scholarly journals Quasi-completeness of the class of problems on the "weight-minimax edge"

2018 ◽  
Author(s):  
V. A. Perepelitsya ◽  
E. V. Tereschenko ◽  
A. E. Ryabenko
Keyword(s):  
General Structure ◽  
Admissible Solution ◽  
Pareto Set ◽  
Polynomial Algorithms ◽  
Constant Number ◽  
Class A ◽  
Complete Problems ◽  
Successful Solution ◽  
Complete Set ◽  
Feasible Solutions

The tasks of multi-criteria optimization in the general formulation do not have a trivial solution, which gives rise to a multitude of approaches in determining the most “successful” solution from a certain set of solutions that satisfy the problem conditions. One of the ways of formal defining of the possible alternative solution set is to isolate the Pareto set, i.e. the set of unimprovable alternatives. The previously developed approach was applied for studying some classes of multi-criteria problems, the objective functions of which have certain properties, and its productivity was confirmed. The concept of complete problems was introduced, for which the equality of the sets of feasible solutions, the Pareto and the full set of alternatives was fulfilled. In previous works, the authors introduced the concept of quasi-completeness. In the article the class of two-criterion problems, for which the admissible solution for the first criterion has a constant number of edges, and objective function contains the criterion of weight and the criterion of the minimax edge, is distinguished. The problem on the graph of the general structure and the problem on the bichromatic graph, for which the feasible solutions have a constant number of edges, were selected as representatives of this class. A method for studying the properties and estimating the powers of an admissible set of solutions, a Pareto set and a complete set of alternatives for the problems of the selected class, has been formulated. A theorem on the quasi-completeness for the selected class problems is proved. There were obtained estimates for two representatives of this class: “about a spanning tree and a minimax edge”, “about a perfect matching on a bichromatic graph and a minimax edge”. Polynomial algorithms for solving the problems under study are proposed. Estimates of the computational complexity of these algorithms are given

scholarly journals Vibration-based damage detection with uncertainty quantification by structural identification using nonlinear constraint satisfaction with interval arithmetic

2018 ◽  
Vol 18 (5-6) ◽  
pp. 1569-1589 ◽  
Author(s):  
Timothy Kernicky ◽  
Matthew Whelan ◽  
Ehab Al-Shaer
Keyword(s):  
Constraint Satisfaction ◽  
Interval Arithmetic ◽  
Model Updating ◽  
Structural Identification ◽  
Inverse Eigenvalue Problem ◽  
Degree Of Freedom ◽  
Nonlinear Constraint ◽  
Complete Set ◽  
Feasible Solutions ◽  
Interval Hull

Structural identification has received increased attention over recent years for performance-based structural assessment and health monitoring. Recently, an approach for formulating the finite element model updating problem as a constraint satisfaction problem has been developed. In contrast to widely used probabilistic model updating through Bayesian inference methods, the technique naturally accounts for measurement and modeling errors through the use of interval arithmetic to determine the set of all feasible solutions to the partially described and incompletely measured inverse eigenvalue problem. This article presents extensions of the constraint satisfaction approach permitting the application to larger multiple degree-of-freedom system models. To accommodate for the drastic increase in the dimensionality of the inverse problem, the extended methodology replaces computation of the complete set of solutions with an approach that contracts the initial search space to the interval hull, which encompasses the complete set of feasible solutions with a single interval vector solution. The capabilities are demonstrated using vibration data acquired through hybrid simulation of a 45-degree-of-freedom planar truss, where a two-bar specimen with bolted connections representing a single member of the truss serves as the experimental substructure. Structural identification is performed using data acquired with the undamaged experimental member as well as over a number of damage scenarios with progressively increased severity developed by exceeding a limit-state capacity of the member. Interval hull solutions obtained through application of the nonlinear constraint satisfaction methodology demonstrate the capability to correctly identify and quantify the extent of the damage in the truss while incorporating measurement uncertainties in the parameter identification.

scholarly journals Phosphonate monoester inhibitors of class A β-lactamases

1991 ◽  
Vol 275 (3) ◽  
pp. 793-795 ◽  
Author(s):  
J Rahil ◽  
R F Pratt
Keyword(s):  
Enzyme Inhibition ◽  
Mechanism Of Action ◽  
Active Site ◽  
General Structure ◽  
Beta Lactamase ◽  
Beta Lactamases ◽  
Inhibitory Ability ◽  
Class A ◽  
Structure Formula ◽  
Slow Turnover

Phosphonate monoesters with the general structure: [formula: see text] are inhibitors of representative class A and class C beta-lactamases. This result extends the range of this type of inhibitor to the class A enzymes. Compounds where X is an electron-withdrawing substituent are better inhibitors than the unsubstituted analogue (X = H), and enzyme inhibition is concerted with stoichiometric release of the substituted phenol. Slow turnover of the phosphonates also occurs. These observations support the proposition that the mechanism of action of these inhibitors involves phosphorylation of the beta-lactamase active site. The inhibitory ability of these phosphonates suggests that the beta-lactamase active site is very effective at stabilizing negatively charged transition states. One of the compounds described also inactivated the Streptomyces R61 D-alanyl-D-alanine carboxypeptidase/transpeptidase.

Actuator fault-tolerance evaluation of linear constrained model predictive control using zonotope-based set computations

2007 ◽  
Vol 221 (6) ◽  
pp. 915-926 ◽  
Author(s):  
C Ocampo-Martinez ◽  
P Guerra ◽  
V Puig ◽  
J Quevedo
Keyword(s):  
Fault Tolerance ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Admissible Solution ◽  
Control Law ◽  
Actuator Fault ◽  
Control Objective ◽  
Constrained Model ◽  
Constrained Model Predictive Control ◽  
Feasible Solutions

This paper presents a computational procedure to evaluate the fault tolerance of a linear-constrained model predictive control (LCMPC) scheme for a given actuator fault configuration (AFC). Faults in actuators cause changes in the constraints related to control signals (inputs), which in turn modify the set of MPC feasible solutions. This fact may result in an empty set of admissible solutions for a given control objective. Therefore, the admissibility of the control law facing actuator faults can be determined by knowing the set of feasible solutions. One of the aims of this paper is to provide methods to compute this set and to evaluate the admissibility of the control law for a given AFC, once the control objective and the admissibility criteria have been established. In particular, the admissible solution set for the predictive control problem, including the effect of faults (either through reconfiguration or accommodation), is determined using an algorithm that is implemented using set computations based on zonotopes. Finally, the proposed method is tested on a real application consisting of a part of the Barcelona sewer network.

scholarly journals Conformal gravity and “gravitational bubbles”

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641004 ◽  
Author(s):  
V. A. Berezin ◽  
V. I. Dokuchaev ◽  
Yu. N. Eroshenko
Keyword(s):  
General Structure ◽  
Momentum Tensor ◽  
Curvature Scalar ◽  
Conformal Gravity ◽  
Curved Space ◽  
Material Sources ◽  
Complete Set ◽  
The One ◽  
Vacuum Solutions ◽  
The Universe

We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson–Walker metrics. We called one of them the “gravitational bubbles”, which is compact and with zero Weyl tensor. These “gravitational bubbles” are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from “nothing”. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We describe the general structure of the energy-momentum tensor in the spherical conformal gravity and construct the vectorial equation that reveals clearly some features of non-vacuum solutions.

Complexity, computational

2018 ◽  
Author(s):  
Alasdair Urquhart
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Propositional Logic ◽  
Common Type ◽  
Combinatorial Games ◽  
Np Completeness ◽  
Complete Problems ◽  
Np Complete ◽  
Feasible Solutions ◽  
Np Problems

The theory of computational complexity is concerned with estimating the resources a computer needs to solve a given problem. The basic resources are time (number of steps executed) and space (amount of memory used). There are problems in logic, algebra and combinatorial games that are solvable in principle by a computer, but computationally intractable because the resources required by relatively small instances are practically infeasible. The theory of NP-completeness concerns a common type of problem in which a solution is easy to check but may be hard to find. Such problems belong to the class NP; the hardest ones of this type are the NP-complete problems. The problem of determining whether a formula of propositional logic is satisfiable or not is NP-complete. The class of problems with feasible solutions is commonly identified with the class P of problems solvable in polynomial time. Assuming this identification, the conjecture that some NP problems require infeasibly long times for their solution is equivalent to the conjecture that P≠NP. Although the conjecture remains open, it is widely believed that NP-complete problems are computationally intractable.

Important Compounds in the Cocaine Class: A Synthesis Overview

1991 ◽  
Author(s):  
F.I. Carroll ◽  
◽  
Anita H. Lewin
Keyword(s):  
Class A
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