold diffusion " has been used to describe the slow diffusion taking place in the space of the actions in hamiltonian nonlinear dynamical systems with three or more degrees of freedom. the present text is an elaborated transcript of the introductory course given in the milano i - celmech school on the topic of arnold diffusion and its relation to nekhoroshev theory. the course introduces basic concepts related to our current understanding of the mechanisms leading to arnold diffusion. emphasis is placed upon the identification of those invariant objects in phase space which drive chaotic diffusion, such as the stable and unstable manifolds emanating from ( partially ) hyperbolic invariant objects. besides a qualitative understanding of the diffusion mechanisms, a precise quantification of the speed of arnold diffusion can be achieved by methods based on canonical perturbation theory, i. e. by the construction of a suitable normal form at optimal order. as an example of such methods, we discuss the ( quasi - ) stationary - phase approximation for the selection of remainder terms acting as driving terms for the diffusion. finally, we discuss the efficiency of such methods through numerical examples in which the optimal normal form is determined by a computer - algebraic implementation of a normalization algorithm. | arxiv:2111.03415 |
transshipment problem is one of the basic operational research problems. in this paper, our first work is to develop a biologically inspired mathematical model for a dynamical system, which is first used to solve minimum cost flow problem. it has lower computational complexity than physarum solver. second, we apply the proposed model to solve the traditional transshipment problem. compared with the conditional methods, experiment results show the provided model is simple, effective as well as handling problem in a continuous manner. | arxiv:1401.2181 |
we construct obliquely reflected brownian motions in all bounded simply connected planar domains, including non - smooth domains, with general reflection vector fields on the boundary. conformal mappings and excursion theory are our main technical tools. a key intermediate step, which may be of independent interest, is an alternative characterization of reflected brownian motions in smooth bounded planar domains with a given field of angles of oblique reflection on the boundary in terms of a pair of quantities, namely an integrable positive harmonic function, which represents the stationary distribution of the process, and a real number that represents, in a suitable sense, the asymptotic rate of rotation of the process around a reference point in the domain. furthermore, we also show that any obliquely reflected brownian motion in a simply connected jordan domain can be obtained as a suitable limit of obliquely reflected brownian motions in smooth domains. | arxiv:1512.02323 |
we consider the problem of optimising functions in the reproducing kernel hilbert space ( rkhs ) of a mat \ ' ern kernel with smoothness parameter $ \ nu $ over the domain $ [ 0, 1 ] ^ d $ under noisy bandit feedback. our contribution, the $ \ pi $ - gp - ucb algorithm, is the first practical approach with guaranteed sublinear regret for all $ \ nu > 1 $ and $ d \ geq 1 $. empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, improved gp - ucb. | arxiv:2001.10396 |
i study a sequence of singularities in dimension 4 and above, each given by a cone of rank 1 tensors of a certain signature, which have crepant resolutions whose exceptional loci are isomorphic to cartesian powers of the projective line. in each dimension n, these resolutions naturally correspond to vertices of an ( n - 2 ) - simplex, and flops between them correspond to edges of the simplex. i show that each face of the simplex may then be associated to a certain relation between flop functors. | arxiv:2108.10541 |
the development of information technology and internet has led to rapidly progressed in e - commerce and online shopping, due to the convenience that they provide consumers. e - commerce and online shopping are still not able to fully replace onsite shopping. in contrast, conventional online shopping websites often cannot provide enough information about a product for the customer to make an informed decision before checkout. 3d virtual shopping environment show great potential for enhancing e - commerce systems and provide customers information about a product and real shopping environment. this paper presents a new type of e - commerce system, which obviously brings virtual environment online with an active 3d model that allows consumers to access products into real physical environments for user interaction. such system with easy process can helps customers make better purchasing decisions that allows users to manipulate 3d virtual models online. the stores participate in the 3d virtual mall by communicating with a mall management. the 3d virtual mall allows shoppers to perform actions across multiple stores simultaneously such as viewing product availability. the mall management can authenticate clients on all stores participating in the 3d virtual mall while only requiring clients to provide authentication information once. 3d virtual shopping online mall convenient and easy process allow consumers directly buy goods or services from a seller in real - time, without an intermediary service, over the internet. the virtual mall with an active 3d model is implemented by using 3d language ( vrml ) and asp. net as the script language for shopping online pages | arxiv:1512.02372 |
modern reconstruction methods for magnetic resonance imaging ( mri ) exploit the spatially varying sensitivity profiles of receive - coil arrays as additional source of information. this allows to reduce the number of time - consuming fourier - encoding steps by undersampling. the receive sensitivities are a priori unknown and influenced by geometry and electric properties of the ( moving ) subject. for optimal results, they need to be estimated jointly with the image from the same undersampled measurement data. formulated as an inverse problem, this leads to a bilinear reconstruction problem related to multi - channel blind deconvolution. in this work, we will discuss some recently developed approaches for the solution of this problem. | arxiv:1705.04081 |
joan w. ( 1971 ), " duality in analysis from the point of view of triples ", journal of algebra, 19 ( 2 ) : 228 – 253, doi : 10. 1016 / 0021 - 8693 ( 71 ) 90105 - 0, issn 0021 - 8693, mr 0280571 rudin, walter ( 1976 ), principles of mathematical analysis ( 3rd ed. ), new york : mcgraw - hill, isbn 0 - 07 - 054235 - x veblen, oswald ; young, john wesley ( 1965 ), projective geometry. vols. 1, 2, blaisdell publishing co. ginn and co., mr 0179666 weibel, charles a. ( 1994 ), an introduction to homological algebra, cambridge university press, isbn 978 - 0 - 521 - 55987 - 4, mr 1269324 edwards, r. e. ( 1965 ). functional analysis. theory and applications. new york : holt, rinehart and winston. isbn 0030505356. | https://en.wikipedia.org/wiki/Duality_(mathematics) |
as subjects perceive the sensory world, different stimuli elicit a number of neural representations. here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. as an example, the subjective distance between different locations in space is calculated from the activity of rodent hippocampal place cells, and lateral septal cells. such a distance is compared to the real distance, between locations. as the number of sampled neurons increases, the subjective distance shows a tendency to resemble the metrics of real space. | arxiv:q-bio/0408008 |
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