Linear Graph Research Articles

Einstein Model of a Graph to Characterize Protein Folded/Unfolded States.

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randić resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.

Split Geodetic Dominating Sets in Path Graphs

Let be the family of split geodetic dominating sets of the path graph . with cardinality i and let . Then the split geodetic polynomial of is defined as = , where is the split geodetic domination number of .In this paper we have determined the family of split geodetic dominating sets of the path graph with cardinality .Also , we have obtained the recursive formula to derive the split geodetic domination polynomials of paths and also obtain some properties of this polynomial.

On reverse shortest paths in geometric proximity graphs

Let S be a set of n geometric objects of constant complexity (e.g., points, line segments, disks, ellipses) in R2, and let ϱ:S×S→R≥0 be a distance function on S. For a parameter r≥0, we define the proximity graphG(r)=(S,E) where E={(e1,e2)∈S×S|e1≠e2,ϱ(e1,e2)≤r}. Given S, s,t∈S, and an integer k≥1, the reverse-shortest-path (RSP) problem asks for computing the smallest value r⁎≥0 such that G(r⁎) contains a path from s to t of length at most k.In this paper we present a general randomized technique that solves the RSP problem efficiently for a large family of geometric objects and distance functions. Using standard, and sometimes more involved, semi-algebraic range-searching techniques, we first give an efficient algorithm for the decision problem, namely, given a value r≥0, determine whether G(r) contains a path from s to t of length at most k. Next, we adapt our decision algorithm and combine it with a random-sampling method to compute r⁎, by efficiently performing a binary search over an implicit set of O(n2) candidate ‘critical’ values that contains r⁎.We illustrate the versatility of our general technique by applying it to a variety of geometric proximity graphs. For example, we obtain (i) an O⁎(n4/3) expected-time randomized algorithm (where O⁎(⋅) hides polylog(n) factors) for the case where S is a set of (possibly intersecting) line segments in R2 and ϱ(e1,e2)=minx∈e1,y∈e2⁡‖x−y‖ (where ‖⋅‖ is the Euclidean distance), and (ii) an O⁎(n+m4/3) expected-time randomized algorithm for the case where S is a set of m points lying on an x-monotone polygonal chain T with n vertices, and ϱ(p,q), for p,q∈S, is the smallest value h such that the points p′:=p+(0,h) and q′:=q+(0,h) are visible to each other, i.e., all points on the segment p′q′ lie above or on the polygonal chain T.

Hybrid path planning based on adaptive visibility graph initialization and edge computing for mobile robots

This paper presents a new initialization method that combines adaptive visibility graphs and the A* algorithm to improve the exploration, accuracy, and computing efficiency of hybrid path planning for mobile robots. First, segments/links in the full visibility graphs are removed randomly in an iterative and adaptive manner, yielding adaptive visibility graphs. Then the A* algorithm is applied to find the shortest paths in these adaptive visibility graphs. Next, high-quality paths featuring low fitness values are chosen to initialize the subsequent heuristic optimization in hybrid path planning. Specifically, in the present study, the genetic algorithm (GA) is implemented on a CPU/GPU edge computing device (Jetson AGX Xavier) to exploit its massively parallel processing threads, and the strategy for judicious CPU/GPU resource utilization is also developed. Numerical experiments are conducted to determine proper hyperparameters and configure GA with balanced performance. Various optimal paths with differential consideration of practical factors for robot path planning are obtained by the proposed method. Compared to the other benchmark methods, ours significantly improves the diversity of initial path and exploration, optimization accuracy, and computing speed (within 5 s with most less than 2 s). Furthermore, real-time experiments are carried out to demonstrate the effectiveness and application of the proposed algorithm on mobile robots.

Introduction of a tool to assess Risk of Bias in Non-randomized Studies-of Exposure (2022)

This article introduces the contents of the latest edition Risk of Bias in Non-randomized Studies-of Exposure (ROBINS-E) published in June 2022 [ROBINS-E (2022)], and gives some examples about its usage. ROBINS-E is a tool for assessing the risk of bias in non-randomized studies-of exposure. Compared with ROBINS-E (2019), ROBINS-E (2022) adds more bias for observational studies, covers a more comprehensive range of bias, and adds the assessment of the external authenticity of the study. ROBINS-E (2022) adds a preliminary evaluation process to improve the efficiency of evaluation. In addition, ROBINS-E (2022) visualizes and instrumentalizes the use of signal problems in the form of path graph, making it more convenient to use. ROBINS-E (2022), although more consideration has been given to the issue of co-exposure, still does not address the problem of effect modification in co-exposure, and there is still room to expand the applicable research.

Partition Dimention of Amalgamation-Side in Cycle Graph

The graph is a pair of sets , where is a finite set whose elements are called vertices, and is the set of pairs of members of . which is called the edge. Let be a simple graph where . The distance between points and is denoted by is the length of the shortest path between and . Given and there is a vertex on the connected graph , then the distance between and is denoted . If is -partition of , then the representation of with respect to is -ordered pairs, . If the -ordered pairs for are all different, then the partition is called a dimension partition. The minimal -number which is the -differentiating partition of is called the partition dimension of and is denoted by . In this study, the partition dimensions of the sided amalgamation result will be determined on an even-order cycle graph. In determining the dimensions of the partition, characterization of the partition dimensions is used in the path graph, the lemma about the distinguishing set and the equivalence point, especially in the even-order cycle graph. The results of this study are pd(Amal(Cn,e,k)) = 3 for n≥4 , pd(Amal(C4,e,k))=4 for k=4 , pd(Amal(C4,e,k))=3+m for k=2m+3 and k=2m+4 where m=1,2,3,...

Graph based routing algorithm for torus topology and its evaluation for the Angara interconnect

Several approaches and techniques exist to resolve load balancing problem in general and torus topology networks. Graph methods are natural ways to perform balancing of routing paths. A routing balancing algorithm must operate within the constraints of the underlying network architecture that limits several parameters, such as the number of logical paths in the network. In this paper, we consider a torus topology that is one of the common topologies that are used in high performance computing systems. We introduce a routing graph that corresponds to a interconnect topology, abstracts interconnect routing rules, providing one-to-one correspondence of network routes and graph paths. We propose a deadlock-free routing algorithm based on a fast single-source shortest path algorithm in a routing graph for the deterministic routing of a torus topology interconnect with a single virtual channel. The proposed algorithm is a tradeoff between two existing routing algorithms, also the algorithm is optimized for multidimensional torus topology and can be applied to any torus topology HPC system. We present a complete description of a routing graph that abstracts the Angara interconnect with 4D torus topology. We evaluated the proposed routing algorithm and benchmarked the maximum performance improvement of 71% for the Alltoall pattern for torus topology systems up to 432 nodes on the Angara interconnect simulator. The performance improvement of more than 5% was obtained for the NPB FT and IS application kernels on a 32-node supercomputer.

Graph Machine Learning for Improved Imputation of Missing Tropospheric Ozone Data.

Gaps in the measurement series of atmospheric pollutants can impede the reliable assessment of their impacts and trends. We propose a new method for missing data imputation of the air pollutant tropospheric ozone by using the graph machine learning algorithm "correct and smooth". This algorithm uses auxiliary data that characterize the measurement location and, in addition, ozone observations at neighboring sites to improve the imputations of simple statistical and machine learning models. We apply our method to data from 278 stations of the year 2011 of the German Environment Agency (Umweltbundesamt - UBA) monitoring network. The preliminary version of these data exhibits three gap patterns: shorter gaps in the range of hours, longer gaps of up to several months in length, and gaps occurring at multiple stations at once. For short gaps of up to 5 h, linear interpolation is most accurate. Longer gaps at single stations are most effectively imputed by a random forest in connection with the correct and smooth. For longer gaps at multiple stations, the correct and smooth algorithm improved the random forest despite a lack of data in the neighborhood of the missing values. We therefore suggest a hybrid of linear interpolation and graph machine learning for the imputation of tropospheric ozone time series.

Hopf Monoids and Generalized Permutahedra

Generalized permutahedra are polytopes that arise in combinatorics, algebraic geometry, representation theory, topology, and optimization. They possess a rich combinatorial structure. Out of this structure we build a Hopf monoid in the category of species.Species provide a unifying framework for organizing families of combinatorial objects. Many species carry a Hopf monoid structure and are related to generalized permutahedra by means of morphisms of Hopf monoids. This includes the species of graphs, matroids, posets, set partitions, linear graphs, hypergraphs, simplicial complexes, and building sets, among others. We employ this algebraic structure to define and study polynomial invariants of the various combinatorial structures.We pay special attention to the antipode of each Hopf monoid. This map is central to the structure of a Hopf monoid, and it interacts well with its characters and polynomial invariants. It also carries information on the values of the invariants on negative integers. For our Hopf monoid of generalized permutahedra, we show that the antipode maps each polytope to the alternating sum of its faces. This fact has numerous combinatorial consequences.We highlight some main applications:We obtain uniform proofs of numerous old and new results about the Hopf algebraic and combinatorial structures of these families. In particular, we give optimal formulas for the antipode of graphs, posets, matroids, hypergraphs, and building sets. They are optimal in the sense that they provide explicit descriptions for the integers entering in the expansion of the antipode, after all coefficients have been collected and all cancellations have been taken into account.We show that reciprocity theorems of Stanley and Billera–Jia–Reiner (BJR) on chromatic polynomials of graphs, order polynomials of posets, and BJR-polynomials of matroids are instances of one such result for generalized permutahedra.We explain why the formulas for the multiplicative and compositional inverses of power series are governed by the face structure of permutahedra and associahedra, respectively, providing an answer to a question of Loday.We answer a question of Humpert and Martin on certain invariants of graphs and another of Rota on a certain class of submodular functions.We hope our work serves as a quick introduction to the theory of Hopf monoids in species, particularly to the reader interested in combinatorial applications. It may be supplemented with Marcelo Aguiar and Swapneel Mahajan’s 2010 and 2013 works, which provide longer accounts with a more algebraic focus.

Multi-Material 3D-Printing Nozzle Design Based on the Theory of Inventive Problem Solving and Knowledge Graph

Fused deposition modeling (FDM) technology is an emerging technology with promising applications, with the nozzle playing a crucial role in extrusion, heating, and material ejection. However, most current extrusion-based 3D printers handle only single-material printing, making the integration of multiple materials through a single nozzle challenging due to compromised quality and clogging risks. This paper introduces a method to design multi-material 3D printing nozzles using the Theory of Inventive Problem Solving (TRIZ) and knowledge graph (KG). By optimizing design and leveraging TRIZ’s contradiction resolution principle, this study addressed bottlenecks and complexities in multi-material nozzle design, providing insightful recommendations. A patent knowledge graph focused on spray nozzles was created, storing material properties, design elements, and constraints for enhanced knowledge sharing. Building on identified challenges and recommendations, the study utilized keyword searches and associative paths in the knowledge graph to guide designers in generating innovative solutions. Validation was achieved through two distinct nozzle design models resulting from guided innovations. The TRIZ-KG methodology presented in this paper provides designers with a systematic cognitive framework to empower designers in overcoming technical obstacles and proposing precise solutions.

SUM CORDIAL LABELING OF CORONA PRODUCT GRAPH OF PATH TO PATH

In this paper the researcher studies on the labeling of Corona Product Graph of Path to Path by admitting the certain condition of Sum cordial labeling. A sum cordial labeling of a graph is a binary labeling with vertex set V, with edge labeling f:E(G) {0,1},defined by f(uv)=(f(u)+f(v))(mod2) if |vf(0)-vf(1)|≤1and |ef(0)-ef(1)|≤1. A graph G is Sum cordial if it admits Sum cordial labeling.

An omics data analysis method based on feature linear relationship and graph convolutional network

Biological networks are known to be highly modular, and the dysfunction of network modules may cause diseases. Defining the key modules from the omics data and establishing the classification model is helpful in promoting the research of disease diagnosis and prognosis. However, for applying modules in downstream analysis such as disease states discrimination, most methods only utilize the node information, and ignore the node interactions or topological information, which may lead to false positives and limit the model performance. In this study, we propose an omics data analysis method based on feature linear relationship and graph convolutional network (LCNet). In LCNet, we adopt a way of applying the difference of feature linear relationships during disease development to characterize physiological and pathological changes and construct the differential linear relation network, which is simple and interpretable from the perspective of feature linear relationship. A greedy strategy is developed for searching the highly interactive modules with a strong discrimination ability. To fully utilize the information of the detected modules, the personalized sub-graphs for each sample based on the modules are defined, and the graph convolutional network (GCN) classifiers are trained to predict the sample labels. The experimental results on public datasets show the superiority of LCNet in classification performance. For Breast Cancer metabolic data, the identified metabolites by LCNet involve important pathways. Thus, LCNet can identify the module biomarkers by feature linear relationship and a greedy strategy, and label samples by personalized sub-graphs and GCN. It provides a new manner of utilizing node (molecule) information and topological information in the defined modules for better disease classification.

Multikernel adaptive filtering over graphs based on normalized LMS algorithm

To address the difficulty and inflexibility associated with choosing kernel parameters for single kernel adaptive filters (KAFs), this article proposes a multikernel adaptive filter for graph signals based on the least mean square (LMS) algorithm. First, normalized by its largest eigenvalue, the combinatorial graph Laplacian is adopted as the graph shift operator (GSO) to preprocess graph input signals. Then, the graph multikernel normalized least mean square (GMKNLMS) algorithm is developed to estimate nonlinear graph filter coefficients. To limit the growth in dictionary size, a coherence-check (CC) based sparsification method is introduced to form the new GMKNLMS-CC algorithm. In addition, numerical simulation examples are presented to demonstrate the improved performance of the proposed algorithms compared with the linear graph least mean square (GLMS) and graph kernel normalized least mean square (GKNLMS) algorithms. Finally, the real sensor measurement data taken from the Intel Lab is used as time-varying graph signals to demonstrate the tracking performance of the GMKNLMS-CC algorithm.

A new graph-theoretic approach for the study of the surface of a thin sheet of a viscous liquid model

In this study, we considered the model of the surface of a thin sheet of viscous liquid which is known as the Buckmaster equation (BME), and presented a new graph-theoretic polynomial collocation method named the Hosoya polynomial collocation method (HPCM) for the solution of nonlinear Buckmaster equation. In the literature, the majority of the developed numerical methods considered small time step sizes like 0.01s and 0.05s to obtain relatively accurate approximations for the nonlinear BME. This study focused on optimizing the time step sizes by adopting bigger time steps sizes like 1.0s,3.0s, and 5.0s, etc without adversely affecting accuracy. First, using the Gram- Schmidt process, we generated the orthonormal functions from the Hosoya polynomial of the path graph. Then developed the functional integration matrix using orthonormal Hosoya polynomials of path graphs. With this active matrix-involved method, the nonlinear BMEs are transformed into a system of nonlinear equations and solved the equations by Newton’s method through the Mathematica software for unknown coefficients. The exactness of the proposed strategy is tested with two numerical examples. The acquired results contrasted with the current analytical solutions to these problems. Also provided the convergence analysis, comparison of error norms, graphical plots of correlation of HPCM results, and the results of other numerical methods in the literature to validate the productivity and accuracy of the newly developed HPCM.

Deep Reinforcement Learning for Intelligent Penetration Testing Path Design

Penetration testing is an important method to evaluate the security degree of a network system. The importance of penetration testing attack path planning lies in its ability to simulate attacker behavior, identify vulnerabilities, reduce potential losses, and continuously improve security strategies. By systematically simulating various attack scenarios, it enables proactive risk assessment and the development of robust security measures. To address the problems of inaccurate path prediction and difficult convergence in the training process of attack path planning, an algorithm which combines attack graph tools (i.e., MulVAL, multi-stage vulnerability analysis language) and the double deep Q network is proposed. This algorithm first constructs an attack tree, searches paths in the attack graph, and then builds a transfer matrix based on depth-first search to obtain all reachable paths in the target system. Finally, the optimal path for target system attack path planning is obtained by using the deep double Q network (DDQN) algorithm. The MulVAL double deep Q network(MDDQN) algorithm is tested in different scale penetration testing environments. The experimental results show that, compared with the traditional deep Q network (DQN) algorithm, the MDDQN algorithm is able to reach convergence faster and more stably and improve the efficiency of attack path planning.

Erratum. Dominator coloring of total graph of path and cycles

Erratum. Dominator coloring of total graph of path and cycles

Patterns and Line-Adjacency Matrix Strategy on a Game of Induced Matching

A matching is an independent set of edges in a graph G; an induced matching is a matching with an additional property that no two of its edges are joined by an edge in G. An induced matching M in a graph G is maximal if no other induced matching in G contains M. In the proposed game, players alternate choose edges on a graph while maintaining an induced matching. They continue until the matching is maximal (i.e. no player can choose another edge), and the last player to choose an edge wins. This paper will discuss patterns for this game and prove results on several categories of graphs including Complete Graphs, Path Graphs, Cycle Graphs, and Ladder Graphs. In addition, a novel Line-Adjacency Matrix method has been defined and proved to calculate all possible edges for the next move in a connected graph. Keywords: Induced Matching, Adjacency Matrix, Line-Adjacency Graph

Synthesis and Analysis of Well‐Defined Copolymers via by Combination ROP Technique

AbstractHerein, the poly(ɛ‐caprolactone)‐poly(ethylene glycol)‐poly(ɛ‐caprolactone) (PCL‐PEG‐PCL) macro xanthate reversible addition–fragmentation chain‐transfer agent is obtained on the polyethylene glycol (PEG) (600, 1000, and 1500 g mol−1) block, after the addition of ɛ‐caprolactone via ring‐opening polymerization. Then, poly (styrene‐b‐ɛ‐caprolactone‐b‐PEG‐b‐ɛ‐caprolactone‐b‐styrene) pentablock copolymer is synthesized reversible addition–fragmentation chain‐transfer (RAFT) solution polymerization technique via mediated PCL‐PEG‐PCL xanthate macro‐RAFT agents and 2,2′‐azobisisobutyronitrile as initiator. The products are demonstrated using Fourier transform infrared spectrophotometer (FT‐IR), proton nuclear magnetic resonance (1H‐NMR), carbon nuclear magnetic resonance (13C‐NMR), differential scanning calorimetry (DSC), and gel permeation chromatography (GPC) analyses. First‐order linear kinetic graphs of the reaction mechanism are observed with an increase in molecular weights (MW) between 16 000 and 36 000 g mol−1. The narrow dispersity (Đ = 1.40–1.48) polymer formation of styrene (St) controlled by RAFT polymerization confirms the increase in molecular weight according to the polymerization time. The reaction kinetics are first order and the rate constants are found to be k1 = 6.16 × 10−4s−1, k2 = 6.91 × 10−4 s−1 and k3 = 7.33 × 10−4 s−1. Thermal and spectroscopic analyses prove that the reactions are carried out successfully.

Preliminary application of three-dimensional venography and fusion navigation technique in May-Thurner syndrome

ObjectiveThe purpose of this study was to report a technique for intraprocedural guidance of endovascular iliac vein stenting procedures using three-dimensional (3D) venography images as an overlay on live biplanar fluoroscopy. MethodsUsing 3D venography and a fusion navigation technique, percutaneous transluminal angioplasty and stent placement were performed to evaluate the feasibility of using 3D venography images and the fusion navigation technique to treat MTS compared with traditional digital subtraction angiography. The general epidemiologic data (ie, age, gender), clinical manifestations (ie, major symptoms, affected extremity, CEAP [clinical, etiology, anatomy, pathophysiology] classification, comorbidity, stenosis rate), intraoperative findings (ie, stent type, stent count, stent to inferior vena cava distance, procedure time, radiation dose, contrast agent dosage), and postoperative recovery were obtained and analyzed. ResultsA total of 30 consecutive patients with symptomatic MTS from our institution were enrolled in the present study. Of the 30 patients, 12 (group A) were treated using 3D venography images and fusion navigation and 18 (group B) were treated with two-dimensional venography images during endovascular management. Significant differences were observed between the two groups with respect to the procedure time (64.42 ± 4.35 minutes vs 76.61 ± 3.47 minutes; P = .04), radiation dose (2152 ± 124.7 mGy vs 2561 ± 105.6 mGy; P = .02), and contrast agent dosage (71.42 ± 4.87 mL vs 86.17 ± 4.14 mL; P = .03). Conclusions3D venography and its fusion navigation technique can improve prediction of the coverage area of the stent. Its use can also shorten the procedure time and reduce the contrast agent dose and radiation exposure, making it a valuable tool for both the diagnosis and the treatment of symptomatic MTS.

Correlation Between COSMIC Rayn Intensity and Geomagnetic Activity Indices

This study conducts an extensive analysis to explore the correlation between the monthly average cosmic ray intensity (CRI) and indicators of geomagnetic activity, primarily focusing on the Ap and Kp indices. The study covers two distinct time intervals, 1996-2008 and 2009-2019. By analyzing the correlation between CRI and geomagnetic indices, we constructed linear graphs depicting their associations. The results consistently reveal a noticeable inverse correlation between monthly average CRI and the Ap index. Correlation coefficients were computed to quantify these relationships using established statistical methods. Between 1996 and 2008, a strong negative correlation of -0.89 was observed between CRI and the Ap index. Similarly, during 2009-2019, a significant negative correlation of -0.39 was noted. The monthly average CRI exhibited a negative correlation of -0.72 with the Kp index during 1996-2008, and a more pronounced negative correlation of -0.70 during 2009-2019. These findings underscore the intricate interplay between cosmic ray intensity and geomagnetic activity, offering insights into the broader understanding of space weather phenomenon