Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Aerosol retrieval experiments in the ESA Aerosol_cci project

Within the ESA Climate Change Initiative (CCI) project Aerosol_cci (2010–2013), algorithms for the production of long-term total column aerosol optical depth (AOD) datasets from European Earth Observation sensors are developed. Starting with eight existing pre-cursor algorithms three analysis steps are conducted to improve and qualify the algorithms: (1) a series of experiments applied to one month of global data to understand several major sensitivities to assumptions needed due to the ill-posed nature of the underlying inversion problem, (2) a round robin exercise of "best" versions of each of these algorithms (defined using the step 1 outcome) applied to four months of global data to identify mature algorithms, and (3) a comprehensive validation exercise applied to one complete year of global data produced by the algorithms selected as mature based on the round robin exercise. The algorithms tested included four using AATSR, three using MERIS and one using PARASOL. This paper summarizes the first step. Three experiments were conducted to assess the potential impact of major assumptions in the various aerosol retrieval algorithms. In the first experiment a common set of four aerosol components was used to provide all algorithms with the same assumptions. The second experiment introduced an aerosol property climatology, derived from a combination of model and sun photometer observations, as a priori information in the retrievals on the occurrence of the common aerosol components. The third experiment assessed the impact of using a common nadir cloud mask for AATSR and MERIS algorithms in order to characterize the sensitivity to remaining cloud contamination in the retrievals against the baseline dataset versions. The impact of the algorithm changes was assessed for one month (September 2008) of data: qualitatively by inspection of monthly mean AOD maps and quantitatively by comparing daily gridded satellite data against daily averaged AERONET sun photometer observations for the different versions of each algorithm globally (land and coastal) and for three regions with different aerosol regimes. The analysis allowed for an assessment of sensitivities of all algorithms, which helped define the best algorithm versions for the subsequent round robin exercise; all algorithms (except for MERIS) showed some, in parts significant, improvement. In particular, using common aerosol components and partly also a priori aerosol-type climatology is beneficial. On the other hand the use of an AATSR-based common cloud mask meant a clear improvement (though with significant reduction of coverage) for the MERIS standard product, but not for the algorithms using AATSR. It is noted that all these observations are mostly consistent for all five analyses (global land, global coastal, three regional), which can be understood well, since the set of aerosol components defined in Sect. 3.1 was explicitly designed to cover different global aerosol regimes (with low and high absorption fine mode, sea salt and dust).

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

On the cutting stock problem under stochastic demand

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem`s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution-VSS-and the expected value of perfect information-EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem.

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests. (C) 2009 Elsevier B.V. All rights reserved.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

Dynamics of Bose-Einstein condensates in double-well potentials

We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.

Corruption, governance and collective sanctions: : can a wicked problem be tamed?

Tackling a problem requires mostly, an ability to read it, conceptualize it, represent it, define it, and then applying the necessary mechanisms to solve it. This may sound self-evident except when the problem to be tackled happens to be “complex, “ “ill-structured,” and/or “wicked.” Corruption is one of those kinds of problems. Both in its global and national manifestations it is ill-structured. Where it is structural in nature, endemic and pervasive, it is perhaps even wicked. Qualities of the kind impose modest expectations regarding possibilities of any definitive solution to this insidious phenomenon. If so, it may not suffice to address the problem of corruption using existing categories of law and/or good governance, which overlook the “long-term memory” of the collective and cultural specific dimensions of the subject. Such socio-historical conditions require focusing on the interactive and self-reproducing networks of corruption and attempting to ‘subvert’ that phenomenon’s entire matrix. Concepts such as collective responsibility, collective punishment and sanctions are introduced as relevant categories in the structural, as well as behavioral, subversion of some of the most prevalent aspects of corruption. These concepts may help in the evolving of a new perspective on corruption fighting strategies.

From XML to relational view updates: applying old solutions to solve a new problem

XML has become an important medium for data exchange, and is frequently used as an interface to - i.e. a view of - a relational database. Although lots of work have been done on querying relational databases through XML views, the problem of updating relational databases through XML views has not received much attention. In this work, we give the rst steps towards solving this problem. Using query trees to capture the notions of selection, projection, nesting, grouping, and heterogeneous sets found throughout most XML query languages, we show how XML views expressed using query trees can be mapped to a set of corresponding relational views. Thus, we transform the problem of updating relational databases through XML views into a classical problem of updating relational databases through relational views. We then show how updates on the XML view are mapped to updates on the corresponding relational views. Existing work on updating relational views can then be leveraged to determine whether or not the relational views are updatable with respect to the relational updates, and if so, to translate the updates to the underlying relational database. Since query trees are a formal characterization of view de nition queries, they are not well suited for end-users. We then investigate how a subset of XQuery can be used as a top level language, and show how query trees can be used as an intermediate representation of view de nitions expressed in this subset.

Contractual solutions to the holdup problem: a survey

In this survey, we presented the general idea and main results from what we understand that are the most important contributions to contractual solutions to the holdup problem literature. The aim of this paper is to push the previous analysis, uniform the notation and provide a snapshot on the most recent literature, as well as bring topics for future inquires on this issue.

Agressão no futebol

o presente tema - "Agressão no jogo de futebol” - teve primeiramente como objetivo investigar o problema da agressão no esporte popular brasileiro. Assim sendo o trabalho oferece uma visão introdutória, exploratória e descritiva dos aspectos principais com relação ao problema. Desta forma a análise está ligada a várias opiniões e posições que já foram expressas por um número de autores, e esta nossa análise está intimamente ligada a tudo que já foi publicado sobre este tema. Contudo, apresentamos uma ligeira inovação, uma contribuição muito especial. Ao dissertarmos de uma maneira, a mais clara possível, nos limitamos num ponto especifico que é o de vivermos a realidade do jogo de futebol. Cuidadosamente, conduzimos o tema principal do trabalho em direção ao papel fundamental dos dirigentes, treinadores, médicos desportistas, juizes de campo, preparadores físicos, advogados desportistas e psicólogos. Em suma, nós conduzimos nossa atenção ,para as pessoas diretamente envolvidas com a prática do esporte em geral na sociedade contemporânea, assim como da luta para combater os problemas cria dos pela agressão, aspecto particularmente relevante para os jogadores de futebol em situações de forte competição. Na segunda parte do trabalho, nós tivemos a oportunidade de fazer alguns contatos diretos 'e pessoais com vários jogadores conhecidos do futebol no Brasil, assim como outros tipos de profissionais que lidam com este esporte. Podemos dizer, que tal ordem de contatos foi desenvolvida através de, várias observações não só na hora dos treinos, mas também durante um número de jogos eliminatórios (finais), juntamente com algumas entrevistas individuais que depois eles concederam. Quando todas as peças foram colocadas nos próprios lugares é que o quadro ficou mais completo, expondo os fatores mútuos e interativos nos jogos. Falando de maneira geral, o modelo de melhor compreensão proposto para este trabalho foi detalhado de forma que pode ser baseado na observação direta da pesquisa de campo mas com um número especifico de dados para este tipo de· pesquisa, cujos principais objetivos foram as simples situações corriqueiras (significatiyas). Com este material, em nossas mãos, nós pudemos reformular algumas questões vitais que poderiam enriquecer o dia-a-dia da psicologia neste campo de conhecimento. Sem dúvida, essa ênfase atual da questão da agressão - e um problema crescente. O significado do combate a agressão não é fácil, digamos, de enquadrar numa simples elaboração de palavras. Na pesquisa que fizemos a conclusão é de que a agressão deve ser combatida desde muito cedo nos estágios das "escolas de futebol".