Related papers: The Capacity of String-Replication Systems
DNA has immense potential as an emerging data storage medium. The principle of DNA storage is the conversion and flow of digital information between binary code stream, quaternary base, and actual DNA fragments. This process will inevitably…
The simplest possible informational heteropolymer requires only a two-letter alphabet to be able to store information. The evolutionary choice of four monomers in the informational biomolecules RNA/DNA or their progenitors is intriguing,…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…
Short tandem repeats (STRs) are low-entropy regions in the genome, consisting of a short (1-6 bp) unit that is consecutively repeated multiple times. They are known for high mutational instability, due to so-called stutter-mutations, in…
Recursive processing is considered a hallmark of human linguistic abilities. A recent study evaluated recursive processing in recurrent neural language models (RNN-LMs) and showed that such models perform below chance level on embedded…
Enumerating characteristic substrings (e.g., maximal repeats, minimal unique substrings, and minimal absent words) in a given string has been an important research topic because there are a wide variety of applications in various areas such…
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…
While GPT-2 generates sentences that are remarkably human-like, longer documents can ramble and do not follow human-like writing structure. We study the problem of imposing structure on long-range text. We propose a novel controlled text…
In biological cells, DNA replication is carried out by the replisome, a protein complex encompassing multiple DNA polymerases. DNA replication is semi-discontinuous: a DNA polymerase synthesizes one (leading) strand of the DNA continuously,…
Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
Recurrent neural networks (RNN) are simple dynamical systems whose computational power has been attributed to their short-term memory. Short-term memory of RNNs has been previously studied analytically only for the case of orthogonal…
Despite the recent achievements in machine learning, we are still very far from achieving real artificial intelligence. In this paper, we discuss the limitations of standard deep learning approaches and show that some of these limitations…
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple…
Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are…
We extend our earlier model of the small scale structure of cosmic string networks through an improved treatment of the separation of long and short scales. We find that the production of small loops (at the gravitational radiation scale)…
Inspired by protein folding, we explored the construction of three-dimensional structures and machines from one-dimensional chains of simple building blocks. This approach not only allows us to recreate the self-replication mechanism…