Linear Graph Research Articles

Low temperature magnetic and structural properties of Sr-doped La2CoMnO6 (La2-xSrxCoMnO6: 0 ≤ x ≤ 0.08) double perovskite nanoparticles

A study on crystal structure and physical properties has been performed on nanoparticles of lead-free double perovskites, La2CoMnO6 (LCMO) and Sr-doped La2-xSrxCoMnO6 (LSMO:0 ≤ x ≤ 0.08) prepared by the sol–gel synthesis method. In preparation for the LSMO nanoparticle, the La site of the LCMO double perovskite was replaced with an increasing concentration of Sr atom. Structural investigation done by employing the X-ray Diffraction technique indicates that the crystallite size decreases as the doping concentration increases. The Rietveld refinement on the XRD pattern shows the formation of the rhombohedral phase of LCMO (S.G. no. 161). Strain in the prepared samples estimated from Williamson Hall (W-H) analysis shows that the strain decreases as crystallite size decreases. The presence of compressive strain is also evident from the blue shift obtained in the Raman spectrum of the nanoparticles. The UV–Vis spectra reveal the maximum absorption in the near UV region of the electromagnetic spectrum. The Bandgap analysis from Tauc’s plot shows an increase in band gap with Sr doping in the LCMO host lattice (from 1.81 eV to 1.92 eV). This is attributed to the decrease in crystallite size and octahedral tilting with Sr doping. Resistivity versus temperature plots reveal the semiconducting nature of the compound. A linear nature graph between lnρ and T-14 indicates that the electric transport mechanism is governed by the variable range Hopping (VRH) model. The M−H curves show that the maximum magnetization decreases as a result of Sr doping due to the anti-site disorder introduced. dM/dT vs T curve shows two magnetic transitions at ∼ 215 K and at ∼ 173 K which are due to Co2+–O2--Mn4+ and Co3+–O2--Mn4+ ferromagnetic superexchange interactions, respectively.

Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators.

Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to investigate these networks, obtaining mathematical descriptions for the dynamics of multilayer and multiplex systems is still an open problem. Here, we combine ideas and concepts from linear algebra and graph theory with nonlinear dynamics to offer a novel approach to study multiplex networks of Kuramoto oscillators. Our approach allows us to study the dynamics of a large, multiplex network by decomposing it into two smaller systems: one representing the connection scheme within layers (intra-layer), and the other representing the connections between layers (inter-layer). Particularly, we use this approach to compose solutions for multiplex networks of Kuramoto oscillators. These solutions are given by a combination of solutions for the smaller systems given by the intra- and inter-layer systems, and in addition, our approach allows us to study the linear stability of these solutions.

Solution to a conjecture on resistance diameter of lexicographic product of paths

The resistance distance R[u,v] between two vertices u and v of a graph G is defined as the net effective resistance between them in the electric network constructed from G by replacing each edge with a unit resistor. The resistance diameter Dr(G) of G is the maximum resistance distance among all pairs of vertices of G. Given two path graphs Pn=a1a2…an and Pm=b1b2…bm, let Pn[Pm] be the lexicographic product of Pn and Pm with vertex set {(ai,bj)|i=1,…,n;j=1,…,m}. In [J. Appl. Math. Comput. 68 (2022) 1743–1755], Li et al. proved that for n>10, Dr(Pn[Pm])=R[(a1,b1),(an,bm)]=R[(a1,b1),(an,b1)]=R[(a1,bm),(an,b1)]=R[(a1,bm),(an,bm)]. In addition, they found that the result is not true for n=2. For 3≤n≤10 and enough small m, they checked by computer that the result is still true. Based on their observation, they conjectured that the result is true for 3≤n≤10. In this paper, by combinatorial and electrical network approaches, we confirm the conjecture.

A new method for vulnerability and risk assessment of IoT

In this paper, we propose a generic vulnerability and risk assessment method for IoT-enabled systems. The main aim is to provide risk detection and vulnerability assessment for IoT-based systems. We present three phases of risk assessment methodology: graph construction, attack path detection, and attack path filtering for high-level attack paths. We give attack path detection, risk level computing, and attack path removing procedures to validate these phases. We represent the IoT-based network as a graphical structure. Then, we construct the topology for a given IoT-based system. The smart home system is considered as a case scenario to present a realistic instance. The National Vulnerability Database (NVD), Common Vulnerability Scoring System (CVSS), and Common Vulnerability Exposures (CVE) metrics are used to assign vulnerabilities to devices. We formulate risk factors to compute risk levels for each node, attack path, and entire graph. We use the modified Depth First Algorithm (DFS) to find all attack paths for a source and target nodes. In addition, we compute risk levels using computing procedures. Further, we filter detected attack paths considering dominance level using computational metrics. We perform the simulation on a custom Python simulator considering the designed IoT-based smart home system. We compare our proposed methods with the state of the art. According to the experimental results, the proposed methods outperform existing vulnerability-based risk assessment models regarding running time complexity and operational cost.

Graph structure reforming framework enhanced by commute time distance for graph classification

As a graph data mining task, graph classification has high academic value and wide practical application. Among them, the graph neural network-based method is one of the mainstream methods. Most graph neural networks (GNNs) follow the message passing paradigm and can be called Message Passing Neural Networks (MPNNs), achieving good results in structural data-related tasks. However, it has also been reported that these methods suffer from over-squashing and limited expressive power. In recent years, many works have proposed different solutions to these problems separately, but none has yet considered these shortcomings in a comprehensive way. After considering these several aspects comprehensively, we identify two specific defects: information loss caused by local information aggregation, and an inability to capture higher-order structures. To solve these issues, we propose a plug-and-play framework based on Commute Time Distance (CTD), in which information is propagated in commute time distance neighborhoods. By considering both local and global graph connections, the commute time distance between two nodes is evaluated with reference to the path length and the number of paths in the whole graph. Moreover, the proposed framework CTD-MPNNs (Commute Time Distance-based Message Passing Neural Networks) can capture higher-order structural information by utilizing commute paths to enhance the expressive power of GNNs. Thus, our proposed framework can propagate and aggregate messages from defined important neighbors and model more powerful GNNs. We conduct extensive experiments using various real-world graph classification benchmarks. The experimental performance demonstrates the effectiveness of our framework. Codes are released on https://github.com/Haldate-Yu/CTD-MPNNs.

Smaller and Denser Speech Graphs in Nondemented Patients with Progressive Supranuclear Palsy.

The well-established semantic fluency test measures the ability to produce a sequence of spoken words from a particular category within a limited period of time. Like patients with Parkinson's disease (PD), patients with progressive supranuclear palsy (PSP) tend to produce fewer correct words than age-matched healthy adults. This study further examined the difference between patients with PSP and PD in their semantic fluency performance using a graph theory-based approach. Twenty-nine patients with PSP Richardson's syndrome (PSP-RS), thirty-eight patients with PD, and fifty-one healthy controls (HC) were recruited. All participants completed a standard semantic fluency test (animals). Their verbal responses were recorded, transcripted, and transformed into directed speech graphs. The speech graphs of the PSP-RS group showed higher density, shorter diameter, and shorter average shortest path than those of the PD and HC groups. It indicates that the PSP-RS group produced smaller and denser speech graphs than the PD and HC groups. In the PSP-RS group, moreover, the average shortest paths of the speech graphs correlated with the severity of motor symptoms. This study shows the potential of the graph theory-based approach in distinguishing the semantic fluency performance of nondemented patients with PSP-RS and PD.

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

We show how to efficiently decompose a parameterized multi-qubit Pauli (PMQP) gate into native parameterized two-qubit Pauli (P2QP) gates minimizing both the circuit depth and the number of P2QP gates. Given a realistic quantum computational model, we argue that the technique is optimal in terms of the number of hardware native gates and the overall depth of the decomposition. Starting from PMQP gate decompositions for the path and star hardware graph, we generalize the procedure to any generic hardware graph and provide exact expressions for the depth and number of P2QP gates of the decomposition. Furthermore, we show how to efficiently combine the decomposition of multiple PMQP gates to further reduce the depth as well as the number of P2QP gates for a combinatorial optimization problem using the Lechner–Hauke–Zoller mapping.

Hierarchical high-point Energy Flow Network for jet tagging

Jet substructure observable basis is a systematic and powerful tool for analyzing the internal energy distribution of constituent particles within a jet. In this work, we propose a novel method to insert neural networks into jet substructure basis as a simple yet efficient interpretable IRC-safe deep learning framework to discover discriminative jet observables. The Energy Flow Polynomial (EFP) could be computed with a certain summation order, resulting in a reorganized form which exhibits hierarchical IRC-safety. Thus inserting non-linear functions after the separate summation could significantly extend the scope of IRC-safe jet substructure observables, where neural networks can come into play as an important role. Based on the structure of the simplest class of EFPs which corresponds to path graphs, we propose the Hierarchical Energy Flow Networks and the Local Hierarchical Energy Flow Networks. These two architectures exhibit remarkable discrimination performance on the top tagging dataset and quark-gluon dataset compared to other benchmark algorithms even only utilizing the kinematic information of constituent particles.

Quantum algorithm for de novo DNA sequence assembly based on quantum walks on graphs

De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to smaller graphs that form a hierarchical structure. We use quantum walks to find paths in low rank graphs and a quantum algorithm that finds Hamiltonian paths in high hierarchical rank. We tested the partitioning quantum algorithm, as well as the quantum algorithm that finds Hamiltonian paths in high hierarchical rank and confirmed its correct operation using Qiskit. We developed a custom simulation for quantum walks to search for paths in low rank graphs. The approach described in this paper may serve as a basis for the development of efficient quantum algorithms that solve the de novo DNA assembly problem.

Highly sensitive zero-order emission system - fluorescence detection-liquid chromatographic method for simultaneous estimation of two banned phenyl xanthene dyes in bottled chili sauce

ABSTRACT. A zero-order emission system was applied to address the variation in emission wavelengths between analytes. Also, it assists to compensate for the drop in emission intensity resulted from the changes in analyte excitation wavelength. So, a high performance liquid chromatography-fluorescence detector (HPLC-FLD) with zero order emission mode was used for the simultaneous estimation of rhodamine B (RhB) and eosin Y (EsY) based on their native fluorescence. The presented method is considered the first fluorescence method for simultaneous determination of RhB and EsY. The efficiency of the developed method was tested by determining the two dyes in a high matrix sample, chili sauce. Under the optimum condition, a linear calibration graphs for RhB and EsY in range of 0.5 -300 ng/mL with r = 0.9994 and 0.9991, respectively, were acquired. The limits of detection for RhB and EsY were 0.344 ng/mL (0.355 ng/g) and 0.215 ng/mL (0.222 ng/g), respectively. The recovery percentage and relative standard deviation of two analytes were obtained in the range of 98.38-101.86% and 0.83-1.66%, respectively. RhB was detected only in one chili sauce sample at a concentration of 0.388 ng/mL while EsY was not found in any sample.
 KEY WORDS: Rhodamine B, Eosin Y, HPLC-FLD, Zero-order emission mode, Solid phase extraction
 Bull. Chem. Soc. Ethiop. 2023, 37(6), 1315-1323. DOI: https://dx.doi.org/10.4314/bcse.v37i6.2

Graceful Labeling of Prime Index Graph of Group Zp × Zpn

The prime index graph π(G) of a finite group G is a special type of undirected simple graph whose vertex set is set of subgroups of G, in which two distinct vertices are adjacent if one has prime index in the other. Let p and q be distinct primes. In this paper, we establish that prime index graph of a finite cyclic p-group Zpn, a finite abelian group Zpn × Zq and a finite abelian p-group Zp × Zpn always have graceful labeling without any condition on n using the concept of path graph or p-layer ladder graph of size n + 1.

Recommendation Method of Power Knowledge Retrieval Based on Graph Neural Network

With the development of the digital and intelligent transformation of the power grid, the structure and operation and maintenance technology of the power grid are constantly updated, which leads to problems such as difficulties in information acquisition and screening. Therefore, we propose a recommendation method for power knowledge retrieval based on a graph neural network (RPKR-GNN). The method first uses a graph neural network to learn the network structure information of the power fault knowledge graph and realize the deep semantic embedding of power entities and relations. After this, it fuses the power knowledge graph paths to mine the potential power entity relationships and completes the power fault knowledge graph through knowledge inference. At the same time, we combine the user retrieval behavior features for knowledge aggregation to form a personal subgraph, and we analyze the user retrieval subgraph by matching the similarity of retrieval keyword features. Finally, we form a fusion subgraph based on the subgraph topology and reorder the entities of the subgraph to generate a recommendation list for the target users for the prediction of user retrieval intention. Through experimental comparison with various classical models, the results show that the models have a certain generalization ability in knowledge inference. The method performs well in terms of the MR and Hit@10 indexes on each dataset, and the F1 value can reach 87.3 in the retrieval recommendation effect, which effectively enhances the automated operation and maintenance capability of the power system.

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.