Tree decompositions of real-world networks from simulated annealing

Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network. Tree and branch decompositions considered here directly represent network structure as trees for recursive computation of network properties. Unlike coarse-graining approximations in terms of community structure or metapopulations, tree decompositions of sufficiently small width allow for exact results on equilibrium processes. Here we use simulated annealing to find tree decompositions of narrow width for a set of medium-size empirical networks. Rather than optimizing tree decompositions directly, we employ a search space constituted by so-called elimination orders being permutations on the network's node set. For each in a database of empirical networks with up to 1000 edges, we find a tree decomposition of low width.Comment: 11 pages, 2 figures, 1 tabl

Modelling single line train operations

Scheduling of trains on a single line involves using train priorities for the resolution of conflicts. The mathematical programming model described in the first part of this paper schedules trains over a single line track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch and bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single line track require the existence of a set of sidings at which trains can cross and/ or overtake each other. Investment decisions on upgrading the number and location of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. The second part of this paper puts forward a model to determine the optimal position of a set of sidings on a single track rail corridor. The sidings are positioned to minimise the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of non-constant train velocities and non-uniform departure times

Tree decompositions of graphs: Saving memory in dynamic programming

AbstractWe propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique” is based on a tree-like set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60% and 98%

Systems Statistical Engineering – Systems Hierarchical Constraint Propagation

Cotter (ASEM-IAC 2012, 2015, 2016, 2017): (1) identified the gaps in knowledge that statistical engineering needed to address and set forth a working definition of and body of knowledge for statistical engineering; (2) proposed a systemic causal Bayesian hierarchical model that addressed the knowledge gap needed to integrate deterministic mathematical engineering causal models within a stochastic framework; (3) specified the modeling methodology through which statistical engineering models could be developed, diagnosed, and applied to predict systemic mission performance; and (4) proposed revisions to and integration of IDEF0 as the framework for developing hierarchical qualitative systems models. In the last work, Cotter (2017) noted that a necessary dimension of the systems statistical engineering body of knowledge is hierarchical constraint propagation to assure that imposed environmental economic, legal, political, social, and technical constraints are consistently decomposed to subsystems , modules, and components and that modules, and subsystems socio-technical constraints are mapped to systemic mission performance. This paper presents systems theory, constraint propagation theory, and Bayesian constrained regression theory relevant to the problem of systemic hierarchical constraint propagation and sets forth the theoretical basis for their integration into the systems statistical engineering body of knowledge

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

Enhancing network robustness via shielding

We consider shielding critical links to guarantee network connectivity under geographical and general failure models. We develop a mixed integer linear program (MILP) to obtain the minimum cost shielding to guarantee the connectivity of a single SD pair under a general failure model, and exploit geometric properties to decompose the shielding problem under a geographical failure model. We extend our MILP formulation to guarantee the connectivity of the entire network, and use Benders decomposition to significantly reduce the running time by exploiting its partial separable structure. We also apply simulated annealing to solve larger network problems to obtain near-optimal solutions in much shorter time. Finally, we extend the algorithms to guarantee partial network connectivity, and observe significant reduction in shielding cost, especially when the failure region is small. For example, when the failure region radius is 60 miles, we observe as much as 75% reduction in shielding cost by relaxing the connectivity requirement to 95% on a major US infrastructure network