Related papers: p-Adic numbers in bioinformatics: from genetic cod…
A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence…
A Bio-metrics system is actually a pattern recognition system that utilizes various patterns like iris, retina and biological traits like fingerprint, voice recognition, facial geometry and hand geometry. What makes Bio-metrics really…
Researchers in the field of biocomputing have, for many years, successfully "harvested and exploited" the natural world for inspiration in developing systems that are robust, adaptable and capable of generating novel and even "creative"…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
Genome rearrangement has been an active area of research in computational comparative genomics for the last three decades. While initially mostly an interesting algorithmic endeavor, now the practical application by applying rearrangement…
The applications of artificial neural networks in the cosmological field have shone successfully during the past decade, this is due to their great ability of modeling large amounts of datasets and complex nonlinear functions. However, in…
How to represent the genetic code? Despite the fact that it is extensively known, the DNA mapping into proteins remains as one of the relevant discoveries of genetics. However, modern genomic signal processing usually requires converting…
We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…
Using machine learning, especially deep learning, to facilitate biological research is a fascinating research direction. However, in addition to the standard classification or regression problems, in bioinformatics, we often need to predict…
Processing-in-memory (PIM) is a transformative architectural paradigm designed to overcome the Von Neumann bottleneck. Among PIM architectures, digital SRAM-PIM emerges as a promising solution, offering significant advantages by directly…
The origin and organizing principles of the genetic code remain fundamental puzzles in life science. The vanishingly low probability of the natural codon-to-amino acid mapping arising by chance has spurred the hypothesis that its structure…
Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even…
The matching distance is a pseudometric on multi-parameter persistence modules, defined in terms of the weighted bottleneck distance on the restriction of the modules to affine lines. It is known that this distance is stable in a reasonable…
In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial…
A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer…
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be…
Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We…
Methods for alignment of protein sequences typically measure similarity by using substitution matrix with scores for all possible exchanges of one amino acid with another. Although widely used, the matrices derived from homologous sequence…