The Oriented and Flux-Weighted Current Density Stagnation Graph of LiH

A scheme is introduced to quantitatively analyze the magnetically induced molecular current density vector field $\mathbf{J}$. After determining the set of zero points of $\mathbf{J}$, which is called its {\em stagnation graph} (SG), the line integrals $\Phi_{\ell_i}=-\frac{1}{\mu_0} \int_{\ell_i} \mathbf{B}_\mathrm{ind}\cdot\mathrm{d}\mathbf{l}$ along all edges $\ell_i$ of the connected subset of the SG are determined. The edges $\ell_i$ are oriented such that all $\Phi_{\ell_i}$ are non-negative and they are weighted with $\Phi_{\ell_i}$. An oriented flux-weighted (current density) stagnation graph (OFW-SG) is obtained. Since $\mathbf{J}$ is in the exact theoretical limit divergence free and due to the topological characteristics of such vector fields the flux of all separate vortices and neighbouring vortex combinations can be determined by adding the weights of cyclic subsets of edges of the OFW-SG. The procedure is exemplified by the case of LiH for a perpendicular and weak homogeneous external magnetic field $\mathbf{B}$}

Topological Characteristics Associated with Intraoperative Stimulation Related Epilepsy of Glioma Patients: A DTI Network Study

Background: Awake craniotomy with intraoperative stimulation has been utilized in glioma surgical resection to preserve the quality of life. Epilepsy may occur in 5–20% of cases, leading to severe consequences. This study aimed to discuss the mechanism of intraoperative stimulation-related epilepsy (ISE) using DTI-based graph theoretical analysis. Methods: Twenty patients with motor-area glioma were enrolled and divided into two groups (Ep and nEp) according to the presence of ISE. Additionally, a group of 10 healthy participants matched by age, sex, and years of education was also included. All participants underwent T1, T2, and DTI examinations. Graph theoretical analysis was applied to reveal the topological characteristics of white matter networks. Results: Three connections were found to be significantly lower in at least one weighting in the Ep group. These connections were between A1/2/3truL and A4ulL, A1/2/3truR and A4tR, and A6mL and A6mR. Global efficiency was significantly decreased, while the shortest path length increased in the Ep group in at least one weighting. Ten nodes exhibited significant differences in nodal efficiency and degree centrality analyses. The nodes A6mL and A6mR showed a marked decrease in total four weightings in the Ep group. Conclusions: The hub nodes A6mL and A6mR are disconnected in patients with ISE, causing subsequent lower efficiency of global and regional networks. These findings provide a basis for presurgical assessment of ISE, for which caution should be taken when it involves hub nodes during intraoperative electrical stimulation.

Improvement of Quantum Approximate Optimization Algorithm for Max–Cut Problems

The objective of this short letter is to study the optimal partitioning of value stream networks into two classes so that the number of connections between them is maximized. Such kind of problems are frequently found in the design of different systems such as communication network configuration, and industrial applications in which certain topological characteristics enhance value–stream network resilience. The main interest is to improve the Max–Cut algorithm proposed in the quantum approximate optimization approach (QAOA), looking to promote a more efficient implementation than those already published. A discussion regarding linked problems as well as further research questions are also reviewed.

Application of matlab for digital images topological characteristics calculation and analysis

The paper describes the practical results received from digital images topographic characteristics calculating in Matlab, such as length and curvature of contour lines, density of lengths and curvature, as well as irregularities of contour lines of the first and second order. Topological characteristics contain complete information about the shape and contours of a digital image, which allows them to be effectively used in solving the problems of remote sensing data processing, analysis of biomedical images, classification and pattern recognition problems.

Neural evidence for image quality perception based on algebraic topology

In this paper, the algebraic topological characteristics of brain networks composed of electroencephalogram(EEG) signals induced by different quality images were studied, and on that basis, a neurophysiological image quality assessment approach was proposed. Our approach acquired quality perception-related neural information via integrating the EEG collection with conventional image assessment procedures, and the physiologically meaningful brain responses to different distortion-level images were obtained by topological data analysis. According to the validation experiment results, statistically significant discrepancies of the algebraic topological characteristics of EEG data evoked by a clear image compared to that of an unclear image are observed in several frequency bands, especially in the beta band. Furthermore, the phase transition difference of brain network caused by JPEG compression is more significant, indicating that humans are more sensitive to JPEG compression other than Gaussian blur. In general, the algebraic topological characteristics of EEG signals evoked by distorted images were investigated in this paper, which contributes to the study of neurophysiological assessment of image quality.

A new approach to vague soft toplogical structures concerning soft points

This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.

On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

New Lens to Reveal the Street Interface. A Morphological-Visual Perception Methodological Contribution for Decoding the Public/Private Edge of Arterial Streets

Streets have different forms that are not defined only by their partitions, furniture, and width, but also by their edges as vital features of their spatiality. The relationship between a street and a building impacts the street interface configurations, resulting in various topological characteristics. Thus, the street interface is a physical entity that is produced by the interrelationship between urban morphological elements (street and building), and the way it is formed and used affects the livability of the street. The methods used in the current study contribute to an empirical urban morphological–visual cognitive investigation of arterial street interface configurations, particularly on the ground floor level, to assess potential relations between variations in the physical configurations that influence pedestrian visual perception using mobile eye-tracking glasses. In conclusion, this study contributes to research into developing a spatial framework for arterial street liveability, addressing the pilot case study of Avenida da República in Lisbon.