Correction to: Parallel optimization of the ray-tracing algorithm based on the HPM model

The Journal of Supercomputing - A correction to this paper has been published: https://doi.org/10.1007/s11227-021-03680-0     

Robustness analysis via the running time of the interior point methods

Let Σ be the set of stable linear time-invariant autonomous systems, equipped with a stability robustness measure ρ. Let be the measure of the computational efficiency of the algorithm that verifies the stability of the elements of Σ. We demonstrate the existence of a robustness measure ρ, algorithm , and a monotonically increasing function h, such that for all stable ,implications of this relationship are then discussed.     

Computational and structural analysis of the contour of graphs

Let be a finite, simple, and connected graph. The closed interval of a set is the set of all vertices lying on a shortest path between any pair of vertices of S. The set S is geodetic if . The eccentricity of a vertex v is the number of edges in the greatest shortest path between v and any vertex w of G. A vertex v is a contour vertex if no neighbor of v has eccentricity greater than v. The contour of G is the set formed by the contour vertices of G. We consider two problems: the problem of determining whether the contour of a graph class is geodetic; the problem of determining if there exists a graph such that is not geodetic. We obtain a sufficient condition that is useful for both problems; we prove a realization theorem related to problem and show two infinite families such that is not geodetic. Using computational tools, we establish the minimum graphs for which is not geodetic; and show that all graphs with , and all bipartite graphs with , are such that is geodetic.     

Full complexity analysis of the diameter‐constrained reliability

Let be a simple graph with nodes and links, a subset of “terminals,” a vector , and a positive integer d, called “diameter.” We assume that nodes are perfect but links fail stochastically and independently, with probabilities . The “diameter‐constrained reliability” (DCR) is the probability that the terminals of the resulting subgraph remain connected by paths composed of d links, or less. This number is denoted by . The general DCR computation belongs to the class of ‐hard problems, since it subsumes the problem of computing the probability that a random graph is connected. The contributions of this paper are twofold. First, a full analysis of the computational complexity of DCR subproblems is presented in terms of the number of terminal nodes and the diameter d. Second, we extend the class of graphs that accept efficient DCR computation. In this class, we include graphs with bounded co‐rank, graphs with bounded genus, planar graphs, and, in particular, Monma graphs, which are relevant to robust network design.     

Remarks on the relationship between stability and internal stability of nonlinear systems

In this paper, we investigate the relationship between stability and internal stability of nonlinear systems. It is shown that under certain conditions, stability implies attractivity of the equilibrium and that local stability with finite gain implies local asymptotic stability of the origin. Copyright © 2012 John Wiley & Sons, Ltd.     

Thin‐slot formalism for the split‐field FDTD analysis of periodic structure

An expression of the thin‐slot formalism is presented to alleviate the gridding of the split‐field finite‐difference time‐domain (FDTD) solution for periodic structure. The varying auxiliary‐field ( , ) and split‐field ( , ) distributions near the slots are analytically derived from the varying field ( , ). The update equations for the split‐field FDTD are obtained by incorporating those varying field distributions into the split‐field equations in integral form. A frequency selective surface (FSS) structure is applied to verify the proposed method. The results indicate that the computational efficiency is improved.     

An application of a reflector for increase of the radiation efficiency of cellular telephone antennas

A reflector placed near a cellular telephone antenna is proposed to increase its radiation efficiency. In this study, a half wavelength dipole antenna at 900 MHz is treated as a cellular telephone model and a small plate reflector is placed between the antenna and a human head‐sized phantom model. By using the finite‐difference time‐domain (FDTD) method, various kinds of materials, such as a dielectric material, a magnetic material, and a conductive material, are investigated for the reflector composition. Among them, a magnetic reflector having high μ and low μ (complex relative permeability: μ−jμ) is shown to be effective for increasing the radiation efficiency. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 253–263, 2000.     

Robust control of the Hill's problem with drag

There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three‐body problem (CRTBP) equations, the Hill's equations support three‐dimensional “halo” orbits that require station‐keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two‐degree‐of‐freedom control strategy is used to maintain a pre‐selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time‐periodic state feedback law, and a time‐periodic feed‐forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.     

Controllability of Semilinear Systems of Parabolic Equations with Delay on the State

In this paper we prove the approximate controllability of the following semilinear system parabolic equations with delay on the state variable where Ω is a bounded domain in is a n × n non diagonal matrix whose eigenvalues are semi‐simple with non negative real part, the control u belongs to and B is a n × m matrix. Here τ≥0 is the maximum delay, which is supposed to be finite. We assume that the operator L:L²([?τ,0];Z)→Z is linear and bounded with and the nonlinear function f:[0,r] × IRⁿ×IR^m→IRⁿ is smooth and bounded.     

Correction to: An evaluation of the formalised AcciMap approach for accident analysis in healthcare

Cognition, Technology & Work - A correction to this paper has been published: https://doi.org/10.1007/s10111-021-00676-x     

Extracting models from clause sets saturated under semantic refinements of the resolution rule

We present an algorithm that—given a set of clauses S saturated under some semantic refinements of the resolution calculus—automatically constructs a Herbrand model of S. is represented by a set of atoms with equality and disequality constraints interpreted over the finite tree algebra, hence the problem of evaluating first-order formulae in is decidable.     

Stabilization of the planar vertical take-off and landing using nonlinear feedback control

This article presents a new control strategy for the well-known problem of the planar vertical take-off and landing. The total thrust is computed using a nonlinear feedback compensation so that the altitude reaches the desired altitude. The horizontal position x is then controlled by choosing the orientation angle as a smooth saturation function of x and . A proof of convergence is presented using a Lyapunov approach. The proposed control strategy is successfully tested in numerical simulations.     

Comparison of metaheuristics for the k‐labeled spanning forest problem

In this paper, we study the k‐labeled spanning forest (kLSF) problem in which an undirected graph whose edges are labeled and an integer‐positive value are given; the aim is to find a spanning forest of the input graph with the minimum number of connected components and the upper bound on the number of labels. The problem is related to the minimum labeling spanning tree problem and has several applications in the real world. In this paper, we compare several metaheuristics to solve this NP‐hard problem. In particular, the proposed intelligent variable neighborhood search (VNS) shows excellent performance, obtaining high‐quality solutions in short computational running time. This approach integrates VNS with other complementary approaches from machine learning, statistics, and experimental algorithmics, in order to produce high‐quality performance and completely automate the resulting optimization strategy.