Multigraph Models Research Articles

Research on Traffic Flow Forecasting Based on Dynamic Spatial-Temporal Transformer

Accurate traffic flow forecasting is crucial for urban traffic control and route planning. Aiming at the difficulty in capturing dynamic spatio-temporal complexity of traffic flow, a dynamic spatio-temporal transformer (DST-Trans) model capable of modeling dynamic correlation of traffic flow is proposed, which consists of gated temporal convolutional network (GTCN), graph convolutional network (GCN), and spatio-temporal transformer (ST-TF). GTCN and GCN are utilized to capture the temporal and spatial characteristics of traffic flow, respectively. ST-TF includes a temporal transformer using temporal gated convolution and temporal multi-head self-attention to capture short-long term temporal features, and spatial transformer using spatial gated graph convolution and spatial multi-head self-attention to capture local-global dynamic spatial features. In addition, to take full advantage of the dynamic and static associations of road networks, multi-graph models of road relationship graph, similarity graph, and adaptive dynamic graph with SGGC are constructed. Experimental results show that the DST-Trans model in this paper shows good prediction performance in short-term (15 min), medium-term (30 min), and long-term (60 min) prediction, outperforming existing state-of-the-art models by up to approximately 7%.

Математические и графовые модели специализированных мультиагентных систем с распределенным решением прикладных задач

The concept of a specialized multi-agent system (SMAS) as a system designed for a distributed solution of either one applied problem or a highly limited range of applied problems is considered. Such problems frequently require a large number of homogeneous operations, which can lead to a significant increase in the size of the system and, as a result, to inefficient control and a drop in performance. Therefore, it is advisable to divide a large-sized open SMAS into classes of agents and find relationships between them. This corresponds to dividing the applied task T into subtasks and determining relations between these subtasks. Such a path entails a two-level distributed control over SMAS agents. At the first and second levels, respectively, the relations of agents within classes and between classes of agents are studied. This paper proposes a multi-model approach to constructing, modeling, and analyzing SMAS. The properties of the agent and its mathematical model, described by a 5-digit set, as well as the mathematical model of the class of agents, described by a 12-digit set, which includes such components as the collective knowledge base of agents, the collective communication environment, mental, social, and other components, are discussed. Relations between classes of agents are reflected in a mathematical model of open SMAS. If a partition of a problem T is represented by an undirected acyclic graph GR′ whose terminal vertices have degree one and whose interior vertices have degree two, then GR′ is defined as a simple tree. In the case when any class of agents is a complete graph К then the Cartesian product CP′ = GR′ × Kn, according to the proved theorem, is a graph model of an open SMAS, consisting of the components К and connectives between them. According to the corollary of this theorem, it is possible to pass from CP′ to the multigraph model MYL′ = (MV′, ME′) of the system, if the components К are associated with the vertices of this model mv′ com  MV′, and the connectives are associated with its edges me′ con1  ME′. Moreover, the number of edges between any two vertices MYL′ is equal to n. The analysis of multigraph models of open SMAS of large sizes will significantly reduce the complexity of their study at the structural level.

Goodness of fit tests for random multigraph models

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic -distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted -distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure.

Multiplexity analysis of networks using multigraph representations

Multivariate networks comprising several compositional and structural variables can be represented as multigraphs by various forms of aggregations based on vertex attributes. We propose a framework to perform exploratory and confirmatory multiplexity analysis of aggregated multigraphs in order to find relevant associations between vertex and edge attributes. The exploration is performed by comparing frequencies of the different edges within and between aggregated vertex categories, while the confirmatory analysis is performed using derived complexity or multiplexity statistics under different random multigraph models. These statistics are defined by the distribution of edge multiplicities and provide information on the covariation and dependencies of different edges given vertex attributes. The presented approach highlights the need to further analyse and model structural dependencies with respect to edge entrainment. We illustrate the approach by applying it on a well known multivariate network dataset which has previously been analysed in the context of multiplexity.

Gauges, loops, and polynomials for partition functions of graphical models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is #P-hard that is of an exponential complexity with respect to the number of variables. In this manuscript, aimed at approximating the partition function, we consider multi-graph models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge function technique from Chertkov and Chernyak (2006 Phys. Rev. E 73 065102; 2006 J. Stat. Mech. 2006 P06009) with the technique developed in Anari and Oveis Gharan 2017 arXiv:1702.02937; Gurvits 2011 arXiv:1106.2844; Straszak and Vishnoi 2017 55th Annual Allerton Conf. on Communication, Control, and Computing, based on the recent progress in the field of real stable polynomials. We show that the Gauge function, representing a single-out term in a finite sum expression for the partition function which achieves extremum at the so-called belief-propagation gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, Gauge function can be used to recover the partition function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists of the application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in multi-graph models on decreasing in size (number of edges) graphs with the same partition function as in the original multi-graph model. Even though the complexity of computing factors in the sequence of the derived multi-graph models and respective Gauge functions grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the partition function.

Using the scenario approach in anti-corruption management processes (on the example of the construction industry)

This study discusses the methodological and applied problems of increasing the effectiveness of the anti-corruption management process. An analysis of the essence and forms of corruption, as well as their negative impacts on the socioeconomic development of the society is offered.
 To increase the effectiveness of anti-corruption problem-solving and assess the decision-making process pertaining to management, a scenario analysis is proposed.
 The analysis of basic multigraph models of anti-corruption management focuses on the construction industry, using functional symbolic graphs.
 According to the results, it is more effective to look more broadly at the criminological problem of combating corruption by linking its solution to developments in the fields of economics, sociology, and psychology.
 The current publication is considered a new approach to the development of specific measures to counter this type of crime.

Closure coefficients in scale-free complex networks

Abstract The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity is another method to measure triadic closure. This statistic measures clustering from the head node of a triangle (instead of from the centre node, as in the often studied clustering coefficient). We perform a first exploratory analysis of the behaviour of the local closure coefficient in two random graph models that create simple networks with power-law degrees: the hidden-variable model and the hyperbolic random graph. We show that the closure coefficient behaves significantly different in these simple random graph models than in the previously studied multigraph models. We also relate the closure coefficient of high-degree vertices to the clustering coefficient and the average nearest neighbour degree.

Scenario Analysis in Control of Complex Geopolitical Information Confrontation

The paper considers methodological and applied problems of increasing the efficiency of information control processes in the context of globalization. The tasks of organizing effective counteraction to information aggression have been set and solved. The results of the scenario analysis study of the developed multigraph models for controlling of information threats counteraction are provided.

Analyzing local and global properties of multigraphs

ABSTRACTThe local structure of undirected multigraphs under two random multigraph models is analyzed and compared. The first model generates multigraphs by randomly coupling pairs of stubs according to a fixed degree sequence so that edge assignments to vertex pair sites are dependent. The second model is a simplification that ignores the dependency between the edge assignments. It is investigated when this ignorance is justified so that the simplified model can be used as an approximation, thus facilitating the structural analysis of network data with multiple relations and loops. The comparison is based on the local properties of multigraphs given by marginal distribution of edge multiplicities and some local properties that are aggregations of global properties.

Multigraph Models of Gas-transport Objects States and Identification Method with Intelligent Processing of Information

This article presents a method for reducing a dimension of the identification problem of gas-transport objects technical condition. Within this method there were created special types of multigraph models with interval-valued states of geometric characteristic of metal shell damages. Depending on gas-transport objects operation time, the behavior of proposed models has been examined and operating performance with due account for states identification has been determined, also the possibility of reducing the scope of diagnostics and repair works was shown.

Classifying multigraph models of secondary RNA structure using graph-theoretic descriptors.

The prediction of secondary RNA folds from primary sequences continues to be an important area of research given the significance of RNA molecules in biological processes such as gene regulation. To facilitate this effort, graph models of secondary structure have been developed to quantify and thereby characterize the topological properties of the secondary folds. In this work we utilize a multigraph representation of a secondary RNA structure to examine the ability of the existing graph-theoretic descriptors to classify all possible topologies as either RNA-like or not RNA-like. We use more than one hundred descriptors and several different machine learning approaches, including nearest neighbor algorithms, one-class classifiers, and several clustering techniques. We predict that many more topologies will be identified as those representing RNA secondary structures than currently predicted in the RAG (RNA-As-Graphs) database. The results also suggest which descriptors and which algorithms are more informative in classifying and exploring secondary RNA structures.

Multigraph models for causal quantum gravity and scale dependent spectral dimension

We study random walks on ensembles of a specific class of random multigraphs which provide an ‘effective graph ensemble’ for the causal dynamical triangulation (CDT) model of quantum gravity. In particular, we investigate the spectral dimension of the multigraph ensemble for recurrent as well as transient walks. We investigate the circumstances in which the spectral dimension and Hausdorff dimension are equal and show that this occurs when ρ, the exponent for anomalous behaviour of the resistance to infinity, is zero. The concept of scale dependent spectral dimension in these models is introduced. We apply this notion to a multigraph ensemble with a measure induced by a size biased critical Galton–Watson process which has a scale dependent spectral dimension of two at large scales and one at small scales. We conclude by discussing a specific model related to four dimensional CDT which has a spectral dimension of four at large scales and two at small scales.

Functional annotation of regulatory pathways

Standardized annotations of biomolecules in interaction networks (e.g. Gene Ontology) provide comprehensive understanding of the function of individual molecules. Extending such annotations to pathways is a critical component of functional characterization of cellular signaling at the systems level. We propose a framework for projecting gene regulatory networks onto the space of functional attributes using multigraph models, with the objective of deriving statistically significant pathway annotations. We first demonstrate that annotations of pairwise interactions do not generalize to indirect relationships between processes. Motivated by this result, we formalize the problem of identifying statistically overrepresented pathways of functional attributes. We establish the hardness of this problem by demonstrating the non-monotonicity of common statistical significance measures. We propose a statistical model that emphasizes the modularity of a pathway, evaluating its significance based on the coupling of its building blocks. We complement the statistical model by an efficient algorithm and software, Narada, for computing significant pathways in large regulatory networks. Comprehensive results from our methods applied to the Escherichia coli transcription network demonstrate that our approach is effective in identifying known, as well as novel biological pathway annotations. Narada is implemented in Java and is available at http://www.cs.purdue.edu/homes/jpandey/narada/.

An expert system for coherent assessment of probabilities in multigraph models

In this paper, we present a method that allows a coherent assessment of probabilistic Bayesian networks over sets of nodes or variables that share a common subset. We motivate and illustrate the models with a diseases-symptoms knowledge base defined by multiple Bayesian networks. Since the parameter values for the joint probability distribution of diseases and symptoms must satisfy some compatibility conditions, the probability assessment becomes complicated and can be monitored by an expert system, in order to maintain coherence in the knowledge base. The bases of this expert system are presented. Once the human expert selects one parameter in the model to be assessed, the expert system calculates and provides the human expert with a range of feasible values of the parameter. Any value of the parameter within this range is coherent with the probability axioms. Then, the human expert can specify either a single value or an interval for that parameter in the feasible range. Accordingly, the expert system then updates the feasible ranges for all other parameters. The process can be repeated until all the parameters have been specified. At the end, the expert system gives a final set of values or intervals for all parameters. We apply the proposed system to the dependent-symptoms and the independent-symptoms probabilistic models. We give two numerical examples to illustrate the method. © 1999 John Wiley & Sons, Inc. Networks 33: 193–206, 1999

Vulnerability of scheduled networks and a generalization of Menger's Theorem

An edge-scheduled network N is a multigraph G = (V, E), where each edge e ϵ E has been assigned two real weights: a start time α(e) and a finish time β(e). Such a multigraph models a communication or transportation network. A multiedge joining vertices u and v represents a direct communication (transportation) link between u and v, and the edges of the multiedge represent potential communications (transportations) between u and v over a fixed period of time. For a, b ϵ V, and k a nonnegative integer, we say that N is k-failure ab-invulnerable for the time period [0, t] if information can be relayed from a to b within that time period, even if up to k edges are deleted, i.e., “fail.” The k-failure ab-vulnerability threshold νab(k) is the earliest time t such that N is k-failure ab-invulnerable for the time period [0, t] [where νab(k) = ∞ if no such t exists]. Let κ denote the smallest k such that νab(k) = ∞. In this paper, we present an O(κ|E|) algorithm for computing νab(i), i = 0, …, κ −1. The latter algorithm constructs a set of κ pairwise edge-disjoint schedule-conforming paths P0, …, Pκ −1 such that the finish time of Pi is νab(i), i = 0, 1, …, κ −1. (A path P = ae1u1e2 ··· Upp−1epb is schedule-conforming if the finish time of edge ei is no greater than the start time of the next edge ei + 1.) The existence of such paths when α(e) = β(e) = 0, for all e ϵ E, implies Menger's Theorem. In this paper, we also show that the obvious analogs of these results for either multiedge deletions or vertex deletions do not hold. In fact, we show that the problem of finding k schedule-conforming paths such that no two paths pass through the same vertex (multiedge) is NP-complete, even for k = 2. © 1996 John Wiley & Sons, Inc.