Related papers: A Class of Random Sequences for Key Generation
Linear recursions of degree $k$ are determined by evaluating the sequence of Generalized Fibonacci Polynomials, $\{F_{k,n}(t_1,...,t_k)\}$ (isobaric reflects of the complete symmetric polynomials) at the integer vectors $(t_1,...,t_k)$. If…
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size $m$. In particular, the size of the sample is allowed to be…
Random number generation is a key technology that is useful in a variety of ways. Random numbers are often used to generate keys for data encryption. Random numbers generated at a sufficiently long length can encrypt sensitive data and make…
We motivate the study of a certain class of random Fibonacci sequences - which we call continuous random Fibonacci sequences - by demonstrating that their exponential growth rate can be used to establish capacity and power scaling laws for…
We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…
Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…
High quality random numbers are necessary in the modern world. Ranging from encryption keys in cyber security to models and simulations for scientific use: it's important that these random numbers are of high quality and quickly attainable.…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
We study an LCM-based analogue of Rowland's GCD-based prime-generating recurrence, introduced by the author in 2008. The multiplicative increments of this sequence are conjectured always to be $1$ or prime, but a complete proof requires a…
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized…
This paper considers some random processes of the form X_{n+1}=TX_n+B_n (mod p) where B_n and X_n are random variables over (Z/pZ)^d and T is a fixed d x d integer matrix which is invertible over the complex numbers. For a particular…
In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
The marginal Bayesian predictive classifiers (mBpc) as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and hence tacitly assumes the independence of the observations. However, due to…
Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is…
We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…
In a recent insightful article, Helmut Prodinger uses sophisticated complex analysis, with residues, to derive convolution identities for Fibonacci, Tribonacci, and k-bonacci numbers. Here we use a naive, "experimental mathematics" (yet…