Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Solving problems collaboratively online : experiences of Australian and Chinese heritage university students

The research reported in this paper is part of a larger project designed to compare the online collaborative learning behaviours of Chinese Heritage Culture (CHC) university students, for whom a Chinese dialect is a first language, with Australian university students of European descent, and for whom English is a first language. The collaborative learning discussion focussed on in the research involved fellow students, rather than tutorial staff, facilitating those discussions.

The first component of the research was quantitative, comprising a questionnaire on readiness for online learning, and a quantitative analysis of student postings to a student-led collaborative problem solving task conducted online. The first component of the research (reported in Smith et at, 2005) showed no differences between the two groups in their willingness to self-manage their own learning, but did show that the CHC students were significantly less comfortable than the Australian students with online learning. Student postings to the online discussions were classified into organisational postings, social postings, and intellectual. There were substantial differences between the two groups in their patterns of online postings among those classifications, as well as differences in the length of postings made.

This paper will explore these findings in more detail through qualitative data generated through interviews with a subset of students from each group. Interview data provided further insight into the lesser comfort with e-learning among CHC students. Students from both groups felt there were inefficiencies in the online discussion, but CHC students also felt rather marginalised by the process. Australian students were more likely to evaluate the experience in terms of its capacity to achieve required learning outcomes in a time efficient way, while CHC students expressed more concern about how the process had impacted upon them personally. The interview data also indicated that a tutor sensitive to cultural difference is important for comfort among the CHC students in particular, since there is need for encouragement to those students to make reflective inputs to the discussion.

Sample subset optimization for classifying imbalanced biological data

Data in many biological problems are often compounded by imbalanced class distribution. That is, the positive examples may largely outnumbered by the negative examples. Many classification algorithms such as support vector machine (SVM) are sensitive to data with imbalanced class distribution, and result in a suboptimal classification. It is desirable to compensate the imbalance effect in model training for more accurate classification. In this study, we propose a sample subset optimization technique for classifying biological data with moderate and extremely high imbalanced class distributions. By using this optimization technique with an ensemble of SVMs, we build multiple roughly balanced SVM base classifiers, each trained on an optimized sample subset. The experimental results demonstrate that the ensemble of SVMs created by our sample subset optimization technique can achieve higher area under the ROC curve (AUC) value than popular sampling approaches such as random over-/under-sampling; SMOTE sampling, and those in widely used ensemble approaches such as bagging and boosting.

A modified Intelligent Water Drops algorithm and its application to optimization problems

The Intelligent Water Drop (IWD) algorithm is a recent stochastic swarm-based method that is useful for solving combinatorial and function optimization problems. In this paper, we investigate the effectiveness of the selection method in the solution construction phase of the IWD algorithm. Instead of the fitness proportionate selection method in the original IWD algorithm, two ranking-based selection methods, namely linear ranking and exponential ranking, are proposed. Both ranking-based selection methods aim to solve the identified limitations of the fitness proportionate selection method as well as to enable the IWD algorithm to escape from local optima and ensure its search diversity. To evaluate the usefulness of the proposed ranking-based selection methods, a series of experiments pertaining to three combinatorial optimization problems, i.e., rough set feature subset selection, multiple knapsack and travelling salesman problems, is conducted. The results demonstrate that the exponential ranking selection method is able to preserve the search diversity, therefore improving the performance of the IWD algorithm. © 2014 Elsevier Ltd. All rights reserved.

A novel approach to maximize the sum-rate for MIMO broadcast channels

This paper considers the sum-rate of wireless broadcast systems with multiple antennas at the base station. In a conventional MIMO-BC system with a large number of users, selecting an optimal subset of users to maximizing the overall system capacity is a key design issue. This paper presents a novel approach to investigate the sum-rate using Eigen Value Decomposition (EVD). Particularly, we derive the lower bound on sum-rate of a conventional MIMO-BC using a completely different approach compared to the existing approaches. The paper formulates the rate maximization problem for any number of users and any number of transmitting antennas using EVD approach of the channel matrix. This also shows the impact of channel angle information on the sum-rate of conventional MIMO-BC. Numerical results confirm the benefits of our technique in various MIMO communication scenarios.

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.

QCD glueball sum rules revisited

We discuss several key problems of conventional QCD glueball sum rules in the spin-0 channels and show how they are overcome by nonperturbative Wilson coefficients. The nonperturbative contributions originate from direct instantons and, in the pseudoscalar channel, additionally from topological charge screening. The treatment of the direct-instanton sector is based on realistic instanton size distributions and renormalization at the operator scale. The resulting predictions for spin-0 glueball properties as well as their implications for experimental glueball searches are discussed.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

On Global Attractors for a Class of Parabolic Problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solving the multiobjective environmental/economic dispatch problem using weighted sum and ε-constraint strategies and a predictor-corrector primal-dual interior point method

This paper proposes a technique for solving the multiobjective environmental/economic dispatch problem using the weighted sum and ε-constraint strategies, which transform the problem into a set of single-objective problems. In the first strategy, the objective function is a weighted sum of the environmental and economic objective functions. The second strategy considers one of the objective functions: in this case, the environmental function, as a problem constraint, bounded above by a constant. A specific predictor-corrector primal-dual interior point method which uses the modified log barrier is proposed for solving the set of single-objective problems generated by such strategies. The purpose of the modified barrier approach is to solve the problem with relaxation of its original feasible region, enabling the method to be initialized with unfeasible points. The tests involving the proposed solution technique indicate i) the efficiency of the proposed method with respect to the initialization with unfeasible points, and ii) its ability to find a set of efficient solutions for the multiobjective environmental/economic dispatch problem.

Are mental health problems and depression associated with bruxism in children?

Renner AC, da Silva AAM, Rodriguez JDM, Simoes VMF, Barbieri MA, Bettiol H, Thomaz EBAF, Saraiva MC. Are mental health problems and depression associated with bruxism in children? Community Dent Oral Epidemiol 2011. (C) 2011 John Wiley & Sons A/S Abstract Objectives: Previous studies have found an association between bruxism and emotional and behavioral problems in children, but reported data are inconsistent. The objective of this study was to estimate the prevalence of bruxism, and of its components clenching and grinding, and its associations with mental problems and depression. Methods: Data from two Brazilian birth cohorts were analyzed: one from 869 children in Ribeirao Preto RP (Sao Paulo), a more developed city, and the other from 805 children in Sao Luis SL (Maranhao). Current bruxism evaluated by means of a questionnaire applied to the parents/persons responsible for the children was defined when the habit of tooth clenching during daytime and/or tooth grinding at night still persisted until the time of the assessment. Additionally, the lifetime prevalence of clenching during daytime only and grinding at night only was also evaluated. Mental health problems were investigated using the Strength and Difficulties Questionnaire (SDQ) and depression using the Childrens Depression Inventory (CDI). Analyses were carried out for each city: with the SDQ subscales (emotional symptoms, conduct problems, peer problems, attention/hyperactivity disorder), with the total score (sum of the subscales), and with the CDI. These analyses were performed considering different response variables: bruxism, clenching only, and grinding only. The risks were estimated using a Poisson regression model. Statistical inferences were based on 95% confidence intervals (95% CI). Results: There was a high prevalence of current bruxism: 28.7% in RP and 30.0% in SL. The prevalence of clenching was 20.3% in RP and 18.8% in SL, and grinding was found in 35.7% of the children in RP and 39.1% in SL. Multivariable analysis showed a significant association of bruxism with emotional symptoms and total SDQ score in both cities. When analyzed separately, teeth clenching was associated with emotional symptoms, peer problems, and total SDQ score; grinding was significantly associated with emotional symptoms and total SDQ score in RP and SL. Female sex appeared as a protective factor for bruxism, and for clenching and grinding in RP. Furthermore, maternal employment outside the home and white skin color of children were associated with increased prevalence of teeth clenching in SL. Conclusions: Mental health problems were associated with bruxism, with teeth clenching only and grinding at night only. No association was detected between depression and bruxism, neither clenching nor grinding. But it is necessary to be cautious regarding the inferences from some of our results.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.