Incidence Matrix Research Articles

A Collaborative Monitoring Method for Traffic Situations under Urban Road Emergencies

The complex and diverse urban road traffic environments make it difficult to accurately assess road traffic situations. This paper proposes a collaborative monitoring method for urban road traffic situational assessment during emergency events. This method is applied to a monitoring network mapped by road geographic relations. When an emergency event is captured by a monitoring node in the network, road traffic situational awareness is completed by an activation function. Then, the Incidence matrix of the emergency event is constructed based on the node degree of this monitoring node. The collaborative node set and collaborative monitoring area are formed dynamically from this Incidence matrix. Finally, the AHP and EM combination weight calculation method based on Game Theory (GT-AHP-EM) is used to fuse the data of various information in the collaborative monitoring area to predict the current road traffic trend. The experiments show that the collaborative monitoring method can effectively assess road traffic conditions and enhance the accuracy of road traffic trend prediction.

Consensus of discrete-time multi-agent systems with consecutive packet losses in directed communication topology

In this paper, consensus analysis and design are investigated for discrete-time multi-agent systems (MASs) with consecutive packet losses in communication links of directed communication topology. It is assumed that at each transmitted instant, the packet loss is stochastic and described by Bernoulli distribution, but during a given time window, the data could be successfully transmitted to the agent from each of its neighbors. First, we utilize the incidence matrix of a directed spanning tree of the communication topology to construct a linear transformation matrix so that the consensus problem is equivalently transformed into a mean square asymptotic stability problem of a reduced-order system. Second, by using Lyapunov–Krasovskii functional approach, we derive some sufficient conditions of consensus criterion in terms of linear matrix inequalities (LMIs). These conditions express the relationship among the control gain matrix, packet loss rate, and the number of consecutive packet losses. Based on the conditions, gain matrix in the consensus protocol is designed to guarantee the MAS with stochastic packet losses to achieve mean square asymptotic consensus. Moreover, for the special case of undirected communication topology, by using the matrix decomposition method, the variables of LMIs are transformed into the low-order conditions independent of the network size. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Incidence matrices and line graphs of mixed graphs

Abstract In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result. The goal of this article is to present aligned definitions of the adjacency matrix, the incidence matrix, and line graph of a mixed graph such that the mentioned theorem is valid for mixed graphs.

Design of Incidence Matrices With Limited Constellation Expansion in Massive Connectivity NOMA Systems

Non-orthogonal multiple-access (NOMA) is designed to transmit massive amounts of user communications. The incidence matrix manages the relationship between users and resources. This study focused on increasing user supportability and complexity reduction using larger incidence matrices. Our approach to optimizing the incidence matrix to improve system capacity and reduce complexity is based on two critical mathematical concepts: Parallel classes in hypergraph theory and combinatorial designs allow us to explore and extend incidence matrices. Frame theory is used to estimate matrix structures. Then, we investigate applications utilizing our incidence matrix designs–Simple Orthogonal Multi-Arrays (SOMA). The characteristics of SOMA reflect the unique Latin Square pattern, allowing us to produce a highly flexible and fair resource allocation matrix. SOMA designs let us support overload factors over 500%. The theoretical performance analysis equations of our NOMA system were established to support dynamic adaptability and optimization. We implemented and evaluated security methods for eavesdroppers. The prototype of the user hierarchy allows a higher-priority group to have a lower error rate without significantly affecting the system’s performance. Finally, the Monte Carlo simulation indicated that our NOMA systems allow higher degrees of freedom and lower complexity than other NOMA schemes while maintaining graceful error rates with a maximum 33% improvement.

Relation between the Branch-to-Node Incidence and Triangular Matrices in Radial Distribution Networks

The power flow solution is a classical problem in electrical engineering that has been studied for more than 60 years [1]. One of the most widely used methods corresponds to the Newton-Raphson approach, which is currently employed for analyzing power systems with meshed configurations and multiple generation sources, i.e., it is typically employed for power systems in high-voltage levels [2].

Online vector bin packing and hypergraph coloring illuminated: simpler proofs and new connections

This paper studies the online vector bin packing (OVBP) problem and the related problem of online hypergraph coloring (OHC). Firstly, we use a double counting argument to prove an upper bound on the competitive ratio of FirstFit for OVBP. Our proof is conceptually simple, and strengthens the result in [1] by removing the dependency on the bin size parameter. Secondly, we introduce a notion of an online incidence matrix that is defined for every instance of OHC. Using this notion, we provide a reduction from OHC to OVBP, which allows us to carry known lower bounds on the competitive ratio of algorithms from OHC to OVBP. Our approach significantly simplifies the previous argument from [1] that relied on using intricate graph structures. In addition, we slightly improve their lower bounds. Lastly, we establish a tight bound on the competitive ratio of algorithms for OHC, where input is restricted to be a hypertree, thus resolving a conjecture in [2]. The crux of this proof lies in solving a certain combinatorial partition problem about multi-family of subsets, which might be of independent interest.

The sum of hamming distance for some composite graphs relative to vertex-edge incidence matrix

Given C be a vertex-edge incidence matrix of a graph Z. The Hamming distance between two rows C(x, :) and C(y, :) of C is the number of coloumn ℓ such that C (x, ℓ) ≠ C (y, ℓ). In this paper, we discuss the sum of Hamming distances between all pairs of rows of C. We present a formula for the sum of the number of edges and the number of vertices of the graph Z. We then use this formula to determine the sum of Hamming distance for composite graphs such as union of graphs, joint of graphs, corona product of graphs and cartesian product of graphs

The maximal spectral radius of the uniform unicyclic hypergraphs with perfect matchings

Let U(n, k) and ?(n, k) be respectively the sets of the k-uniform connected linear and nonlinear unicyclic hypergraphs having perfect matchings with n vertices, where n ? k(k?1) and k ? 3. By using some techniques of transformations and constructing the incidence matrices for the hypergraphs considered, we get the hypergraphs with the maximal spectral radii among three kinds of hypergraphs, namely U(n, k) with n = 2k(k ? 1) and n ? 9k(k ? 1), ?(n, k) with n ? k(k ? 1), and U(n, k) ? ?(n, k) with n ? 2k(k ? 1), where k ? 3.

ПОИСК ЭКСТРЕМАЛЬНОГО СОДЕРЖАНИЯ КОМПОНЕНТА В РЕАГИРУЮЩЕЙ СИСТЕМЕ С ПОМОЩЬЮ ГРАФА ХИМИЧЕСКИХ РЕАКЦИЙ

The article presents a technique for calculating a maximum amount of a substance in a closed system using a step-by-step graph of chemical reactions. A list of probable one- and two-particle reversible reactions is generated based on the substances that may be a part of the reacting system. The list is narrowed down according to the research objectives and conditions of the reacting system. The obtained list corresponds to the incidence matrix, which is suitable for analyzing the graph via a computer. The search for the maximum amount of the component in question is conducted through the comparison of weights of the graph’s edges at each stage of its intermediate reactions. The graph’s weights are calculated based on the kinetic coefficients of reactions. They also determine the dominant reaction. The amount is calculated under the premise that the dominant reaction is equilibrium. The maximum amount of hydroperoxyl radical HO2 in a hydrogen H and oxygen O reacting system is calculated.

IDriveGenes: Cancer Driver Genes Prediction Using Machine Learning

The development of high throughput sequencing technologies i.e. Next Generation Sequencing (NGS) is revolutionizing the exploration of cancer. Though sequence datasets are highly complex, mutation can occur randomly in DNA or RNA sequences that can make cells sicker or less fit. The unusual growth and behavior of genes in cells cause cancer. Cancer-driver gene cells grow when mutation occurs. Identification of cancer driver genes is a critical and challenging issue for researchers. In the proposed work, initially, robust features are extracted from the sequence dataset through Position Relative Incidence Matrix (PRIM) integrated with Accumulative Absolute Position Incidence Vector (AAPIV) generation. PRIM and AAPIV convert the single-dimensional sequence data into 2-dimensional numeric data. Support Vector Machine (SVM), Neural Network (NN), and Random Forest (RF) are used to train the model. The proposed model is validated with different validation methods i.e., independent testing, k-fold cross-validation, self-consistency, and jackknife testing. The proposed model predicts whether the given primary structure corresponds to cancer driver genes or not. Results analyses show 95%, 92%, and 69% accuracy on RF, Artificial Neural Networks (ANN), and SVM respectively. The comparative analysis with existing state-of-the-art models i.e., 20/20+ and Multimodal Deep Neural Network by integrating Multi-dimensional Data (NDNNMD) shows that the proposed model outperforms the existing techniques.

Brain Network Analysis of Schizophrenia Patients Based on Hypergraph Signal Processing.

Since high-order relationships among multiple brain regions-of-interests (ROIs) are helpful to explore the pathogenesis of neurological diseases more deeply, hypergraph-based brain networks are more suitable for brain science research. Unlike the existing hypergraph based brain network (brain hypernetwork), where hyperedges containing the same number of ROIs are assumed to have equal weights (to some extent, the network is unweighted), and the underlying structure is described only by an incidence/adjacency matrix, in this paper, we propose a framework for constructing a truly weighted brain hypernetwork described by an adjacency tensor. Considering the relationships among vertices within a hyperedge, we propose a novel hyperedge weight estimation method and convert the incidence matrix into a weighted adjacency tensor. On the basis of tensor decomposition, we apply hypergraph signal processing tools, such as hypergraph Fourier transform, to analyze and compare the spectrum between schizophrenia patients and normal controls. It is found that there are more high frequency components in the spectrum of patients than controls, and the average amplitude is significantly greater than that of controls. Instead of extracting some simple topological features from brain hypernetworks for classification, we innovatively use the hypergraph spectrum and the spectral signal as classification features, and the classification results on two public datasets demonstrate the effectiveness of our proposed method.

Hamming index of graphs with respect to its incidence matrix

Let $B(G)$ be the incidence matrix of a graph $G$. The row in $B(G)$ corresponding to a vertex $v$, denoted by $s(v)$ is the string which belongs to $\Bbb{Z}_2^n$, a set of $n$-tuples over a field of order two. The Hamming distance between the strings $s(u)$ and $s(v)$ is the number of positions in which $s(u)$ and $s(v)$ differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.

Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2

In this note, we report the classification of all symmetric 2-(36, 15, 6) designs that admit an automorphism of order 2 and their incidence matrices generate an extremal ternary self-dual code. It is shown that up to isomorphism, there exists only one such design, having a full automorphism group of order 24, and the ternary code spanned by its incidence matrix is equivalent to the Pless symmetry code.

INFORMATION TECHNOLOGY FOR THE SCHEDULE GENERATION BASED ON THE ALGEBRA OF ADDITIVE-DISJUNCTIVE FORMS AND THE MODIFIED METHOD OF PERMANENT DECOMPOSITION

To improve the information technology of drawing up class schedules, there is a need to develop methods that allow significantly reduce the number of combinatorial objects in the process of algorithms for generating schedules matrices. For example, the result of applying the method of permanent decomposition is a collection of combinatorial objects - permutations, combinations, and placements. For the task of drawing up lesson schedules in the part of forming timetable matrices, the method provides a memory-recorded set of all possible systems of various representatives of sets, which are the columns of the timetable matrices (SRPS). Since the algorithm of permanent decomposition gives all possible SRPS, it creates the problem of forming the final schedule based on SRPS or all possible variants of schedules and requires the development of special algorithms. Certain known approaches to solving such a problem are associated with significant computational complexity in the general case. This also applies to the approach based on the order relation of the set of decomposition matrices.
 The basis of the information technology proposed in the work is the further modification of the incidence matrices and, accordingly, such a modification of the permanent decomposition method, which allows generating ready versions of the schedule matrices at the output. This is achieved due to the introduction of a special algebra of additive-disjunctive forms and, accordingly, the possibility of generating such forms in the process of permanent decomposition. In fact, in this context, ADF is a formal representation of a ready-made version of an admissible schedule that satisfies some additional requirements.

Matrix representation of operations on graphs

This article considers the possibility of matrix execution of both unary and binary operations on graphs. Graphs, as an abstract mathematical construction, have a very wide range of practical applications. First of all, it is algorithmization and computer processing of information, electrical engineering, etc. Therefore, it is important to have a mathematical apparatus that allows you to transform the graphical presentation of information about objects into algebraic models for their further research using purely mathematical methods. If necessary, it is always possible to return from such an algebraic model to a graphical representation of the object (for example, to a graphical representation of a circuit diagram in electronics). For each of the considered operations on graphs, either a combination of algebraic operations or an easily programmable matrix processing algorithm is proposed, which can be used to represent any graph. Attention is also paid to the differences in such processing depending on the type of graphs involved in the considered operations. Some operations are more convenient to perform with adjacency matrices, and some - with incidence matrices. This article also considers these features of matrix execution of operations on graphs. All the proposed algorithms are illustrated with specific detailed examples. Thus, it is shown that for all operations on graphically presented objects, their matrix interpretation is possible. This result greatly facilitates the possibility of software implementation of work with such graphic objects.

Compositions and decompositions of binary relations

It is well-known that to every binary relation on a non-void set I there can be assigned its incidence matrix, also in the case when I is infinite. We show that a certain kind of multiplication of such incidence matrices corresponds to the composition of the corresponding relations. Using this fact we investigate the solvability of the equation R o X = S for given binary relations R and S on I and derive an algorithm for solving this equation by using the connections between the corresponding incidence matrices. Moreover, we describe how one can obtain the incidence matrix of a product of binary relations from the incidence matrices of its factors.

The Markov complexity of book graphs

Let A be the incidence matrix of a book graph with expandable pages, A(r) its r-th Lawrence lifting and IA(r) the corresponding toric ideal, where r≥3. We compute the minimal systems of generators for the double family of toric ideals IA(r). We prove that toric ideals of book graphs with expandable pages may have arbitrary large Markov complexity, by explicitly computing it.

Steady turnover in a bird community in a periurban landscape in Northern Italy: a look at the change in species richness over time

From November 2017 until February 2022, with a partial interruption during 2020 linked to the COVID 19 pandemic, the bird community was monitored in a 30 hectares periurban plot in north-western Lombardy, in the province of Varese. The study area consists of a mosaic of farmland/ urban habitat (Luino and Germignaga municipalities) with scattered strips of woodland on the east side of Lake Maggiore. The farmland is mainly cultivated ryegrass or maize and permanent grassland. The turnover and phenology of the avifauna was regularly monitored. The year was divided up 4 seasons: winter, spring migration, breeding season and autumn migration. Each season was further divided into 10-day periods, giving a total of 37 ten-day periods over the whole year. For each ten-day period, there was a minimum of 4 surveys, alternating a 500m transect over 30 minutes with a single point count for 30 minutes. A total of 134 species were observed. The trend in species richness follows a sinusoidal curve relating to the migration periods. The area of farmland, while not having any regularly breeding species, supported 65 foraging species, with permanent grassland being more species rich than either maize or ryegrass. The Sorensen Similarity Index, based on incidence matrices, ranged from the lowest value of 0.6480 (during the winter of 2018/19 to spring migration in 2019) to the highest value of 0.8572 (from spring migration 2019 to the breeding period in 2019). Most of the nesting species are synanthropic, occupying the urban areas of this plot, including a colony of northern house martins.

Model-Based Fault Analysis and Diagnosis of PEM Fuel Cell Control System

This paper presents a systematic fault analysis and diagnosis method of a PEM fuel cell control system using a model-based approach. With a model-based approach, it is possible to analyze the causal relationship and effect of probable faults in the system, and to diagnose them under the assumption that the model and the process are similar. With a model-based approach, it is possible to analyze the causal relationship and effect of probable faults in the system and diagnose them under the assumption that the model and the process are similar. In this work, a model-based approach was adopted for fault analysis and diagnosis, and its methods are suggested. A PEM fuel cell is mathematically modelled, analyzed, and verified for the analysis and simulations. Relationships among variables are shown using an incidence matrix and with a Dulmage–Mendelsohn decomposition of the matrix. When it is difficult to detect faults due to a deficient degree of redundancy, a bi-partite graph is used to analyze the effect of faults and to assess the possibility of fault detection through the appropriate redundant sensor placement. Thereafter, residuals are obtained based on analytical redundancies of the system, and a fault signature matrix is subsequently constructed. A fault detection and isolation (FDI) algorithm is developed based on a fault signature matrix that describes the connection between faults and residuals. The simulation results demonstrate the validity and effectiveness of the proposed FDI algorithm for diagnosing faults. With the proposed FDI algorithm, eight faults could be diagnosed by FDI algorithm with given sensors in the system.

PERMANENT DECOMPOSITION ALGORITHM FOR THE COMBINATORIAL OBJECTS GENERATION

Context. The problem of generating vectors consisting of different representatives of a given set of sets is considered. Such problems arise, in particular, in scheduling theory, when scheduling appointments. A special case of this problem is the problem of generating permutations.
 Objective. Problem is considered from the point of view of a permanent approach and a well-known one, based on the concept of lexicographic order.
 Method. In many tasks, it becomes necessary to generate various combinatorial objects: permutations, combinations with and without repetitions, various subsets. In this paper we consider a new approach to the combinatorial objects generation, which is based on the procedure of the permanent decomposition. Permanent is built for the special matrix of incidence. The main idea of this approach is including to the process of the algebraic permanent decomposition by row additional function for the column identifiers writing into corresponding data structures. In this case, the algebraic permanent in not calculated, but we get a specific recursive algorithm for generating a combinatorial object. The computational complexity of this algorithm is analyzed.
 Results. It is investigated a new approach to the generation of complex combinatorial objects, based on the procedure of decomposition of the modified permanent of the incidence matrix by line with memorization of index elements.
 Conclusions. The permanent algorithms of the combinatorial objects generation is investigated. The complexity of our approach in the case of permutation is compared with the lexicographic algorithm and the Johnson-Trotter algorithm.
 The obtained results showed that our algorithm belongs to the same complexity class as the lexicographic algorithm and the Johnson-Trotter method. Numerical results confirmed the effectiveness of our approach.