scholarly journals The linearization problem of a binary quadratic problem and its applications

2021 ◽  
Author(s):  
Hao Hu ◽  
Renata Sotirov
Keyword(s):  
Shortest Path ◽  
Quadratic Function ◽  
Directed Acyclic Graphs ◽  
Complete Characterization ◽  
Shortest Path Problem ◽  
Quadratic Problem ◽  
Lower Bounding ◽  
Linearization Problem ◽  
Binary Quadratic Problem

AbstractWe provide several applications of the linearization problem of a binary quadratic problem. We propose a new lower bounding strategy, called the linearization-based scheme, that is based on a simple certificate for a quadratic function to be non-negative on the feasible set. Each linearization-based bound requires a set of linearizable matrices as an input. We prove that the Generalized Gilmore–Lawler bounding scheme for binary quadratic problems provides linearization-based bounds. Moreover, we show that the bound obtained from the first level reformulation linearization technique is also a type of linearization-based bound, which enables us to provide a comparison among mentioned bounds. However, the strongest linearization-based bound is the one that uses the full characterization of the set of linearizable matrices. We also present a polynomial-time algorithm for the linearization problem of the quadratic shortest path problem on directed acyclic graphs. Our algorithm gives a complete characterization of the set of linearizable matrices for the quadratic shortest path problem.

scholarly journals Mixed-integer optimal control problems with switching costs: a shortest path approach

2020 ◽  
Author(s):  
Felix Bestehorn ◽  
Christoph Hansknecht ◽  
Christian Kirches ◽  
Paul Manns
Keyword(s):  
Optimal Control ◽  
Shortest Path ◽  
Switching Costs ◽  
Optimal Control Problems ◽  
Directed Acyclic Graphs ◽  
Shortest Path Problem ◽  
Mixed Integer ◽  
Programming Approach ◽  
Control Problems ◽  
Decomposition Approach

Abstract We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns out to be difficult in the presence of switching costs or switching constraints as the underlying problem is an Integer Program. We therefore reformulate the rounding problem into a shortest path problem on a parameterized family of directed acyclic graphs (DAGs). Solving the shortest path problem then allows to minimize switching costs and still maintain approximability with respect to the tunable DAG parameter $$\theta $$ θ . We provide a proof of a runtime bound on equidistant rounding grids, where the bound is linear in time discretization granularity and polynomial in $$\theta $$ θ . The efficacy of our approach is demonstrated by a comparison with an integer programming approach on a benchmark problem.

scholarly journals Minimum weight resolving sets of grid graphs

2016 ◽  
Vol 08 (03) ◽  
pp. 1650048
Author(s):  
Patrick Andersen ◽  
Cyriac Grigorious ◽  
Mirka Miller
Keyword(s):  
Shortest Path ◽  
Minimum Weight ◽  
Weighted Graph ◽  
Complete Characterization ◽  
Simple Graph ◽  
Resolving Set ◽  
Maximum Cardinality ◽  
Grid Graphs ◽  
Characterization Of Solutions

For a simple graph [Formula: see text] and for a pair of vertices [Formula: see text], we say that a vertex [Formula: see text] resolves [Formula: see text] and [Formula: see text] if the shortest path from [Formula: see text] to [Formula: see text] is of a different length than the shortest path from [Formula: see text] to [Formula: see text]. A set of vertices [Formula: see text] is a resolving set if for every pair of vertices [Formula: see text] and [Formula: see text] in [Formula: see text], there exists a vertex [Formula: see text] that resolves [Formula: see text] and [Formula: see text]. The minimum weight resolving set problem is to find a resolving set [Formula: see text] for a weighted graph [Formula: see text] such that [Formula: see text] is minimum, where [Formula: see text] is the weight of vertex [Formula: see text]. In this paper, we explore the possible solutions of this problem for grid graphs [Formula: see text] where [Formula: see text]. We give a complete characterization of solutions whose cardinalities are 2 or 3, and show that the maximum cardinality of a solution is [Formula: see text]. We show that the grid has the property that given a landmark set, we only need to investigate whether or not all pairs of vertices that share common neighbors are resolved to determine if the whole graph is resolved. We use this result to provide a characterization of a class of minimals whose cardinalities range from [Formula: see text] to [Formula: see text] and show that the number of such minimals is [Formula: see text].

scholarly journals Path homologies of motifs and temporal network representations

2022 ◽  
Vol 7 (1) ◽  
Author(s):  
Samir Chowdhury ◽  
Steve Huntsman ◽  
Matvey Yutin
Keyword(s):  
Complex Networks ◽  
Directed Acyclic Graphs ◽  
Complete Characterization ◽  
Temporal Network ◽  
Temporal Networks ◽  
Acyclic Graphs ◽  
Bona Fide ◽  
Insight Into ◽  
Theoretical Developments

AbstractPath homology is a powerful method for attaching algebraic invariants to digraphs. While there have been growing theoretical developments on the algebro-topological framework surrounding path homology, bona fide applications to the study of complex networks have remained stagnant. We address this gap by presenting an algorithm for path homology that combines efficient pruning and indexing techniques and using it to topologically analyze a variety of real-world complex temporal networks. A crucial step in our analysis is the complete characterization of path homologies of certain families of small digraphs that appear as subgraphs in these complex networks. These families include all digraphs, directed acyclic graphs, and undirected graphs up to certain numbers of vertices, as well as some specially constructed cases. Using information from this analysis, we identify small digraphs contributing to path homology in dimension two for three temporal networks in an aggregated representation and relate these digraphs to network behavior. We then investigate alternative temporal network representations and identify complementary subgraphs as well as behavior that is preserved across representations. We conclude that path homology provides insight into temporal network structure, and in turn, emergent structures in temporal networks provide us with new subgraphs having interesting path homology.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

scholarly journals Complete characterization of spin chains with two Ising symmetries

2019 ◽  
Vol 125 (1) ◽  
pp. 10008 ◽  
Author(s):  
Bat-el Friedman ◽  
Atanu Rajak ◽  
Emanuele G. Dalla Torre
Keyword(s):  
Complete Characterization ◽  
Spin Chains

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Protein complex formation in methionine chain-elongation and leucine biosynthesis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
Shweta Chhajed ◽  
Tong Zhang ◽  
Joseph M. Collins ◽  
Qiuying Pang ◽  
...  
Keyword(s):  
Protein Complexes ◽  
Complete Characterization ◽  
Bimolecular Fluorescence Complementation ◽  
Chain Elongation ◽  
Substrate Channeling ◽  
Leucine Biosynthesis ◽  
Protein Complex Formation ◽  
Genes Encoding ◽  
Isopropylmalate Dehydrogenase

AbstractDuring the past two decades, glucosinolate (GLS) metabolic pathways have been under extensive studies because of the importance of the specialized metabolites in plant defense against herbivores and pathogens. The studies have led to a nearly complete characterization of biosynthetic genes in the reference plant Arabidopsis thaliana. Before methionine incorporation into the core structure of aliphatic GLS, it undergoes chain-elongation through an iterative three-step process recruited from leucine biosynthesis. Although enzymes catalyzing each step of the reaction have been characterized, the regulatory mode is largely unknown. In this study, using three independent approaches, yeast two-hybrid (Y2H), coimmunoprecipitation (Co-IP) and bimolecular fluorescence complementation (BiFC), we uncovered the presence of protein complexes consisting of isopropylmalate isomerase (IPMI) and isopropylmalate dehydrogenase (IPMDH). In addition, simultaneous decreases in both IPMI and IPMDH activities in a leuc:ipmdh1 double mutants resulted in aggregated changes of GLS profiles compared to either leuc or ipmdh1 single mutants. Although the biological importance of the formation of IPMI and IPMDH protein complexes has not been documented in any organisms, these complexes may represent a new regulatory mechanism of substrate channeling in GLS and/or leucine biosynthesis. Since genes encoding the two enzymes are widely distributed in eukaryotic and prokaryotic genomes, such complexes may have universal significance in the regulation of leucine biosynthesis.

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