Related papers: On the optimality of the standard genetic code: th…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
The standard genetic code is well known to be optimized for minimizing the phenotypic effects of single nucleotide substitutions, a property that was likely selected for during the emergence of a universal code. Given the fitness advantage…
It has been repeatedly proposed to expand the scope for SETI, and one of the suggested alternatives to radio is the biological media. Genomic DNA is already used on Earth to store non-biological information. Though smaller in capacity, but…
It has been known that the insufficiency of linear coding in achieving the optimal rate of the general index coding problem is rooted in its rate's dependency on the field size. However, this dependency has been described only through the…
Automatic code generation is to generate the program code according to the given natural language description. The current mainstream approach uses neural networks to encode natural language descriptions, and output abstract syntax trees…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
The maximum clique problem (MCP) is a fundamental problem in graph theory and in computational complexity. Given a graph G, the problem is that of finding the largest clique (complete subgraph) in G. The MCP has many important applications…
Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the…
The Standard Model has three generations of fermions and although it does not contain any explicit reason for this, the existence of additional generations is now very constrained by experiment. Present measurements are saturating…
Rich information on the prebiotic evolution is still stored in contemporary genomic data. The statistical mechanism at the sequence level may play a significant role in the prebiotic evolution. Based on statistical analysis of genome…
We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later…
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we…
A new class of error-correcting quantum codes is introduced capable of stabilizing qubits against spontaneous decay arising from couplings to statistically independent reservoirs. These quantum codes are based on the idea of using an…
In the near future, all the human genes will be identified. But understanding the functions coded in the genes is a much harder problem. For example, by using block entropy, one has that the DNA code is closer to a random code then written…
A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the…
Molecular codes translate information written in one type of molecules into another molecular language. We introduce a simple model that treats molecular codes as noisy information channels. An optimal code is a channel that conveys…
Many transcription factors bind to DNA with a remarkable lack of specificity, so that regulatory binding sites compete with an enormous number of non-regulatory 'decoy' sites. For an auto-regulated gene, we show decoy sites decrease noise…
We present a model of the evolution of control systems in a genome under environmental constraints. The model conceptually follows the Jacob and Monod model of gene control. Genes contain control elements which respond to the internal state…
The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…
Coding information is the main source of heterogeneity (non-randomness) in the sequences of bacterial genomes. This information can be naturally modeled by analysing cluster structures in the "in-phase" triplet distributions of relatively…