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We consider DNA codes based on the nearest-neighbor (stem) similarity model which adequately reflects the "hybridization potential" of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a…
High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…
This book draft gives the theory of a new method for p dimensional adaptive integration by repeated 2^p subdivision of simplexes and hypercubes. A new method of constructing high order integration routines for these geometries permits…
Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation (WAP) property which is necessary and sufficient condition for uniform two-grid convergence. This paper studies a…
Medical Informatics and the application of modern signal processing in the assistance of the diagnostic process in medical imaging is one of the more recent and active research areas today. This thesis addresses a variety of issues related…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation.…
We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are…
We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of C{\alpha}…
Using the differential precision methods developed previously by the same authors, we study the p-adic stability of standard operations on matrices and vector spaces. We demonstrate that lattice-based methods surpass naive methods in many…
In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to…
The incorporation of subarrays in Direct Radiating Arrays for satellite missions is fundamental in reducing the number of Radio Frequency chains, which correspondingly diminishes cost, power consumption, space, and mass. Despite the…
This paper is a sequel to arXiv:2501.14444, in which we shall give proofs of several results stated in arXiv:2501.14444 (Theorems D--L) which, for brevity and clarity, we postponed to this sequel paper. These results were the following: for…
Genetic Programming (GP) is a computationally intensive technique which also has a high degree of natural parallelism. Parallel computing architectures have become commonplace especially with regards Graphics Processing Units (GPU). Hence,…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
We discuss how to handle matching-adjusted indirect comparison (MAIC) from a data analyst's perspective. We introduce several multivariate data analysis methods to assess the appropriateness of MAIC for a given data set. These methods focus…
This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo p^a and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic…
Deep learning affords enormous opportunities to augment the armamentarium of biomedical imaging, albeit its design and implementation have potential flaws. Fundamentally, most deep learning models are driven entirely by data without…
Bound states in the continuum (BICs) have some unusual properties and important applications in photonics. A periodic structure sandwiched between two homogeneous media is the most popular platform for observing BICs and realizing their…
This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix…