相关论文: Discrete logarithms in free groups

We present a simple variant of the Gaussian mechanism for answering differentially private queries when the sensitivity space has a certain common structure. Our motivating problem is the fundamental task of answering $d$ counting queries…

We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function…

Gaussian copulas are widely used to estimate multivariate distributions and relationships. We present algorithms for estimating Gaussian copula correlations that ensure differential privacy. We first convert data values into sets of two-way…

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…

Graph cuts are among the most prominent tools for clustering and classification analysis. While intensively studied from geometric and algorithmic perspectives, graph cut-based statistical inference still remains elusive to a certain…

A new proof is given for the correctness of the powers of two descent method for computing discrete logarithms. The result is slightly stronger than the original work, but more importantly we provide a unified geometric argument,…

We find separation rates for testing multinomial or more general discrete distributions under the constraint of local differential privacy. We construct efficient randomized algorithms and test procedures, in both the case where only…

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…

We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical…

We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single…

We prove that the modular symbols appropriately normalized and ordered have a Gaussian distribution for all cofinite subgroups of SL_2(R). We use spectral deformations to study the poles and the residues of Eisenstein series twisted by…

In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by…

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain…

We introduce a geometrically natural probability measure on the group of all M\"obius transformations of the circle. Our aim is to study "random" groups of M\"obius transformations, and in particular random two-generator groups. By this we…

Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic…

Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to…

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…

Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.

This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($\mu$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian…