The Randić index of a graph G is the sum of (dG(u)dG(v))−1/2 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease Randić index of graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs, and characterize the corresponding extremal graphs.

In the realm of molecular science, intricate relationships between molecular structures and their biomedical and pharmacological characteristics have been revealed through empirical experiments. This exploration hinges on the application of numerical descriptors, known as Topological Indices, which illuminate the inherent properties of diverse molecular structures. With particular significance in the medical and pharmaceutical domains, these indices facilitate the prediction of biological features for new chemical compounds and drugs by quantifying weighted entropies. In the context of this paper, we delve into the concept of graph entropy, weaving it intricately with the topological properties of the crystalline framework of the copper oxide molecule, denoted as Cu\textsubscript{2}O$[i,j,t]$. Our primary objective is to unravel the mathematical symphony underlying the structural intricacies of Cu\textsubscript{2}O$[i,j,t]$ and to imbue it with the conceptual essence of entropy. We accomplish this through the computation of entropy, leveraging various topological indices, including weight. In addition to our analytical journey, we present a graphical comparison that juxtaposes the computed indices and entropies, shedding light on the interplay between mathematical analysis and the structural elegance of Cu\textsubscript{2}O$[i,j,t]$. This endeavor contributes to a deeper understanding of the material's multifaceted applications, spanning domains from chemical sensors to solar cells, photocatalysis, and batteries, where Cu\textsubscript{2}O's crystallographic structure plays a pivotal role.

This study aims to refine our understanding of evolutionary processes, particularly as they apply to complex organisms, using an innovative graph-based simulation approach. We model the topological evolution of simple (5-node ring graph) and complex (20-node dense random graph) organisms over 10 generations, applying different mutation rates to reflect biological realities. Our results provide intriguing insights into the potentially different evolutionary dynamics at play in simple versus complex organisms. While simple organisms demonstrate high topological flexibility and rapid adaptability, aligning with classical evolutionary models, complex organisms exhibit a surprising degree of structural stability. This stability persists even under mutation rates that would typically drive significant changes in simpler systems. The simulation highlights an important consideration: the intricate, interdependent networks characteristic of complex organisms may create a form of evolutionary buffering. This buffering could modulate the impact of random mutations and natural selection – processes that are cornerstones of evolutionary theory. Our findings suggest that the high degree of complexity in advanced life forms may necessitate a more nuanced view of how evolutionary processes operate across different levels of biological organization. Furthermore, the emergence of new structural motifs in simple organisms, contrasted with the relative conservation in complex topologies, indicates that evolutionary mechanisms may manifest differently across the spectrum of biological complexity. This observation invites a more detailed exploration of how evolutionary principles apply to diverse life forms.These results contribute to the ongoing refinement of evolutionary theory, especially in its application to complex organisms. They suggest that additional mechanisms, such as constrained mutations, epigenetic changes, or higher-order organizational principles, may play significant roles alongside random mutations and natural selection in the evolution of complex life forms.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

In this article we compute many topological indices for the family of Möbius ladder. At first we give general closed form of M-polynomial of this family and recover many degree based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family.

The part of this article dealing with topological insulators and topological superconductors was first written about two years ago - the ideas in the part about the topological universe originated six years ago or more. It’s rather strange that I never put the two parts together in writing before. My belief in unification is unshakeable - I’ve been convinced for years that the universe must be composed of topology. Since Earth is part of the cosmos, entanglement means it must have topological materials. The reverse is also true: topological materials on Earth are well known to science - so in a unification, space and time inevitably possess topological composition. Topological materials (topological insulators, topological superconductors) can be less mystifying if they’re related to the paradigm-shifting deterministic view of quantum mechanics which is described in the universal topology (the “rubber-sheet geometry” of the cosmos): see my previous submission “Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories" at https://www.preprints.org/manuscript/202105.0239/v1 (the first section of this present article is a quick summary of the relevant parts).

Graph visualization has evolved significantly over time, offering various methods to effectively represent complex data structures. This study introduces a novel force-directed algorithm for 3D data visualization, specifically tailored for commonly used datasets in linked data visualization. Leveraging the power of graph theory and methods, the algorithm aims to address the challenge of creating visually appealing and easily interpretable visualizations, which often necessitate advanced user interaction. By utilizing 3D space and the Unity Engine, the research successfully visualizes data and develops interactive visualizations, overcoming limitations of basic force-directed implementations. The main contribution of presented research is in the force-directed algorithm with springs and controlled placement as a visualization technique that combines the use of springs and attractive forces to stabilize a graph in a 3D environment. The combination of these two techniques also helps prevent the formation of a single large cluster within the graph, enhancing the overall visualization quality.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

Vertex-degree-based (VDB) topological indices have been applied in QSPR/QSAR. As an important category, the general logarithmic VDB topological index $T_{lnf}(G)$, is defined as the summation of $ln{f(d(u),d(v))}$, where the summation over all $uv\in E(G)$. In this paper, we give the sufficient conditions for that (1) the path $P_{n}$ is the only tree with the minimal $T_{lnf}$; (2) the star $S_n$ is the only tree with the maximal and the minimal $T_{lnf}$, respectively. As applications, the minimal and maximal trees of some logarithmic VDB indices are determined.

The electronic properties of calcium intercalated graphite (CaC6) as a function of pressure are revisited using density functional theory (DFT). The electronic band structures of CaC6, like many other layered superconducting materials, display cosine-shaped bands at or near the Fermi level (FL). Such bands encompass bonding/antibonding information with a strong connection to superconducting properties. Using an hexagonal cell representation for CaC6, construction of a double supercell in the c-direction effects six-folding in reciprocal space of the full cosine function, explicitly revealing the bonding/antibonding relationship divide at the cosine midpoint. Similarly, folding of the Fermi surface (FS) reveals physical phenomena relevant to electronic topological transitions (ETT) with application of pressure. For CaC6, the peak value for the superconducting transition temperature, Tc, occurs at about 7.5 GPa, near to the observed pressure of the calculated ETT. At this pressure, the radius of the nearly spherical Ca 4s-orbital FS coincides with three times the distance from the G centre point to the Brillouin zone (BZ) boundary of the 2c supercell (which is equal to half the identically defined distance for the primitive rhombohedral BZ). In addition, the ETT coincides with alignment of the non-bonding (inflection) point of the cosine band (the point at which the sign of the cosine amplitude modulation is reversed) with the FL. At other calculated pressure conditions, the Ca 4s-orbital FS undergoes topological changes that correspond and can be correlated to experimentally determined changes in Tc. The ETT is a key mechanism that circumscribes the known significant drop in Tc for CaC6 as a function of increasing pressure.

Constructing new graph from the graph's parameters and related notions in the way that, the study on the new graph and old graph in their parameters could be facilitated. As graph, new graph has some characteristics and results which are related to the structure of this graph. For this purpose, regular graph is considered so the internal relation and external relation on this new graph are studied. The kind of having same number of edges when this number is originated by common number of graphs like maximum degree, minimum degree, domination number, coloring number and clique number, is founded in the word of having regular graph

Against the background of the sky, imaging and perception of aircraft are cru- cial. Among these, the location of aircrafts is not a very difficult problem in general, because that deep learning algorithms and object detection models based on convolutional neural network(CNN) are ever-evolving. In order to have a better identification of various aircrafts, or to accurately locate different types of flying targets in the sky, it becomes significant to distinguish and recognize different types of aircrafts. One question is that, distinguishing and recognizing between sub-categories of aircrafts pose great challenges. Although fine-grained recognition focuses on exploring and studying such problems, aircrafts under different sub-categories and granularities lead us to rethink the application of features. We noticed that features in swin-transformer demonstrates the under- standing and processing of images, fully showcasing the encoding and indexing of information. Through this research and proposed approach, we discovered a better understanding of features encoding and use, which are inspired by the feature encoding and computation in swin-transformer. In our paper, our ap- proach has achieved effects on features encoded graphically, manifested from the architecture design and convolutional neural network computation, and outper- forms other famous fine-graiend classification models on this issue. Not only approach we proposed has demonstrated superior performance in fine-grained aicraft classification, but also the mechanisms of the feature encoding under different sample space partitions is revealed for this issue, which provides a re- search for the representation of aircraft fineness characteristics. The relationship between representation orientation of aircraft feature information under various grained divisions, shows that the recognition of different categories according to man-made, such as aircraft, can be achieved by means of the feature represen- tations studied in this paper, for more specific defined classification tasks and various man-made targets partition criteria, which may influences the princi- ple of design for calculation and feature extraction in fine-grained classification models.

We study the coupling of two topologcal subsystems in distinct topological states, and show that it leads to a precursor behavior of the topological phase transition in the overall system. This behavior is solely determined by the symmetry classes of the subsystem Hamiltonians and coupling terms, and is marked by the persistent existence of subgap states within the bulk energy gap. By investigating the critical current of Josephson junctions involving topological superconductors, we also illustrate that such subgap states play crucial roles in physical properties of nanoscale devices or materials.

：Non-Euclidean data, such as social networks, and citation relationships between documents, has node information and structural information. Graph Convolutional Network(GCN) can automatically learn node features and association information between nodes. The core ideology of the graph convolutional network is to aggregate node information by using edge information, thereby generating a new node feature. In the process of updating node features, there are two core influencing factors. One is the number of neighboring nodes of the central node, the other is the contribution of the neighboring nodes to the central node. Due to the previous GCN methods not simultaneously considering the numbers and different contributions of neighboring nodes to the central node, we design the Adaptive Attention Mechanism(AAM). To further enhance the representational capability of the model, we utilize Multi-Head Graph Convolution(MHGC). Finally, we adopt cross-entropy(CE) loss function to describe the difference between the predicted results of node categories and the ground truth (GT). Combined with backpropagation, this ultimately achieves accurate node classification. Based on AAM, MHGC and CE, we contrive the novel Graph Adaptive Attention Network (GAAN). Experiments show that the classification accuracy has achieved outstanding performances on Cora, Citeseer and Pubmed datasets.

Graph theory plays significant role in every field of science as well as technology. Every situation can be articulated in terms of suitable graphs by using various approaches of graph theory. Considering the recent pandemic in the world and the precautions taken for prevention of the COVID 19, it is the most appropriate way to exercise the graph models with theoretical as well as practical aspects to control this epidemic. This paper defines the variable set, variable graphs and their types with respect to variable vertex sets and variable edge sets. Depending upon the nature of the pandemic, there are four types of Virus graphs. Virus graph I and III are not so perilous for all living beings. Although, Virus graphs II and IV are extremely hazardous for the harmony of the world. In view of different aspects for expand of pandemic, growth types of virus graphs are divided in 1-1, 1-P and 1-all growth types. The COVID19 initially was in Virus graph-I type, but presently it is in Virus graph-II types. We present the table involving the number of infected people after n days with respect to different values of P and growth rates with I0 = 100. Moreover, the country wise starting dates of stages of the virus graph-I and II are specified. The concept of cut sets is applicable for prevention of COVID19 and the whole world is using the same analogy.

Graph Neural Networks (GNNs) are powerful models capable of managing intricate connections in non-Euclidean data, such as social networks, physical systems, chemical structures, and communication networks. Despite their effectiveness, the large-scale and complex nature of graph data demands substantial computational resources and high performance during both training and inference stages, presenting significant challenges, particularly in the context of embedded systems. Recent studies on GNNs have investigated both software and hardware solutions to enhance computational efficiency. Earlier studies on Deep Neural Networks (DNNs) have indicated that methods like reconfigurable hardware and quantization are beneficial in addressing these issues. Unlike DNN research, studies on efficient computational methods for GNNs are less developed and require more exploration. This survey reviews the latest developments in quantization and FPGA-based acceleration for GNNs, showcasing the capabilities of reconfigurable systems (often FPGAs) to offer customized solutions in environments marked by significant sparsity and the necessity for dynamic load management. It also emphasizes the role of quantization in reducing both computational and memory demands through the use of fixed-point arithmetic and streamlined vector formats. This paper concentrates on low-power, resource-limited devices over general hardware accelerators and reviews research applicable to embedded systems. Additionally, it provides a detailed discussion of potential research gaps, foundational knowledge, obstacles, and prospective future directions.

With the development of deep learning, several Graph Neural Networks (GNN)-based approaches have been utilized for text classification. However, GNNs encounter challenges in capturing contextual text information within a document sequence. To address this, a novel text classification model RB-GAT is proposed by combining RoBERTa-BiGRU embedding and a multi-head Graph ATtention Network (GAT). First, the pre-trained RoBERTa model is exploited to learn word and text embeddings in different contexts. Second, the Bidirectional Gated Recurrent Unit (BiGRU) is employed to capture long-term dependencies and bidirectional sentence information from the text context. Next, the multi-head graph attention network is applied to analyze this information, which serves as a node feature for the document. Finally, the classification results are generated through a Softmax layer. Experimental results on three benchmark datasets demonstrate that our method can achieve an accuracy of 71.48%, 98.45%, and 80.32% on Ohsumed, R8, and MR, which is superior to the existing nine text classification approaches.

We recently proposed that topological quantum computing might be based on $SL(2,\mathbb{C})$ representations of the fundamental group $\pi_1(S^3\setminus K)$ for the complement of a link $K$ in the $3$-sphere. The restriction to links whose associated $SL(2,\mathbb{C})$ character variety $\mathcal{V}$ contains a Fricke surface $\kappa_d=xyz -x^2-y^2-z^2+d$ is desirable due to the connection of Fricke spaces to elementary topology. Taking $K$ as the Hopf link $L2a1$, one of the three arithmetic two-bridge links [the Whitehead link $5_1^2$, the Berge link $6_2^2$, the double-eight link $6_3^2$] or the link $7_3^2$, the $\mathcal{V}$ for those links contains the reducible component $\kappa_4$, the so-called Cayley cubic. In addition, the $\mathcal{V}$ for the later two links contains the irreducible component $\kappa_3$, or $\kappa_2$, respectively. Taking $\rho$ to be a representation with character $\kappa_d$ ($d<4$), with $|x|,|y|,|z| \le 2$, then $\rho(\pi_1)$ fixes a unique point in the hyperbolic space $\mathcal{H}_3$ and is conjugate to a $SU(2)$ representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the $4$-punctured sphere and Painlev\'e VI equation. The $0$-surgery on the $3$ circles of the Borromean rings L6a4 is taken as an example.

People have always hoped to be able to fill an entire plane with ``single unit cells'' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single unit cell'' named `einstein'. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.

Selecting road networks in cartographic generalization has consistently posed formidable challenges, driving research towards the application of intelligent models. Despite previous efforts, the accuracy and connectivity preservation in these studies, particularly when dealing with road types of similar sample sizes, still warrant improvement. To address these shortcomings, we introduce a Heterogeneous Graph Attention Network (HAN) for road selection, where feature masking method is initially utilized to assess the significance of road features. Concentrating on the most relevant features, two meta-paths are introduced within the HAN framework: one for aggregating features of the same road type within the first-order neighborhood, emphasizing local connectivity, and another extending this aggregation to the second-order neighborhood, capturing a broader spatial context. For a comprehensive evaluation, we introduce a set of metrics considering both quantitative and qualitative aspects of the road network. Compared to traditional neural networks, our HAN model demonstrates superior accuracy and F1-score, particularly for road types with comparable samples. Additionally, it enhances the overall connectivity of the selected network. In summary, our HAN-based method provides an advanced solution for road network selection, surpassing previous approaches in terms of accuracy and connectivity preservation.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

This paper investigates five different GARCH models (GARCH, EGARCH, IGARCH, Component GARCH (CGARCH) and GJR-GARCH) along with six distributions (Normal, Student’s t, GED and their skewed forms), which are used to forecast the volatility for the Bulgarian Stock index SOFIX. We use a GARCH model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data covers the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at forecasting the volatility of SOFIX and which distribution is most appropriate. The results, based on BIC and AIC information criteria, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student t-distribution is preferred for forecasting. With the help of 5000 simulations, it is estimated that the chances of Index SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087.

Background: The modified Duke index derived from coronary computed tomography angiography (CCTA) was designed to predict cardiovascular outcomes based on the severity of coronary ste-nosis. However, it does not take into consideration the presence or severity of peri-coronary in-flammation. The peri-coronary fat attenuation index (FAI) is a novel imaging marker determined by CCTA which reflects the degree of inflammation in the coronary tree in patients with coronary artery disease. Purpose: To assess the association between the modified Duke index assessed by CCTA, cardiovascular risk factors and peri-coronary inflammation in the coronary arteries of pa-tients with coronary artery disease. Methods: One hundred seventy-two patients who underwent CCTA for typical angina were assigned into two groups based on the modified Duke index: group 1 – patients with low index ≤ 3 (n=107) and group 2 – patients with high index > 3 (n=65). Demo-graphic, clinical and CCTA data were collected for all patients, and FAI analysis of coronary in-flammation was performed. Results: Patients with increased values of the modified Duke index were significantly older compared to those with a low index (61.83 ± 9.89 vs. 64.78 ± 8.9; p = 0.002). No differences were found between the two groups in terms of gender distribution, hypertension, hypercholesterolemia or smoking history (all p > 0.5). The FAI score was significantly higher in patients from group 2, who presented a significantly higher score of inflammation compared to the patients in group 1, especially at the level of the right coronary artery (FAI score 20.85 ± 15.80 vs. 14.61 ± 16.66; p = 0.01 for the right coronary artery, 13.85 ± 8.04 vs. 10.91 ± 6.5; p = 0.01 for the circumflex artery, and 13.26 ±10.18 vs. 11.37 ± 8.84; p = 0.2 for the left anterior descending artery). CaRi-Heart® analysis identified a significantly higher risk of future events among patients with a high modified Duke index (34.84 % ± 25.86 % versus 16.87 % ± 15.80 %; p

Annually, the oak forests of the Zagros Mountain chains, in western Iran and northeastern Iraq, face recurring challenges posed by forest fires, particularly in the Kurdo-Zagrosian forests situated in western Iran and northeastern Iraq. Assessing fire susceptibility relies significantly on vegetation condition. Integrating in situ data, Remote Sensing (RS) data, alongside the integration of Geographical Information Systems (GIS), presents a cost-effective and precise approach to capturing environmental conditions before, during, and after fire events, minimizing the need for extensive fieldwork. This study refines and applies the Zagros Grass Index (ZGI), a local vegetation index tailored to discern between grass-covered surfaces from tree canopies in Zagros forests, identifying the grass masses as the most flammable fuel type. Utilizing Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) product as input, from 2013 to 2022, the ZGI aims to mitigate the influence of tree canopies, isolating NDVI values solely attributable to grass cover. By incorporating phenological characteristics of forest trees and grass species, the ZGI outperforms NDVI in mapping grass-covered areas that are crucial for fire susceptibility assessment in the study region. Results demonstrate a strong overlap between ZGI-based maps and recorded fire occurrences, validating the efficacy of the index in fire susceptibility estimation.

The objective of person re-identification (ReID) tasks is to match a specific individual across different times, locations, or camera viewpoints. The prevalent issue of occlusion in real-world scenarios affects image information, rendering the affected features unreliable. The difficulty and core challenge lie in how to effectively discern and extract visual features from human images under various complex conditions, including cluttered backgrounds, diverse postures, and the presence of occlusions. Some works have employed pose estimation or human keypoint detection to construct graph-structured information to counteract the effects of occlusions. However, this approach introduces new noise due to issues such as the invisibility of keypoints. Our proposed module, in contrast, does not require the use of additional feature extractors. Our module employs multi-scale graph attention for the reweighting of feature importance. This allows features to concentrate on areas genuinely pertinent to the re-identification task, thereby enhancing the model's robustness against occlusions. To address these problems, a model that employs multi-scale graph attention to re-weight the importance of features is proposed in this study, significantly enhancing the model’s robustness against occlusions. Our experimental results demonstrate that, compared to baseline models, the method proposed herein achieves a notable improvement in mAP on occluded data sets, with increases of 0.5%, 31.5%, and 12.3% in mAP scores.

With recent advancements in network technology and spread of Internet, use of social network services and Internet of Things devices has flourished, leading to a continuous generation of large volumes of graph stream data, where changes, such as additions or deletions of vertices and edges occur over time. Additionally, owing to the need for efficient use of storage space and security requirements, graph stream data compression has become essential in various applications. Even though various studies on graph compression methods have been conducted, most of them do not fully reflect the dynamic characteristics of graph streams and complexity of large graphs. In this paper, we propose a compression scheme using provenance data to efficiently process and analyze large graph stream data. It obtains provenance data by analyzing graph stream data and builds a pattern dictionary based on this to perform dictionary-based compression. By improving the existing dictionary-based graph compression methods, it enables more efficient dictionary management through tracking pattern changes and evaluating their importance using provenance. Furthermore, it considers the relationships among sub-patterns using an FP-tree and performs pattern dictionary management that updates pattern scores based on time. Our experiments show that the proposed scheme outperforms existing graph compression methods in key performance metrics, such as compression rate and processing time.

Topological indices are invariant numerical fields of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of the aluminophosphates are similar to those of zeolites. Two examples of current applications are natural gas dehydration and humidity sensor. New frameworks are being synthesised by researchers in chemistry and materials science. There are many layers and holes in these substances. In this study, Vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis are explained.

Abstract: The VSI represents a significant advancement in the assessment of gastrointestinal-specific anxiety among patients with Irritable Bowel Syndrome (IBS) and other Chronic Inflammatory Bowel Diseases (IBD). However, an Italian version of the instrument is not yet available for the reference population. This study utilized a national sample of 500 individuals, including healthy controls and patients with Ulcerative Colitis and Crohn's Disease, to test the validity and reliability of the Italian VSI. Using back-translation methodology to ensure translation fidelity, the research applied a questionnaire and the VSI through an online format to 500 participants. Data analysis revealed that the Italian VSI had excellent psychometric properties, demonstrating high internal consistency (Cronbach’s α = 0.95) and construct validity. The scale proved sensitive in detecting significant differences in visceral sensitivity among groups, highlighting its utility as a clinical and research assessment tool. Specifically, the Italian VSI exhibited a unidimensional factorial structure and maintained a strong correlation with other measures of anxiety and the severity of gastrointestinal symptoms, confirming its role in enhancing the understanding and management of IBS and IBD in Italy.

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

Multimodal knowledge graph completion necessitates the integration of information from multiple modalities (such as images and text) into the structural representation of entities to improve link prediction. However, most existing studies have overlooked the interaction between different modalities. To address this issue, this paper proposed a Transformer-based knowledge graph link prediction model (MM-Transformer) that fuses multimodal features. Different modal encoders are employed to extract structural, visual and textual features, and hybrid key-value calculations are performed on features from different modalities based on the Transformer architecture. The similarities of textual tags to structural tags and visual tags are calculated and aggregated respectively, and multimodal entity representations are modeled and optimized to reduce the heterogeneity of the representations. Experimental results demonstrate that, compared to the current multimodal state-of-the-art methods, the proposed method achieves significant performance improvements in knowledge graph link prediction tasks. This proves that the proposed method effectively addresses the problem of multimodal feature fusion in knowledge graph link prediction tasks.

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.

In GNSS/IMU integrated navigation systems, factors such as satellite occlusion and non-line-of-sight conditions can lead to degradation of satellite positioning results, Subsequently affecting the overall accuracy of the integrated navigation system. To address this issue and ef-fectively utilize historical pseudorange information from satellites, this paper proposes a graph optimization-based GNSS/IMU model with virtual constraints. These virtual constraints are con-structed using satellite ‘s position from previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint can serve as an alternative solution for individual satellites in case of signal anomalies, ensuring the integrity and continuity of the graph optimi-zation model. Additionally, this paper conducts an analysis of the graph optimization model constructed using these virtual constraints, comparing it with traditional integrated navigation graph optimization model, and analyzes and reconstructs the marginalization process based on these virtual constraints. The experimental results, compared with tightly coupled Kalman fil-tering and the original graph optimization method on a set of real-world data, demonstrate that the introduction of virtual pseudoranges maintains high positioning accuracy. The RMSE error between it and the original graph optimization remains within 5%, affirming the high feasibility of this approach.

Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested to solve this problem using sequential Monte Carlo (SMC, a.k.a. particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper extends the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance.

While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a ground state. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan-Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has non-zero divergence when phonons or shear stress are present. A possible system where the present kind of monopoles could be observed is BiCu$_2$PO$_6$.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the ev-degree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi–Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree Narumi-Katayama and Zagreb indices.

.Bacground: Sepsis remains a major health challenge worldwide, characterized by a dysre-gulated host response to infection, leading to high mortality and morbidity in intensive care units (ICUs). The Fibrosis 4 (FIB-4) index, originally developed to assess liver fibrosis in hepatitis C patients, has recently been explored for its potential prognostic value in sepsis patients. Method: This study retrospectively analyzed 309 sepsis patients admitted to the Internal Me-dicine and Anaesthesia ICUs between December 12, 2021, and December 15, 2023, to inves-tigate the relationship between FIB-4 levels, Acute Physiology and Chronic Health Evaluation (APACHE), and Sequential Organ Failure Assessment (SOFA) and clinical outcomes. Results: The study found that higher FIB-4 measurements were statistically significantly asso-ciated with increased 28-day mortality, with a cut-off value of 4.9 providing a sensitivity of 54.92% and specificity of 74.25%. Logistic regression analysis indicated that elevated Conclusion:FIB-4 levels were a significant predictor of early mortality, suggesting that the FIB-4 index could serve as a valuable prognostic tool in assessing the severity and prognosis of sepsis patients.

Although Lov\'{a}sz introduced the graph exponential $G^K$ in 1967, this product has received little attention. This paper focuses on the number of components in $G^K$ when exponent $K$ is a complete graph $K_n$. For a connected bipartite $G$, when $K$ is $K_2$, $G^{K_2}$ has three components; and when $K$ is $K_n$ with $n>2$, $G^{K_n}$ produces $\lceil\frac{n+1}{2}\rceil$ components. A connected $G$ with an odd cycle produces one component in $G^{K_n}$.

Floods are a common natural disaster whose severity in terms of duration, water resource volume, peak and accumulated rainfall-based damage are likely to differ significantly for different geographical regions. In this paper, we first propose a novel hourly flood index (SWRI24−hr−S), derived from normalising the existing 24-hourly water resources index (WRI24−hr−S) in literature, to monitor flash flood risks on an hourly scale. The proposed SWRI24−hr−S is adopted to identify a flood situation and derive its characteristics, such as the duration (D), volume (V) and peak (Q). The comprehensive result analysis establishes the practical utility of SWRI24−hr−S in identifying flood situations at seven study sites in Fiji between 2014 and 2018 and deriving their characteristics (i.e., D, V, and Q). Secondly, this study develops a vine copula-probabilistic risk analysis system that models the joint distribution of flood characteristics (i.e., D, V, and Q) to extract their joint exceedance probability for the seven study sites in Fiji, enabling probabilistic flood risk assessment. The vine copula approach, particularly suited to Fiji’s study sites, introduces a novel probabilistic framework for flood risk assessment. The results show moderate differences in the spatial patterns of joint exceedance probability of flood characteristics in different combination scenarios generated by the proposed vine copula approach. In the worst-case scenario, the probability of any flood event occurring where the flood volume, peak and duration are likely to exceed the 95th-quantile value (representing an extreme flood event) is found to be less than 5% for all study sites. The proposed hourly flood index and the vine copula approach can be feasible and cost-effective tools for flood risk monitoring and assessment. The methodologies proposed in this study can be applied to other data-scarce regions where only rainfall data is available, offering crucial information for flood risk monitoring, assessment, and the development of effective mitigation strategies.

:. Background and Objectives: Pulmonary embolism, PE, incidence had been increasing in the last ten years. Computed thoracic pulmonary angiography, CTPA, had a major role in confirming PE di-agnosis.The main purpose of the study was to establish the prognostic value of a CTPA parameter: pulmonary artery obstruction index, PAOI, for PE risk assessment . A second objective of the re-search was to investigate the predictive accuracy of biomarkers (D-dimer, and cardiac Troponin T, c-TnT ), and PAOI, in 7-day mortality. The third objective of the study was the relationship between PAOI, and these biomarkers, in different etiologies of PE. Materials and Methods: The study com-prised 109 patients with PE, hospitalized, and treated between February 2021, and August 2022. They had different etiologies: deep vein thrombosis, DVT; persistent atrial fibrillation, AF; chronic obstructive pulmonary disease, COPD, exacerbation; Covid; and cancers. The investigations were the following: clinical examination; D-dimer testing, as a mandatory method for PE suspicion( values ≥ 500 µg/L were highly suggestive for PE); c-TnT , as a marker of myocardial injury(values ≥ 14 ng/L were abnormal); CTPA, with right ventricle dysfunction, RVD, signs, and PAOI. Treat-ments were according to PE risk: systemic thrombolysis (in high risk , and hemodynamic instability); low weight molecular heparins, LWMH, after systemic thrombolysis, or in high risk PE, with he-modynamic stability; direct oral anticoagulants, DOAC (in low, and intermediate risk). Results: The relationship PAOI- D-dimer, and PAOI- c-TnT, had very strong statistical correlation, for the entire sample, and for DVT, AF, COPD, Covid subgroups ( Rho = 0.815-0.982). PAOI had a high predic-tive accuracy for intermediate , and high risk together (area under curve, AUC=0.948), and high risk PE (AUC= 0.993). For 7-day mortality, D-dimer , and c-TnT had high predictive accura-cy(AUC=0.921, and 0.979). PAOI had statistical significance for 7-day mortality in Covid (p=0.045), and cancer (p=0.038) patients. Conclusions: PAOI was an important tool for PE risk as-sessment. D-dimer , and c-TnT were valuable predictors, for 7-day mortality in PE. PAOI, and D-dimer; PAOI, and c-TnT were strongly correlated, for the entire PE sample, and for DVT, AF, COPD, and Covid patients.

Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.

Background: The Advanced Lung Cancer Inflammation Index (ALI) is a novel, comprehensive index that integrates inflammation and nutritional status, incorporating parameters such as albumin, body mass index (BMI), and the neutrophil-to-lymphocyte ratio (NLR). Unlike traditional inflammation biomarkers, this study aims to evaluate the prognosis of IPF patients by considering both inflammation and nutritional status. Method: A total of 102 patients with IPF were included in the study. Clinical data were obtained from the patients’ medical records. NLR and ALI score were calculated based on data collected at the initiation of antifibrotic treatment using the following formula: Neut/Lym and albumin × BMI / NLR. Results: IPF subject subgroups in terms of ALI based on gender–age–physiology (GAP) stages (1,2,3), FVC (median split, <70% vs ≥70%), DLCO (<51% vs ≥51%), 6-Minute Walk Test (6MWT) (<350 vs ≥350) and CCI (≤1 vs >1). ALI showed significant difference depending on the categories of GAP stage, FVC, DLCO, and 6MWT but these differences were not observed based on the charlson comorbidity index (CCI) categories (sırasıyla p=0.000, p=0.000, p=0.000, p=0.001, p=0.233). Receiver Operating Characteristic (ROC) curve analysis was performed to evaluate the sensitivity and specificity of ALI, albumin, NLR, and BMI in determining the mortality risk in IPF patients. ALI demonstrated a sensitivity of 63.6% and a specificity of 98.9% at a threshold of 11.2 (AUC = 0.945, 95% CI 0.892–0.998, p < 0.000). Conclusion: We determined that ALI levels are significantly associated with disease severity and mortality in patients with IPF.

In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily

In the paper the verification of forecasts of precipitation conditions measured by the standardized precipitation index SPI is presented. For the verification of categorical forecasts a contingency table was used. Standard verification measures were used for the SPI value forecast. The 30 day SPI moved every 10 days by 10 days was calculated in 2013-2015 from April to September on the basis of precipitation data from 35 meteorological stations in Poland. Predictions of the 30 day SPI were created in which precipitation was forecasted in the next 10 days (the SPI 10-day forecast) and 20 days (the SPI 20-day forecast). Both for the 10 and 20 days, the forecasts were skewed towards drier categories at the expense of wet categories. There was a good agreement between observed and 10-day forecast categories of precipitation. Less agreement is obtained for 20-day forecasts – these forecasts evidently “over-dry” the assessment of precipitation anomalies. The 10-day SPI value forecast accuracy is acceptable, whereas for the 20-day forecast is unsatisfactory. Both for the SPI categorical and the SPI value forecast, the 10-day SPI forecast is reliable and the 20-day forecast should be accepted with reservation and used with caution.

Finite element discretizations of problems in computational physics often rely on hand-generated initial mesh and adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. We propose Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aid Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate - Linear elasticity) and fluid mechanics (Flow around cylinders - steady-state Stokes) problems. Our results show it can accurately predict the dynamics of the system and adapt the mesh accordingly. The adaptivity of the model supports learning resolution-independent dynamics and can scale to more complex state spaces at test time.

Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider alternative scenarios such as variable speed of light models and canonical quantum gravity effects and their implications for runnings of the spectral index.

The root system plays an irreplaceable role in plant growth. Its improvement can increase crop productivity. However, such system is still mysterious for us. The underlying mechanism has not been fully uncovered. The investigation on proteins related to the root system is an important means to complete this task. In the previous time, lack of root-related proteins makes it impossible to adopt machine learning methods for designing efficient models for the discovery of novel root-related proteins. Recently, a public database on root-related proteins was set up and machine learning methods can be applied in this field. In this study, we proposed a machine learning based model, named Graph-Root, for identification of root-related proteins. The features derived from protein sequences and one network were extracted, where the former features were processed by graph convolutional neural network and multi-head attention, and the later features abstracted the linkage between proteins. These features were fed into the fully connected layer to make prediction. The 5-fold cross-validation and independent tests suggested its good performance. It also outperformed the only one previous model, SVM-Root. Furthermore, the importance of each feature type and component in the proposed model was investigated.

Climate change is challenging the agricultural sector worldwide. The pressure exerted by the altered thermal conditions drives the zonal shift for various cultivations. This study presents the multiyear analysis of the Growing Degree Days (GDD) index over the Northern Mediterranean Basin (NMB), focused on the high-value vine cultivation derived from the E-OBS dataset. To handle this extensive environmental dataset, R-language scripts and packages were applied, along with the capabilities of the GIS software. The investigated time period spans from 1969 to 2018, and the performed analysis indicates a broad shift/expansion in areas of GDD exceeding 2000 heat units. The extracted results specify the viticultural areas where the GDD index surpasses the suitable values for vine cultivation, owing to the increase of the thermal stress risk. In addition to mapping areas with GDD ≥ 2000, spatial calculations of the surface of areas meeting this criterion per country in the study area were made. In the northern parts of the NMB, the rise of the GDD index values indicates the establishment of vine plantations in the future.

Aim: To investigate inflammation indices and erythropoietin (EPO) levels for their potential role in distinguishing polycythemia vera (PV) from secondary polycythemia (SP), and to compare different parameter combinations in terms of diagnostic accuracy. Methods: This retrospective cohort was created from patients assessed for polycythemia from January 2020 to December 2023. PV diagnosis was made according to the 2016 WHO criteria (n=145). Those who did not fulfill the criteria were defined as having SP (n=84). Results: NLR, PLR and SII were significantly higher in the PV group (p

Purpose: The purpose of this study is to apply the Composite Radiographic Index modified (CRIm) in CBCT scans of patients with Medication related osteonecrosis of the jaws (MRONJ) in order to detect its validity, and corelate the radiologic findings with the clinical staging of the disease. Methods: This study included 43 patients with MRONJ diagnosis and CBCT scans performed in the School of Dentistry and approved by the Research Ethics Committee. Clinical staging for every patient (0-3) was provided according to AAOMS 2022 guidelines. In cases of patients with both jaws affected, each jaw was evaluated independently resulting to 52 CBCT scans. The 52 CBCT scans were assessed under standardized viewing conditions by 2 observers who evaluated independently the following 8 radiologic features: lytic changes, sclerosis, periosteal reaction, sequestration, non-healing extraction sockets and other findings (sinus implication, inferior alveolar canal involvement, jaw fracture). The CRIm index was constructed to assess the extent of osseous changes. The radiologic features were scored as absent (0), localized/single (1), extensive/multiple (2), yielding a theoretical range of 0–12. For statistical analysis Fisher’s exact test and Spearman’s correlation coefficient were performed. Results: A statistically significant association of clinical stage with lytic changes, sequestration and inferior alveolar canal involvement was found. Also, a statistically significant correlation of clinical stage with CRIm index classification was obtained. Conclusions: The CRIm index tends to increase as the clinical stages of MRONJ advance, suggesting a correlation between the clinical stage of MRONJ and the CRIm index.

COPD is currently the fourth leading cause of death in the world. Globally, due to continued exposure to COPD risk factors and an aging population, the burden of COPD is expected to increase in the coming decades. The BODE (body mass index, airflow obstruction, dyspnea, and exercise capacity) index is a practical and multidimensional predictor for prognosis of COPD, and better than FEV1.We used the database of Kaohsiung Chang Gung Memorial Hospital medical center, Taiwan to analyze the correlation between BODE index, healthcare resource utilization, and Charlson comorbidity index (CCI). This retrospective study to collect COPD patients with complete BODE index data who had undergone a 6-minute walk examination in our hospital from January 2015 to December 2016. The medical cost and comorbidities database were analyzed from January 1, 2015, to August 31, 2017. Of 396 patients, 382 (96.5%) were male, with an average age of 71.3 ± 8.4 years. There was a significant association between the BODE index and the CCI of COPD patients (p < 0.001). Healthcare resource utilization was positively correlated with the BODE index during the 32 months of retrospective clinical outcomes: positively correlated with the number of hospitalizations (p<0.001), hospitalization days (p<0.001), hospitalization expenses (p=0.005), and total medical expenses (p=0.024), respectively. Our findings provide the crucial information for clinician to predict medical burden and comorbidities in patients with COPD by using BODE index.

We propose a method for creating parallel Bessel-like vortical optical needles with an arbitrary axial intensity distribution via superposition of different cone-angle Bessel vortices. We analyze the interplay between the separation of individual optical vortical needles and their respective lengths and introduce a super-Gaussian function as their axial profile. We also analyze the physical limitations to observe well-separated optic needles, as they are influenced by mutual interference of the individual beams. To verify our theoretical and numerical results, we generate controllable spatial arrays of individual Bessel beams with various numbers and spatial separations by altering the spectrum of the incoming laser beam via the spatial light modulator. We demonstrate experimentally how to implement such beams using a diffractive mask. The presented method facilitates the creation of diverse spatial intensity distributions in three dimensions, potentially finding applications in specific microfabrication tasks or other contexts. These beams may have benefits in laser material processing applications such as nanochannel machining, glass via production, modification of glass refractive indices, and glass dicing.

Topological interlocking assembly (TIA) and computational architecture treat form as an emergent property of a material system, where the final shape results from the interplay of geometries and geometric interdependencies influenced by material, structural, and fabrication constraints. This paper posits that TIA is an ideal pedagogical tool for introducing students to computational architecture, its theoretical foundations and design principles. Specifically, defining TIA as a material system provides a robust educational approach for engaging students with computation, fostering design processes through bottom-up, hands-on investigations and procedural logic, understanding generative geometric rules, and exploring the flexibility of parametric variations. The methodology is illustrated through a Design Workshop and study unit from the Bachelor’s and Master’s programs at the Faculty for the Built Environment, University of Malta. The paper presents four investigations of defining a material system based on TIA - of tetrahedra, cones, octahedra, and osteomorphic blocks—as case studies to demonstrate how these exercises introduce students to computational thinking, parametric design, and fabrication techniques. Finally, the paper discusses the advantages and limitations of this pedagogical methodology.

Physical measurements might display range values extending towards infinite. The occurrence of infinity in physical equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on physical geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical equations. In this unconventional approach, a continuous monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations.

3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map's semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of both geometry, topology and semantics by incorporating the C-Map data structure in the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

Structured science summaries or research contributions using properties or dimensions beyond traditional keywords enhances science findability. Current methods, such as those used by the Open Research Knowledge Graph (ORKG), involve manually curating properties to describe research papers' contributions in a structured manner, but this is labor-intensive and inconsistent between the domain expert human curators. We propose using Large Language Models (LLMs) to automatically suggest these properties. However, it's essential to assess the readiness of LLMs like GPT-3.5, Llama 2, and Mistral for this task before application. Our study performs a comprehensive comparative analysis between ORKG's manually curated properties and those generated by the aforementioned state-of-the-art LLMs. We evaluate LLM performance through four unique perspectives: semantic alignment and deviation with ORKG properties, fine-grained properties mapping accuracy, SciNCL embeddings-based cosine similarity, and expert surveys comparing manual annotations with LLM outputs. These evaluations occur within a multidisciplinary science setting. Overall, LLMs show potential as recommendation systems for structuring science, but further finetuning is recommended to improve their alignment with scientific tasks and mimicry of human expertise.

Graph databases (GDBs) are becoming increasingly popular across scientific disciplines, being highly suitable to store and connect complex heterogeneous data. In systems biology, they are used as a backend solution for biological data repositories, ontologies, networks, pathways, and knowledge graph (KG) databases. In this review, we analyse all publications using or mentioning graph databases retrieved from PubMed and PubMed Central full-text search, focusing on the top 16 available GDB technologies. Relevant publications are then categorised according to their domain and application. We detail different approaches and highlight advantages of outstanding resources, such as UniProtKB, Disease Ontology, and Reactome, which provide graph-based solutions. We discuss ongoing efforts of the systems biology community to standardise and harmonise KG creation and the maintenance of integrated resources. Outlining prospects, including the use of GDBs as a way of communication between biological data repositories, we conclude that efficient design, querying, and maintenance of GDBs will be key for knowledge generation in systems biology and other research fields with heterogeneous data.

This research aimed to investigate the relationship between climate policy uncertainty (CPU), clean energy (ENERGY), carbon emission allowance prices (CARBON), and Bitcoin returns (BTC) for the period from August 2012 to August 2022. The empirical analysis strategies utilized in this study included the Fourier Bootstrap ARDL long-term coefficient estimator, Fourier Granger Causality, and Fourier Toda Yamamoto Causality methods. Following the confirmation of cointegration among the variables, we observed a positive relationship between BTC and CARBON, a positive relationship between BTC and CPU, and a negative relationship between BTC and ENERGY. In terms of causal associations, we identified one-way causality running from CARBON to BTC, BTC to CPU, and BTC to the ENERGY variable. The study underscores the potential benefits and revenue opportunities for investors seeking diversified investment strategies in light of climate change concerns. Furthermore, it suggests actionable strategies for policymakers, such as implementing carbon taxes and educational campaigns, to foster a transition towards clean energy sources within the cryptocurrency mining sector and thereby mitigate environmental impacts.

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph N_n, for n ≥ 2 has been determined. It is further shown that N₃ is chromatically unique.

We present a Deep Learning generative model specialized to work with graphs with a regular geometry. It is build on a Variational Autoencoder framework and employs Graph convolutional layers in both encoding and decoding phases. We also introduce a pooling technique (ReNN-Pool), used in the encoder, that allows to downsample graph nodes in a spatially uniform and highly interpretable way. In the decoder, a symmetrical un-pooling technique is used to retrieve the original dimensionality of graphs. Performance of the model are tested on the standard Sprite benchmark dataset, a set of 2D images of video game characters, adequately transforming images data into graphs, and on the more realistic use-case of a dataset of cylindrical-shaped graph data that describe the distributions of the energy deposited by a particle beam in a medium.

Background: Obesity remains a widely debated issue, often criticized for the limitations in its identification and classification. This study aims to compare two distinct systems for classifying obesity: Body Mass Index (BMI) and body fat percentage (BFP) as assessed by bioelectrical impedance analysis (BIA). By examining these measures, the study seeks to clarify how different metrics of body composition influence the identification of obesity-related risk factors. Methods: The study enrolled 1255 adults, comprising 471 males and 784 females, with a mean age of 36 ± 11.90 years. Participants exhibited varying degrees of weight status, including optimal weight, overweight, and obesity. Body composition analysis was conducted using the TANITA Body Composition Analyzer BC-418 MA III device (T5896, Tokyo, Japan), evaluating the following parameters: current weight, basal metabolic rate (BMR), adipose tissue (%), muscle mass (%), and hydration status (%). Results: Age and psychological factors like cravings, fatigue, stress, and compulsive eating were significant predictors of obesity in the BMI model but not in the BFP model. Additionally, having a family history of diabetes was protective in the BMI model (OR: 0.33) but increased risk in the BFP model (OR: 1.66). The BMI model demonstrates exceptional predictive ability (AUC=0.998). In contrast, the BFP model, while still performing well, exhibits a lower AUC (0.975), indicating slightly reduced discriminative power compared to the BMI model. Conclusions:BMI classification demonstrates superior predictive accuracy, specificity, and sensitivity. This suggests that BMI remains a more reliable measure for identifying obesity-related risk factors compared to the BFP model.

Hyperspectral small target detection (HSTD) is a promising pixel-level detection task. However, due to the low contrast and imbalance number between the target and background spatially and high dimensions spectrally, it is a challenging one. To address these issues, this work proposes a representation learning-based graph and generative network for hyperspectral small target detection. The model builds a fusion network through frequency representation for HSTD, where the novel architecture incorporates irregular topological data and the spatial-spectral feature to improve its representation ability. Firstly, a graph convolutional network (GCN) module better models the non-local topological relationship between samples to represent the hyperspectral scene’s underlying data structure. The mini-batch-training pattern of the GCN decreases the high computational cost of building an adjacency matrix for high-dimensional data sets. In parallel, the generative model enhances the differentiation reconstruction and the deep feature representation ability with respect to the target spectral signature. Finally, a fusion module compensates for the extracted different types of HS features and integrates their complementary merits for hyperspectral data interpretation while increasing detection and background suppression capabilities. Experiments on different hyperspectral data sets demonstrate the advantages of the proposed architecture.

Floods are among the most serious natural disasters worldwide; they cause enormous crop losses every year and threaten world food security. There are many studies focused on flood impact assessments for administrative districts but fewer on postdisaster impact assessments for specific crops. Therefore, this study used remote sensing data, including the normalized difference vegetation index (NDVI), elevation data, slope data, and rainfall data, combined with crop growing season data to construct a crop flood damage assessment index (CFAI). First, an analytic hierarchy process (AHP) was used to assign weights to the impact factors; then, the weighted composite score method was used to calculate the CFAI; and finally, the impact was classified as slight, moderate, or severe based on the magnitude of the CFAI . This method was used for the Missouri River floods of 2019 in the U.S. Due to the lack of measured data, the disaster vegetation damage index (DVDI) was used to validate the results. The combined approach achieved a high degree of consistency in spatial distribution. The CFAI can respond well to the degree of crop impact after flooding, providing new ideas and reference standards for agriculture-related departments.

Plant leaf area index (LAI) is a key characteristic affecting field canopy microclimate. In addition to traditional professional measuring instruments, smartphone camera sensors have been used to measure plant LAI. However, when smartphone methods were used to measure conifer forest LAI, very different performances were obtained depending on whether the smartphone was held at the zenith angle or at a 57.5° angle. To validate further the potential of smartphone sensors for measuring conifer LAI and to find the limits of this method, this paper reports the results of a comparison of two smartphone methods with an LAI-2000 instrument. It is shown that both methods can be used to reveal the conifer leaf-growing trajectory. However, the method with the phone oriented vertically upwards always produced better consistency in magnitude with LAI-2000. The bias of the LAI between the smartphone method and the LAI-2000 instrument was explained with regard to four aspects that can affect LAI: gap fraction, leaf projection ratio, sensor field of view (FOV), and viewing zenith angle (VZA). It was concluded that large FOV and large VZA cause the 57.5° method to overestimate the gap fraction and hence underestimate conifer LAI, especially when tree height is greater than 2.0 m. For the vertically upward method, the bias caused by the overestimated gap fraction is compensated for by an underestimated leaf projection ratio.

Public transportation scheduling aims to optimize the allocation of transportation resources, enhance transportation efficiency, and increase passenger satisfaction, which is crucial for building a sustainable urban transportation system. As a complement to public transportation, shared bikes provide users with a solution for the last mile of travel, compensating for the lack of flexibility in public transportation and helping to improve its utilization rate. Due to the characteristics of shared bikes, such as peak usage periods in the morning and evening and significant fluctuations in demand across different areas, the optimization of shared bike dispatch can better meet user needs, thereby reducing vehicle vacancy rates and increasing operating revenue. Addressing this issue, this paper designs a comprehensive decision-making approach for spatio-temporal demand prediction and bike dispatch optimization. For demand prediction, we designed a T-GCN based bike demand prediction model. In terms of dispatch optimization, we considered factors such as dispatch capacity, distance restrictions, and dispatch costs, and designed an optimization solution based on genetic algorithms. Finally, this paper validates the approach using shared bike operating data, shows that T-GCN can effectively predict short-term demand for shared bikes. Meanwhile, the optimization model based on genetic algorithms provides a complete dispatch solution verifying the model’s effectiveness. The shared bike dispatch approach proposed in this paper, which combines demand prediction with resource scheduling. This scheme can also be extended to other transportation scheduling problems with uncertain demand, such as store replenishment delivery and intercity inventory dispatch.

A topological quantum interplay between the magnetic flux and the mass has been investigated, for the case of an electron, by evaluating a gauge-invariant phase factor (a Wilson loop) linked to the electromagnetic gauge field of the particle. In particular, from this phase factor and the quantization of the magnetic flux variations, a relationship between the mass at rest of the electron and its self-energy , arising from radiative corrections, has been obtained also within a QED approach. Besides, a formulation of an energy scale comparable to the energy at rest of an electron-positron pair is proposed. Remarkably, a reckoning of the Bohr energy of a W⁺ W^- pair is compatible with constants and parameters usually employed within the electroweak theory and comparable to the energy at rest of an electron-positron pair.

In this work the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a current flux injected into the system using an external normal lead and derived from it via a superconducting electrode. After discussing the topological phase diagram of the isolated systems, using a scattering technique within the Bogoliubov-de Gennes formulation, we analyze the differential conductance properties of these topological devices as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize topological systems is also addressed by studying the system electrical response as a function of the position and the distance of the normal electrode (tip). The results show how the signatures of topological order affect the electrical response of the analyzed systems, a subset of such signatures being robust also against the effects of a moderate amount of disorder. The analysis of the internal modes of the nanodevices demonstrates that topological protection can be lost when quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. The conclusions of this work could be useful in understanding the topological phases of nanowire-based mesoscopic devices.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets, based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structure in a broad range of data analytics problems including the study of cardiovascular signals. This review aims to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA has shown great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

The study of photonic crystals has emerged as an attractive area of research in nanoscience in the last years. In this work we study the properties of a two-dimensional photonic crystal composed of dielectric rods. The unit cell of the system is composed of six rods organized on the sites of a C6 triangular lattice. We induce a topological phase by introducing an angular perturbation ϕ in the pristine system. The topology of the system is then determined by using the so-called k.p perturbed model. Our results show that the system presents a topological and a trivial phases, depending on the sign of the angular perturbation ϕ. The topological character of the system is probed by evaluating the electromagnetic energy density and analyzing its distribution in the real space, in particular on the maximal Wyckoff points. We also find two edge modes at the interface between the trivial and topological photonic crystals, which present a pseudospin topological behavior. By applying the Bulk-Edge correspondence, we study the pseudospin edge modes and conclude that they are robust against defects, disorder and reflection. Moreover, the localization of the edge modes leads to the confinement of light and the interface behaves as a waveguide for the propagation of electromagnetic waves. Finally, we show that the two edge modes present energy flux propagating in opposite directions, which is the photonic analogue of the quantum spin Hall effect.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

Abstract: Doppler renal resistive index (RRI) has been used for several decades as a potential indi-cator for renal disease and progression. In recent years, RRI has emerged as a useful prognostic indicator for a range of co-morbidities in patients who are acutely unwell and as a potential marker for sub-clinical acute kidney injury (AKI) and post procedural AKI risk. Despite this, the clinical and theoretical determinants of RRI are poorly understood and remain contentious. Method: A narrative review of studies exploring the theoretical, experimental, and clinical evidence for factors affecting RRI. No date restrictions were set. Findings: Both experimental and clinical data confirm that RRI is markedly affected by a range of systemic and renal determinants and is influenced closely by the underlying risk factors and sys-temic vascular changes that lead to progressive renal damage. Discussion: This paper provides an overview of the key haemodynamic determinants of renal re-sistive index and aims to clarify their relative importance. With reference to a simplified theoretical model, evidence from experimental and clinical studies is reviewed. Pathophysiological factors and patient characteristics that influence RRI are explored to provide a better understanding of why RRI values change in the presence of common or complex pathologies. Conclusion: By gaining a better understanding of the complex systemic and renal factors that influ-ence RRI, ultrasound users will be better prepared to understand and interpret changes in RRI across a range of patient presentations.

Properties of time domain parameters of the vibration signal have been extensively studied for the fault diagnosis of rolling element bearings (REB). Parameters like kurtosis and Envelope Harmonic-to-Noise Ratio are most widely applied in this field and some important progress has been made. However, since only one-sided information is contained in these parameters respectively, problems still exist in practice when the signals collected are of complicated structure and/or contaminated by strong background noises. A new parameter, named Shock pulse index (SPI), is proposed in this paper. It integrates the mutual advantage of both parameters above and can help effectively identify fault related impulse components under the interference of strong background noises, unrelated harmonic components and random impulses. The SPI optimizes the parameters of Maximum Correlated Kurtosis Deconvolution (MCKD), which is used to filter the signals under consideration. Finally, the interested transient information contained in the filtered signal can be highlighted through demodulation with Teager Energy Operator (TEO). Fault related impulse components can therefore be extracted accurately. Simulations and experiment analyses verify the effectiveness and correctness of the SPI.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

Surface water distribution extracted from remote sensing data has been used in water resource assessment, coastal management, and environmental change studies. Traditional manual methods for extracting water bodies cannot satisfy the requirements for mass processing of remote sensing data; therefore, accurate automated extraction of such water bodies has remained a challenge. The histogram bimodal method (HBM) is a frequently used objective tool for threshold selection in image segmentation. The threshold is determined by seeking twin peaks, and the valley values between them; however, automatically calculating the threshold is difficult because complex surfaces and image noise which lead to not perfect twin peaks (single or multiple peaks). We developed an operational automated water extraction method, the modified histogram bimodal method (MHBM). The MHBM defines the threshold range of water extraction through mass static data; therefore, it does not require the identification of twin histogram peaks. It then seeks the minimum values in the threshold range to achieve automated threshold. We calibrated the MHBM for many lakes in China using Landsat 8 Operational Land Imager (OLI) images, for which the relative error (RE) and squared correlation coefficient (R2) for threshold accuracy were found to be 2.1% and 0.96, respectively. The RE and root-mean-square error (RMSE) for the area accuracy of MHBM were 0.59% and 7.4 km2. The results show that the MHBM could easily be applied to mass time-series remote sensing data to calculate water thresholds within water index images and successfully extract the spatial distribution of large water bodies automatically.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

: Biological networks such as protein interaction networks, gene regulation networks and metabolic pathways are examples of complex networks which are large graphs with small-world and scale-free properties. Analysis of these networks has a profound effect on our understanding the origins of life, health and disease states of organisms, and diagnose diseases to aid the search for remedial processes. In this review, we describe main analysis methods of biological networks using graph theory by first defining main parameters such as clustering coefficient, modularity and centrality. We then survey fundamental graph clustering methods and algorithms followed by the network motif search algorithms with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function carried out by that small network and discovering such a function provides an insight to the overall function of the organism. Lastly, we review network alignment algorithms that achieve to find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor and finding such relationship may help researchers derive ancestral relationships and predict the future evolution of organisms to enable designing new drugs. We conclude by the current challenging areas of biological network analysis using graph theory and parallel processing for high performance analysis

The hybrid bond graph has been studied in depth for scalar bond graphs, but how does this translate to the multi-bond graph? Here, the controlled junction – used to model structural switching such as contact – is extended to the multi-bond case. This is a simple process, assuming that all bonds switch simultaneously (which makes physical sense). A controlled 0-junction is applied to multi-bond graph of a car, which can lose contact with the ground in cornering. Dynamic causality features, but this can be accommodated using an equational submodel in 20-Sim (in a manner similar to that used with scalar bond graphs). The junction is proposed for subsequent work to develop a validated multi-body dynamics car model in cornering.

Droughts have negative impacts on agricultural productivity and economic growth. Effective monitoring and accurate forecasting of drought occurrences and trends are crucial for minimizing drought losses and mitigating their spatial and temporal effects. In this study, trend dynamics in monthly total rainfall time series measured at Cape Town International Airport were analyzed using Mann-Kendall (MK) test, Modified Mann-Kendall (MMK) and innovative trend analysis (ITA) were examined. Additionally, we utilized hybrid prediction method that combined the model with the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique, the autoregressive integrated moving average (ARIMA) model, the long short-term memory (LSTM) network (i.e. CEEMDAN-ARIMA-LSTM) to forecast SPI values of 6-, 9-, and 12-months using rainfall data between 1995 and 2020 from Cape Town International Airport meteorological rainfall stations. The results demonstrate the following essential points: (1) The trend analysis results of the total monthly rainfall values indicate a significant decreasing trend with the negative z-score (MK= -3.7541 and MMK= - 4.0773). ITA also indicated a significant downwards trend of rainfall in the study area. (2) As the forecasting horizon increases, the prediction accuracy of the models and CEEMDAN-combined models gradually improves, reaching their optimum performance at the 12-month horizon. (3) CEEMDAN efficiently stabilizes time-series data, resulting in greater prediction accuracy in the hybrid model compared to individual models at all timescales. (4) The RMSE and R2 values for the hybrid CEEMDAN-ARIMA-LSTM model at a 12-month forecasting horizon are 0.042 and 0.995, demonstrating the applicability of this hybrid approach for drought forecasting.

Objective: To analyse the association between maternal risk factors such as age, body mass index (BMI) and cigarette smoking, with perinatal outcomes. Materials and Methods: This a retrospective analysis from prospectively collected data performed at Hospital Universitario de Torrejón (Madrid, Spain), between September 2017 and December 2019. All pregnant women with singleton pregnancies and non-malformed live fetuses attending their routine ultrasound examination at 11+0 to 13+6 weeks' gestation were invited to participate. Association between preeclampsia, preterm birth, gestational diabetes mellitus (GDM), small for gestational age (SGA) or fetal growth restricted (FGR) neonates and type of delivery according to maternal age, BMI, and cigarrete smoking was studied. Logistic mixed models were used to analyze the data. Results: 1921 patients were included in the analysis. Women of 40 years old had a significantly higher risk of having GDM (Odds Ratio (OR) 1.61, 95% Confidence Interval (CI) 1.08 to 2.36), and SGA neonates (OR 1.54, 95% CI 1.00 to 2.37). Women with a BMI &lt;18 had an increased rate of birth SGA and FGR neonates (OR 3.28, 95% CI 1.51 to 7.05, and OR 3.73, 95% CI 1.54 to 8.37, respectively), whereas women with a BMI ≥35 had a higher risk of GDM (OR 3.10, 95% CI 1.95 to 4.89). Smoking increased the risk of having SGA and FGR neonates (OR 1.83, 95% CI 1.36 to 2.46, and OR 1.91, 95% CI 1.29 to 2.78). Conclusions: Advanced maternal age, low or high BMI, and smoking status are significant risk factors for pregnancy complications. Both clinicians and society should concentrate their efforts on addressing these factors to enhance reproductive health.

The fetal splenic artery pulsatility index (PI) is a parameter that reflects fetal well-being and has been used as a predictor of adverse pregnancy outcomes. The aim of this study was to investigate the predictive value of splenic artery PI in GDM class A1 cases for NICU admission. In this prospective case controlled study, only sixty single pregnancy cases diagnosed with gestational diabetes mellitus class A1 were evaluated. Fetal splenic artery Doppler parameters Peak systolic velocity (PSV), Pulsatility index (PI), Resistivity index (RI) and End diastolic velocity (EDV) were measured in all cases. The rate of re-quirement of need of neanoatal intensive care unit was noted. In cases with need fetal intensive care, fetal splenic PI index was found to be statistically significantly lower than in healthy cases without it (0.94 ± 0.29 vs. 1.70 ± 0.53, respectively, p

Droughts are a common occurrence in various climates and are primarily caused by a prolonged decrease in rainfall. Several factors contribute to droughts, including temperature, wind speed, relative humidity, rainfall timing, amount, and intensity during the growing season. The objective of this study is to establish a new index, named soil moisture and evapotranspiration revealed drought index (SERDI), for displaying dry and wet conditions based on combining both soil moisture and evapotranspiration (Penman-Monteith) to improve drought early warning and its severity globally. For validation of the SERDI with other indices such as LST, VHI, NDVI, and NDWI, different ways used such as R-square, RMSE, MAPE, and P-value to estimate the accuracy, variability of data, the forecast conditions, and how the significance of data. The results showed that the low RMSE and high r² were found between SERDI with LST and VHI. In contrast, the low R- square and high RMSE were between SERDI with NDVI and NDWI in most of the semi-arid areas. Furthermore, most of the semi-arid areas from Iran, Iraq, Syria, Jordan, and Israel experienced moderate and severe dry conditions, except some parts of these regions had normal conditions in Iran and Syria. The SERDI analysis revealed a strong correlation between (LST) and a moderate correlation with (VHI) across all study areas. However, the relationship between other indices, like (NDWI) and (NDVI), varied depending on the regions. To conclude, SERDI can be used globally for detecting drought based on soil moisture and evapotranspiration.

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

We discuss a possible scale of gravitational origin at around 10 MeV, or 10⁻¹² cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago.~A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10⁻¹² cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of ~10¹²⁰ multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1–2 MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S². Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

Here we present a fast and highly scalable community structure preserving network module detection that recursively integrates graph sparsification and clustering. Our algorithm, called SparseClust, participated in the most recent DREAM community challenge on disease module identification, an open competition to comprehensively assess module identification methods across a wide range of biological networks.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

Advanced persistent threat (APT) attacks are sophisticated and organized attacks commonly motivated by political, financial, and strategic objectives. In order to comprehend their tactics, techniques, and procedures (TTP) and indicators, APT reports are valuable sources. While blue teams typically rely on server logs, firewall rules and user authorizations managed in database tables, attackers have a graph-based mindset. In this work, we propose a framework for discovering and evaluating APTs using graph-based algorithms. Cyber threat intelligence (CTI) was extracted from 40,358 pages of APT reports and transformed into a graph. Centrality, community, and similarity analyses were executed on the graph. As a result, critical and influential APT groups and indicators of compromise (IoC) were discovered. Similar attacks and APT groups were revealed. Analysis results were interpreted to create new strategic CTI that can be utilized in future security operations.

(1) Background: Parents of children with autism spectrum disorders often experience psychological distress, which can affect the quality of childcare they provide. It is crucial to screen for psychiatric symptoms among these parents. The Core Symptom Index (CSI) is a widely used tool for assessing general symptoms such as depression, anxiety, and somatic symptoms, with demonstrated validity and reliability across various populations. However, there is limited research on the validity and reliability of the CSI in the general Chinese population. This study aimed to investigate the psychometric properties of the Chinese version of the CSI among parents of children with autism spectrum disorders using Confirmatory Factor Analysis (CFA). (2) Methods: A total of 794 Chinese parents raising children with autism participated in this study. All completed the CSI, along with the social inhibition subscale of the Interpersonal Problems Inventory and the Couple Satisfaction Index. Factorial validity was assessed using CFA to determine how well the bifactor three-factor model fits the data. Various structural models were compared using model fit indices. Convergent and discriminant validity were examined by exploring correlations with the social inhibition subscale and the Couple Satisfaction Index. Invariance testing of the CSI was conducted across multiple groups based on gender, age, and education using CFA. The reliability of the CSI was evaluated using McDonald’s omega coefficients. (3) Results: The bifactor model emerged as the best-fitting model for the data, suggesting that the total score of the CSI adequately represents overall psychiatric symptoms. The CSI exhibited significant correlations with the social inhibition subscale (r = 0.41, p &lt; 0.01) and smaller correlation coefficients with the Couple Satisfaction Index (r = -0.16, p &lt; 0.05), indicating both convergent and discriminant validity. Invariant tests supported scalar invariance levels based on gender and age but only partial invariance for education. The Chinese version of the CSI demonstrated high consistency, with McDonald's omega coefficients ranging between 0.86 and 0.95. (4) Conclusions: The bifactor model of the Chinese version of the CSI is validated, making it a suitable tool for measuring depression, anxiety, and somatization symptoms among parents of children with autism spectrum disorders. Further research on other Chinese populations is encouraged.

For disciplines like biological science, security, and the medical field, link prediction is a popular research area. To demonstrate the link prediction many methods have been proposed. Some of them that have been demonstrated through this review paper are TransE, Complex, DistMult, and DensE models. Each model defines link prediction with different perceptions. We argue that the practical performance potential of these methods, having similar parameter values, using the fine-tuning technique to evaluate their reliability and reproducibility of results. We describe those methods and experiments; provide theoretical proofs and experimental examples, demonstrating how current link prediction methods work in such settings. We use the standard evaluation metrics for testing the model's ability.

Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. Identification of fields in the quantized theory is occurred directly as usual in terms of superconnection and its supercurvature components with the double covering of the general affine group GA¯(4,R). Then, by means of an appropriate decomposition of the metalinear double-covering group SL¯(5,R) with respect to the general linear double-covering group GL¯(4,R) one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations allowing us to build the observables of the theory by means of the BRST algebra constructed using a sa¯(5,R) algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion.

In this research, we investigate the bending of photon light and/or time-like geodesics within the context of four-dimensional space-time geometry, specifically in the presence of topological defects. These topological defects manifest as cosmic string space-time configurations, encompassing screw dislocation, spiral dislocation, and spacelike dislocation. Our primary objective is to determine the extent of deflection experienced by light-like and time-like geodesics and analyze how this deflection is affected by the cosmic string parameter, screw dislocation parameter, and spacelike dislocation parameter. To accomplish this, we employ a derivation technique that centers on the observation that photon rays (light-like geodesics) and/or time-like geodesics follow paths parallel to the z-axis while maintaining a constant radius along the cylinder.