KT-invexity in optimal control problems

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

A class of multiobjective control problems

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

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

Condições suficientes de otimalidade em cálculo variacional

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Condições de otimalidade para controle ótimo via formalismo de Dubovitskii-Milyutin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Automatic Audio Segmentation Using the Generalized Likelihood Ratio

This paper presents a novel technique for segmenting an audio stream into homogeneous regions according to speaker identities, background noise, music, environmental and channel conditions. Audio segmentation is useful in audio diarization systems, which aim to annotate an input audio stream with information that attributes temporal regions of the audio into their specific sources. The segmentation method introduced in this paper is performed using the Generalized Likelihood Ratio (GLR), computed between two adjacent sliding windows over preprocessed speech. This approach is inspired by the popular segmentation method proposed by the pioneering work of Chen and Gopalakrishnan, using the Bayesian Information Criterion (BIC) with an expanding search window. This paper will aim to identify and address the shortcomings associated with such an approach. The result obtained by the proposed segmentation strategy is evaluated on the 2002 Rich Transcription (RT-02) Evaluation dataset, and a miss rate of 19.47% and a false alarm rate of 16.94% is achieved at the optimal threshold.