Size Functions and Morphological Transformations

A combined diffraction and geometrical optics approach for lidar overlap function computation

Chapter 17 - Investigating the common pathogenic mechanism for drug design between different strains of Candida albicans infection in OKF6/TERT-2 cells by comparing their genetic and epigenetic host/pathogen networks: Big data mining and computational systems biology approaches

In 1950 Nelson raised the problem of coloring the Euclidean plane in such a way that no two points of distance 1 receive the same color. How many colors are needed? This problem was often mentioned in Paul Erdos' famous lectures on unsolved combinatorial problems. The history of the problem is described in [2] and [3]. Clearly, three colors are needed. To see that four colors are needed, we consider seven points x1, X2,..., X7 in the Euclidean plane such that the following pairs are of distance 1: X1x2,x1x3,xXx4,x3x4,X2X5,X2X6,X5X6,X3X7,X4X7,X5X7, x6x7. It follows from the theorem of de Bruijn and Erdos [1] that the number of colors needed for the whole plane is the maximum number of colors needed for the finite subsets. The half-century old upper bound 7 is obtained by drawing an appropriate graph in the plane such that each face (region) is bounded by a cycle of (Euclidean) diameter less than one and then coloring each face and part of the boundary by the same color in such a way that only faces of distance > 1 receive the same color. We prove that colorings of this type always need at least 7 colors. More generally, 7 colors are needed for any surface and any metric of large diameter provided there are no short noncontractible curves and no short contractible curves whose interior have large area. The upper bound 7 is obtained from a hexagonal tiling of the plane such that the hexagons are regular and of diameter slightly less than 1. All points inside a hexagon are colored with the same color. Two hexagons are colored differently if the distance between them is less than one. A coloring of this type will be called nice. More generally, we consider any metric space S, d such that S is a surface, i.e., S is an arcwise connected Hausdorff space such that each element of S has a neighborhood homeomorphic to an open disc in the Euclidean plane. We let G be a connected graph on S, i.e., the vertices of G are elements of S, and the edges of G are simple arcs on S that are pairwise disjoint except at a common vertex. Moreover, we assume that each face (i.e., arcwise connected component of S\G) has diameter less than 1, is homeomorphic to a disc, and is bounded by a cycle in G. Now a nice coloring of S obtained from G is a coloring such that each color class is the union of faces (and part of their boundaries) such that the distance between any two of these faces is greater than 1. We define the area of subset A of S as the maximum number of pairwise disjoint open discs of radius 2 that are contained in A. (If this maximum does not exist we say that A has infinite area.) We say that a simple closed curve C is contractible if S\C has precisely two arcwise connected components such that one of them is homeomorphic to an open disc in the Euclidean plane. That component is called the interior of C and is denoted int(C). (If S is a sphere, then int(C) denotes any component of S\C of

The proliferation-specific oncogenic transcription factor, FOXM1 is overexpressed in primary and recurrent breast tumors across all breast cancer (BC) subtypes. Intriguingly, FOXM1 overexpression was found to be highest in Triple-negative breast cancer (TNBC), the most aggressive BC with the worst prognosis. However, FOXM1-mediated TNBC pathogenesis is not completely elucidated. Single nucleotide polymorphisms (SNPs) are the most common genetic variations causing functional and structural aberrations in proteins enhancing cancer susceptibility. This computational investigation attempted to identify the malignant FOXM1 non-synonymous SNPs (nsSNPs) and evaluate their role in affecting the conformational and functional stability, evolutionary conservation, post-translational modifications, and malignant susceptibility of the protein. Out of a huge data pool of 8826 FOXM1 SNPs using several in-silico sequence-based tools and structural approaches, four SNPs viz. E235Q, R256C, G429E and S756P were identified as pathogenic nsSNPs and among the shortlisted variants molecular dynamics simulations identified E235Q as the most damaging malignant SNP, followed by S756P. Additionally, the defective drug and DNA binding motif of E235Q and S756P were also determined in our study. Thus, although further in-vitro validations are awaited the findings of this in-silico work can be used as a blueprint for malignant nsSNP identification of FOXM1 aiding in clinical TNBC therapeutics.

This paper presents a comprehensive theoretical and computational study on the sequential representation of arrays within the algebraic framework of Galois Fields (GF), with a primary focus on GF(7). By employing modular arithmetic, symmetry principles, and binary encoding techniques, the work demonstrates how discrete array elements can be systematically mapped to finite field structures to achieve efficient and fault-tolerant data representation. The proposed methodology integrates sequential indexing with field operations to ensure closure, invertibility, and predictable algebraic transformations. Through detailed mathematical formulations and computational simulations, the study validates that array differences and mappings preserve the cyclic structure intrinsic to GF(7). Furthermore, the research highlights the applicability of this representation in several domains, including digital communication systems, cryptographic primitives, coding theory, and error-resilient computation. Sequential binary encodings derived from modular residues provide an additional layer of structure suitable for hardware-level implementation and secure data processing pipelines. The study also connects these representations to Perfect Difference Sets (PDS) and Perfect Difference Networks (PDN), illustrating how modular differences support highly symmetric interconnection topologies. Overall, the framework provides a unified perspective on finite-field-based array representation, offering both analytical clarity and practical relevance for modern computational architectures and secure information systems.

Protein chemical shift perturbations (CSPs), upon ligand binding, can be used to refine the structure of a protein-ligand complex by comparing experimental CSPs with calculated CSPs for any given set of structural coordinates. Herein, we describe a fast and accurate methodology that opens up new opportunities for improving the quality of protein-ligand complexes using nuclear magnetic resonance (NMR)-based approaches by focusing on the effect of the ligand on the protein. The new computational approach, 1H empirical chemical shift perturbation (HECSP), has been developed to rapidly calculate ligand binding-induced 1H CSPs in a protein. Given the dearth of experimental information by which a model could be derived, we employed high-quality density functional theory (DFT) computations using the automated fragmentation quantum mechanics/molecular mechanics approach to derive a database of ligand-induced CSPs on a series of protein-ligand complexes. Overall, the empirical HECSP model yielded correlation coefficients between its predicted and DFT-computed values of 0.897 (1HA), 0.971 (1HN), and 0.945 (side chain 1H) with root-mean-square errors of 0.151 (1HA), 0.199 (1HN), and 0.257 ppm (side chain 1H), respectively. Using the HECSP model, we developed a scoring function (NMRScore_P). We describe two applications of NMRScore_P on two complex systems and demonstrate that the method can distinguish native ligand poses from decoys and refine protein-ligand complex structures. We provide further refined models for both complexes, which satisfy the observed 1H CSPs in experiments. In conclusion, HECSP coupled with NMRScore_P provides an accurate and rapid platform by which protein-ligand complexes can be refined using NMR-derived information.

Ebola virus (EBOV), one of the deadliest diseases, is responsible for infecting individuals with hemorrhagic fever syndrome, which remains an ongoing worldwide health concern. The extremely deadly nature and virulence of EBOV illness illuminate the imperative need to evolve effective curative agents. Viral protien (VP35) acts as an Achilles heel for EBOV reproduction and also interacts with numerous human proteins, which leads to impairing the immune system. Herein, the DrugBank database, containing >14000 investigational and approved drugs, is mined to hunt prospective inhibitors toward VP35 utilizing various computational approaches. Docking technique performance is initially validated to predict the VP35‐inhibitor binding pose upon the accessible experimental data. Molecular dynamics simulations (MDS) are then conducted in triplicate on the top potent drug candidates, followed by binding energy (ΔGbinding) estimations using molecular mechanics/generalized Born surface area (MM/GBSA) approach. Upon MM/GBSA//250 ns MDS, DB14875 and DB07800 revealed better binding energy against VP35 than 1D9, reference inhibitor, with ΔGbinding values of −36.6, −35.6, and −29.3 kcal mol−1, respectively. Post‐MD analyses demonstrate great stability for the identified drug candidates complexed with VP35 over 250 ns MDS. Ultimately, the density functional theory computations are executed, and their outcomes elucidate favorable molecular reactivity of the identified drug candidates. Conclusively, these findings suggest promising inhibitors for VP35, warranting further experimental assays.

Catalytic properties of noble-metal nanoparticles (NPs) are largely determined by their surface morphology. The latter is probed by surface-sensitive spectroscopic techniques in different spectra regions. A fast and precise computational approach enabling the prediction of surface–adsorbate interaction would help the reliable description and interpretation of experimental data. In this work, we applied Machine Learning (ML) algorithms for the task of adsorption-energy approximation for CO on Pd nanoclusters. Due to a high dependency of binding energy from the nature of the adsorbing site and its local coordination, we tested several structural descriptors for the ML algorithm, including mean Pd–C distances, coordination numbers (CN) and generalized coordination numbers (GCN), radial distribution functions (RDF), and angular distribution functions (ADF). To avoid overtraining and to probe the most relevant positions above the metal surface, we utilized the adaptive sampling methodology for guiding the ab initio Density Functional Theory (DFT) calculations. The support vector machines (SVM) and Extra Trees algorithms provided the best approximation quality and mean absolute error in energy prediction up to 0.12 eV. Based on the developed potential, we constructed an energy-surface 3D map for the whole Pd55 nanocluster and extended it to new geometries, Pd79, and Pd85, not implemented in the training sample. The methodology can be easily extended to adsorption energies onto mono- and bimetallic NPs at an affordable computational cost and accuracy.

Megawite, a recently discovered perovskite-structured mineral with Ca(Ti0.07, Sn0.6, Zr0.33)O3, was identified in a xenolith. Its end members, CaTiO3, CaSnO3, and CaZrO3, represent GdFeO3-type perovskites (A2+B4+O3), which have garnered significant attention for their structural and physical properties. Among these, CaSnO3 stands out due to its exceptional optical and electrical properties, supported by its high physical and chemical stability. Despite its increasing applications, critical physical properties such as the elastic moduli (Cij) of single-crystal CaSnO3 have yet to be determined experimentally. Available data on CaSnO3 elasticity stems from polycrystalline measurements or computational predictions. This gap underscores the need for experimental determination of single-crystal elastic moduli better to understand its mechanical behavior and implications for future applications.Here, we report the elastic moduli of single-crystal CaSnO3 perovskite measured using Brillouin scattering at ambient conditions. Crystals of CaSnO3 were synthesized at 1200 °C over 24 hours from a starting mixture of CaCl2 and SnO2 in a 2:1 molar ratio. Four high-quality crystals were selected for Brillouin scattering measurements. Full elastic moduli were derived via least squares regression of sound velocity data against the Christoffel equation. The obtained values for the elastic moduli include longitudinal moduli (C11, C22, C33) ranging from 270 to 290 GPa, shear moduli (C44, C55, C66) between 90 and 98 GPa, and off-diagonal moduli (C12, C13, C23) ranging from 100 to 120 GPa. These measurements' aggregate bulk modulus, shear modulus, and sound velocities align well with previous polycrystalline results obtained through ultrasonic interferometry (Kung et al., 2001; Schneider et al., 2008).A key step in Brillouin scattering data analysis is the establishment of an initial Cij model. For a new material such as CaSnO3, setting up an effective starting model requires experience. In this study, the starting Cij model was derived from density functional theory (DFT) computations to serve the purpose. Elasticity and electronic ground states were calculated using the CASTEP code integrated within the Materials Studio software package. These calculations employed LDA, GGA, and mGGA functionals, with norm-conserving and ultrasoft pseudopotentials modeling electron-ion interactions. The computationally predicted Cij values served as the initial input for data fitting. The final best-fit Cij model was determined by minimizing residual differences across iterative fitting steps. The close agreement between experimental and computational results highlights the utility of computational predictions as a starting point for Brillouin scattering analyses.This study presents the first experimental determination of the elastic moduli for single-crystal CaSnO3 perovskite, supported by computational insights. The integration of experimental and computational approaches offers a robust framework for characterizing the mechanical properties of new materials. Our findings contribute to the broader understanding of perovskite materials, with implications for geosciences and advanced material applications.

The geometric and electronic structures of the six-coordinate azide adduct of oxidized manganese superoxide dismutase (Mn3+ SOD) that is formed at low temperatures, LT N3-Mn3+ SOD, has been examined in detail through a combined spectroscopic/computational approach. Electronic absorption, circular dichroism (CD), magnetic CD (MCD) and variable-temperature, variable-field (VTVH) MCD spectroscopies were used to determine electronic transition energies and to obtain an estimate of zero-field splitting parameters for LT N3-Mn3+ SOD. These experimental data were utilized in conjunction with semiempirical intermediate neglect of differential overlap/spectroscopic parametrization-configuration interaction (INDO/S-CI) and time-dependent density functional theory (TD-DFT) computations to evaluate hypothetical active-site models of LT N3-Mn3+ SOD generated by constrained DFT geometry optimizations. Collectively, our spectroscopic/computational results indicate that N3- binding to Mn3+ SOD at low temperatures promotes neither protonation of the axial solvent ligand nor reorientation of the redox-active molecular orbital, both of which had been previously suggested. Using the same experimentally validated computational approach, models of the product-inhibited form of MnSOD were also developed and evaluated by their relative energies and TD-DFT-computed absorption spectra. On the basis of our computational results as well as previously published kinetic data, we propose that the product-inhibited form of MnSOD is best described as a side-on peroxo-Mn3+ adduct possessing an axial H2O ligand. Notably, attempts to generate a stable hydroperoxo-Mn3+ SOD species by protonation of the proximal O atom of the hydroperoxo ligand resulted in dissociation of HOO- and eventual H+ transfer from Tyr34 to HOO-, generating deprotonated Tyr34 and H2O2. The implications of these results with respect to the mechanism of O2*- dismutation by MnSOD are discussed.

This study explores how an active pharmaceutical ingredient-ionic liquid (API-IL), cholinium taurate ([Cho]+[Tau]-) IL, may alter the structural and functional stability of histone deacetylase 2 (HDAC2), which is a crucial enzyme linked to alcohol use disorder (AUD). A particular hallmark of AUD, which is a worldwide health burden, is epigenetic dysregulation, in which HDAC2 plays a significant role in gene silencing and chronic neuroplastic alterations. Leveraging the unique physicochemical properties of [Cho]+[Tau]-IL, including hydrogen bond (H-bond) formation and structural reinforcement, we explored its therapeutic potential through comprehensive computational approaches. Density functional theory (DFT) analyses provided insights into the hydration and stability profiles of [Cho]+[Tau]-IL, while 200 ns molecular dynamics (MD) simulations elucidated its interaction with HDAC2 at the molecular level. Strikingly, the [Tau]- ion emerged as a key modulator of HDAC2 stability, facilitating conformational transitions in the enzyme's secondary structure, notably from turns to helices. This stabilisation was mediated by intricate hydration networks, water-mediated H-bonds, and diverse non-covalent interactions (NCIs). The rigorous nature of our structural analyses confirmed the potential of [Cho]+[Tau]-IL as a robust stabiliser of HDAC2, offering a novel therapeutic avenue for AUD treatment. This work underscores the promise of API-ILs in targeting epigenetic regulators and advancing strategies for AUD, providing a solid foundation for future research in this area.

Density functional theory computations at the B3LYP/6-311+G(2d,2p) and BPW91/6-311G(d,p) levels were carried out for a series of 15 monosubstituted benzene derivatives to study dependencies between electronic structure parameters and experimental reactivity constants. An efficient and accurate computational approach for the evaluation of sigma(0) substituent constants for substituted benzene systems is outlined. It is based on the excellent linear correlation between the experimental reactivity constants and the theoretical electrostatic potential values (EPN) at the carbon atoms in the para and meta positions. The results underline the usefulness of the EPN as a local reactivity descriptor. Theoretical computations to assess the influence of water solvent using the SCIPCM method showed that the solvent enhances the overall effect of polar substituents by about 30%. The results obtained indicate also that the relative values of the sigma(0) constants are predominantly determined by intramolecular influences.

We report computational test results for several graph-based a priori heuristics for the Euclidean plane versions of two well-known stochastic optimization problems, the probabilistic traveling salesman problem (PTSP) and the probabilistic (or stochastic) vehicle routing problem (PVRP). These heuristics are termed a priori because they design vehicle routes prior to realization of demands. Our tests compare the quality of such solutions to sample averages of a posteriori solutions of the deterministic realizations—the underlying TSPs and VRPs. Our results indicate that the simplest implementations give average cost performance within 5% of the latter, while the best implementations show a gap of only about 1%. Since running times are modest, we conclude that the a priori approaches offer a large potential benefit to the practitioner seeking to obtain good performance in a situation where solving repeated deterministic instances of the TSP or VRP is impractical or otherwise undesirable.

The nearby-friend problem for a user in the context of location based services is to learn the location of a nearby-friend only if (s)he is actually nearby, while simultaneously maintaining the privacy of their respective locations. The existing works address the problem for two users only. In this paper, we present for the first time a solution which caters to multiple users. We use techniques from Euclidean plane geometry and graph theory to develop a secure multi-party computation approach towards solving the nearby-friend problem efficiently for many users. Our solution ensures users' location privacy by enforcing k-anonymity.