Related papers: The Capacity of Some P\'olya String Models
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
Replication of genetic material is an important process for all living organisms. Origins of replication initiate the copying of DNA at many points on a chromosome, and it is the distribution of these points that is relevant here, as it…
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate…
In our paper selected linguistic features of genomes to study the statistics of the gene codes are considered. We present the information theory from which it follows that if the system is described by distributions of hyperbolic type it…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a…
The population is composed of individuals characterised by their genetic strings, phenotypes and ages. We discuss the influence of probabilities of survival of the individuals on the dynamics and phenotypic variability of the population. We…
While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
Molecular generative models, often employing GPT-style language modeling on molecular string representations, have shown promising capabilities when scaled to large datasets and model sizes. However, it remains unclear and subject to debate…
A host-parasite model is considered for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be…
Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…
In this paper we describe ideas about the string landscape, and how to relate it to the physics of the Standard Model of particle physics. First, we give a short status report about heterotic string compactifications. Then we focus on the…
Despite the growing prevalence of large language model (LLM) architectures, a crucial concern persists regarding their energy and power consumption, which still lags far behind the remarkable energy efficiency of the human brain. Recent…
The influence of tension on DNA looping has been studied both experimentally and theoretically in the past. However, different theoretical models have yielded different predictions, leaving uncertainty about their validity. We briefly…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Foundation models in genomics have shown mixed success compared to their counterparts in natural language processing. Yet, the reasons for their limited effectiveness remain poorly understood. In this work, we investigate the role of…
We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum…