相关论文: Deterministic Randomness Extraction from Generaliz…
Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These…
Statistical mechanics of relative species abundance (RSA) patterns in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies…
Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…
Many engineering problems require the prediction of realization-to-realization variability or a refined description of modeled quantities. In that case, it is necessary to sample elements from unknown high-dimensional spaces with possibly…
We study a distributed sampling problem where a set of processors want to output (approximately) independent and identically distributed samples from a joint distribution with the help of a common message from a coordinator. Each processor…
We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related interval algorithm proposed by Han and Hoshi has asymptotically…
In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
By proposing device-independent protocols, S. Pironio et al. [Nature 464, 1021-1024 (2010)] and R. Colbeck et al. [Nature Physics 8, 450-453 (2012)] proved that new randomness can be generated by using perfectly free random sources or…
One of the earliest models of weak randomness is the Chor-Goldreich (CG) source. A $(t,n,k)$-CG source is a sequence of random variables $X=(X_1,\dots,X_t)\sim(\{0,1\}^n)^t$, where each $X_i$ has min-entropy $k$ conditioned on any fixing of…
Liverani-Saussol-Vaienti (L-S-V) maps form a family of piecewise differentiable dynamical systems on $[0,1]$ depending on one parameter $\omega\in\mathbb R^+$. These maps are everywhere expanding apart from a neutral fixed point. It is well…
Interest in the random-order model (ROM) leads us to initiate a study of utilizing random-order arrivals to extract random bits with the goal of derandomizing algorithms. Besides producing simple algorithms, simulating random bits through…
The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This…