Related papers: Maximum-order Complexity and Correlation Measures
In 2002, Kamae and Zamboni introduced maximal pattern complexity and determined that any aperiodic sequence must have maximal pattern complexity at least $2k$. In 2006, Kamae and Rao examined the maximal pattern complexity of sequences over…
In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult…
Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new…
This paper presents a new approach to combine cross-correlation functions. The combination is based on a maximum-likelihood approach and uses a non-linear combination scheme. It can be effective for radial-velocity analysis of multi-order…
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
According to theoretical considerations, multiplicity of hierarchical stellar systems can reach, depending on masses and orbital parameters, several hundred, while observational data confirm existence of at most septuple (seven-component)…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
In this paper we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection.…
We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of…
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…
This commentary discusses a recently proposed measure of heterogeneity of DNA sequences and compares with the measures of complexity.
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery,…
The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques…
Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…