Perturbations Of Operators Research Articles

Evolutionary algorithm for example-based painterly rendering

NPR may be seen as any attempt to create images to convey a scene without directly rendering a physical simulation. This paper describes an evolutionary algorithm (EA) for learning painting styles from example images. The evolutionary algorithm has two main stages: learning and painting. By learning the painting style from a source pair of training images (a source photograph and its artistic style), a style approximation can then be accomplished to another target image. The mechanism of evolutionary algorithms is used here to learn or capture different characters used to depict different regions of the source painting and use them to convert similar regions with similar texture statistics of the target image into artistic rendering. Two main perturbation operators are used in the proposed EA: a multi-sexual recombination and mutation operators. On overall, the algorithm, with its implementation simplicity and computation efficiency, can provide acceptable results with perceived artistic rendering.

Generalized solution of non‐autonomous photon transport problem

AbstractThe purpose of this paper is to show the existence of a generalized solution of a non‐autonomous transport problem. By means of the theory of equicontinuous evolution system on a sequentially complete locally convex topological vector space, we show that the perturbed abstract non‐autonomous Cauchy problem has a unique solution when the perturbation operator and forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the non‐autonomous photon transport problem. Copyright © 2009 John Wiley & Sons, Ltd.

SPECTRAL PROPERTIES AND LINEAR STABILITY OF SELF-SIMILAR WAVE MAPS

We study co-rotational wave maps from (3 + 1)-Minkowski space to the three-sphere S3. It is known that there exists a countable family {fn} of self-similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well-posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from fn by letting n → ∞.

Techniques for restricting multiple overtaking conflicts and performing compound moves when constructing new train schedules

In this paper a discrete sequencing approach for train scheduling is extended firstly by incorporating essential composite perturbation operations and secondly by restricting unnecessary multiple overtaking. Unnecessary multiple overtaking occurs when a train overtakes another train using a siding but is itself overtaken at a later time on a different siding by the train that it previously passed. Compound perturbation operations may be needed in order to restrict precedence impossibilities from occurring when passing facilities do not separate adjacent sections of rail since the sequences are linked by common precedences. Both features affect the sequencing process and can significantly improve the solution quality if handled efficiently and correctly. From a numerical investigation significant benefits are demonstrated on benchmark problems of a previous paper.

Dilatation operator in 3d

The three dimensional perturbative dilatation operator is constructed at the leading two-loop order.

Generalized operator for the interaction of electromagnetic fields and molecules

A previously described, new approach to the theoretical description of Raman spectra as the result of resonant absorption of the energy of an electromagnetic field described by a modulated signal, is extended. It is shown that, on this basis, one can introduce a perturbation operator in the form of a matrix that simultaneously accounts for both absorption and scattering.

Stochastic problems in H ∞ and H 2/H ∞ control

We consider stochastic control systems subjected simultaneously to stochastic and determinate perturbations. Stochastic perturbations are assumed to be state-multiplicative stochastic processes, while determinate perturbations can be any processes with finite energy on infinite time interval. The results of the determinate H ?-theory are compared to their stochastic analogs. The determinate and stochastic theories are linked together by the lemma that establishes the equivalence between the stability and boundness of the ?L?? < ? norm of the perturbation operator L, from one side, and the solvability of certain linear matrix inequalities (LMIs), from the other side. As soon as the stochastic version of the lemma is proven, the ?-controller analysis and design problems are solved, in general, identically in the frame of the united LMI methodology.

Stochastic Optimization Algorithms for Support Vector Machines Classification

In this paper, we consider the problem of semi-supervised binary classification by Support Vector Machines (SVM). This problem is explored as an unconstrained and non-smooth optimization task when part of the available data is unlabelled. We apply non-smooth optimization techniques to classification where the objective function considered is non-convex and non-differentiable and so difficult to minimize. We explore and compare the properties of Simulated Annealing and of Simultaneous Perturbation Stochastic Approximation (SPSA) algorithms (SPSA with the Lipschitz Perturbation Operator, SPSA with the Uniform Perturbation Operator, Standard Finite Difference Approximation) for semi-supervised SVM classification. Numerical results are given, obtained by running the proposed methods on several standard test problems drawn from the binary classification literature. The performance of the classifiers were evaluated by analyzing Receiver Operating Characteristics (ROC).

The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications

The main result in this paper is the determination of the Fréchet derivative of an analytic function of a bounded operator, tangentially to the space of all bounded operators. Some applied problems from statistics and numerical analysis are included as a motivation for this study. The perturbation operator (increment) is not of any special form and is not supposed to commute with the operator at which the derivative is evaluated. This generality is important for the applications. In the Hermitian case, moreover, some results on perturbation of an isolated eigenvalue, its eigenprojection, and its eigenvector if the eigenvalue is simple, are also included. Although these results are known in principle, they are not in general formulated in terms of arbitrary perturbations as required for the applications. Moreover, these results are presented as corollaries to the main theorem, so that this paper also provides a short, essentially self-contained review of these aspects of perturbation theory.

Stochastic approximation algorithms for support vector machines semi-supervised binary classification

In this paper,we consider the problem of semi-supervisedbinary classificationby Support Vector Machines (SVM). This problem is explored as an unconstrained and non-smooth optimization task when part of the available data is unlabelled. We apply non-smooth optimization techniques to classification problems where the objective function considered is non-convex and non-differentiable and so difficult to minimize. We explore and compare the properties of Stochastic Approximation algorithms (Simultaneous Perturbation Stochastic Approximation (SPSA) with the Lipschitz Perturbation Operator, SPSA with the Uniform Perturbation Operator, and Standard Finite Difference Approximation) for semi-supervised SVM classification. We present some numerical results obtained by running the proposed methods on several standard test problems drawn from the binary classification literature.

Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component. III. Introduction of gauge-including atomic orbitals and a finite-size nuclear model

The relativistic calculation of nuclear magnetic shielding tensors in hydrogen halides is performed using the second-order regular approximation to the normalized elimination of the small component (SORA-NESC) method with the inclusion of the perturbation terms from the metric operator. This computational scheme is denoted as SORA-Met. The SORA-Met calculation yields anisotropies, Delta sigma = sigma(parallel) - sigma(perpendicular), for the halogen nuclei in hydrogen halides that are too small. In the NESC theory, the small component of the spinor is combined to the large component via the operator sigma x piU/2c, in which pi = p + A, U is a nonunitary transformation operator, and c approximately = 137.036 a.u. is the velocity of light. The operator U depends on the vector potential A (i.e., the magnetic perturbations in the system) with the leading order c(-2) and the magnetic perturbation terms of U contribute to the Hamiltonian and metric operators of the system in the leading order c(-4). It is shown that the small Delta sigma for halogen nuclei found in our previous studies is related to the neglect of the U(0,1) perturbation operator of U, which is independent of the external magnetic field and of the first order with respect to the nuclear magnetic dipole moment. Introduction of gauge-including atomic orbitals and a finite-size nuclear model is also discussed.

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.

Multi-objective fuzzy particle swarm optimization based on elite archiving and its convergence *

A fuzzy particle swarm optimization (PSO) on the basis of elite archiving is proposed for solving multi-objective optimization problems. First, a new perturbation operator is designed, and the concepts of fuzzy global best and fuzzy personal best are given on basis of the new operator. After that, particle updating equations are revised on the basis of the two new concepts to discourage the premature convergence and enlarge the potential search space; second, the elite archiving technique is used during the process of evolution, namely, the elite particles are introduced into the swarm, whereas the inferior particles are deleted. Therefore, the quality of the swarm is ensured. Finally, the convergence of this swarm is proved. The experimental results show that the nondominated solutions found by the proposed algorithm are uniformly distributed and widely spread along the Pareto front.

Constrained optimization with an improved particle swarm optimization algorithm

PurposeThe purpose of this paper is to present a new constrained optimization algorithm based on a particle swarm optimization (PSO) algorithm approach.Design/methodology/approachThis paper introduces a hybrid approach based on a modified ring neighborhood with two new perturbation operators designed to keep diversity. A constraint handling technique based on feasibility and sum of constraints violation is adopted. Also, a special technique to handle equality constraints is proposed.FindingsThe paper shows that it is possible to improve PSO and keeping the advantages of its social interaction through a simple idea: perturbing the PSO memory.Research limitations/implicationsThe proposed algorithm shows a competitive performance against the state‐of‐the‐art constrained optimization algorithms.Practical implicationsThe proposed algorithm can be used to solve single objective problems with linear or non‐linear functions, and subject to both equality and inequality constraints which can be linear and non‐linear. In this paper, it is applied to various engineering design problems, and for the solution of state‐of‐the‐art benchmark problems.Originality/valueA new neighborhood structure for PSO algorithm is presented. Two perturbation operators to improve PSO algorithm are proposed. A special technique to handle equality constraints is proposed.

A sequencing approach for creating new train timetables

Train scheduling is a complex and time consuming task of vital importance. To schedule trains more accurately and efficiently than permitted by current techniques a novel hybrid job shop approach has been proposed and implemented. Unique characteristics of train scheduling are first incorporated into a disjunctive graph model of train operations. A constructive algorithm that utilises this model is then developed. The constructive algorithm is a general procedure that constructs a schedule using insertion, backtracking and dynamic route selection mechanisms. It provides a significant search capability and is valid for any objective criteria. Simulated Annealing and Local Search meta-heuristic improvement algorithms are also adapted and extended. An important feature of these approaches is a new compound perturbation operator that consists of many unitary moves that allows trains to be shifted feasibly and more easily within the solution. A numerical investigation and case study is provided and demonstrates that high quality solutions are obtainable on real sized applications.

New model describing interaction between an electromagnetic wave and a molecule

The expediency of refining some basic concepts of the common theory of interaction between an electromagnetic field and a substance using a quasi-classical model for the phenomena of absorption and emission of energy and Raman scattering (RS) is considered. The use of the time-dependent Schrodinger equation for obtaining the transition probability constants is discussed. A new model that describes the intensities of the RS lines and involves the explicit introduction of the perturbation operator for the RS spectrum is proposed.

Quantum Thermodynamics of the Spontaneous Approach to the Equilibrium State – Irreversible Exponential Decay of a Discrete Quantum State of Entropy Production into a Continuum

We consider the temporal evolution of the entropy S of an isolated system from an initial non-equilibrium state 2· of entropy S = S i to the equilibrium state of maximum entropy S = S max &gt; S i. The application of usual density matrix theory of quantum mechanics leads us to the surprising result P = dS/dt = 0. The entropy does not change in time. This result is valid in case of the equilibrium state. However it is wrong for a non-equilibrium state, because the entropy of the isolated system could not spontaneously increase from S i to S max by entropy production P &gt; 0. This contradicts the second law of thermodynamics. We avoid this discrepancy by changing from quantum mechanics to quantum thermodynamics. Now the entropy production P = dS/dt and the time t are the relevant observables. In order to treat the temporal development of S and P, we at first prepare an initial state i of entropy production P i at time t &lt; 0. Subsequently at ϑ t ≥ 0 the initial state i interacts with a continuum of final states f, which transfers the entropy production from i to f. The temporal evolution of the entropy production P(t) of our system is treated by means of the time-dependent perturbation theory. For that reason we split the operator of entropy production P = P 0 + W into two parts. The operator P 0 describes the unperturbed basic vectors of entropy production | i &gt; and | f &gt;, while the perturbation operator W determines the interaction between | i &gt; and | f &gt;. We expand the time-dependent state function &lt; t | ψ &gt; of the isolated system into the complete set of stationary eigenvectors | i &gt; and | f &gt; and calculate the time-dependent expansion coefficients c i(t) and c(f, t) by means of the dynamic equation of quantum thermodynamics − i k (d/dt) &lt; t | ψ &gt; = &lt; t | P | ψ &gt;. Here k means the Boltzmann constant, which is characteristic of quantum thermodynamics and represents the atomic entropy unit. The expansion coefficients are given by a system of coupled differential equations, from which we deduce an integral-differential equation for the coefficient c i(t) of the initial state i. Unfortunately it has been impossible to obtain an analytic solution of the complicated equation. However approximations are available. Accordingly, in the vicinity of the equilibrium state, the probability of still finding the initial state i of entropy production P i at time t is given by ω i(t) = | c i(t) |2 = exp (−Lt). The rate constant L ≥ σ depends on the density ρ(P f) of final states f of entropy production P f near by P i, and on the squared modulus of the perturbation matrix elements W if = &lt; i | W | f &gt;, which determines the interaction between | i &gt; and | f &gt;. The entropy production P(t) = P i ω i(t) = P i exp (−ϑLt) of the isolated system decreases exponentially and irreversibly with proceeding time t. Its rate-determining step is the transfer of entropy production from i to f. The integral over the entropy production of the final states f vanishes. Therefore the continuum states f do not contribute to the total entropy production P(t). The temporal evolution of the entropy S(t) can easily be calculated by integration of P(t). In conclusion, the entropy production of a non-equilibrium state is finite P(t) &gt; 0 and only vanishes in the case of the equilibrium state P(∞) = 0. Thus, quantum thermodynamics agrees with the second law of thermodynamics.

Théorème de renouvellement pour chaînes de Markov fortement ergodiques : application aux modèles itératifs lipschitziens

Let Q be a transition probability on a measurable space E. Let ( X n ) n ∈ N be a stationary Markov chain associated to Q. Let ξ : E → R measurable. Under a moment condition of order 1 + ε on ξ and under functional hypotheses on the action of Q and the Fourier kernels associated to ( Q , ξ ) , on a certain Banach space, we establish a renewal theorem for ( ξ ( X n ) ) n ∈ N ∗ . We use Fourier techniques and a perturbation operator method based on a result by Keller–Liverani. An application to Lipschitz iterative models is given. To cite this article: D. Guibourg, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

An iterated local search heuristic for the logistics network design problem with single assignment

In the logistics network design problem (LNDP), decisions must be made regarding the selection of suppliers, the location of plants and warehouses, the assignment of activities to these facilities, and the flows of raw materials and finished products in the network. This article introduces an iterated local search (ILS) heuristic for the LNDP variant arising when each raw material should be supplied by a unique supplier, and each finished product should be produced and distributed by a unique plant and a unique warehouse, respectively. The ILS heuristic exploits the combinatorial nature of the problem and relies on simple moves combined within a descent algorithm. Several perturbation operators are used to allow a broad exploration of the solution space. The performance of the algorithm is evaluated on randomly generated instances, and the solutions are compared with lower bounds computed by solving the LP relaxation of the problem.

A perturbation theorem for local C-regularized cosine functions

Motivated by the previous works on C–regularized semigroups and C–regularized cosine functions, this paper presents a new result concerning the multiplicative perturbation of local C–regularized cosine functions on a Banach space X. Two cases are considered: (1) the range of the regularizing operator C is not dense in X; (2) the operator C may not commute with the perturbation operator.