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in previous work, we developed a deep neural network classifier that only relies on phase - space information to obtain a catalog of accreted stars based on the second data release of gaia ( dr2 ). in this paper, we apply two clustering algorithms to identify velocity substructure within this catalog. we focus on the subset of stars with line - of - sight velocity measurements that fall in the range of galactocentric radii $ r \ in [ 6. 5, 9. 5 ] $ kpc and vertical distances $ | z | < 3 $ kpc. known structures such as gaia enceladus and the helmi stream are identified. the largest previously - unknown structure, nyx, is a vast stream consisting of at least 90 stars in the region of interest. this study displays the power of the machine learning approach by not only successfully identifying known features, but also discovering new kinematic structures that may shed light on the merger history of the milky way.
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arxiv:1907.07681
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trappist - 1 hosts seven earth - sized planets transiting an m8 star. we observed mid - transit times of each of the inner two planets with the astrophysical research consortium ( arc ) 3. 5 m telescope at apache point observatory ( apo ) to help constrain the planet masses with transit timing variations, and we outline a procedure for analyzing transit observations of late - m stars with apo. the transit times of trappist - 1 b and c are $ \ mathrm { bjd } _ { \ mathrm { tdb } } = 2457580. 87634 ^ { + 0. 00034 } _ { - 0. 00034 } $ and $ 2457558. 89477 ^ { + 0. 00080 } _ { - 0. 00085 } $, respectively, which will help constrain the planet masses.
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arxiv:1801.04460
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this paper introduces the fft - enhanced kalman filter ( fftkf ), a differentially private optimization method that addresses the challenge of preserving performance in dp - sgd, where added noise typically degrades model utility. fftkf integrates frequency - domain noise shaping with kalman filtering to enhance gradient quality while preserving $ ( \ varepsilon, \ delta ) $ - dp guarantees. it employs a high - frequency shaping mask in the fourier domain to concentrate differential privacy noise in less informative spectral components, preserving low - frequency gradient signals. a scalar - gain kalman filter with finite - difference hessian approximation further refines the denoised gradients. with a per - iteration complexity of $ \ mathcal { o } ( d \ log d ) $, fftkf demonstrates improved test accuracy over dp - sgd and disk across mnist, cifar - 10, cifar - 100, and tiny - imagenet datasets using cnns, wide resnets, and vision transformers. theoretical analysis confirms that fftkf maintains equivalent privacy guarantees while achieving a tighter privacy - utility trade - off through reduced noise and controlled bias.
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arxiv:2505.04468
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the bender - dunne basis operators, $ \ mathsf { t } _ { - m, n } = 2 ^ { - n } \ sum _ { k = 0 } ^ n { n \ choose k } \ mathsf { q } ^ k \ mathsf { p } ^ { - m } \ mathsf { q } ^ { n - k } $ where $ \ mathsf { q } $ and $ \ mathsf { p } $ are the position and momentum operators respectively, are formal integral operators in position representation in the entire real line $ \ mathbb { r } $ for positive integers $ n $ and $ m $. we show, by explicit construction of a dense domain, that the operators $ \ mathsf { t } _ { - m, n } $ ' s are densely defined operators in the hilbert space $ l ^ 2 ( \ mathbb { r } ) $.
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arxiv:1509.00340
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we say that wiener ' s property holds for the exponent $ p > 0 $ if we have that whenever a positive definite function $ f $ belongs to $ l ^ p ( - \ epsilon, \ epsilon ) $ for some $ \ epsilon > 0 $, then $ f $ necessarily belongs to $ l ^ p ( \ tt ) $, too. this holds true for $ p \ in 2 \ nn $ by a classical result of wiener. recently various concentration results were proved for idempotents and positive definite functions on measurable sets on the torus. these new results enable us to prove a sharp version of the failure of wiener ' s property for $ p \ notin 2 \ nn $. thus we obtain strong extensions of results of wainger and shapiro, who proved the negative answer to wiener ' s problem for $ p \ notin 2 \ nn $.
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arxiv:0711.0676
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1 : k \ in \ mathbb { z } \ } } the set of even numbers is a prime ideal of z { \ displaystyle \ mathbb { z } } and the quotient ring z / 2 z { \ displaystyle \ mathbb { z } / 2 \ mathbb { z } } is the field with two elements. parity can then be defined as the unique ring homomorphism from z { \ displaystyle \ mathbb { z } } to z / 2 z { \ displaystyle \ mathbb { z } / 2 \ mathbb { z } } where odd numbers are 1 and even numbers are 0. the consequences of this homomorphism are covered below. = = properties = = the following laws can be verified using the properties of divisibility. they are a special case of rules in modular arithmetic, and are commonly used to check if an equality is likely to be correct by testing the parity of each side. as with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic, and multiplication is distributive over addition. however, subtraction in modulo 2 is identical to addition, so subtraction also possesses these properties, which is not true for normal integer arithmetic. = = = addition and subtraction = = = even ± even = even ; even ± odd = odd ; odd ± odd = even ; = = = multiplication = = = even × even = even ; even × odd = even ; odd × odd = odd ; by construction in the previous section, the structure ( { even, odd }, +, × ) is in fact the field with two elements. = = = division = = = the division of two whole numbers does not necessarily result in a whole number. for example, 1 divided by 4 equals 1 / 4, which is neither even nor odd, since the concepts of even and odd apply only to integers. but when the quotient is an integer, it will be even if and only if the dividend has more factors of two than the divisor. = = history = = the ancient greeks considered 1, the monad, to be neither fully odd nor fully even. some of this sentiment survived into the 19th century : friedrich wilhelm august frobel ' s 1826 the education of man instructs the teacher to drill students with the claim that 1 is neither even nor odd, to which frobel attaches the philosophical afterthought, it is well
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https://en.wikipedia.org/wiki/Parity_(mathematics)
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modern machine learning ( ml ) models are becoming increasingly popular and are widely used in decision - making systems. however, studies have shown critical issues of ml discrimination and unfairness, which hinder their adoption on high - stake applications. recent research on fair classifiers has drawn significant attention to developing effective algorithms to achieve fairness and good classification performance. despite the great success of these fairness - aware machine learning models, most of the existing models require sensitive attributes to pre - process the data, regularize the model learning or post - process the prediction to have fair predictions. however, sensitive attributes are often incomplete or even unavailable due to privacy, legal or regulation restrictions. though we lack the sensitive attribute for training a fair model in the target domain, there might exist a similar domain that has sensitive attributes. thus, it is important to exploit auxiliary information from a similar domain to help improve fair classification in the target domain. therefore, in this paper, we study a novel problem of exploring domain adaptation for fair classification. we propose a new framework that can learn to adapt the sensitive attributes from a source domain for fair classification in the target domain. extensive experiments on real - world datasets illustrate the effectiveness of the proposed model for fair classification, even when no sensitive attributes are available in the target domain.
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arxiv:2206.03656
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most of the current transformer - based chemical language models are pre - trained on millions to billions of molecules. however, the improvement from such scaling in dataset size is not confidently linked to improved molecular property prediction. the aim of this study is to investigate and overcome some of the limitations of transformer models in predicting molecular properties. specifically, we examine the impact of pre - training dataset size and diversity on the performance of transformer models and investigate the use of domain adaptation as a technique for improving model performance. first, our findings indicate that increasing pretraining dataset size beyond 400k molecules from the guacamol dataset does not result in a significant improvement on four adme endpoints, namely, solubility, permeability, microsomal stability, and plasma protein binding. second, our results demonstrate that using domain adaptation by further training the transformer model on a small set of domain - relevant molecules, i. e., a few hundred to a few thousand, using multi - task regression of physicochemical properties was sufficient to significantly improve performance for three out of the four investigated adme endpoints ( p - value < 0. 001 ). finally, we observe that a model pre - trained on 400k molecules and domain adopted on a few hundred / thousand molecules performs similarly ( p - value > 0. 05 ) to more complicated transformer models like molbert ( pre - trained on 1. 3m molecules ) and molformer ( pre - trained on 100m molecules ). a comparison to a random forest model trained on basic physicochemical properties showed similar performance to the examined transformer models. we believe that current transformer models can be improved through further systematic analysis of pre - training and downstream data, pre - training objectives, and scaling laws, ultimately leading to better and more helpful models.
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arxiv:2503.03360
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graph convolutional networks ( gcns ) are powerful tools for graph - structured data. however, they have been recently shown to be vulnerable to topological attacks. to enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. by challenging the classical graph laplacian, we propose a new convolution operator that is provably robust in the spectral domain and is incorporated in the gcn architecture to improve expressivity and interpretability. by extending the original graph to a sequence of graphs, we also propose a robust training paradigm that encourages transferability across graphs that span a range of spatial and spectral characteristics. the proposed approaches are demonstrated in extensive experiments to simultaneously improve performance in both benign and adversarial situations.
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arxiv:1905.10029
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in this paper, we study the following two hypercube coloring problems : given $ n $ and $ d $, find the minimum number of colors, denoted as $ { \ chi } ' _ { d } ( n ) $ ( resp. $ { \ chi } _ { d } ( n ) $ ), needed to color the vertices of the $ n $ - cube such that any two vertices with hamming distance at most $ d $ ( resp. exactly $ d $ ) have different colors. these problems originally arose in the study of the scalability of optical networks. using methods in coding theory, we show that $ { \ chi } ' _ { 4 } ( 2 ^ { r + 1 } - 1 ) = 2 ^ { 2r + 1 } $, $ { \ chi } ' _ { 5 } ( 2 ^ { r + 1 } ) = 4 ^ { r + 1 } $ for any odd number $ r \ geq3 $, and give two upper bounds on $ { \ chi } _ { d } ( n ) $. the first upper bound improves on that of kim, du and pardalos. the second upper bound improves on the first one for small $ n $. furthermore, we derive an inequality on $ { \ chi } _ { d } ( n ) $ and $ { \ chi } ' _ { d } ( n ) $.
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arxiv:1001.2209
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an analytic phenomenological shell model mass formula for light nuclei is constructed., the formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely : a ) charge and mass distributions are closer to a gaussian shape than to the shape characteristic in medium and heavy nuclei ; b ) the central charge and mass densities are larger than, and decrease towards, the " asymptotic " values that are the reference parameters for nuclear matter ; and c ) after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin - orbit couplings. a correlation between the " skin effect " and the symmetry dependence of the optical potential is established. towards the neutron drip line the potential well depth, the spin - orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. the ensuing shift and contraction of the single particle level scheme may lead to : a ) to strong configuration mixing and new magic numbers, and b ) the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.
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arxiv:1207.6050
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aims. excitation of far - infrared and submillimetric molecular lines may originate from nonreactive collisions, chemical formation, or far infrared, near - infrared, and optical fluorescences. as a template, we investigate the impact of each of these processes on the excitation of the methylidyne cation ch + and on the intensities of its rotational transitions recently detected in emission in dense photodissociation regions ( pdrs ) and in planetary nebulae. methods. we have developed a nonlocal thermodynamic equilibrium ( non - lte ) excitation model that includes the entire energy structure of ch +, i. e. taking into account the pumping of its vibrational and bound and unbound electronic states by near - infrared and optical photons. the model includes the theoretical cross - sections of nonreactive collisions with h, h2, he, and e -, and a boltzmann distribution is used to describe the probability of populating the excited levels of ch + during its chemical formation by hydrogenation of c +. to confirm our results we also performed an extensive analytical study, which we use to predict the main excitation process of several diatomic molecules, namely hf, hcl, sio, cs, and co. results. at densities nh = 10 ^ 4 cm - 3, the excitation of the rotational levels of ch + is dominated by the radiative pumping of its electronic, vibrational, and rotational states if the intensities of the radiation field at \ sim 0. 4, \ sim 4, and \ sim 300 \ mum are stronger than 10 ^ 5, 10 ^ 8, and 10 ^ 4 times those of the local interstellar radiation field ( isrf ). below these values, the chemical pumping is the dominant source of excitation of the j > 1 levels, even at high kinetic temperatures ( \ sim 1000 k ). the far - infrared emission lines of ch + observed in the orion bar and the ngc 7027 pdrs are consistent with the predictions of our excitation model assuming an incident far - ultraviolet ( fuv ) radiation field of \ sim 3 \ times 10 ^ 4 ( in draine ' s unit ) and densities of \ sim 5 \ times 10 ^ 4 and \ sim 2 \ times 10 ^ 5 cm - 3. in the case of ngc 7027, the estimate of the density is 10 to 100 times lower than those deduced by traditional excitation codes
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arxiv:1211.5528
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we study the problem of realizing the full spectrum of bipedal locomotion on a real robot with sim - to - real reinforcement learning ( rl ). a key challenge of learning legged locomotion is describing different gaits, via reward functions, in a way that is intuitive for the designer and specific enough to reliably learn the gait across different initial random seeds or hyperparameters. a common approach is to use reference motions ( e. g. trajectories of joint positions ) to guide learning. however, finding high - quality reference motions can be difficult and the trajectories themselves narrowly constrain the space of learned motion. at the other extreme, reference - free reward functions are often underspecified ( e. g. move forward ) leading to massive variance in policy behavior, or are the product of significant reward - shaping via trial - and - error, making them exclusive to specific gaits. in this work, we propose a reward - specification framework based on composing simple probabilistic periodic costs on basic forces and velocities. we instantiate this framework to define a parametric reward function with intuitive settings for all common bipedal gaits - standing, walking, hopping, running, and skipping. using this function we demonstrate successful sim - to - real transfer of the learned gaits to the bipedal robot cassie, as well as a generic policy that can transition between all of the two - beat gaits.
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arxiv:2011.01387
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recent studies have extended the use of the stochastic hamilton - jacobi - bellman ( hjb ) equation to include complex variables for deriving quantum mechanical equations. however, these studies often assume that it is valid to apply the hjb equation directly to complex numbers, an approach that overlooks the fundamental problem of comparing complex numbers when finding optimal controls. this paper explores the application of the hjb equation in the context of complex variables. it provides an in - depth investigation of the stochastic movement of quantum particles within the framework of stochastic optimal control theory. we obtain the complex diffusion coefficient in the stochastic equation of motion using the cauchy - riemann theorem, considering that the particle ' s stochastic movement is described by two perfectly correlated real and imaginary stochastic processes. during the development of the covariant form of the hjb equation, we demonstrate that if the temporal stochastic increments of the two processes are perfectly correlated, then the spatial stochastic increments must be perfectly anti - correlated, and vice versa. the diffusion coefficient we derive has a form that enables the linearization of the hjb equation. the method for linearizing the hjb equation, along with the subsequent derivation of the dirac equation, was developed in our previous work [ v. yordanov, scientific reports 14, 6507 ( 2024 ) ]. these insights deepen our understanding of quantum dynamics and enhance the application of stochastic optimal control theory to quantum mechanics.
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arxiv:2404.15964
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convolutional neural networks ( cnns ) have demonstrated their effectiveness in numerous vision tasks. however, their high processing requirements necessitate efficient hardware acceleration to meet the application ' s performance targets. in the space of fpgas, streaming - based dataflow architectures are often adopted by users, as significant performance gains can be achieved through layer - wise pipelining and reduced off - chip memory access by retaining data on - chip. however, modern topologies, such as the unet, yolo, and x3d models, utilise long skip connections, requiring significant on - chip storage and thus limiting the performance achieved by such system architectures. the paper addresses the above limitation by introducing weight and activation eviction mechanisms to off - chip memory along the computational pipeline, taking into account the available compute and memory resources. the proposed mechanism is incorporated into an existing toolflow, expanding the design space by utilising off - chip memory as a buffer. this enables the mapping of such modern cnns to devices with limited on - chip memory, under the streaming architecture design approach. smof has demonstrated the capacity to deliver competitive and, in some cases, state - of - the - art performance across a spectrum of computer vision tasks, achieving up to 10. 65 x throughput improvement compared to previous works.
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arxiv:2403.18921
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we consider a family of linear control systems $ \ dot { x } = ax + \ alpha bu $ where $ \ alpha $ belongs to a given class of persistently exciting signals. we seek maximal $ \ alpha $ - uniform stabilisation and destabilisation by means of linear feedbacks $ u = kx $. we extend previous results obtained for bidimensional single - input linear control systems to the general case as follows : if the pair $ ( a, b ) $ verifies a certain lie bracket generating condition, then the maximal rate of convergence of $ ( a, b ) $ is equal to the maximal rate of divergence of $ ( - a, - b ) $. we also provide more precise results in the general single - input case, where the above result is obtained under the sole assumption of controllability of the pair $ ( a, b ) $.
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arxiv:1308.3758
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quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. in this paper, we generalize important results in multipartite entanglement theory to their counterparts in quantum coherence theory. first, we give a necessary and sufficient condition for when two pure multipartite states are equivalent under local quantum incoherent operations and classical communication ( licc ), i. e., two states can be deterministically transformed to each other under licc operations. next, we investigate and give the conditions in which such a transformation succeeds only stochastically. different from entanglement case for two - qubit states, we find that the slicc equivalence classes are infinite. moreover, it ' s possible that there are some classes of states in multipartite entanglement can convert into each other, while, they cannot convert into each other in multipartite coherence. in order to show the difference among slicc classes, we introduce two coherence monotones : accessible coherence and source coherence, following the logistics given in [ \ emph { phys. ~ rev. ~ lett. 115, ~ 150502 ( 2015 ) } ]. these coherence monotones have a straightforward operational interpretation, namely, the accessible coherence characterizes the proficiency of a state to generate other states via quantum incoherent operations, while the source coherence characterizes the set of states that can be reached via quantum incoherent operations acting on the given state of interest.
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arxiv:1807.06308
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given a graph $ g $, a hypergraph $ \ mathcal { h } $ is a berge copy of $ f $ if $ v ( g ) \ subset v ( \ mathcal { h } ) $ and there is a bijection $ f : e ( g ) \ rightarrow e ( \ mathcal { h } ) $ such that for any edge $ e $ of $ g $ we have $ e \ subset f ( e ) $. we study ramsey problems for berge copies of graphs, i. e. the smallest number of vertices of a complete $ r $ - uniform hypergraph, such that if we color the hyperedges with $ c $ colors, there is a monochromatic berge copy of $ g $. we obtain a couple results regarding these problems. in particular, we determine for which $ r $ and $ c $ the ramsey number can be super - linear. we also show a new way to obtain lower bounds, and improve the general lower bounds by a large margin. in the specific case $ g = k _ n $ and $ r = 2c - 1 $, we obtain an upper bound that is sharp besides a constant term, improving earlier results.
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arxiv:1906.02465
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we present near - infrared speckle interferometry of the oh / ir star oh 104. 9 + 2. 4 in the k ' band obtained with the 6m telescope of the special astrophysical observatory ( sao ). at a wavelength of lambda = 2. 12 micron the diffraction - limited resolution of 74 mas was attained. the reconstructed visibility reveals a spherically symmetric, circumstellar dust shell ( cds ) surrounding the central star. the visibility function shows that the stellar contribution to the total flux at lambda = 2. 12 micron is less than ~ 50 %, indicating a rather large optical depth of the cds. the azimuthally averaged 1 - dimensional gaussian visibility fit yields a diameter of 47 + / - 3mas ( fhwm ), which corresponds to 112 + / - 13 au for an adopted distance of d = 2. 38 + / - 0. 24 kpc. to determine the structure and the properties of the cds of oh 104. 9 + 2. 4, radiative transfer calculations using the code dusty were performed to simultaneously model its visibility and the spectral energy distribution ( sed ). we found that both the iso spectrum and the visibility of oh 104. 9 + 2. 4 can be well reproduced by a radiative transfer model with an effective temperature t _ eff = 2500 + / - 500 k of the central source, a dust temperature t _ in = 1000 + / - 200 k at the inner shell boundary r _ in = 9. 1 r _ star = 25. 4 au, an optical depth tau = 6. 5 + / - 0. 3 at 2. 2 micron, and dust grain radii ranging from a _ min = 0. 005 + / - 0. 003 micron to a _ max = 0. 2 + / - 0. 02 micron with a power law with index - 3. 5. it was found that even minor changes in a _ max have a major impact on both the slope and the curvature of the visibility function, while the sed shows only minor changes. our detailed analysis demonstrates the potential of dust shell modeling constrained by both the sed and visibilities.
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arxiv:astro-ph/0406092
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the fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. using the divergence theorem and stokes ' theorem, closed expressions are obtained. apparent singularities, all removable, are discussed in detail. loss of precision due to cancellation near the singularities can be avoided by using series expansions.
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arxiv:1703.00255
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we studied the magnetoresistance of normal metal ( nm ) / ferromagnet ( fm ) bilayers in the linear and nonlinear ( current - dependent ) regimes and compared it with the amplitude of the spin - orbit torques and thermally induced electric fields. our experiments reveal that the magnetoresistance of the heavy nm / co bilayers ( nm = ta, w, pt ) is phenomenologically similar to the spin hall magnetoresistance ( smr ) of yig / pt, but has a much larger anisotropy, of the order of 0. 5 %, which increases with the atomic number of the nm. this smr - like behavior is absent in light nm / co bilayers ( nm = ti, cu ), which present the standard amr expected of polycrystalline fm layers. in the ta, w, pt / co bilayers we find an additional magnetoresistance, directly proportional to the current and to the transverse component of the magnetization. this so - called unidirectional smr, of the order of 0. 005 %, is largest in w and correlates with the amplitude of the antidamping spin - orbit torque. the unidirectional smr is below the accuracy of our measurements in yig / pt.
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arxiv:1510.06285
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in 2002, a method has been proposed by buchholz et al. in the context of local quantum physics, to characterize states that are locally in thermodynamic equilibrium. it could be shown for the model of massless bosons that these states exhibit quite interesting properties. the mean phase - space density satisfies a transport equation, and many of these states break time reversal symmetry. moreover, an explicit example of such a state, called the hot bang state, could be found, which models the future of a temperature singularity. however, although the general results carry over to the fermionic case easily, the proof of existence of an analogue of the hot bang state is not quite that straightforward. the proof will be given in this paper. moreover, we will discuss some of the mathematical subtleties which arise in the fermionic case.
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arxiv:math-ph/0504074
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we show that if $ x $ is an arc - like continuum which can be represented as an inverse limit of a simplicial inverse system on arcs, then for every point $ x \ in x $ there is a plane embedding of $ x $ in which $ x $ is accessible. this answers a special case of the nadler - quinn question from 1972.
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arxiv:2311.14128
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we consider the { \ em correlated knapsack orienteering } ( csko ) problem : we are given a travel budget $ b $, processing - time budget $ w $, finite metric space $ ( v, d ) $ with root $ \ rho \ in v $, where each vertex is associated with a job with possibly correlated random size and random reward that become known only when the job completes. random variables are independent across different vertices. the goal is to compute a $ \ rho $ - rooted path of length at most $ b $, in a possibly adaptive fashion, that maximizes the reward collected from jobs that are processed by time $ w $. to our knowledge, csko has not been considered before, though prior work has considered the uncorrelated problem, { \ em stochastic knapsack orienteering }, and { \ em correlated orienteering }, which features only one budget constraint on the { \ em sum } of travel - time and processing - times. we show that the { \ em adaptivity gap of csko is not a constant, and is at least $ \ omega \ bigl ( \ max \ sqrt { \ log { b } }, \ sqrt { \ log \ log { w } } \ } \ bigr ) $ }. complementing this, we devise { \ em non - adaptive } algorithms that obtain : ( a ) $ o ( \ log \ log w ) $ - approximation in quasi - polytime ; and ( b ) $ o ( \ log w ) $ - approximation in polytime. we obtain similar guarantees for csko with cancellations, wherein a job can be cancelled before its completion time, foregoing its reward. we also consider the special case of csko, wherein job sizes are weighted bernoulli distributions, and more generally where the distributions are supported on at most two points ( 2 - csko ). although weighted bernoulli distributions suffice to yield an $ \ omega ( \ sqrt { \ log \ log b } ) $ adaptivity - gap lower bound for ( uncorrelated ) { \ em stochastic orienteering }, we show that they are easy instances for csko. we develop non - adaptive algorithms that achieve $ o ( 1 ) $ - approximation in polytime for weighted bernoulli distributions, and in $ ( n + \ log b ) ^ { o ( \ log w ) } $ - time for the more general case of 2 - csko.
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arxiv:2408.16566
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we study vanishing results for l2 - cohomology of countable groups under the presence of subgroups that satisfy some weak normality condition. as a consequence we show that the l2 - betti numbers of sl ( n, r ) for any infinite integral domain r vanish below degree n - 1. we also give a uniform proof for the vanishing of l2 - betti numbers of thompson ' s groups f and t.
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arxiv:1206.4793
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in merger - driven models of massive galaxy evolution, the luminous quasar phase is expected to be accompanied by vigorous star formation in quasar host galaxies. in this paper, we use high column density damped lyman alpha ( dla ) systems along quasar sight lines as natural coronagraphs to directly study the far - uv ( fuv ) radiation from the host galaxies of luminous background quasars. we have stacked the spectra of $ \ sim $ 2, 000 dla systems ( n _ hi > 10 ^ { 20. 6 } cm ^ { - 2 } ) with a median absorption redshift < z > = 2. 6 selected from quasars observed in the sdss - iii baryon oscillation spectroscopic survey. we detect residual flux in the dark troughs of the composite dla spectra. the level of this residual flux significantly exceeds systematic errors in the sdss fiber sky subtraction ; furthermore, the residual flux is strongly correlated with the continuum luminosity of the background quasar, while uncorrelated with dla column density or metallicity. we conclude that the flux could be associated with the average fuv radiation from the background quasar host galaxies ( with medium redshift < z > = 3. 1 ) that is not blocked by the intervening dla. assuming all of the detected flux originates from quasar hosts, for the highest quasar luminosity bin ( < l > = 2. 5x 10 ^ { 13 } l _ sun ), the host galaxy has a fuv intensity of 1. 5 + / - 0. 2 x 10 ^ { 40 } erg s ^ { - 1 } a ^ { - 1 } ; this corresponds to an unobscured uv star formation rate of 9 m _ sun / yr.
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arxiv:1408.0829
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in this work we study invertible bloom lookup tables ( iblts ) with small failure probabilities. iblts are highly versatile data structures that have found applications in set reconciliation protocols, error - correcting codes, and even the design of advanced cryptographic primitives. for storing $ n $ elements and ensuring correctness with probability at least $ 1 - \ delta $, existing iblt constructions require $ \ omega ( n ( \ frac { \ log ( 1 / \ delta ) } { \ log ( n ) } + 1 ) ) $ space and they crucially rely on fully random hash functions. we present new constructions of iblts that are simultaneously more space efficient and require less randomness. for storing $ n $ elements with a failure probability of at most $ \ delta $, our data structure only requires $ \ mathcal { o } \ left ( n + \ log ( 1 / \ delta ) \ log \ log ( 1 / \ delta ) \ right ) $ space and $ \ mathcal { o } \ left ( \ log ( \ log ( n ) / \ delta ) \ right ) $ - wise independent hash functions. as a key technical ingredient we show that hashing $ n $ keys with any $ k $ - wise independent hash function $ h : u \ to [ cn ] $ for some sufficiently large constant $ c $ guarantees with probability $ 1 - 2 ^ { - \ omega ( k ) } $ that at least $ n / 2 $ keys will have a unique hash value. proving this is non - trivial as $ k $ approaches $ n $. we believe that the techniques used to prove this statement may be of independent interest. we apply our new iblts to the encrypted compression problem, recently studied by fleischhacker, larsen, simkin ( eurocrypt 2023 ). we extend their approach to work for a more general class of encryption schemes and using our new iblt we achieve an asymptotically better compression rate.
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arxiv:2306.07583
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in their 1995 paper, jean - beno \ ^ { i } t bost and alain connes ( bc ) constructed a quantum dynamical system whose partition function is the riemann zeta function $ \ zeta ( \ beta ) $, where $ \ beta $ is an inverse temperature. we formulate riemann hypothesis ( rh ) as a property of the low temperature kubo - martin - schwinger ( kms ) states of this theory. more precisely, the expectation value of the bc phase operator can be written as $ $ \ phi _ { \ beta } ( q ) = n _ { q - 1 } ^ { \ beta - 1 } \ psi _ { \ beta - 1 } ( n _ q ), $ $ where $ n _ q = \ prod _ { k = 1 } ^ qp _ k $ is the primorial number of order $ q $ and $ \ psi _ b $ a generalized dedekind $ \ psi $ function depending on one real parameter $ b $ as $ $ \ psi _ b ( q ) = q \ prod _ { p \ in \ mathcal { p, } p \ vert q } \ frac { 1 - 1 / p ^ b } { 1 - 1 / p }. $ $ fix a large inverse temperature $ \ beta > 2. $ the riemann hypothesis is then shown to be equivalent to the inequality $ $ n _ q | \ phi _ \ beta ( n _ q ) | \ zeta ( \ beta - 1 ) > e ^ \ gamma \ log \ log n _ q, $ $ for $ q $ large enough. under rh, extra formulas for high temperatures kms states ( $ 1. 5 < \ beta < 2 $ ) are derived.
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arxiv:1012.4665
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magnetic chemically peculiar ( mcp ) stars exhibit complex atmospheres that allow the investigation of such diverse phenomena as atomic diffusion, magnetic fields, and stellar rotation. the advent of space - based photometry provides the opportunity for the first precise characterizations of the photometric variability properties of these stars. we carried out a search for new mcp stars in the kepler field with the ultimate aim of investigating their photometric variability properties using kepler data. as an aside, we describe criteria for selecting mcp star candidates based on light curve properties, and assess the accuracy of the spectral classifications provided by the mkclass code. as only very few known mcp stars are situated in the kepler field, we had to depend largely on alternative ( nonspectroscopic ) means of identifying suitable candidates that rely mostly on light curve properties ; in particular we relied on monoperiodic variability and light curve stability. newly acquired and archival spectra were used to confirm most of our mcp star candidates. linear ephemeris parameters and effective amplitudes were derived from detrended kepler data. our final sample consists of 41 spectroscopically confirmed mcp stars of which 39 are new discoveries, 5 candidate mcp stars, and 7 stars in which no chemical peculiarities could be established. our targets populate the whole age range from zero - age main sequence to terminal - age main sequence and are distributed in the mass interval from 1. 5 m _ sun to 4 m _ sun. about 25 % of the mcp stars show a hitherto unobserved wealth of detail in their light curves indicative of complex surface structures. we identified light curve stability as a primary criterion for identifying mcp star candidates among early - type stars in large photometric surveys, and prove the reliability of the spectral classifications provided by the mkclass code.
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arxiv:1808.05669
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in this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. this is the function field analog of the euler - zagier multiple zeta function of depth d.
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arxiv:math/0512027
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we study the open string extension of the mirror map for n = 1 supersymmetric type ii vacua with d - branes on non - compact calabi - yau manifolds. its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. the solutions describe the flat coordinates on the n = 1 parameter space, and the exact disc instanton corrected superpotential on the d - brane world - volume. a gauged linear sigma model for the combined open - closed string system is also given. it allows to use methods of toric geometry to describe d - brane phase transitions and the n = 1 k \ " ahler cone. applications to a variety of d - brane geometries are described in some detail.
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arxiv:hep-th/0111113
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the variational determination of the two - particle density matrix is an interesting, but not yet fully explored technique that allows to obtain ground - state properties of a quantum many - body system without reference to an $ n $ - particle wave function. the one - dimensional fermionic hubbard model has been studied before with this method, using standard two - and three - index conditions on the density matrix [ j. r. hammond { \ it et al. }, phys. rev. a 73, 062505 ( 2006 ) ], while a more recent study explored so - called subsystem constraints [ n. shenvi { \ it et al. }, phys. rev. lett. 105, 213003 ( 2010 ) ]. these studies reported good results even with only standard two - index conditions, but have always been limited to the half - filled lattice. in this letter we establish the fact that the two - index approach fails for other fillings. in this case, a subset of three - index conditions is absolutely needed to describe the correct physics in the strong - repulsion limit. we show that applying lifting conditions [ j. r. hammond { \ it et al. }, phys. rev. a 71, 062503 ( 2005 ) ] is the most economical way to achieve this, while still avoiding the computationally much heavier three - index conditions. a further extension to spin - adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. at the same time we establish the feasibility of such studies to the more complicated phase diagram in two - dimensional hubbard models.
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arxiv:1110.5732
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global strings ( those which couple to goldstone modes ) may play a role in cosmology. in particular, if the qcd axion exists, axionic strings may control the efficiency of axionic dark matter abundance. the string network dynamics depend on the string intercommutation efficiency ( whether strings re - connect when they cross ). we point out that the velocity and angle in a collision between global strings " renormalize " between the network scale and the microscopic scale, and that this plays a significant role in their intercommutation dynamics. we also point out a subtlety in treating intercommutation of very nearly antiparallel strings numerically. we find that the global strings of a o ( 2 ) - breaking scalar theory do intercommute for all physically relevant angles and velocities.
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arxiv:1604.02356
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we examine the regge ( high energy ) limit of 4 - point scattering in both qcd and gravity, using recently developed techniques to systematically compute all corrections up to next - to - leading power in the exchanged momentum i. e. beyond the eikonal approximation. we consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. in qcd, our calculation describes power - suppressed corrections to the reggeisation of the gluon. in gravity, we confirm a previous conjecture that next - to - soft corrections correspond to two independent deflection angles for the incoming particles. our calculations in qcd and gravity are consistent with the well - known double copy relating amplitudes in the two theories.
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arxiv:1611.02172
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we have previously found in the hubble deep field a significant angular correlation of faint, high color - redshift objects on scales below one arcsecond, or several kiloparsecs in metric size. we examine the correlation and nearest neighbor statistics to conclude that 38 % of these objects in the hdf have a companion within one arcsecond, three times the number expected in a random distribution with the same number of objects. we examine three dynamical scenarios for these object multiplets : 1 ) the objects are star - forming regions within normal galaxies, whose disks have been relatively dimmed by k - correction and surface brightness dimming ; 2 ) they are fragments merging into large galaxies ; 3 ) they are satellites accreting onto normal l _ * galaxies. we find that hypothesis 1 is most tenable. first, large galaxies in the process of a merger formation would have accumulated too much mass in their centers ( 5e12 m _ sun inside 2 kpc ) to correspond to present day objects. second, accretion by dynamical friction occurs with a predictable density vs. radius slope, not seen among the faint hdf objects. since the dynamical friction time is roughly ( 1 gyr ), a steady - state should have been reached by redshift z < 5. star - forming regions within galaxies clearly present no dynamical problems. since large spirals would still appear as such in the hdf, we favor a scenario in which the faint compact sources in the hdf are giant starforming regions within small normal galaxies, such as magellanic irregulars. finally we checked that reduction in mass - to - light from induced star - formation cannot alone explain the luminosity overdensity.
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arxiv:astro-ph/9702030
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we investigate the properties of a static, cylindrically symmetric majumdar - papapetrou - type solution of einstein - maxwell equations. we locate its singularities, establish its algebraic type, find its asymptotic properties and weak - field limit, study the structure of electrogeodesics, and determine the mass and charge of its sources. we provide an interpretation of the spacetime and discuss the parameter appearing in the metric.
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arxiv:1611.07192
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transfer learning for partial differential equations ( pdes ) is to develop a pre - trained neural network that can be used to solve a wide class of pdes. existing transfer learning approaches require much information of the target pdes such as its formulation and / or data of its solution for pre - training. in this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using pde information. the construction of the feature space involves re - parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space. theoretical analysis shows the high quality of the produced feature space, i. e., uniformly distributed neurons. extensive numerical experiments verify the outstanding performance of our method, including significantly improved transferability, e. g., using the same feature space for various pdes with different domains and boundary conditions, and the superior accuracy, e. g., several orders of magnitude smaller mean squared error than the state of the art methods.
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arxiv:2301.11701
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we discuss a few examples of rich newly developing field of double parton scattering. we start our presentation from production of two pairs of charm quark - antiquark and argue that it is the golden reaction to study the double parton scattering effects. in addition to the dps we consider briefly also mechanism of single parton scattering and show that it gives much smaller contribution to the $ c \ bar c c \ bar c $ final state. next we discuss a perturbative parton - splitting mechanism which should be included in addition to the conventional dps mechanism. we show that the presence of this mechanism unavoidably leads to collision energy and other kinematical variables dependence of so - called $ \ sigma _ { eff } $ parameter being extracted from different experiments. next we briefly discuss production of four jets. we concentrate on estimation of the contribution of dps for jets remote in rapidity. understanding of this contribution is very important in the context of searches for bfkl effects known under the the name mueller - navelet jets. we discuss the situation in a more general context. finally we briefly mention about dps effects in production of $ w ^ + w ^ - $. outlook closes the presentation.
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arxiv:1504.06491
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recent works on predictive uncertainty estimation have shown promising results on out - of - distribution ( ood ) detection for semantic segmentation. however, these methods struggle to precisely locate the point of interest in the image, i. e, the anomaly. this limitation is due to the difficulty of finegrained prediction at the pixel level. to address this issue, we build upon the recent obsnet approach by providing object instance knowledge to the observer. we extend obsnet by harnessing an instance - wise mask prediction. we use an additional, class agnostic, object detector to filter and aggregate observer predictions. finally, we predict an unique anomaly score for each instance in the image. we show that our proposed method accurately disentangles in - distribution objects from ood objects on three datasets.
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arxiv:2207.08782
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we study the sensitivity of the hellaz and borexino solar neutrino experiments on discriminating the neutrino species nu _ e, anti - nu _ e, nu _ { mu, tau }, anti - nu _ { mu, tau }, and nu _ { sterile } using the difference in the recoil electron kinetic energy spectra in elastic neutrino - electron scattering. we find that one can observe a non - vanishing nu _ { mu, tau } component in the solar neutrino flux, especially when the nu _ e survival probability is low. also, if the data turn out to be consistent with nu _ e < - > nu _ { mu, tau } oscillations, an anti - nu _ e component can be excluded effectively.
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arxiv:hep-ph/0003210
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we test the holographic conjecture for brane black holes : that a full classical 5d solution will correspond to a quantum corrected 4d black hole. we show that a schwarzschild - ads black string in the bulk can be consistently interpreted as a quantum - corrected black hole on the brane, but the form of the quantum corrections is unlike what we would expect. the stress tensor extracted from the bulk solution does not have a thermal component corresponding to hawking radiation outside the black hole. we compare this strong coupling prediction to a weak coupling calculation to study the differences in detail. we comment on implications for asymptotically flat black holes and for black holes localised in the extra dimension.
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arxiv:0802.2037
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we propose a new cryptosystem by combing the lissajous map, which is the asymptotic model of deterministic randomness, with the one - way coupled map lattice ( ocml ) system. the key space, the encryption efficiency, and the security are investigated. we find that the parameter sensitivity can reach the computational precision when the system size is only three, all the lattice outputs can be treated as key stream parallelly, and the system is resistible against various attacks including the differential - like chosen cipher attack. the findings of this paper are a strong indication of the importance of deterministic randomness in secure communications.
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arxiv:nlin/0507063
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in this paper we deal with the problem of axiomatizing the preference relations modelled through choquet integral with respect to a $ k $ - additive capacity, i. e. whose m \ " obius transform vanishes for subsets of more than $ k $ elements. thus, $ k $ - additive capacities range from probability measures ( $ k = 1 $ ) to general capacities ( $ k = n $ ). the axiomatization is done in several steps, starting from symmetric 2 - additive capacities, a case related to the gini index, and finishing with general $ k $ - additive capacities. we put an emphasis on 2 - additive capacities. our axiomatization is done in the framework of social welfare, and complete previous results of weymark, gilboa and ben porath, and gajdos.
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arxiv:0711.2489
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we study in this paper a variant of wasserstein barycenter problem, which we refer to as tree - wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for wasserstein distance. drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree - wasserstein barycenter and its variants. the proposed approach is not only fast for computation but also efficient for memory usage. exploiting the tree - wasserstein barycenter and its variants, we scale up multi - level clustering and scalable bayes, especially for large - scale applications where the number of supports in probability measures is large. empirically, we test our proposed approach against other baselines on large - scale synthetic and real datasets.
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arxiv:1910.04483
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a holomorphic 1 - form on a compact riemann surface s naturally defines a flat metric on s with cone - type singularities. we present the following surprising phenomenon : having found a geodesic segment ( saddle connection ) joining a pair of conical points one can find with a nonzero probability another saddle connection on s having the same direction and the same length as the initial one. the similar phenomenon is valid for the families of parallel closed geodesics. we give a complete description of all possible configurations of parallel saddle connections ( and of families of parallel closed geodesics ) which might be found on a generic flat surface s. we count the number of saddle connections of length less than l on a generic flat surface s ; we also count the number of admissible configurations of pairs ( triples,... ) of saddle connections ; we count the analogous numbers of configurations of families of closed geodesics. by the previous result of a. eskin and h. masur these numbers have quadratic asymptotics with respect to l. here we explicitly compute the constant in this quqadratic asymptotics for a configuration of every type. the constant is found from a siegel - - veech formula. to perform this computation we elaborate the detailed description of the principal part of the boundary of the moduli space of holomorphic 1 - forms and we find the numerical value of the normalized volume of the tubular neighborhood of the boundary. we use this for evaluation of integrals over the moduli space.
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arxiv:math/0202134
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discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. we introduce discovery of dynamical systems via moving horizon optimization ( dysmho ), a scalable machine learning framework for identifying governing laws in the form of differential equations from large - scale noisy experimental data sets. dysmho consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. the sequential nature of dysmho allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. canonical nonlinear dynamical system examples are used to demonstrate that dysmho can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.
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arxiv:2108.00069
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lidar semantic segmentation provides 3d semantic information about the environment, an essential cue for intelligent systems during their decision making processes. deep neural networks are achieving state - of - the - art results on large public benchmarks on this task. unfortunately, finding models that generalize well or adapt to additional domains, where data distribution is different, remains a major challenge. this work addresses the problem of unsupervised domain adaptation for lidar semantic segmentation models. our approach combines novel ideas on top of the current state - of - the - art approaches and yields new state - of - the - art results. we propose simple but effective strategies to reduce the domain shift by aligning the data distribution on the input space. besides, we propose a learning - based approach that aligns the distribution of the semantic classes of the target domain to the source domain. the presented ablation study shows how each part contributes to the final performance. our strategy is shown to outperform previous approaches for domain adaptation with comparisons run on three different domains.
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arxiv:2010.12239
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using data collected with the hypercp ( e871 ) spectrometer during the 1997 fixed - target run at fermilab, we report the first observation of the decay k - - > pi - mu + mu - and new measurements of the branching ratios for k + / - - > pi + / - mu + mu -. by combining the branching ratios for the k + and k - decays, we measure the ratio ( k + / - - > pi + / - mu + mu - ) / ( k + / - - > all ) = ( 9. 8 + / - 1. 0 + / - 0. 5 ) x10 ^ ( - 8 ). the cp asymmetry between the k + and k - decay modes = - 0. 02 + / - 0. 11 + / - 0. 04.
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arxiv:hep-ex/0110033
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traffic analysis attacks can counteract end - to - end encryption and use leaked communication metadata to reveal information about communicating parties. with an ever - increasing amount of traffic by an ever - increasing number of networked devices, communication privacy is undermined. therefore, anonymous communication systems ( acss ) are proposed to hide the relationship between transmitted messages and their senders and receivers, providing privacy properties known as anonymity, unlinkability, and unobservability. this article aims to review research in the acss field, focusing on dining cryptographers networks ( dcns ). the dcn - based methods are information - theoretically secure and thus provide unconditional unobservability guarantees. their adoption for anonymous communications was initially hindered because their computational and communication overhead was deemed significant at that time, and scalability problems occurred. however, more recent contributions, such as the possibility to transmit messages of arbitrary length, efficient disruption handling and overhead improvements, have made the integration of modern dcn - based methods more realistic. in addition, the literature does not follow a common definition for privacy properties, making it hard to compare the approaches ' gains. therefore, this survey contributes to introducing a harmonized terminology for acs privacy properties, then presents an overview of the underlying principles of acss, in particular, dcn - based methods, and finally, investigates their alignment with the new harmonized privacy terminologies. previous surveys did not cover the most recent research advances in the acs area or focus on dcn - based methods. our comprehensive investigation closes this gap by providing visual maps to highlight privacy properties and discussing the most promising ideas for making dcns applicable in resource - constrained environments.
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arxiv:2212.08275
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soft prompt tuning achieves superior performances across a wide range of few - shot tasks. however, the performances of prompt tuning can be highly sensitive to the initialization of the prompts. we also empirically observe that conventional prompt tuning methods cannot encode and learn sufficient task - relevant information from prompt tokens. in this work, we develop an information - theoretic framework that formulates soft prompt tuning as maximizing mutual information between prompts and other model parameters ( or encoded representations ). this novel view helps us to develop a more efficient, accurate and robust soft prompt tuning method infoprompt. with this framework, we develop two novel mutual information based loss functions, to ( i ) discover proper prompt initialization for the downstream tasks and learn sufficient task - relevant information from prompt tokens and ( ii ) encourage the output representation from the pretrained language model to be more aware of the task - relevant information captured in the learnt prompt. extensive experiments validate that infoprompt can significantly accelerate the convergence of the prompt tuning and outperform traditional prompt tuning methods. finally, we provide a formal theoretical result for showing to show that gradient descent type algorithm can be used to train our mutual information loss.
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arxiv:2306.04933
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we propose the approach of model - based differentially private synthesis ( modips ) in the bayesian framework for releasing individual - level surrogate / synthetic datasets with privacy guarantees given the original data. the modips technique integrates the concept of differential privacy into model - based data synthesis. we introduce several variants for the general modips approach and different procedures to obtaining privacy - preserving posterior samples, a key step in modips. the uncertainty from the sanitization and synthetic process in modips can be accounted for by releasing multiple synthetic datasets and quantified via an inferential combination rule that is proposed in this paper. we run empirical studies to examine the impacts of the number of synthetic sets and the privacy budget allocation schemes on the inference based on synthetic data.
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arxiv:1606.08052
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the essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. in the present paper we discuss this interplay as it is present in three major departments of contemporary physics : general relativity, quantum mechanics and some attempts at quantizing gravity ( especially geometrodynamics and its recent successors in the form of various pregeometry conceptions ). it turns out that all big interpretative issues involved in this problem point towards the necessity of changing from the standard space - time geometry to some radically new, most probably non - local, generalization. we argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. noncommutative spaces are, in general, non - local, and their applications to physics, known at present, seem very promising. one would expect that beneath the planck threshold there reigns a ` ` noncommutative pregeometry ' ', and only when crossing this threshold the usual space - time geometry emerges.
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arxiv:gr-qc/9702047
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this paper describes an engine to optimize web publisher revenues from second - price auctions. these auctions are widely used to sell online ad spaces in a mechanism called real - time bidding ( rtb ). optimization within these auctions is crucial for web publishers, because setting appropriate reserve prices can significantly increase revenue. we consider a practical real - world setting where the only available information before an auction occurs consists of a user identifier and an ad placement identifier. the real - world challenges we had to tackle consist mainly of tracking the dependencies on both the user and placement in an highly non - stationary environment and of dealing with censored bid observations. these challenges led us to make the following design choices : ( i ) we adopted a relatively simple non - parametric regression model of auction revenue based on an incremental time - weighted matrix factorization which implicitly builds adaptive users ' and placements ' profiles ; ( ii ) we jointly used a non - parametric model to estimate the first and second bids ' distribution when they are censored, based on an on - line extension of the aalen ' s additive model. our engine is a component of a deployed system handling hundreds of web publishers across the world, serving billions of ads a day to hundreds of millions of visitors. the engine is able to predict, for each auction, an optimal reserve price in approximately one millisecond and yields a significant revenue increase for the web publishers.
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arxiv:2006.07083
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recent experiments observe the spin - wave - meissner - current modes in ferromagnetic insulator - superconductor heterostructures, in which the coherently excited spin waves seemingly do not decay as usual beneath the superconductor strip [ borst et al., science 382, 430 ( 2023 ) ]. we interpret this phenomenon by demonstrating that the stray magnetic field emitted by the magnetization dynamics is reflected, focused, and enhanced inside the ferromagnet by the supercurrent induced in the superconductor, such that the group velocity of spin waves is strongly enhanced. analytical and numerical calculations based on this model predict that the coherent transport of magnons is enhanced by close to 500 % for yttrium iron garnet capped by superconducting nbn with a decay length exceeding millimeters. our finding may augment the performance of magnons in quantum information and quantum transport processing.
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arxiv:2404.02598
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a systematic study of 160 heavy and super - heavy nuclei is performed in the hartree - fock - bogoliubov approach with the finite range and density dependent gogny force with the d1s parameter set. we show calculations in several approximations : with axially symmetric and reflexion symmetric wave functions, with axially symmetric and non - reflexion symmetric wave functions and finally some representative examples with triaxial wave functions are also discussed. relevant properties of the ground state and along the fission path are thoroughly analyzed. fission barriers, q $ _ \ alpha $ - factors and lifetimes with respect to fission and $ \ alpha $ - decay as well as other observables are discussed. larger configuration spaces and more general hfb wave functions as compared to previous studies provide a very good agreement with the experimental data.
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arxiv:1204.5867
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a two - variable stochastic model for diffusion - limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. the model is a direct generalization of the standard classical nucleation theory. the nucleation rate and pathway are calculated in the weak - noise approximation and are shown to be in good agreement with direct numerical simulations for the weak - solution / strong - solution transition in globular proteins. we find that classical nucleation theory underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.
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arxiv:1409.5562
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the action potential is widely considered a purely electrical phenomenon. however, one also finds mechanical and thermal changes that can be observed experimentally. in particular, nerve membranes become thicker and axons contract. the spatial length of the action potential can be quite large, ranging from millimeters to many centimeters. this suggests to employ macroscopic thermodynamics methods to understand its properties. the pulse length is several orders of magnitude larger than the synaptic gap, larger than the distance of the nodes of ranvier, and even larger than the size of many neurons such as pyramidal cells or brain stem motor neurons. here, we review the mechanical changes in nerves, theoretical possibilities to explain them, and implications of a mechanical nerve pulse for the neuron and for the brain. in particular, the contraction of nerves gives rise to the possibility of fast mechanical synapses.
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arxiv:2408.07615
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large numbers of ground states of two - dimensional ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40 ^ 2. a combination of a genetic algorithm and cluster - exact approximation is used. for each quenched realization of the bonds up to 40 independent ground states are obtained. for the infinite system a ground - state energy of e = - 1. 4015 ( 3 ) is extrapolated. the ground - state landscape is investigated using a finite - size scaling analysis of the distribution of overlaps. the mean - field picture assuming a complex landscape describes the situation better than the droplet - scaling model, where for the infinite system mainly two ground states exist. strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three - dimensional spin glasses.
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arxiv:cond-mat/9810037
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in this note, we show that there exist cusped hyperbolic $ 3 $ - manifolds that embed geodesically, but cannot bound geometrically. thus, being a geometric boundary is a non - trivial property for such manifolds. our result complements the work by long and reid on geometric boundaries of compact hyperbolic $ 4 $ - manifolds, and by kolpakov, reid and slavich on embedding arithmetic hyperbolic manifolds.
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arxiv:1811.05509
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let x and x ' be compact riemann surfaces of genus at least three. let g and g ' be nontrivial connected semisimple linear algebraic groups over c. if some components $ m _ { dh } ^ d ( x, g ) $ and $ m _ { dh } ^ { d ' } ( x ', g ' ) $ of the associated deligne - - hitchin moduli spaces are biholomorphic, then x ' is isomorphic to x or to the conjugate riemann surface $ \ bar { x } $.
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arxiv:1202.6518
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control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks - - a property presumably optimized by biological evolution. we here ask to what extent the property of a stochastic dynamical network to produce reliable dynamics is an evolvable trait. using an evolutionary algorithm based on a deterministic selection criterion for the reliability of dynamical attractors, we evolve dynamical networks of noisy discrete threshold nodes. we find that, starting from any random network, reliability of the attractor landscape can often be achieved with only few small changes to the network structure. further, the evolvability of networks towards reliable dynamics while retaining their function is investigated and a high success rate is found.
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arxiv:0707.1407
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access to continuous, quality assessed meteorological data is critical for understanding the climatology and atmospheric dynamics of a region. research facilities like oak ridge national laboratory ( ornl ) rely on such data to assess site - specific climatology, model potential emissions, establish safety baselines, and prepare for emergency scenarios. to meet these needs, on - site towers at ornl collect meteorological data at 15 - minute and hourly intervals. however, data measurements from meteorological towers are affected by sensor sensitivity, degradation, lightning strikes, power fluctuations, glitching, and sensor failures, all of which can affect data quality. to address these challenges, we conducted a comprehensive quality assessment and processing of five years of meteorological data collected from ornl at 15 - minute intervals, including measurements of temperature, pressure, humidity, wind, and solar radiation. the time series of each variable was pre - processed and gap - filled using established meteorological data collection and cleaning techniques, i. e., the time series were subjected to structural standardization, data integrity testing, automated and manual outlier detection, and gap - filling. the data product and highly generalizable processing workflow developed in python jupyter notebooks are publicly accessible online. as a key contribution of this study, the evaluated 5 - year data will be used to train atmospheric dispersion models that simulate dispersion dynamics across the complex ridge - and - valley topography of the oak ridge reservation in east tennessee.
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arxiv:2502.05191
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= = prominent practitioners and advocates of recreational mathematics have included professional and amateur mathematicians : = = see also = = list of recreational number theory topics mathematics of paper folding ( origami ) = = references = = = = further reading = = w. w. rouse ball and h. s. m. coxeter ( 1987 ). mathematical recreations and essays, thirteenth edition, dover. isbn 0 - 486 - 25357 - 0. henry e. dudeney ( 1967 ). 536 puzzles and curious problems. charles scribner ' s sons. isbn 0 - 684 - 71755 - 7. sam loyd ( 1959. 2 vols. ). in martin gardner : the mathematical puzzles of sam loyd. dover. oclc 5720955. raymond m. smullyan ( 1991 ). the lady or the tiger? and other logic puzzles. oxford university press. isbn 0 - 19 - 286136 - 0. = = external links = = recreational mathematics from mathworld at wolfram research
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https://en.wikipedia.org/wiki/Recreational_mathematics
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several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. in this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an expanding background. we take a detailed and formal approach by deriving the equations describing gravity in ( d + 1 ) dimensions using the action principle of einstein. we then consider the newtonian limit of these equations and finally obtain the necessary fluid equations required to describe structure formation. these equations are solved for the density perturbation in both the linearised form and in the spherical top hat model of nonlinear growth. we find that, when the special case of d = 2 is considered, no structures can grow. we therefore conclude that, within the frame work of einstein ' s theory of gravity in ( 2 + 1 ) dimensions, formation of structures cannot take place. finally, we indicate the different possible ways of getting around this difficulty so that growing structures can be obtained in two dimensional cosmological gravitational simulations and discuss their implications.
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arxiv:astro-ph/9805192
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sr2iro4 was predicted to be a high temperature superconductor upon electron doping since it highly resembles the cuprates in crystal structure, electronic structure and magnetic coupling constants. here we report a scanning tunneling microscopy / spectroscopy ( stm / sts ) study of sr2iro4 with surface electron doping by depositing potassium ( k ) atoms. at the 0. 5 - 0. 7 monolayer ( ml ) k coverage, we observed a sharp, v - shaped gap with about 95 % loss of density of state ( dos ) at efand visible coherence peaks. the gap magnitude is 25 - 30 mev for 0. 5 - 0. 6 ml k coverage and it closes around 50 k. these behaviors exhibit clear signature of superconductivity. furthermore, we found that with increased electron doping, the system gradually evolves from an insulating state to a normal metallic state, via a pseudogap - like state and possible superconducting state. our data suggest possible high temperature superconductivity in electron doped sr2iro4, and its remarkable analogy to the cuprates.
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arxiv:1506.06557
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in the vast expanse of our galaxy, white dwarfs ( wds ) are natural sentinels, capturing the enigmatic dark matter ( dm ) particles that incessantly traverse their interiors. these celestial bodies provide a unique vantage point for probing interactions between dm particles and their constituents - nuclei or electrons - should such interactions exist. the captured dm particles may accumulate, undergo mutual annihilation, or be evaporated by the wd ' s own nuclei or electrons, thereby perturbing the standard cooling sequence predicted by stellar evolution theory. this letter reports pioneering constraints on dm - electron interactions derived from an in - depth analysis of four pulsating wds. by leveraging the period variation rates of their pulsation modes, we delineate the following constraints : for a form factor $ f ( q ) = 1 $, in the dm mass range $ 20 \ mathrm { mev } / c ^ { 2 } \ lesssim m _ { \ chi } \ lesssim 80 \ mathrm { mev } / c ^ { 2 } $ with a cross - section limit of $ \ sigma _ { \ chi, e } \ lesssim 10 ^ { - 56 } \ mathrm { cm } ^ { 2 } $ ; for a form factor $ f ( q ) = ( \ alpha m _ { e } ) ^ { 2 } / q ^ { 2 } $, in a the dm mass range $ 20 \ mathrm { mev } / c ^ { 2 } \ lesssim m _ { \ chi } \ lesssim 70 \ mathrm { mev } / c ^ { 2 } $ with a limit of $ \ sigma _ { \ chi, e } \ lesssim 10 ^ { - 52 } \ mathrm { cm } ^ { 2 } $. these newly established constraints surpass current direct detection experiments by over fifteen orders of magnitude, forging a path into the uncharted territories of the dm parameter space. this work not only advances our understanding of light dark matter - electron interactions but also exemplifies the potential of wds as important astrophysical laboratories for probing the elusive nature of dm.
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arxiv:2406.03100
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this paper investigates the optimization of reconfigurable intelligent surface ( ris ) in an integrated sensing and communication ( isac ) system. \ red { to meet the demand of growing number of devices, power domain non - orthogonal multiple access ( noma ) is considered. however, traditional noma with a large number of devices is challenging due to large decoding delay and propagation error introduced by successive interference cancellation ( sic ). thus, oma is integrated into noma to support more devices }. we formulate a max - min problem to optimize the sensing beampattern \ red { with constraints on communication rate }, through joint power allocation, active beamforming and ris phase shift design. to solve the non - convex problem with a non - smooth objective function, we propose a low complexity alternating optimization ( ao ) algorithm, where a closed form expression for the intra - cluster power allocation ( intra - cpa ) is derived, and penalty and successive convex approximation ( sca ) methods are used to optimize the beamforming and phase shift design. simulation results show the effectiveness of the proposed algorithm in terms of improving minimum beampattern gain ( mbpg ) compared with other baselines. furthermore, the trade - off between sensing and communication is analyzed and demonstrated in the simulation results.
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arxiv:2309.06080
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the p300 speller is being considered as an independent brain - computer interface. that means it measures the user ' s intent, and does not require the user to move any muscles. in particular it should not require eye fixation of the desired character. however, it has been shown that posterior electrodes provide significant discriminative information, which is likely related to visual processing. these findings imply the need for studies controlling the effect of eye movements. in experiments with a 3x3 character matrix, attention and eye fixation was directed to different characters. in the event - related potentials, a p300 occurred for the attended character, and n200 was seen for the trials showing the focussed character. it occurred at posterior sites, reaching its peak at 200ms after stimulus onset. the results suggest that gaze direction plays an important role in p300 speller paradigm. by controlling gaze direction it is possible to separate voluntary and involuntary eeg responses to the highlighting of characters.
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arxiv:1006.3688
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existence and non - existence of integrable stationary solutions to smoluchowski ' s coagulation equation with source are investigated when the source term is integrable with an arbitrary support in ( 0, $ \ infty $ ). besides algebraic upper and lower bounds, a monotonicity condition is required for the coagulation kernel. connections between integrability properties of the source and the corresponding stationary solutions are also studied.
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arxiv:2006.15879
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a novel framework for performance analysis and code design is proposed to address the sneak path ( sp ) problem in resistive random - access memory ( reram ) arrays. the main idea is to decompose the reram channel, which is both non - ergodic and data - dependent, into multiple stationary memoryless channels. a finite - length performance bound is derived by analyzing the capacity and dispersion of these stationary memoryless channels. furthermore, leveraging this channel decomposition, a practical sparse - graph code design is proposed using density evolution. the obtained channel codes are not only asymptotic capacity approaching but also close to the derived finite - length performance bound.
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arxiv:2412.06275
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using a new spectroscopic sample and methods accounting for spectroscopic sampling fractions that vary in magnitude and surface brightness, we present r - band galaxy luminosity functions ( glfs ) for six nearby galaxy clusters with redshifts 4000 < cz < 20000 km / s and velocity dispersions 700 < sigma < 1250 km / s. in the case of the nearest cluster, abell 1060, our sample extends to m _ r = - 14 ( 7 magnitudes below m * ), making this the deepest spectroscopic determination of the cluster glf to date. our methods also yield composite glfs for cluster and field galaxies to m _ r = - 17 ( m * + 4 ), including the glfs of subsamples of star forming and quiescent galaxies. the composite glfs are consistent with schechter functions ( m * _ r = - 21. 14 ^ { + 0. 17 } _ { - 0. 17 }, alpha = - 1. 21 ^ { + 0. 08 } _ { - 0. 07 } for the clusters, m * _ r = - 21. 15 ^ { + 0. 16 } _ { - 0. 16 }, alpha = - 1. 28 ^ { + 0. 12 } _ { - 0. 11 } for the field ). all six cluster samples are individually consistent with the composite glf down to their respective absolute magnitude limits, but the glf of the quiescent population in clusters is not universal. there are also significant variations in the glf of quiescent galaxies between the field and clusters that can be described as a steepening of the faint end slope. the overall glf in clusters is consistent with that of field galaxies, except for the most luminous tip, which is enhanced in clusters versus the field. the star formation properties of giant galaxies are more strongly correlated with the environment than those of fainter galaxies.
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arxiv:astro-ph/0304031
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we experimentally observed the enhanced contact angle hysteresis ( cah ) of dilute aqueous salt solution on graphite surface, i. e., 40. 6 $ ^ \ circ $, 34. 6 $ ^ \ circ $, and 27. 8 $ ^ \ circ $, for licl, nacl, and kcl, indicating the effective tuning of the cahs by cations. molecular dynamics simulations reveal that the preferential adsorption of cations on the hopg surface due to the cation - { \ pi } interaction pins the water at the backward liquid - gas - solid interfaces, reducing the receding contact angle and hence enhancing the cah. this finding provides a simple method to control the contact angle and the cah of aqueous drops on graphitic surfaces such as graphene, carbon nanotube, biomolecules, and airborne pollutants.
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arxiv:2004.02148
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deep convolutional neural networks ( convnets ) have been recently shown to attain state - of - the - art performance for action recognition on standard - resolution videos. however, less attention has been paid to recognition performance at extremely low resolutions ( elr ) ( e. g., 16 x 12 pixels ). reliable action recognition using elr cameras would address privacy concerns in various application environments such as private homes, hospitals, nursing / rehabilitation facilities, etc. in this paper, we propose a semi - coupled filter - sharing network that leverages high resolution ( hr ) videos during training in order to assist an elr convnet. we also study methods for fusing spatial and temporal convnets customized for elr videos in order to take advantage of appearance and motion information. our method outperforms state - of - the - art methods at extremely low resolutions on ixmas ( 93. 7 % ) and hmdb ( 29. 2 % ) datasets.
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arxiv:1610.03898
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we introduce an analogue $ k _ n ( x, z ; q, t ) $ of the cauchy - type kernel function for the macdonald polynomials, being constructed in the tensor product of the ring of symmetric functions and the commutative algebra $ \ mathcal { a } $ over the degenerate $ \ mathbb { c } \ mathbb { p } ^ 1 $. we show that a certain restriction of $ k _ n ( x, z ; q, t ) $ with respect to the variable $ z $ is neatly described by the tableau sum formula of macdonald polynomials. next, we demonstrate that the integer level representation of the ding - iohara quantum algebra naturally produces the currents of the deformed $ \ mathcal { w } $ algebra. then we remark that the $ k _ n ( x, z ; q, t ) $ emerges in the highest - to - highest correlation function of the deformed $ \ mathcal { w } $ algebra.
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arxiv:1002.2485
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a first order phase transition usually proceeds by nucleating bubbles of the new phase which then rapidly expand. in confining gauge theories with a gravity dual, the deconfined phase is often described by a black hole. if one starts in this phase and lowers the temperature, the usual description of how the phase transition proceeds violates the area theorem. we study the dynamics of this phase transition using the insights from the dual gravitational description, and resolve this apparent contradiction.
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arxiv:hep-th/0701099
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it is well known that many machine learning systems demonstrate bias towards specific groups of individuals. this problem has been studied extensively in the facial recognition area, but much less so in automatic speech recognition ( asr ). this paper presents initial speech recognition results on " casual conversations " - - a publicly released 846 hour corpus designed to help researchers evaluate their computer vision and audio models for accuracy across a diverse set of metadata, including age, gender, and skin tone. the entire corpus has been manually transcribed, allowing for detailed asr evaluations across these metadata. multiple asr models are evaluated, including models trained on librispeech, 14, 000 hour transcribed, and over 2 million hour untranscribed social media videos. significant differences in word error rate across gender and skin tone are observed at times for all models. we are releasing human transcripts from the casual conversations dataset to encourage the community to develop a variety of techniques to reduce these statistical biases.
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arxiv:2111.09983
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we obtain large n asymptotics for products of powers of the absolute values of the characteristic polynomials in the gaussian unitary ensemble of n \ times n matrices. our results can also be interpreted as asymptotics of the determinant of a hankel matrix whose symbol is supported on the real line and possesses power - like ( fisher - hartwig ) singularities.
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arxiv:math-ph/0411016
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we construct the creation operator of a vortex for su ( 2 ) pure gauge theory using the methods developed for monopoles. we interpret its vacuum expectation value as a disorder parameter for the deconfinement phase transition and find that it behaves in the vacuum in a similar way to monopoles. results are extrapolated to the thermodynamical limit using finite - size scaling.
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arxiv:hep-lat/0010044
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the quasiparticle band structures of four polytypes 3c, 6h, 4h, and 2h of gap, gaas, gasb, inp, inas, and insb are computed with high accuracy including spin - orbit interaction applying a recently developed approximate calculation scheme, the lda - 1 / 2 method. the results are used to derive band offsets $ \ delta e _ c $ and $ \ delta e _ v $ for the conduction and valence bands between two polytypes. the alignment of the band structures is based on the branch - point energy $ e _ { \ rm bp } $ for each polytype. the aligned electronic structures are used to explain properties of heterocrystalline but homomaterial junctions. the gaps and offsets allow to discuss spectroscopic results obtained recently for such junctions in iii - v nanowires.
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arxiv:1206.2209
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the visual object category reports of artificial neural networks ( anns ) are notoriously sensitive to tiny, adversarial image perturbations. because human category reports ( aka human percepts ) are thought to be insensitive to those same small - norm perturbations - - and locally stable in general - - this argues that anns are incomplete scientific models of human visual perception. consistent with this, we show that when small - norm image perturbations are generated by standard ann models, human object category percepts are indeed highly stable. however, in this very same " human - presumed - stable " regime, we find that robustified anns reliably discover low - norm image perturbations that strongly disrupt human percepts. these previously undetectable human perceptual disruptions are massive in amplitude, approaching the same level of sensitivity seen in robustified anns. further, we show that robustified anns support precise perceptual state interventions : they guide the construction of low - norm image perturbations that strongly alter human category percepts toward specific prescribed percepts. these observations suggest that for arbitrary starting points in image space, there exists a set of nearby " wormholes ", each leading the subject from their current category perceptual state into a semantically very different state. moreover, contemporary ann models of biological visual processing are now accurate enough to consistently guide us to those portals.
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arxiv:2308.06887
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we present the first lattice - qcd $ x $ - dependent pion valence - quark generalized parton distribution ( gpd ) calculated directly at physical pion mass using the large - momentum effective theory ( lamet ) with next - to - next - to - leading order perturbative matching correction. we use clover fermions for the valence action on $ 2 + 1 + 1 $ flavors of highly improved staggered quarks ( hisq ), generated by milc collaboration, with lattice spacing $ a \ approx 0. 09 $ fm and box size $ l \ approx 5. 5 $ fm ; the pion two - point measurements number up to $ o ( 10 ^ 6 ) $ with boost momentum 1. 73gev. the pion valence distribution is renormalized in hybrid scheme with wilson - line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the $ \ overline { \ text { ms } } $ scheme. we focus on the zero - skewness limit, where the gpd has a probability - density interpretation in the longitudinal bjorken $ x $ and the transverse impact - parameter distributions. we take the integral of our gpd functions to generate leading moment so that we can make comparisons with past lattice - qcd and experimental determinations of the pion form factors and found consistent agreement among them. we predict the higher gpd moments and reveal $ x $ - dependent tomography of the pion for the first time using lattice qcd.
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arxiv:2310.10579
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we present a first - principles density functional study of the structural, electronic and magnetic properties of the ferroelectric domain walls in multiferroic bifeo3. we find that domain walls in which the rotations of the oxygen octahedra do not change their phase when the polarization reorients are the most favorable, and of these the 109 degree domain wall centered around the bio plane has the lowest energy. the 109 degree and 180 degree walls have a significant change in the component of their polarization perpendicular to the wall ; the corresponding step in the electrostatic potential is consistent with a recent report of electrical conductivity at the domain walls. finally, we show that changes in the fe - o - fe bond angles at the domain walls cause changes in the canting of the fe magnetic moments which can enhance the local magnetization at the domain walls.
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arxiv:0909.5294
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understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity. we investigate the condition and latent heat of phase transition for non - linear charged ads black holes using the maxwell ' s equal - area law, and analysis the boundary and curve of the two - phase coexistence area in the expanded phase space. we suggest that the phase transition of the non - linear charged ads black hole with the fixed temperature ( $ t < t _ c $ ) is related to the electric potential at the horizon, not only to the location of horizon. recently, the molecular number density was introduced to study the phase transition and microstructure of black holes. on this basis, we discuss the continuous phase transition of a non - linear charged ads black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.
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arxiv:2112.10403
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network available, and with probability p { \ displaystyle p }, connects to each. thus, e [ ⟨ k ⟩ ] = e [ k ] = p ( n − 1 ) { \ displaystyle \ mathbb { e } [ \ langle k \ rangle ] = \ mathbb { e } [ k ] = p ( n - 1 ) }. degree distribution the degree distribution p ( k ) { \ displaystyle p ( k ) } is a fundamental property of both real networks, such as the internet and social networks, and of theoretical models. the degree distribution p ( k ) of a network is defined to be the fraction of nodes in the network with degree k. the simplest network model, for example, the ( erdos – renyi model ) random graph, in which each of n nodes is independently connected ( or not ) with probability p ( or 1 − p ), has a binomial distribution of degrees k ( or poisson in the limit of large n ). most real networks, from the www to the protein interaction networks, however, have a degree distribution that are highly right - skewed, meaning that a large majority of nodes have low degree but a small number, known as " hubs ", have high degree. for such scale - free networks the degree distribution approximately follows a power law : p ( k ) k − γ { \ displaystyle p ( k ) \ sim k ^ { - \ gamma } }, where γ is the degree exponent, and is a constant. such scale - free networks have unexpected structural and dynamical properties, rooted in the diverging second moment of the degree distribution. = = = average shortest path length ( or characteristic path length ) = = = the average shortest path length is calculated by finding the shortest path between all pairs of nodes, and taking the average over all paths of the length thereof ( the length being the number of intermediate edges contained in the path, i. e., the distance d u, v { \ displaystyle d _ { u, v } } between the two vertices u, v { \ displaystyle u, v } within the graph ). this shows us, on average, the number of steps it takes to get from one member of the network to another. the behavior of the expected average shortest path length ( that is, the ensemble average of the average shortest path length ) as a function of the number of vertices n { \ displaystyle n } of a random network model defines whether that model
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https://en.wikipedia.org/wiki/Network_science
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we introduce and study the concept of generating function for natural elements in a dedekind complete riesz space equipped with a conditional expectatnion operator. this allows to study discrete processes in free - measure setting. in particular we improve a result obtained by kuo, vardy and watson concerning poisson approximation.
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arxiv:2212.00673
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the resistivity, magnetoresistance, and magnetic susceptibility are measured in single crystals of fete0. 65se0. 35 with cu, ni, and co substitutions for fe. the crystals are grown by bridgman ' s method. the resistivity measurements show that superconductivity disappears with the rate which correlates with the nominal valence of the impurity. from magnetoresistance we evaluate doping effect on the basic superconducting parameters, such as upper critical field and coherence length. we find indications that doping leads to two component superconducting behavior, possibly because of local charge depression around impurities.
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arxiv:1205.6295
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we introduce the notion of metric lie algebras of killing type, which are characterized by the fact that all conformal killing symmetric tensors are sums of killing tensors and multiples of the metric tensor. we show that if a lie algebra is either 2 - step nilpotent, or 2 - or 3 - dimensional, or 4 - dimensional non - solvable, or 4 - dimensional solvable with 1 - dimensional derived ideal, or has an abelian factor, then it is of killing type with respect to any positive definite metric.
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arxiv:2012.08337
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standard stochastic loewner evolution ( sle ) is driven by a continuous brownian motion, which then produces a continuous fractal trace. if jumps are added to the driving function, the trace branches. we consider a generalized sle driven by a superposition of a brownian motion and a stable levy process. the situation is defined by the usual sle parameter, $ \ kappa $, as well as $ \ alpha $ which defines the shape of the stable levy distribution. the resulting behavior is characterized by two descriptors : $ p $, the probability that the trace self - intersects, and $ \ tilde { p } $, the probability that it will approach arbitrarily close to doing so. using dynkin ' s formula, these descriptors are shown to change qualitatively and singularly at critical values of $ \ kappa $ and $ \ alpha $. it is reasonable to call such changes ` ` phase transitions ' '. these transitions occur as $ \ kappa $ passes through four ( a well - known result ) and as $ \ alpha $ passes through one ( a new result ). numerical simulations are then used to explore the associated touching and near - touching events.
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arxiv:cond-mat/0509187
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expanding the receptive field to capture large - scale context is key to obtaining good performance in dense prediction tasks, such as human pose estimation. while many state - of - the - art fully - convolutional architectures enlarge the receptive field by reducing resolution using strided convolution or pooling layers, the most straightforward strategy is adopting large filters. this, however, is costly because of the quadratic increase in the number of parameters and multiply - add operations. in this work, we explore using learnable box filters to allow for convolution with arbitrarily large kernel size, while keeping the number of parameters per filter constant. in addition, we use precomputed summed - area tables to make the computational cost of convolution independent of the filter size. we adapt and incorporate the box filter as a differentiable module in a fully - convolutional neural network, and demonstrate its competitive performance on popular benchmarks for the task of human pose estimation.
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arxiv:1906.11367
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let $ \ xi = ( \ xi _ t ) $ be a locally finite $ ( 2, \ beta ) $ - superprocess in $ \ rr ^ d $ with $ \ beta < 1 $ and $ d > 2 / \ beta $. then for any fixed $ t > 0 $, the random measure $ \ xi _ t $ can be a. s. approximated by suitably normalized restrictions of lebesgue measure to the $ \ varepsilon $ - neighborhoods of $ { \ rm supp } \, \ xi _ t $. this extends the lebesgue approximation of dawson - watanabe superprocesses. our proof is based on a truncation of $ ( \ alpha, \ beta ) $ - superprocesses and uses bounds and asymptotics of hitting probabilities.
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arxiv:1201.6437
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large language models ( llms ) have shown remarkable comprehension abilities but face challenges in gpu memory usage during inference, hindering their scalability for real - time applications like chatbots. to accelerate inference, we store computed keys and values ( kv cache ) in the gpu memory. existing methods study the kv cache compression to reduce memory by pruning the pre - computed kv cache. however, they neglect the inter - layer dependency between layers and huge memory consumption in pre - computation. to explore these deficiencies, we find that the number of crucial keys and values that influence future generations decreases layer by layer and we can extract them by the consistency in attention weights. based on the findings, we propose pyramidinfer, a method that compresses the kv cache by layer - wise retaining crucial context. pyramidinfer saves significant memory by computing fewer keys and values without sacrificing performance. experimental results show pyramidinfer improves 2. 2x throughput compared to accelerate with over 54 % gpu memory reduction in kv cache.
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arxiv:2405.12532
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a class of models is presented, in the form of continuation monads polymorphic for first - order individuals, that is sound and complete for minimal intuitionistic predicate logic. the proofs of soundness and completeness are constructive and the computational content of their composition is, in particular, a $ \ beta $ - normalisation - by - evaluation program for simply typed lambda calculus with sum types. although the inspiration comes from danvy ' s type - directed partial evaluator for the same lambda calculus, the there essential use of delimited control operators ( i. e. computational effects ) is avoided. the role of polymorphism is crucial - - dropping it allows one to obtain a notion of model complete for classical predicate logic. the connection between ours and kripke models is made through a strengthening of the double - negation shift schema.
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arxiv:1102.1061
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the solution of energy - balance model of the earth global climate and the epica dome c and vostok experimental data of the earth surface palaeotemperature evolution over past 420 and 740 kyr are compared. in the framework of proposed bifurcation model ( i ) the possible sharp warmings of the dansgaard - oeschger type during the last glacial period due to stochastic resonance is theoretically argued ; ( ii ) the concept of climatic sensitivity of water in the atmosphere, whose temperature instability has the form of so - called hysteresis loop, is proposed, and based of this concept the time series of global ice volume over the past 1000 kyr, which is in good agreement with the time series of delta o - 18 concentration in the sea sediments, is obtained ; ( iii ) the so - called " co2 doubling " problem is discussed
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arxiv:0803.2766
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we report an all - fiber - based experimental setup to generate a correlated photon - pair comb using four wave mixing ( fwm ) in highly non - linear fiber ( hnlf ). temporal correlations of the generated photons were confirmed through coincidence measurements. we observed a maximum of 32 kcps, with a coincidence to accidental ratio of 17 $ \ pm $ 1. to further understand the underlying processes, we also simulated a generalized fwm event involving the interaction between an arbitrary frequency comb and a continuous wave ( cw ) pump. non - linear dynamics through the hnlf were modelled using schr \ " odinger propagation equations, with numerical predictions agreeing with our experimental results.
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arxiv:2412.03323
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the aim of this work is to develop deep learning - based algorithms for high - dimensional stochastic control problems based on physics - informed learning and dynamic programming. unlike classical deep learning - based methods relying on a probabilistic representation of the solution to the hamilton - - jacobi - - bellman ( hjb ) equation, we introduce a pathwise operator associated with the hjb equation so that we can define a problem of physics - informed learning. according to whether the optimal control has an explicit representation, two numerical methods are proposed to solve the physics - informed learning problem. we provide an error analysis on how the truncation, approximation and optimization errors affect the accuracy of these methods. numerical results on various applications are presented to illustrate the performance of the proposed algorithms.
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arxiv:2402.15592
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fungal symbionts are often overlooked in studies of plant invasion. nevertheless, their role could be essential to the competitive success of the invader. we studied fungal endophytes in the widespread invasive centaurea stoebe ( common knapweed ). a preliminary experiment showed that endophytes in roots of c. stoebe significantly reduced the biomass of evolutionarily na \ " ive neighbours ( festuca idahoensis ), compared to endophyte - free c. stoebe. in the main experiment non - clavicipitaceous endophytes belonging to six phylotypes, were employed as root inoculants. each of these endophytes again reduced the growth of na \ " ive neighbours ( f. idahoensis ) ; and remarkably, each also increased the growth of adapted neighbours ( f. ovina ) that were tested for the first time. four of the six endophytes caused c. stoebe to gain a competitive advantage over its na \ " ive neighbour that was significantly greater than the endophyte - free c. stoebe over that same neighbour. however, endophyte - free c. stoebe had no greater competitive advantage over f. idahoensis than it had over f. ovina. therefore, plant - plant interactions were dramatically affected by the presence of endophytes in a way that would favor invasion.
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arxiv:1209.1617
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to detect anomalies in real - world graphs, such as social, email, and financial networks, various approaches have been developed. while they typically assume static input graphs, most real - world graphs grow over time, naturally represented as edge streams. in this context, we aim to achieve three goals : ( a ) instantly detecting anomalies as they occur, ( b ) adapting to dynamically changing states, and ( c ) handling the scarcity of dynamic anomaly labels. in this paper, we propose slade ( self - supervised learning for anomaly detection in edge streams ) for rapid detection of dynamic anomalies in edge streams, without relying on labels. slade detects the shifts of nodes into abnormal states by observing deviations in their interaction patterns over time. to this end, it trains a deep neural network to perform two self - supervised tasks : ( a ) minimizing drift in node representations and ( b ) generating long - term interaction patterns from short - term ones. failure in these tasks for a node signals its deviation from the norm. notably, the neural network and tasks are carefully designed so that all required operations can be performed in constant time ( w. r. t. the graph size ) in response to each new edge in the input stream. in dynamic anomaly detection across four real - world datasets, slade outperforms nine competing methods, even those leveraging label supervision.
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arxiv:2402.11933
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in this paper, we introduce a " partially disorder - averaged " syk model. this model has a real parameter that smoothly interpolates between the ordinary totally disorder - averaged syk model and the totally fixed - coupling model. for the large $ n $ effective description, in addition to the usual bi - local collective fields, we also introduce a new additional set of local collective fields. these local fields can be understood as " half " of the bi - local collective fields, and in the totally fixed - coupling limit, they represent the " half - wormholes " which were found in recent studies. we find that the large $ n $ saddles of these local fields vanish in the total - disorder - averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. we argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic ads boundary. this illuminates how the half - wormhole saddles emerge in the syk model with fixed couplings.
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arxiv:2111.11705
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here we report that the source of si impurities commonly observed on ( 010 ) $ \ beta - ga _ 2o _ 3 $ is from exposure of the surface to air. moreover, we find that a 15 minute hf ( 49 % ) treatment reduces the si density by approximately 1 order of magnitude on ( 010 ) $ \ beta - ga _ 2o _ 3 $ surfaces. this reduction in si is critical for the elimination of the often observed parasitic conducting channel, which negatively affects transport properties and lateral transistor performance. after the hf treatment the sample must be immediately put under vacuum, for the si fully returns within 10 minutes of additional air exposure. lastly, we demonstrate that performing a 30 minute hf ( 49 % ) treatment on the substrate before growth has no deleterious effect on the structure or on the epitaxy surface after subsequent $ ga _ 2o _ 3 $ growth.
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arxiv:2312.06851
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optical cross - talk is a critical characteristic of silicon photomultipliers ( sipms ) and represents a significant source of the excess noise factor, exerting a substantial influence on detector performance. during the avalanche process of sipms, photons generated can give rise to both internal cross - talk within the same sipm and external cross - talk when photons escape from one sipm and trigger avalanches in others. in scenarios where sipms are arranged in a compact configuration and positioned facing each other, the external cross - talk could even dominate the cross - talk phenomenon. this paper investigates two distinct methods for measuring external cross - talk : the counting method, which involves operating sipms face - to - face and measuring their coincident signals, and the reflection method, which employs a highly reflective film attached to the surface of the sipms. external cross - talk measurements have been conducted on several types of sipms, including vacuum ultra - violet ( vuv ) sensitive sipms that fondazione bruno kessler ( fbk ) and hamamatsu photonics inc ( hpk ) produced for nexo as well as visible - sensitive sipms provided by fbk, hpk and sensl technologies ltd ( sensl ) for juno - tao. the results reveal a significant presence of external cross - talk in all tested sipms, with hpk ' s sipms exhibiting a dominant external cross - talk component due to the implementation of optical trenches that effectively suppress internal cross - talk. furthermore, we found that the number of fired pixels resulting from internal cross - talk can be described by combining geometric and borel models for all tested sipms, while the external cross - talk can be predicted using a pure borel model. these distinct probability distributions lead to different excess noise factors, thereby impacting the detector performance in varying ways.
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arxiv:2312.12901
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