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Introduction: molecular geometry, the three-dimensional arrangement of atoms within a molecule, is fundamental to understanding chemical reactivity, physical properties, and biological activity. The prevailing models used to describe…
Limited by the operation and measurement conditions, numerical simulation is often the only feasible approach for studying plasma behavior and mechanisms. Although artificial intelligence methods, especially physics-informed neural network…
Single-particle electron microscopy is a modern technique that biophysicists employ to learn the structure of proteins. It yields data that consist of noisy random projections of the protein structure in random directions, with the added…
This paper describes a geometrical method for finding the roots $r_1$, $r_2$ of a quadratic equation in one complex variable of the form $x^2+c_1 x+c_2=0$, by means of a Line $L$ and a Circumference $C$ in the complex plane, constructed…
This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is…
Protein structure determination has long been one of the primary challenges of structural biology, to which deep machine learning (ML)-based approaches have increasingly been applied. However, these ML models generally do not incorporate…
The solution in sense of Prager&Synge is the alternative to the commonly used notion of the numerical solution, which is considered as a limit of grid functions at mesh refinement. Prager&Synge solution is defined as a hypersphere…
This paper presents a one-dimensional analog of the Rectangular-Polar (RP) integration strategy and its convergence analysis for weakly singular convolution integrals. The key idea of this method is to break the whole integral into integral…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
Machine learning (ML) has seen promising developments in materials science, yet its efficacy largely depends on detailed crystal structural data, which are often complex and hard to obtain, limiting their applicability in real-world…
Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as $\alpha$-helices and $\beta$-sheets. Secondary structure is characterized by the local rotational state of the protein…
This work is an update of the 2000 publication of magnetic-rotational bands by Amita et al. [1], followed by an unpublished update of 2006 [2], and reviews detailed experimental data extracted from original publications for 228…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
We propose a multi-objective global pattern search algorithm for the task of locating and quantifying damage in flexible mechanical structures. This is achieved by identifying eigenfrequencies and eigenmodes from measurements and matching…
Despite the success of deep learning methods in quantum chemistry, their representational capacity is most often confined to neutral, closed-shell molecules. However, real-world chemical systems often exhibit complex characteristics,…
Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or…
Given a set $\mathsf{P}$ of $n$ points in $\mathbb{R}^d$, we show how to insert a set $\mathsf{X}$ of $O( n^{1-1/d} )$ additional points, such that $\mathsf{P}$ can be broken into two sets $\mathsf{P}_1$ and $\mathsf{P}_2$, of roughly equal…