Journal articles: 'Chain graph models'

1

Drton, Mathias. "Discrete chain graph models." Bernoulli 15, no. 3 (August 2009): 736–53. http://dx.doi.org/10.3150/08-bej172.

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Skornyakov, Vladimir, Maria Skornyakova, Antonina Shurygina, and Pavel Skornyakov. "Finite-state discrete-time Markov chain models of gene regulatory networks." F1000Research 3 (September 12, 2014): 220. http://dx.doi.org/10.12688/f1000research.4669.1.

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In this study, Markov chain models of gene regulatory networks (GRN) are developed. These models make it possible to apply the well-known theory and tools of Markov chains to GRN analysis. A new kind of finite interaction graph called a combinatorial net is introduced to represent formally a GRN and its transition graphs constructed from interaction graphs. The system dynamics are defined as a random walk on the transition graph, which is a Markov chain. A novel concurrent updating scheme (evolution rule) is developed to determine transitions in a transition graph. The proposed scheme is based on the firing of a random set of non-steady-state vertices in a combinatorial net. It is demonstrated that this novel scheme represents an advance in asynchronicity modeling. The theorem that combinatorial nets with this updating scheme can asynchronously compute a maximal independent set of graphs is also proved. As proof of concept, a number of simple combinatorial models are presented here: a discrete auto-regression model, a bistableswitch, an Elowitz repressilator, and a self-activation model, and it is shown that these models exhibit well-known properties.

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Ferrándiz, Juan, Enrique F. Castillo, and Pilar Sanmartín. "Temporal aggregation in chain graph models." Journal of Statistical Planning and Inference 133, no. 1 (July 2005): 69–93. http://dx.doi.org/10.1016/j.jspi.2004.03.012.

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Wang, Yuhao, and Arnab Bhattacharyya. "Identifiability of Linear AMP Chain Graph Models." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10080–89. http://dx.doi.org/10.1609/aaai.v36i9.21247.

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We study identifiability of linear Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are equal (or more generally, monotone non-decreasing in topological order). This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.

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Lauritzen, Steffen L., and Thomas S. Richardson. "Chain graph models and their causal interpretations." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64, no. 3 (August 2002): 321–48. http://dx.doi.org/10.1111/1467-9868.00340.

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Vo, Thi Phuong Thuy. "Chain-referral sampling on stochastic block models." ESAIM: Probability and Statistics 24 (2020): 718–38. http://dx.doi.org/10.1051/ps/2020025.

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The discovery of the “hidden population”, whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling (CRS) method, where participants recommend the people they know. This leads to the study of a Markov chain on a random graph where vertices represent individuals and edges connecting any two nodes describe the relationships between corresponding people. We are interested in the study of CRS process on the stochastic block model (SBM), which extends the well-known Erdös-Rényi graphs to populations partitioned into communities. The SBM considered here is characterized by a number of vertices N, a number of communities (blocks) m, proportion of each community π = (π1, …, πm) and a pattern for connection between blocks P = (λkl∕N)(k,l)∈{1,…,m}2. In this paper, we give a precise description of the dynamic of CRS process in discrete time on an SBM. The difficulty lies in handling the heterogeneity of the graph. We prove that when the population’s size is large, the normalized stochastic process of the referral chain behaves like a deterministic curve which is the unique solution of a system of ODEs.

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Knudsen, Michael, and Carsten Wiuf. "A Markov Chain Approach to Randomly Grown Graphs." Journal of Applied Mathematics 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/190836.

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A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree0,1,…,in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.

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KhudaBukhsh, Wasiur R., Arnab Auddy, Yann Disser, and Heinz Koeppl. "Approximate lumpability for Markovian agent-based models using local symmetries." Journal of Applied Probability 56, no. 3 (September 2019): 647–71. http://dx.doi.org/10.1017/jpr.2019.44.

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AbstractWe study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. Recently, Simon, Taylor, and Kiss [40] used the automorphisms of the underlying graph to generate a lumpable partition of the joint state space, ensuring Markovianness of the lumped process for binary dynamics. However, many large random graphs tend to become asymmetric, rendering the automorphism-based lumping approach ineffective as a tool of model reduction. In order to mitigate this problem, we propose a lumping method based on a notion of local symmetry, which compares only local neighbourhoods of vertices. Since local symmetry only ensures approximate lumpability, we quantify the approximation error by means of the Kullback–Leibler divergence rate between the original Markov chain and a lifted Markov chain. We prove the approximation error decreases monotonically. The connections to fibrations of graphs are also discussed.

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Höfler, Michael, Tanja Brückl, Antje Bittner, and Roselind Lieb. "Visualizing Multivariate Dependencies with Association Chain Graphs." Methodology 3, no. 1 (January 2007): 24–34. http://dx.doi.org/10.1027/1614-2241.3.1.24.

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In a recent paper, a new type of graph to visualize the results from graphical models was proposed. Association chain graphs (ACGs) provide a richer visualization than conventional graphs (directed acyclic and recursive regression graphs) if the data can be described with only a small number of parameters. ACGs display not only which associations reach statistical significance, but also the magnitude of associations (confidence intervals for statistical main effects) as the contrast color to the background color of the graph. In this paper, the ACG visualization is extended especially for the case where all variables are binary by illustrating their relative frequencies. This shows the degrees of associations not only on the individual (as expressed by odds ratios or other indexes of association) but also on the community level. We applied the approach to an extensive example of birth and childhood factors for the onset of affective mental disorders using data from the EDSP (Early Developmental Stages of Psychopathology) Study.

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10

Anacleto, Osvaldo, and Catriona Queen. "Dynamic Chain Graph Models for Time Series Network Data." Bayesian Analysis 12, no. 2 (June 2017): 491–509. http://dx.doi.org/10.1214/16-ba1010.

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11

Andersson, Steen A., and Michael D. Perlman. "Characterizing Markov equivalence classes for AMP chain graph models." Annals of Statistics 34, no. 2 (April 2006): 939–72. http://dx.doi.org/10.1214/009053606000000173.

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12

Marchetti, Giovanni M., and Monia Lupparelli. "Chain graph models of multivariate regression type for categorical data." Bernoulli 17, no. 3 (August 2011): 827–44. http://dx.doi.org/10.3150/10-bej300.

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13

Studený, Milan, and Remco R. Bouckaert. "On chain graph models for description of conditional independence structures." Annals of Statistics 26, no. 4 (August 1998): 1434–95. http://dx.doi.org/10.1214/aos/1024691250.

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14

Cerqueira, Andressa, Aurélien Garivier, and Florencia Leonardi. "A note on perfect simulation for Exponential Random Graph Models." ESAIM: Probability and Statistics 24 (2020): 138–47. http://dx.doi.org/10.1051/ps/2019024.

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In this paper, we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling from the past method of Propp and Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the monotonicity of the ERGM for a subset of the parametric space. We also obtain an upper bound on the running time of the algorithm that depends on the mixing time of the Markov chain.

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15

Rezaei, Navid, and Marek Z. Reformat. "Utilizing Language Models to Expand Vision-Based Commonsense Knowledge Graphs." Symmetry 14, no. 8 (August 17, 2022): 1715. http://dx.doi.org/10.3390/sym14081715.

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The introduction and ever-growing size of the transformer deep-learning architecture have had a tremendous impact not only in the field of natural language processing but also in other fields. The transformer-based language models have contributed to a renewed interest in commonsense knowledge due to the abilities of deep learning models. Recent literature has focused on analyzing commonsense embedded within the pre-trained parameters of these models and embedding missing commonsense using knowledge graphs and fine-tuning. We base our current work on the empirically proven language understanding of very large transformer-based language models to expand a limited commonsense knowledge graph, initially generated only on visual data. The few-shot-prompted pre-trained language models can learn the context of an initial knowledge graph with less bias than language models fine-tuned on a large initial corpus. It is also shown that these models can offer new concepts that are added to the vision-based knowledge graph. This two-step approach of vision mining and language model prompts results in the auto-generation of a commonsense knowledge graph well equipped with physical commonsense, which is human commonsense gained by interacting with the physical world. To prompt the language models, we adapted the chain-of-thought method of prompting. To the best of our knowledge, it is a novel contribution to the domain of the generation of commonsense knowledge, which can result in a five-fold cost reduction compared to the state-of-the-art. Another contribution is assigning fuzzy linguistic terms to the generated triples. The process is end to end in the context of knowledge graphs. It means the triples are verbalized to natural language, and after being processed, the results are converted back to triples and added to the commonsense knowledge graph.

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16

Ormonova, E. "Analysis of Assessing the Reliability Quality of the Software Product Based on the Graphs Theory and Markov Chains." Bulletin of Science and Practice 6, no. 4 (April 15, 2020): 12–17. http://dx.doi.org/10.33619/2414-2948/53/01.

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In this paper, we use graph theory and Markov chain methods to determine the quality of a software product based on a mathematical model. Since modern programming, developing a data structure and creating a mathematical model of a software product, we cannot do without graph theory. As an object of research, the PascalABC programming language is used. We have created a mathematical model of a software product using graph theory. The principles of software quality assessment by methods of graph theory, as well as Markov chains, are developed. Models of probabilistic assessment of the quality of computer programs using the Kolmogorov equations, based on graph theory.

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17

Nicolussi, Federica, and Roberto Colombi. "Type II chain graph models for categorical data: A smooth subclass." Bernoulli 23, no. 2 (May 2017): 863–83. http://dx.doi.org/10.3150/15-bej762.

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18

Stefanini, Federico M. "Chain Graph Models to Elicit the Structure of a Bayesian Network." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/749150.

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Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts’ degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features.

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19

Levitz, Michael, Michael D. Perlman, and David Madigan. "Correction: Separation and completeness properties for AMP chain graph Markov models." Annals of Statistics 31, no. 1 (February 2003): 348. http://dx.doi.org/10.1214/aos/1046294468.

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20

Burgarth, Daniel. "Identifying combinatorially symmetric Hidden Markov Models." Electronic Journal of Linear Algebra 34 (February 21, 2018): 393–98. http://dx.doi.org/10.13001/1081-3810.3651.

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A sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models, based on the structure of their transition matrix, is provided. If the observed states of the chain form a zero forcing set of the graph of the Markov model, then it is uniquely identifiable and an explicit reconstruction method is given.

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21

Mukminov, T. F. "The chain of embedded invariant submodels for conic motions." Multiphase Systems 14, no. 4 (2019): 268–73. http://dx.doi.org/10.21662/mfs2019.4.034.

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The equations of continuum mechanics are invariant in relation to the Galilean group generalized by extention. Its 11-dimensional Lie algebra has many subalgebras, which form the optimal system of dissimilar subalgebras. Subalgebras from the optimal system form the graph of embedded subalgebras. There are many chains of subalgebras in the graph. We consider the chain of embedded subalgebras containing operators of space and time translation, the rotation and uniform extension of all independent variables for the models of the continuous medium mechanics. We choose concordant invariants for each subalgebra from the chain. The chain of invariant submodels is constructed in a cylindrical coordinates based on chosen invariants. It is proved that solutions of a submodel constructed on a subalgebra of higher dimension will be part of solutions of submodels constructed on subalgebra of smaller dimensions for the considered chain. Thus, the chain of embedded invariant submodels is constructed by the example of equations of ideal gas dynamics.

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22

La Rocca, Luca, and Alberto Roverato. "Chain graph models: topological sorting of meta-arrows and efficient construction of $${\mathcal{B}}$$ -essential graphs." Statistical Methods and Applications 17, no. 1 (April 3, 2007): 73–83. http://dx.doi.org/10.1007/s10260-007-0050-z.

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23

Karanam, Malleswari, Lanka Krishnanand, Vijaya Kumar Manupati, Katarzyna Antosz, and Jose Machado. "Identification of the Critical Enablers for Perishable Food Supply Chain Using Deterministic Assessment Models." Applied Sciences 12, no. 9 (April 29, 2022): 4503. http://dx.doi.org/10.3390/app12094503.

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Today’s perishable food supply chains must be resilient to handle volatile demands, environmental restrictions, and disruptions in order to meet customers’ requirements. The enablers of the perishable food supply chain have not yet been explored. In this paper, a bibliometric systematic literature review has been conducted to identify the articles related to the perishable food supply chain. Next, with these identified articles, a map is created with bibliographic data using Vosviewer network visualization software, and then the enablers were identified by conducting keyword co-occurrence analysis. Later, a total interpretive structural modeling (TISM) is employed to analyze the interrelationships among enablers and then determine each enabler’s hierarchies, further representing them in a diagraph. Finally, the identified enablers are classified using cross-impact matrix multiplication applied to classification (MICMAC) analysis, and the graph is plotted. The results obtained from the deterministic assessment model provide the critical enablers for the perishable food supply chain. The obtained critical enablers and their hierarchies provide valuable insights for researchers in the context of perishable food supply chain for further study.

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Vasudevan, K., M. Cavers, and A. Ware. "Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs." Nonlinear Processes in Geophysics 22, no. 5 (September 8, 2015): 499–512. http://dx.doi.org/10.5194/npg-22-499-2015.

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Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model with phase lag to the non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behavior of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and, subsequently, point out the role of the Kuramoto model in understanding the evolution of synchronous and asynchronous regions. We surmise that one implication of the emergence of chimera states will lead to investigation of the present and other mathematical models in detail to generate global chimera-state maps similar to global seismicity maps for earthquake forecasting studies.

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Wang, Cong, Fangyue Yu, Zaixu Zhang, and Jian Zhang. "Multiview Graph Learning for Small- and Medium-Sized Enterprises’ Credit Risk Assessment in Supply Chain Finance." Complexity 2021 (February 13, 2021): 1–13. http://dx.doi.org/10.1155/2021/6670873.

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In recent years, supply chain finance (SCF) is exploited to solve the financing difficulties of small- and medium-sized enterprises (SMEs). SME credit risk assessment is a critical part in the SCF system. The diffusion of SME credit risk may cause serious consequences, leading the whole supply chain finance system unstable and insecure. Compared with traditional credit risk assessment models, the supply chain relationship, credit condition of SME, and core enterprises should all be considered to rate SME credit risk in SCF. Traditional methods mix all indicators from different index systems. They cannot give a quantitative result on how these index systems work. Furthermore, traditional credit risk assessment models are heavily dependent on the number of annotated SME data. However, it is implausible to accumulate enough credit risky SMEs in advance. In this paper, we propose an adaptive heterogenous multiview graph learning method to tackle the small sample size problem for SMEs’ credit risk forecasting. Three graphs are constructed by using indicators from supply chain operation, SME financial indicator, and nonfinancial indicator individually. All the graphs are integrated in an adaptive manner, providing a quantitative explanation on how the three parts cooperate. The experimental analysis shows that the proposed method has good performance for determining whether SME is risky or nonrisky in SCF. From the perspective of SCF, SME financing ability is still the main factor to determine the credit risk of SME.

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Xiao, Ya-Qi, Sun-Wei Li, and Zhen-Zhong Hu. "Automatically Generating a MEP Logic Chain from Building Information Models with Identification Rules." Applied Sciences 9, no. 11 (May 29, 2019): 2204. http://dx.doi.org/10.3390/app9112204.

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In mechanical, electrical, and plumbing (MEP) systems, logic chains refer to the upstream and downstream connections between MEP components. Generating the logic chains of MEP systems can improve the efficiency of facility management (FM) activities, such as locating components and retrieving relevant maintenance information for prompt failure detection or for emergency responses. However, due to the amount of equipment and components in commercial MEP systems, manually creating such logic chains is tedious and fallible work. This paper proposes an approach to generate the logic chains of MEP systems using building information models (BIMs) semi-automatically. The approach consists of three steps: (1) the parametric and nonparametric spatial topological analysis within MEP models to generate a connection table, (2) the transformation of MEP systems and custom information requirements to generate the pre-defined and user-defined identification rules, and (3) the logic chain completion of MEP model based on the graph data structure. The approach was applied to a real-world project, which substantiated that the approach was able to generate logic chains of 15 MEP systems with an average accuracy of over 80%.

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27

DRTON, MATHIAS, and MICHAEL EICHLER. "Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property." Scandinavian Journal of Statistics 33, no. 2 (June 2006): 247–57. http://dx.doi.org/10.1111/j.1467-9469.2006.00482.x.

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28

Nicolussi, Federica, and Fulvia Mecatti. "A smooth subclass of graphical models for chain graph: towards measuring gender gaps." Quality & Quantity 50, no. 1 (November 21, 2014): 27–41. http://dx.doi.org/10.1007/s11135-014-0135-3.

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29

Flaccadoro, Diana, Cristiano Cervellera, Giorgio Bosia, and Eva Riccomagno. "Modelling of Fault Detection and Diagnostics for Hybrid Bus Using Chain Graph Models." Quality and Reliability Engineering International 30, no. 7 (July 18, 2014): 975–83. http://dx.doi.org/10.1002/qre.1691.

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30

Vasudevan, K., M. Cavers, and A. Ware. "Earthquake sequencing: Chimera states with Kuramoto model dynamics on directed graphs." Nonlinear Processes in Geophysics Discussions 2, no. 1 (February 20, 2015): 361–98. http://dx.doi.org/10.5194/npgd-2-361-2015.

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Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model, and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress-interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behaviour of weakly-coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly-coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model to the non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behaviour of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and subsequently, point out the role of Kuramoto model in understanding the evolution of synchronous and asynchronous regions.

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31

Beaumont, Olivier, Julien Herrmann, Guillaume Pallez (Aupy), and Alena Shilova. "Optimal memory-aware backpropagation of deep join networks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2166 (January 20, 2020): 20190049. http://dx.doi.org/10.1098/rsta.2019.0049.

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Deep learning training memory needs can prevent the user from considering large models and large batch sizes. In this work, we propose to use techniques from memory-aware scheduling and automatic differentiation (AD) to execute a backpropagation graph with a bounded memory requirement at the cost of extra recomputations. The case of a single homogeneous chain, i.e. the case of a network whose stages are all identical and form a chain, is well understood and optimal solutions have been proposed in the AD literature. The networks encountered in practice in the context of deep learning are much more diverse, both in terms of shape and heterogeneity. In this work, we define the class of backpropagation graphs, and extend those on which one can compute in polynomial time a solution that minimizes the total number of recomputations. In particular, we consider join graphs which correspond to models such as siamese or cross-modal networks. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

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Papadonikolaki, Eleni, Ruben Vrijhoef, and Hans Wamelink. "Supply chain integration with BIM: a graph-based model." Structural Survey 33, no. 3 (July 13, 2015): 257–77. http://dx.doi.org/10.1108/ss-01-2015-0001.

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Purpose – The purpose of this paper is to propose a methodology to integrate the construction Supply Chain (SC) through the application of Building Information Modeling (BIM) and Supply Chain Management (SCM). It features a renovation case as a proof-of-concept. Design/methodology/approach – After analyzing the relevant gaps in the literature, the research followed a modeling approach. The proposed model merged product-, process- and organizational models in a graph-based model to represent and analyze a BIM-based SCM project. Findings – Presently, the information flows of the construction SC are vague. BIM is an aspiring integrator of information flows for construction. The proposed model for SC integration with BIM, offers an approach to identify the project complexities in relation to organizational structures, roles and interactions and integrate the industry. Practical implications – Currently BIM-enabled SCM is not very widely applied in the industry. However, the authors report the increasing interest of most construction stakeholders to engage in the application of the two, after acknowledging the benefits from the individual approaches. Since this combination is quite rare, the research uses a retrospective real-world case study of a SC project with an imaginary application of BIM. Originality/value – Thus far, there is no formal model to represent the interactions of the SC actors along with BIM. The unique combination of a product and a process model, i.e. BIM, with an organizational model aims at integrating the information flows of the SC. The proposed model aims at analyzing and supporting the BIM-enabled SCM in Architecture Engineering and Construction.

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Zhao, Bo, Jianhou Gan, and Hualong Wu. "Redefined Zagreb indices of Some Nano Structures." Applied Mathematics and Nonlinear Sciences 1, no. 1 (June 2, 2016): 291–300. http://dx.doi.org/10.21042/amns.2016.1.00024.

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AbstractIn theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and redefined Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of redefined Zagreb indices for certain important chemical structures like nanotube and nanostar. As supplement, the redefined Zagreb indices of polyomino chain and benzenoid series are manifested.

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Ma, Hao, Juncheng Jia, Xinhao Yang, Weipeng Zhu, and Hong Zhang. "MC-NILM: A Multi-Chain Disaggregation Method for NILM." Energies 14, no. 14 (July 18, 2021): 4331. http://dx.doi.org/10.3390/en14144331.

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Non-intrusive load monitoring (NILM) is an approach that helps residents obtain detailed information about household electricity consumption and has gradually become a research focus in recent years. Most of the existing algorithms on NILM build energy disaggregation models independently for an individual appliance while neglecting the relation among them. For this situation, this article proposes a multi-chain disaggregation method for NILM (MC-NILM). MC-NILM integrates the models generated by existing algorithms and considers the relation among these models to improve the performance of energy disaggregation. Given the high time complexity of searching for the optimal MC-NILM structure, this article proposes two methods to reduce the time complexity, the k-length chain method and the graph-based chain generation method. Finally, we use the Dataport and UK-DALE datasets to evaluate the feasibility, effectiveness, and generality of the MC-NILM.

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Zaourar, Lilia, Yann Kieffer, and Chouki Aktouf. "A Graph-Based Approach to Optimal Scan Chain Stitching Using RTL Design Descriptions." VLSI Design 2012 (December 20, 2012): 1–11. http://dx.doi.org/10.1155/2012/312808.

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The scan chain insertion problem is one of the mandatory logic insertion design tasks. The scanning of designs is a very efficient way of improving their testability. But it does impact size and performance, depending on the stitching ordering of the scan chain. In this paper, we propose a graph-based approach to a stitching algorithm for automatic and optimal scan chain insertion at the RTL. Our method is divided into two main steps. The first one builds graph models for inferring logical proximity information from the design, and then the second one uses classic approximation algorithms for the traveling salesman problem to determine the best scan-stitching ordering. We show how this algorithm allows the decrease of the cost of both scan analysis and implementation, by measuring total wirelength on placed and routed benchmark designs, both academic and industrial.

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Bouvier, Guillaume, Benjamin Bardiaux, Riccardo Pellarin, Chiara Rapisarda, and Michael Nilges. "Building Protein Atomic Models from Cryo-EM Density Maps and Residue Co-Evolution." Biomolecules 12, no. 9 (September 13, 2022): 1290. http://dx.doi.org/10.3390/biom12091290.

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Electron cryo-microscopy (cryo-EM) has emerged as a powerful method by which to obtain three-dimensional (3D) structures of macromolecular complexes at atomic or near-atomic resolution. However, de novo building of atomic models from near-atomic resolution (3–5 Å) cryo-EM density maps is a challenging task, in particular because poorly resolved side-chain densities hamper sequence assignment by automatic procedures at a lower resolution. Furthermore, segmentation of EM density maps into individual subunits remains a difficult problem when the structure of the subunits is not known, or when significant conformational rearrangement occurs between the isolated and associated form of the subunits. To tackle these issues, we have developed a graph-based method to thread most of the C-α trace of the protein backbone into the EM density map. The EM density is described as a weighted graph such that the resulting minimum spanning tree encompasses the high-density regions of the map. A pruning algorithm cleans the tree and finds the most probable positions of the C-α atoms, by using side-chain density when available, as a collection of C-α trace fragments. By complementing experimental EM maps with contact predictions from sequence co-evolutionary information, we demonstrate that this approach can correctly segment EM maps into individual subunits and assign amino acid sequences to backbone traces to generate atomic models.

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Essa, Ehab, and Xianghua Xie. "Deep Collaborative Learning for Randomly Wired Neural Networks." Electronics 10, no. 14 (July 13, 2021): 1669. http://dx.doi.org/10.3390/electronics10141669.

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A deep collaborative learning approach is introduced in which a chain of randomly wired neural networks is trained simultaneously to improve the overall generalization and form a strong ensemble model. The proposed method takes advantage of functional-preserving transfer learning and knowledge distillation to produce an ensemble model. Knowledge distillation is an effective learning scheme for improving the performance of small neural networks by using the knowledge learned by teacher networks. Most of the previous methods learn from one or more teachers but not in a collaborative way. In this paper, we created a chain of randomly wired neural networks based on a random graph algorithm and collaboratively trained the models using functional-preserving transfer learning, so that the small network in the chain could learn from the largest one simultaneously. The training method applies knowledge distillation between randomly wired models, where each model is considered as a teacher to the next model in the chain. The decision of multiple chains of models can be combined to produce a robust ensemble model. The proposed method is evaluated on CIFAR-10, CIFAR-100, and TinyImageNet. The experimental results show that the collaborative training significantly improved the generalization of each model, which allowed for obtaining a small model that can mimic the performance of a large model and produce a more robust ensemble approach.

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Fried, Daniel, Peter Jansen, Gustave Hahn-Powell, Mihai Surdeanu, and Peter Clark. "Higher-order Lexical Semantic Models for Non-factoid Answer Reranking." Transactions of the Association for Computational Linguistics 3 (December 2015): 197–210. http://dx.doi.org/10.1162/tacl_a_00133.

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Lexical semantic models provide robust performance for question answering, but, in general, can only capitalize on direct evidence seen during training. For example, monolingual alignment models acquire term alignment probabilities from semi-structured data such as question-answer pairs; neural network language models learn term embeddings from unstructured text. All this knowledge is then used to estimate the semantic similarity between question and answer candidates. We introduce a higher-order formalism that allows all these lexical semantic models to chain direct evidence to construct indirect associations between question and answer texts, by casting the task as the traversal of graphs that encode direct term associations. Using a corpus of 10,000 questions from Yahoo! Answers, we experimentally demonstrate that higher-order methods are broadly applicable to alignment and language models, across both word and syntactic representations. We show that an important criterion for success is controlling for the semantic drift that accumulates during graph traversal. All in all, the proposed higher-order approach improves five out of the six lexical semantic models investigated, with relative gains of up to +13% over their first-order variants.

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Yin, Fan, and Carter T. Butts. "Highly scalable maximum likelihood and conjugate Bayesian inference for ERGMs on graph sets with equivalent vertices." PLOS ONE 17, no. 8 (August 26, 2022): e0273039. http://dx.doi.org/10.1371/journal.pone.0273039.

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The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme.

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Burton, Robert M., and David C. Plaehn. "One-dimensional Kohonen maps are super-stable with exponential rate." Advances in Applied Probability 31, no. 2 (June 1999): 367–93. http://dx.doi.org/10.1239/aap/1029955140.

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Kohonen self-organizing interval maps are considered. In this model a linear graph is embedded randomly into the unit interval. At each time a point is chosen randomly according to a fixed distribution. The nearest vertex and some of its nearby neighbors are moved closer to the point. These models have been proposed as models of learning in the audio-cortex. The models possess not only the structure of a Markov chain, but also the added structure of a random dynamical system. This structure is used to show that for a large class of these models, in a strong way, the initial conditions are unimportant and only the dynamics govern the future. A contractive condition is proven in spite of the fact that the maps are not continuous. This, in turn, shows that the Markov chain is uniformly ergodic.

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Burton, Robert M., and David C. Plaehn. "One-dimensional Kohonen maps are super-stable with exponential rate." Advances in Applied Probability 31, no. 02 (June 1999): 367–93. http://dx.doi.org/10.1017/s0001867800009162.

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Kohonen self-organizing interval maps are considered. In this model a linear graph is embedded randomly into the unit interval. At each time a point is chosen randomly according to a fixed distribution. The nearest vertex and some of its nearby neighbors are moved closer to the point. These models have been proposed as models of learning in the audio-cortex. The models possess not only the structure of a Markov chain, but also the added structure of a random dynamical system. This structure is used to show that for a large class of these models, in a strong way, the initial conditions are unimportant and only the dynamics govern the future. A contractive condition is proven in spite of the fact that the maps are not continuous. This, in turn, shows that the Markov chain is uniformly ergodic.

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Hong, Weiwei, Jinxi Chen, Bingliang Ye, and Rongjiang Cui. "Innovative design method for planar mechanism configuration based on component similarity discrimination." Mechanical Sciences 13, no. 1 (April 13, 2022): 353–59. http://dx.doi.org/10.5194/ms-13-353-2022.

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Abstract. Obtaining new models of mechanical equipment to conduct mechanical innovative design through kinematic chain configuration synthesis is an effective method. However, in practice, due to the existence of similar components, existing innovative design methods easily produce redundant design schemes, which require extensive isomorphic discrimination operations, and the design process is complex. In view of existing problems, this study analyzes a method for discriminating between similar components of mechanisms from the perspective of graph theory and then applies it to the specialization of topological graphs to solve the problem of redundant design schemes. Finally, using the innovation of a drilling rig drilling arm mechanism as an example, 52 feasible schemes without redundancy are obtained. This paper provides a reference for the innovation of the configuration of planar mechanisms without design redundancy.

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Javidian, Mohammad Ali, Marco Valtorta, and Pooyan Jamshidi. "AMP Chain Graphs: Minimal Separators and Structure Learning Algorithms." Journal of Artificial Intelligence Research 69 (October 7, 2020): 419–70. http://dx.doi.org/10.1613/jair.1.12101.

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This paper deals with chain graphs (CGs) under the Andersson–Madigan–Perlman (AMP) interpretation. We address the problem of finding a minimal separator in an AMP CG, namely, finding a set Z of nodes that separates a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. We propose several modifications of the PC-like algorithm that remove part or all of this order-dependence. We also extend the decomposition-based approach for learning Bayesian networks (BNs) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified versions of) PC-like algorithm. The LCD-AMP algorithm usually outperforms the PC-like algorithm, and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stabler when the sample size is reasonably large and the underlying graph is sparse

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Schmidt, A., F. Rottensteiner, U. Soergel, and C. Heipke. "A GRAPH BASED MODEL FOR THE DETECTION OF TIDAL CHANNELS USING MARKED POINT PROCESSES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3/W3 (August 19, 2015): 115–21. http://dx.doi.org/10.5194/isprsarchives-xl-3-w3-115-2015.

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In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach.

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Verho, Tuukka, and Jukka Vaari. "Analytical and Numerical Modeling of Degradation and Pyrolysis of Polyethylene: Measuring Aging with Thermogravimetry." Polymers 14, no. 13 (July 1, 2022): 2709. http://dx.doi.org/10.3390/polym14132709.

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Aging reactions due to heat and radiation cause chain scissions and cross-linking in cross-linked polyethylene (XLPE). We have developed theoretical and numerical graph models to study the evolution of the gel fraction and network properties during aging as well as the mass loss during thermogravimetric analysis (TGA). Our analytical and kinetic Monte Carlo (KMC) based models that combine degradation reactions and a simple vaporization model can quantitatively predict TGA curves for aged XLPE. Fitting the model to experimental TGA data yields the number of scission reactions, showing that thermogravimetry combined with our models can present a nondestructive aging characterization tool for lifetime prediction.

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Toba, Ange-Lionel, Rajiv Paudel, Yingqian Lin, Rohit V. Mendadhala, and Damon S. Hartley. "Integrated Land Suitability Assessment for Depots Siting in a Sustainable Biomass Supply Chain." Sensors 23, no. 5 (February 22, 2023): 2421. http://dx.doi.org/10.3390/s23052421.

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A sustainable biomass supply chain would require not only an effective and fluid transportation system with a reduced carbon footprint and costs, but also good soil characteristics ensuring durable biomass feedstock presence. Unlike existing approaches that fail to account for ecological factors, this work integrates ecological as well as economic factors for developing sustainable supply chain development. For feedstock to be sustainably supplied, it necessitates adequate environmental conditions, which need to be captured in supply chain analysis. Using geospatial data and heuristics, we present an integrated framework that models biomass production suitability, capturing the economic aspect via transportation network analysis and the environmental aspect via ecological indicators. Production suitability is estimated using scores, considering both ecological factors and road transportation networks. These factors include land cover/crop rotation, slope, soil properties (productivity, soil texture, and erodibility factor) and water availability. This scoring determines the spatial distribution of depots with priority to fields scoring the highest. Two methods for depot selection are presented using graph theory and a clustering algorithm to benefit from contextualized insights from both and potentially gain a more comprehensive understanding of biomass supply chain designs. Graph theory, via the clustering coefficient, helps determine dense areas in the network and indicate the most appropriate location for a depot. Clustering algorithm, via K-means, helps form clusters and determine the depot location at the center of these clusters. An application of this innovative concept is performed on a case study in the US South Atlantic, in the Piedmont region, determining distance traveled and depot locations, with implications on supply chain design. The findings from this study show that a more decentralized depot-based supply chain design with 3depots, obtained using the graph theory method, can be more economical and environmentally friendly compared to a design obtained from the clustering algorithm method with 2 depots. In the former, the distance from fields to depots totals 801,031,476 miles, while in the latter, it adds up to 1,037,606,072 miles, which represents about 30% more distance covered for feedstock transportation.

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Chong, Siang Yew, Peter Tiňo, Jun He, and Xin Yao. "A New Framework for Analysis of Coevolutionary Systems—Directed Graph Representation and Random Walks." Evolutionary Computation 27, no. 2 (June 2019): 195–228. http://dx.doi.org/10.1162/evco_a_00218.

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Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains—random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

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Maguire, Jack B., Daniele Grattarola, Vikram Khipple Mulligan, Eugene Klyshko, and Hans Melo. "XENet: Using a new graph convolution to accelerate the timeline for protein design on quantum computers." PLOS Computational Biology 17, no. 9 (September 27, 2021): e1009037. http://dx.doi.org/10.1371/journal.pcbi.1009037.

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Graph representations are traditionally used to represent protein structures in sequence design protocols in which the protein backbone conformation is known. This infrequently extends to machine learning projects: existing graph convolution algorithms have shortcomings when representing protein environments. One reason for this is the lack of emphasis on edge attributes during massage-passing operations. Another reason is the traditionally shallow nature of graph neural network architectures. Here we introduce an improved message-passing operation that is better equipped to model local kinematics problems such as protein design. Our approach, XENet, pays special attention to both incoming and outgoing edge attributes. We compare XENet against existing graph convolutions in an attempt to decrease rotamer sample counts in Rosetta’s rotamer substitution protocol, used for protein side-chain optimization and sequence design. This use case is motivating because it both reduces the size of the search space for classical side-chain optimization algorithms, and allows larger protein design problems to be solved with quantum algorithms on near-term quantum computers with limited qubit counts. XENet outperformed competing models while also displaying a greater tolerance for deeper architectures. We found that XENet was able to decrease rotamer counts by 40% without loss in quality. This decreased the memory consumption for classical pre-computation of rotamer energies in our use case by more than a factor of 3, the qubit consumption for an existing sequence design quantum algorithm by 40%, and the size of the solution space by a factor of 165. Additionally, XENet displayed an ability to handle deeper architectures than competing convolutions.

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Kovalchuk, Alexander, and F. Akhmetova. "Denavit-Hartenberg Coordinate System for Robots with Tree-like Kinematic Structure." IAES International Journal of Robotics and Automation (IJRA) 5, no. 4 (December 1, 2016): 244. http://dx.doi.org/10.11591/ijra.v5i4.pp244-254.

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<p class="MDPI17abstract"><span lang="EN-US">The paper presents a modified Denavit-Hartenberg coordinate system resulted from joint application of graph theory and the Denavit-Hartenberg coordinate system, which was developed to describe the kinematics of robot actuators with a linear open kinematic chain. It allows forming mathematical models of actuating mechanisms for the robots with tree-like kinematic structures. The work introduces the concept of primary and auxiliary coordinate systems. It considers an example of making the links’ reachability matrix and reachability graph for the tree-like actuating mechanism of a robotic mannequin. The use efficiency of the proposed modified Denavit-Hartenberg coordinate system is illustrated by the examples giving the mathematical description of the kinematics and dynamics of specific robots’ tree-like actuating mechanisms discussed in the previously published papers. It is shown that the proposed coordinate system can also be successfully applied to describe the actuating mechanisms of robots with a linear open kinematic chain, which is a particular case of the tree-like kinematic structure. The absence of branching joints in it does not require introducing auxiliary coordinate systems and the parameters f(i) and ns(i) are necessary only for the formal notation of equations, which have similar forms for the tree-like and linear chains. In this case, the modified and traditional coordinate systems coincide.</span></p>

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Neustroev, S. S., V. I. Serdyukov, N. A. Serdyukova, and S. I. Shishkina. "Mathematical Modeling-based Analysis from the Great Patriotic War Events." Mathematics and Mathematical Modeling, no. 3 (August 25, 2019): 25–35. http://dx.doi.org/10.24108/mathm.0319.0000189.

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When fighting against terrorism in modern armed conflicts, combat vehicles, including tanks, are widely used. To minimise own losses of vehicles and personnel for overthrowing enemy is a relevant task. To solve it, the paper considers certain events in the history of the Great Patriotic War, which are associated with battle of tanks that spring an ambush. A mathematical model of the battle is built. The state graph of the system is given. Using this graph, a probability of tank kills and a ratio of mathematical expectations of losses have been calculated. This mathematical model generalizes the models, previously published in this journal, based on the Markov chain apparatus. The paper gives an example of calculations for this model in the particular case in which experimental data are used as a basis. The ratios of mathematical expectations of losses of the warring parties are obtained. Further, we consider the mathematical models, in which it is assumed that probabilities for tank crews to provide operations of targets detection in firing are known. With technology development and its mathematical support it becomes increasingly more real. The formulas to obtain the probability of tank kills are given according to the graph of states using the known probabilities of transition from one state to another. In each of the three mathematical models under consideration there is a graph of the system state, which allows calculation of the tank kills probability. We have analysed the models to prove a significant dependence of the loss ratio of the warring parties on the number of firing positions used by the tank in ambush in case re-siting is unnoticeable for the enemy. The authors-considered models that use the examples of historical events confirm that the tactics of organising and conducting ambushes in tank battles can be successfully used nowadays, when the technology intensiveness of the opposing forces significantly grows. The obtained results can be applied to organise and conduct tank ambushes in modern armed conflicts and fight against terrorist army.

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Journal articles on the topic 'Chain graph models'

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