Related papers: An estimate for the multiplicity of binary recurre…
Erraticity analysis of multiparticle production data is introduced as a way of extracting the maximum amount of information on self-similar fluctuations. It is presented as the next logical step to take beyond the intermittency analysis. An…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to…
In this paper, we enumerate the pairs of permutations that are long cycles and whose product has a given cycle-type. Our main result is a simple relation concerning the desired numbers for a few related cycle-types. The relation refines a…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We…
Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…
In this paper, we determine the almost sure multifractal spectrum of a class of random functions constructed as sums of pulses with random dilations and translations. In addition, the continuity modulii of these functions is investigated.
This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet…
We present analytical derivation of the minimal and maximal number of items retained in recently introduced Retroactive Interference Model of Forgetting. Also we computed the probability that two items presented at different times are…
We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We…
Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that…
Mixture models have received considerable attention recently and Newton [Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive…
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the M\"obius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the M\"obius function.…
We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in determining measures of algebraic independence of values of…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.