Related papers: The Capacity of String-Replication Systems
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…
The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…
The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the…
With the number of fully-sequenced genomes now well over a hundred it has become possible to start investigating if there are any quantitative regularities in the genetic make-up of genomes. In (physics/0307001), I originally showed that…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
Novel technologies in genomics allow creating data in exascale dimension with relatively minor effort of human and laboratory and thus monetary resources compared to capabilities only a decade ago. While the availability of this data…
Highly-repetitive collections of strings are increasingly being amassed by genome sequencing and genetic variation experiments, as well as by storing all versions of human-generated files, like webpages and source code. Existing indexes for…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
We present an algorithm for building the extended BWT (eBWT) of a string collection from its grammar-compressed representation. Our technique exploits the string repetitions captured by the grammar to boost the computation of the eBWT.…
All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…
Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is…
In this article, we review existing probabilistic models for modeling abundance of fixed-length strings (k-mers) in DNA sequencing data. These models capture dependence of the abundance on various phenomena, such as the size and repeat…
In an extant population, how much information do extant individuals provide on the pedigree of their ancestors? Recent work by Kim, Mossel, Ramnarayan and Turner (2020) studied this question under a number of simplifying assumptions,…
We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on…
We study the amount of reliable information that can be stored in a DNA-based storage system composed of short DNA molecules. In this regime, Shomorony and Heckel (2022) put forward a conjecture on the scaling of the number of information…
Motivation The Burrows-Wheeler transform (BWT) is the foundation of many algorithms for compression and indexing of text data, but the cost of computing the BWT of very large string collections has prevented these techniques from being…
Humans can systematically generalize to novel compositions of existing concepts. Recent studies argue that neural networks appear inherently ineffective in such cognitive capacity, leading to a pessimistic view and a lack of attention to…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
Recent tumor genome sequencing confirmed that one tumor often consists of multiple cell subpopulations (clones) which bear different, but related, genetic profiles such as mutation and copy number variation profiles. Thus far, one tumor has…
The fall of prices of the high-throughput genome sequencing changes the landscape of modern genomics. A number of large scale projects aimed at sequencing many human genomes are in progress. Genome sequencing also becomes an important aid…