Linear Graph Research Articles

Prevalence Trends of Foodborne Pathogens Bacillus cereus, Non-STEC Escherichia coli and Staphylococcus aureus in Ready-to-Eat Foods Sourced from Restaurants, Cafés, Catering and Takeaway Food Premises

Foodborne pathogens of Bacillus cereus (B. cereus), non-STEC Escherichia coli (non-STEC E. coli) and Staphylococcus aureus (S. aureus) are currently non-notifiable in Australia unless attributed to a food poisoning outbreak. Due to the lack of data around individual cases and isolations in foods, any changes in prevalence may go undetected. The aim of this study was to determine any changes in the prevalence of B. cereus, non-STEC E. coli and S. aureus in ready-to-eat (RTE) foods sampled from Western Australian restaurants, cafés, catering facilities and takeaway food premises from July 2009 to June 2022. A total of 21,822 microbiological test results from 7329 food samples analysed over this 13-year period were reviewed and analysed. Linear trend graphs derived from the annual prevalence and binary logistic regression models were used to analyse the sample results, which indicated an increase in prevalence for B. cereus. In contrast, a decrease in prevalence for both S. aureus and non-STEC E. coli was determined. Additionally, there were changes in prevalence for the three bacteria in specific months, seasons, specific RTE foods and food premises types. Further research is needed to gain a better understanding of the potential drivers behind these changes in prevalence, including the potential impacts of climate change, COVID-19, legislation and guidelines targeting specific RTE foods, and the difficulty of differentiating B. cereus from B. thuringeniesis using standard testing methods.

GTasm: a genome assembly method using graph transformers and HiFi reads

MotivationGenome assembly aims to reconstruct the whole chromosome-scale genome sequence. Obtaining accurate and complete chromosome-scale genome sequence serve as an indispensable foundation for downstream genomics analyses. Due to the complex repeat regions contained in genome sequence, the assembly results commonly are fragmented. Long reads with high accuracy rate can greatly enhance the integrity of genome assembly results.ResultsHere we introduce GTasm, an assembly method that uses graph transformer network to find optimal assembly results based on assembly graphs. Based on assembly graph, GTasm first extracts features about vertices and edges. Then, GTasm scores the edges by graph transformer model, and adopt a heuristic algorithm to find optimal paths in the assembly graph, each path corresponding to a contig. The graph transformer model is trained using simulated HiFi reads from CHM13, and GTasm is compared with other assembly methods using real HIFI read set. Through experimental result, GTasm can produce well assembly results, and achieve good performance on NA50 and NGA50 evaluation indicators. Applying deep learning models to genome assembly can improve the continuity and accuracy of assembly results. The code is available from https://github.com/chu-xuezhe/GTasm.

An optimized siamese neural network with deep linear graph attention model for gynaecological abdominal pelvic masses classification.

An adnexal mass, also known as a pelvic mass, is a growth that develops in or near the uterus, ovaries, fallopian tubes, and supporting tissues. For women suspected of having ovarian cancer, timely and accurate detection of a malignant pelvic mass is crucial for effective triage, referral, and follow-up therapy. While various deep learning techniques have been proposed for identifying pelvic masses, current methods are often not accurate enough and can be computationally intensive. To address these issues, this manuscript introduces an optimized Siamese circle-inspired neural network with deep linear graph attention (SCINN-DLGN) model designed for pelvic mass classification. The SCINN-DLGN model is intended to classify pelvic masses into three categories: benign, malignant, and healthy. Initially, real-time MRI pelvic mass images undergo pre-processing using semantic-aware structure-preserving median morpho-filtering to enhance image quality. Following this, the region of interest (ROI) within the pelvic mass images is segmented using an EfficientNet-based U-Net framework, which reduces noise and improves the accuracy of segmentation. The segmented images are then analysed using the SCINN-DLGN model, which extracts geometric features from the ROI. These features are classified into benign, malignant, or healthy categories using a deep clustering algorithm integrated into the linear graph attention model. The proposed system is implemented on a Python platform, and its performance is evaluated using real-time MRI pelvic mass datasets. The SCINN-DLGN model achieves an impressive 99.9% accuracy and 99.8% recall, demonstrating superior efficiency compared to existing methods and highlighting its potential for further advancement in the field.

Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach

Objectives: We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. Methods: In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combination positions of vertex obeying the mean cordial labeling condition using this Python module. We have drawn the graph between the number of vertices and the number of combination positions of the vertex. Findings: We have found that the different graph types like Path, Cycle, and Subdivision of Star graph satisfy the mean cordial labeling condition. The result indicates that the number of combination positions of the Path and cycle graph fulfill the power equation Y=a*xb and the Subdivision of the Star graph meets the exponential growth equation Y=a*bx. Novelty: In this paper, a new method has been developed to find the number of combination position of varies graphs using the Python module. This computational approach will be useful to analyze the biological networking and protein-protein interaction study. Keywords: Mean Cordial, Path, Cycle, Subdivision of Star graph, Computational graph theory

Polynomial Time Algorithm for Shortest Paths in Interval Temporal Graphs

We develop a polynomial time algorithm for the single-source all destinations shortest paths problem for interval temporal graphs (ITGs). While a polynomial time algorithm for this problem is known for contact sequence temporal graphs (CSGs), no such prior algorithm is known for ITGs. We benchmark our ITG algorithm against that for CSGs using datasets that can be solved using either algorithm. Using synthetic datasets, experimentally, we show that our algorithm for ITGs obtains a speedup of up to 32.5 relative to the state-of-the-art algorithm for CSGs.

The hamiltonian path graph is connected for simple s, t paths in rectangular grid graphs

The hamiltonian path graph is connected for simple s, t paths in rectangular grid graphs

Knowledge-Enhanced Conversational Recommendation via Transformer-Based Sequential Modeling

In conversational recommender systems (CRSs), conversations usually involve a set of items and item-related entities or attributes, e.g., director is a related entity of a movie. These items and item-related entities are often mentioned along the development of a dialog, leading to potential sequential dependencies among them. However, most of existing CRSs neglect these potential sequential dependencies. In this article, we first propose a Transformer-based sequential conversational recommendation method, named TSCR, to model the sequential dependencies in the conversations to improve CRS. In TSCR, we represent conversations by items and the item-related entities, and construct user sequences to discover user preferences by considering both the mentioned items and item-related entities. Based on the constructed sequences, we deploy a Cloze task to predict the recommended items along a sequence. Meanwhile, in certain domains, knowledge graphs formed by the items and their related entities are readily available, which provide various different kinds of associations among them. Given that TSCR does not benefit from such knowledge graphs, we then propose a knowledge graph enhanced version of TSCR, called TSCRKG. In specific, we leverage the knowledge graph to offline initialize our model TSCRKG, and augment the user sequence of conversations (i.e., sequence of the mentioned items and item-related entities in the conversation) with multi-hop paths in the knowledge graph. Experimental results demonstrate that our TSCR model significantly outperforms state-of-the-art baselines, and the enhanced version TSCRKG further improves recommendation performance on top of TSCR.

Upper Bounds for Linear Graph Codes

ABSTRACTA linear graph code is a family of graphs on vertices with the property that the symmetric difference of the edge sets of any two graphs in is also the edge set of a graph in . In this article, we investigate the maximal size of a linear graph code that does not contain a copy of a fixed graph . In particular, we show that if has an even number of edges, the size of the code is , making progress on a question of Alon. Furthermore, we show that for almost all graphs with an even number of edges, there exists such that the size of a linear graph code without a copy of is at most .

On the Energy Behaviors of the Bellman–Ford and Dijkstra Algorithms: A Detailed Empirical Study

The Single-Source Shortest Paths (SSSP) graph problem is a fundamental computation. This study attempted to characterize concretely the energy behaviors of the two primary methods to solve it, the Bellman–Ford and Dijkstra algorithms. The very different interactions of the algorithms with the hardware may have significant implications for energy. The study was motivated by the multidisciplinary nature of the problem. Gaining better insights should help vital applications in many domains. The work used reliable embedded sensors in an HPC-class CPU to collect empirical data for a wide range of sizes for two graph cases: complete as an upper-bound case and moderately dense. The findings confirmed that Dijkstra’s algorithm is drastically more energy efficient, as expected from its decisive time complexity advantage. In terms of power draw, however, Bellman–Ford had an advantage for sizes that fit in the upper parts of the memory hierarchy (up to 2.36 W on average), with a region of near parity in both power draw and total energy budgets. This result correlated with the interaction of lighter logic and graph footprint in memory with the Level 2 cache. It should be significant for applications that rely on solving a lot of small instances since Bellman–Ford is more general and is easier to implement. It also suggests implications for the design and parallelization of the algorithms when efficiency in power draw is in mind.

Fixed-Parameter Tractability of Maximum Colored Path and Beyond

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as follows. We give a randomized algorithm, that given a colored \(n\) -vertex undirected graph, vertices \(s\) and \(t\) , and an integer \(k\) , finds an \((s,t)\) -path containing at least \(k\) different colors in time \(2^{k}n^{\mathcal{O}(1)}\) . This is the first FPT algorithm for this problem, and it generalizes the algorithm of Björklund, Husfeldt, and Taslaman on finding a path through \(k\) specified vertices. It also implies the first \(2^{k}n^{\mathcal{O}(1)}\) time algorithm for finding an \((s,t)\) -path of length at least \(k\) . Our method yields FPT algorithms for even more general problems. For example, we consider the problem where the input consists of an \(n\) -vertex undirected graph \(G\) , a matroid \(M\) whose elements correspond to the vertices of \(G\) and which is represented over a finite field of order \(q\) , a positive integer weight function on the vertices of \(G\) , two sets of vertices \(S,T\subseteq V(G)\) , and integers \(p,k,w\) , and the task is to find \(p\) vertex-disjoint paths from \(S\) to \(T\) so that the union of the vertices of these paths contains an independent set of \(M\) of cardinality \(k\) and weight \(w\) , while minimizing the sum of the lengths of the paths. We give a \(2^{p+\mathcal{O}(k^{2}\log(q+k))}n^{\mathcal{O}(1)}w\) time randomized algorithm for this problem.

Research on Evaluation Method of Natural Gas Hydrate Resources Based on Probability Distribution Model

Natural gas hydrate, as a highly efficient and clean energy source, has garnered significant attention from both developed and energy-deficient nations. However, to achieve industrial application, several technical challenges must be addressed, including resource exploration, spatial positioning, resource assessment, economic production evaluation, and climate change impact assessment. Currently, our exploration and evaluation system for gas hydrate resources remains immature. This study aims to determine the probability distribution of effective thickness, porosity, and saturation of natural gas hydrate resource parameters in the study area and their variations. Utilizing probability statistics theory, we calculated specific values for all gas hydrate resource parameters from open-source data of 14 exploration well locations, determined their probability distributions, and conducted distribution detection to identify specific distributions. Data analysis was performed using linear graphs and bar charts to summarize patterns. Subsequently, by applying the mathematical formula Q = A×Z×∅×S×E, we categorized natural gas hydrate resource parameters, calculated gas hydrate resources at each effective depth, determined the probability distribution of each obtained data point, and ultimately solved for the total natural gas hydrate resources, yielding a final solution of 31875763695.08.

Rainbow Mean Index of Some Classes of Graphs

In this article, we determine the rainbow mean index of cartesianproductG◻Pn, where G is a regular graph;Pm◻Pn; Wn◻K2;total graph of paths; chain of cycles and complete graphs; triangular treeand join graphs tCs∨K1.

Injective coloring of subclasses of chordal graphs

An injective k-coloring of a graph G=(V,E) is a function f:V→{1,2,…,k} such that for every pair of vertices u and v having a common neighbor, f(u)≠f(v). The injective chromatic number χi(G) of a graph G is the minimum k for which G admits an injective k-coloring. Given a graph G and a positive integer k, Decide Injective Coloring Problem is to decide whether G admits an injective k-coloring. Decide Injective Coloring Problem is known to be NP-complete for chordal graphs. In this paper, we strengthen this result by proving that Decide Injective coloring Problem remains NP-complete for undirected path graphs, a proper subclass of chordal graphs. Moreover, we show that it is not possible to approximate the injective chromatic number of an undirected path graph within a factor of n1/3−ε in polynomial time for every ε>0 unless ZPP = NP. On the positive side, we prove that the injective chromatic number of an interval graph is either Δ(G) or Δ(G)+1, where Δ(G) is the maximum degree of G. We also characterize the interval graphs having χi(G)=Δ(G) and χi(G)=Δ(G)+1. As a consequence of this characterization, we obtain a linear time algorithm to find the injective chromatic number of an interval graph.

Finding meaningful paths in heterogeneous graphs with PathWays

Graphs, and notably RDF graphs, are a prominent way of sharing data. As data usage democratizes, users need help figuring out the useful content of a graph dataset. In particular, journalists with whom we collaborate are interested in identifying, in a graph, the connections between entities, e.g., people, organizations, emails, etc. We present a novel method for exploring data graphs through their data paths connecting Named Entities (NEs, in short); each data path leads to a tabular-looking set of results. NEs are extracted from the data through dedicated Information Extraction modules. Our method builds upon the pre-existing ConnectionLens platform and follow-up work in the Abstra project, which builds simple, visual ER-style summaries of semi-structured data. The contribution of the present work, and its novelty, is twofold. First, we propose a novel analysis of entity-to-entity paths contained in datasets of any nature, and propose a new method for ranking paths, leveraging a novel Information Extraction (IE) module we built on top of ChatGPT. Second, we present an efficient approach to enumerate and compute NE paths, based on an algorithm which automatically recommends sub-paths to materialize, and rewrites the path queries using these subpaths. Our experiments demonstrate the interest of NE paths and the efficiency of our method for computing and ranking them.

Decomposition of Complete Graphs into Paths and Stars with Different Number of Edges

Let P n and K n respectively denote a path and complete graph on n vertices. By a { p H 1 , q H 2 } -decomposition of a graph G , we mean a decomposition of G into p copies of H 1 and q copies of H 2 for any admissible pair of nonnegative integers p and q , where H 1 and H 2 are subgraphs of G . In this paper, we show that for any admissible pair of nonnegative integers p and q , and positive integer n ≥ 4 , there exists a { p P 4 , q S 4 } -decomposition of K n if and only if 3 p + 4 q = ( n 2 ) , where S 4 is a star with 4 edges.

Applying the Diamond Product of Graphs to the Round Robin Tournament Scheduling Problem

The diamond product of a graph G(V,E) with a graph H(V′,E′) denoted by G⋄H is a graph whose a vertex set V(G⋄H) is a Hom(G,H) and an edge set E(G⋄H)={{f,g}|f,g∈Hom(G,H) and {f(x),g(x)}∈E′, for all x∈V(G)}. A round robin tournament problem involves creating a schedule where each participant plays against every other participant exactly once. This research represents the application of the diamond product of path graph and complete graph to 2n-participants round robin tournament problem. Moreover, the research also represents an algorithm to find a solution of 2n-participants round robin tournament problem.

Computing Zagreb Connection Indices for the Cartesian Product of Path and Cycle Graphs

Topological indices ( ) are a class of graph-based descriptors widely used in chemiformatics and Quantitative Structure-Activity Relationship (QSAR) studies. TIs capture key structural features of molecules by encoding graph-theoretic information, offering a quantitative representation of molecular topology. Each mathematical network is associated with a specific numerical value determined by a function. Among the Zagreb connection indices have been extensively researched. This study delves into the Cartesian product of cycle graphs with path graphs, elucidating the comprehensive implications of . These indices encompass the first , second , and third . Furthermore, comprehensive results of the modified first , modified second , and modified third are presented, along with the first multiplicative ZCI second multiplicative ZCI (SMZCI), and third multiplicative ZCI Moreover, modified first multiplicative ZCI ), modified second multiplicative ZCI and modified third multiplicative ZCI ( are also calculated. To provide precision, both the graphical and numerical analyses of the computed findings are aligned for the two Cartesian products. The foundation for mathematically modeling complex networks and chemical structures lies in graph theory. Topological indices ( ) are a class of graph-based descriptors widely used in chemiformatics and quantitative structure-activity relationship (QSAR) studies. TIs capture key structural features of molecules by encoding graph-theoretic information, offering a quantitative representation of molecular topology. Each mathematical network is associated with a specific numerical value determined by a topological index function. Among these the Zagreb connection indices are extensively researched TIs. This article delves into the Cartesian product of cycle graphs with path graphs, elucidating the comprehensive implications of . These indices encompass the first, Second and third. Furthermore, we present the comprehensive results of the modified , modified and modified , and also present the first multiplicative Zagreb connection index , and , along with their modified counterparts like modified first multiplicative Zagreb connection index , and . These analysis encompass two distinct types of graphs: cycle graphs and path graphs. To provide further precision, we align both the graphical and numerical analysis of our computed findings for these two Cartesian products.

Removal of acidic dyes; acid yellow 25 and acid red 4 from wastewater by degassed activated carbon

Abstract Activated carbon was prepared at 300 °C and 600 °C, characterized by SEM, EDX and XRD, and was then used as an adsorbent for the removal of acidic dyes; acid yellow 25 and acid red 4. The activated carbon prepared at high temperature (600 °C) due to its high carbon contents and surface area was subsequently used as adsorbent for the selected dyes adsorption using batch adsorption approaches to estimate different adsorption parameters. For the estimation of kinetics and equilibrium parameters a number of kinetics and isotherm models were employed. Dyes were adsorbed on activated carbon surface at a high rate for the first 15 min, after which it began to diffuse into the micro pores and thus the process became steady. The rate constant was estimated for first and second order kinetics models. The maximum adsorption capacities recorded were 526.32 mg g−1 for acid red 4 and 555.55 mg g−1 for acid yellow 25. The enthalpy change values recorded were; 19.44 kJ mol−1 for acid yellow 25 adsorption and 16 kJ mol−1 for acid red 4 adsorption, meant that the process is endothermic. The negative values of Gibbs free energy change (−393.28, −1,515.48, −2,634.68 J mol−1) of acid red 4 and acid yellow 25 (−251.72, −1,058.06, −2,367.84 J mol−1) at tested temperatures, confirmed the feasibility and spontaneity of the adsorption processes. The adsorption of dyes on the carbon surface was diffusion-controlled process, as demonstrated by the linear graph of intraparticle diffusion model.

A general formula for the index of depth stability of edge ideals

By a classical result of Brodmann, the function d e p t h R / I t depthR/I^t is asymptotically a constant, i.e. there is a number s s such that d e p t h R / I t = d e p t h R / I s depthR/I^t = depthR/I^s for t > s t > s . One calls the smallest number s s with this property the index of depth stability of I I and denotes it by d s t a b ( I ) dstab(I) . This invariant remains mysterious till now. The main result of this paper gives an explicit formula for d s t a b ( I ) dstab(I) when I I is an arbitrary ideal generated by squarefree monomials of degree 2. That is the first general case where one can characterize d s t a b ( I ) dstab(I) explicitly. The formula expresses d s t a b ( I ) dstab(I) in terms of the associated graph. The proof involves new techniques which relate different topics such as simplicial complexes, systems of linear inequalities, graph parallelizations, and ear decompositions. It provides an effective method for the study of powers of edge ideals.

Parallel finite-element codes for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

We present and distribute a parallel finite-element toolbox written in the free software FreeFEM for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions. The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFEM with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method. Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFEM with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states. Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox's results with known theoretical and numerical findings that have been reported in the literature. Program summaryProgram Title: FFEM_BdG_ddm_toolbox.zipCPC Library link to program files:https://doi.org/10.17632/w9hg964wpb.1Licensing provisions: GPLv3Programming language:FreeFEM (v 4.12) free software (www.freefem.org)Nature of problem: Among the plethora of configurations that may exist in Gross-Pitaevskii (GP) equations modeling one or two-component Bose-Einstein condensates, only the ones that are deemed spectrally stable (or even, in some cases, weakly unstable) have high probability to be observed in realistic ultracold atoms experiments. To investigate the spectral stability of solutions requires the numerical study of the linearization of GP equations, the latter commonly known as the Bogoliubov-de Gennes (BdG) spectral problem. The present software offers an efficient and reliable tool for the computation of eigenvalues (or modes) of the BdG problem for a given two- or three-dimensional GP configuration. Then, the spectral stability (or instability) can be inferred from its spectrum, thus predicting (or not) its observability in experiments.Solution method: The present toolbox in FreeFEM consists of the following steps. At first, the GP equations in two (2D) and three (3D) spatial dimensions are discretized by using P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. For a given configuration of interest, mesh adaptivity in FreeFEM is deployed in order to reduce the size of the problem, thus reducing the toolbox's execution time. Then, stationary states of the GP equations are obtained by a Newton method whose backbone involves the use of a reliable and efficient linear solver judiciously selected from the PETSc1 library. Upon identifying stationary configurations, to trace branches of such solutions a parameter continuation method over the chemical potential in the GP equations (effectively controlling the number of atoms in a BEC) is employed with step-size adaptivity of the continuation parameter. Finally, the computation of the stability of branches of solutions (i.e. the BdG spectrum), is carried out by accurately solving, at each point in the parameter space, the underlying eigenvalue problem by using the SLEPc2 library. Three-dimensional computations are made affordable in the present toolbox by using the domain decomposition method (DDM). In the course of the computation, the toolbox stores not only the solutions but also the eigenvalues and respective eigenvectors emanating from the solution to the BdG problem. We offer examples for computing stationary configurations and their BdG spectrum in one- and two-component GP equations.Running time: From minutes to hours depending on the mesh resolution and space dimension.