Related papers: The Capacity of Some P\'olya String Models
This note illustrates the possibility in simple loaded string models of trapping most of the system energy in a single degree of freedom for very long times, demonstrating in particular that the robustness of the trapping is enhanced by…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory,…
This work analyses the text memorization behavior of large language models (LLMs) when subjected to nucleus sampling. Stochastic decoding methods like nucleus sampling are typically applied to overcome issues such as monotonous and…
We perform large-scale field theoretical simulations in expanding universe to characterize a network of strings that can form composed bound states. The network consists of two copies of Abelian Higgs strings (which we label p and q,…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
Random Boolean networks (RBNs) have been a popular model of genetic regulatory networks for more than four decades. However, most RBN studies have been made with random topologies, while real regulatory networks have been found to be…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is…
String sorting is an important part of tasks such as building index data structures. Unfortunately, current string sorting algorithms do not scale to massively parallel distributed-memory machines since they either have latency (at least)…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
Network systems and their control are highly important and appear in a variety of applications, including vehicle platooning and formation con- trol. Especially vehicle platoons are highly investigated and an interesting problem that arises…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities…
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…
Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is…
DNA data storage systems encode digital data into DNA strands, enabling dense and durable storage. Efficient data retrieval depends on coverage depth, a key performance metric. We study the random access coverage depth problem and focus on…
Probabilistic deterministic finite automata (PDFA) are discrete event systems modeling conditional probabilities over languages: Given an already seen sequence of tokens they return the probability of tokens of interest to appear next.…