Related papers: The Capacity of Some P\'olya String Models
We embed the large N Chern-Simons/topological string duality in ordinary superstrings. This corresponds to a large $N$ duality between generalized gauge systems with N=1 supersymmetry in 4 dimensions and superstrings propagating on…
String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
Understanding whether and to what extent large language models (LLMs) have memorised training data has important implications for the reliability of their output and the privacy of their training data. In order to cleanly measure and…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…
Dynamic linear models with Gaussian observations and Gaussian states lead to closed-form formulas for posterior simulation. However, these closed-form formulas break down when the response or state evolution ceases to be Gaussian. Dynamic,…
A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…
Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…
In this paper, we study capacity scaling laws of the deterministic dissemination (DD) in random wireless networks under the generalized physical model (GphyM). This is truly not a new topic. Our motivation to readdress this issue is…
It is shown that different ways of interacting strings formed in high energy nucleus-nucleus collisions cause a different strength of the chaoticity parameter lambda of Bose-Einstein correlations. In particular, in the case of percolation…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing…
We define and prove limit results for a class of dominant P\'olya sequences, which are randomly reinforced urn processes with color-specific random weights and unbounded number of possible colors. Under fairly mild assumptions on the…
P\'olya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of…
We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as a reservoir computers. A multivariate correlation analysis in tailored replica tests reveals consistency spectra and…
We discuss a class of cellular automata (CA) able to produce long random strings, starting from short "seed" strings. The approach uses two principles borrowed from cryptography: diffusion and confusion. We show numerically that the strings…
Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively…