Related papers: A CF-Based Randomness Measure for Sequences
We present an approach for regression problems that employs analytic continued fractions as a novel representation. Comparative computational results using a memetic algorithm are reported in this work. Our experiments included fifteen…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
The focus of this paper is the random sequences in the form $\{X_{0},X_{1},$ $X_{n}=X_{n-2}+X_{n-1},n=2,3,..\dot{\}},$ referred to as Fibonacci Random Sequence (FRS). The initial random variables $X_{0}$ and $X_{1}$ are assumed to be…
This paper investigates the use of different transformations for improving the randomness of sequences. In particular, convolutional codes are used for increasing the size of a given sequence and then a random mapping function is used for…
Concentration of measure is studied, and obtained, for stable and related random vectors.
By a classical result of Gauss and Kuzmin, the continued fraction expansion of a ``random'' real number contains each digit $a\in\mathbb{N}$ with asymptotic frequency $\log_2(1+1/(a(a+2)))$. We generalize this result in two directions:…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…
The coherence factor (CF) is defined as the ratio of coherent power to incoherent power received by the radar aperture. The incoherent power is computed by the multi-antenna receiver based on only the spatial variable. In this respect, it…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…