Related papers: Likelihood that a pseudorandom sequence generator …
In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…
We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…
A nonlinear detector derived within a maximum likelihood estimation framework is shown to be effective in retrieving the channel coefficients and data of users on the uplink channel of a noncooperative wireless system without the access…
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over…
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…
This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.
Motivation: The reconstruction of gene networks from gene expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
In this paper we present experiments in order to show how some pseudo random number generators can improve the effectiveness of a statistical cryptanalysis algorithm. We deduce mainly that a better generator enhance the accuracy of the…
The Parks-McClellan algorithm provides an efficient method for designing a linear phase FIR filter with a pre-specified weight function on the approximation error. For the given filter order and the specified weight function, the filter…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
We introduce the Romu family of pseudo-random number generators (PRNGs) which combines the nonlinear operation of rotation with the linear operations of multiplication and (optionally) addition. Compared to conventional linear-only PRNGs,…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
An important statistical test on the pseudo-random number generators is called the spectral test. The test is aimed at answering the question of distribution of the generated pseudo-random vectors in dimensions $d$ that are larger than the…
We propose a class of estimators for the parameters of a GARCH(p,q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on…
We prove that bootstrap type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness…
The properties of maximum Lempel-Ziv complexity strings are studied for the binary case. A comparison between MLZs and random strings is carried out. The length profile of both type of sequences show different distribution functions. The…
Biological cells are able to accurately sense chemicals with receptors at their surfaces, allowing cells to move towards sources of attractant and away from sources of repellent. The accuracy of sensing chemical concentration is ultimately…