Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

Neural coding tools, based on Information Theory, applied to discrete time series: from electrophysiology to neuroethology

This work is supported by Brazilian agencies Fapesp, CAPES and CNPq

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance. Journal of the Operational Research Society (2012) 63, 1613-1630. doi:10.1057/jors.2011.159 published online 7 March 2012

Linear viscoelasticity of immiscible blends: The application of creep

A new method to characterize the long-time linear relaxation mechanisms of immiscible blends based on creep experiment was developed. Small-amplitude oscillatory shear and incomplete creep/recovery experiments were combined to characterize immiscible blends of polypropylene with dispersed droplets of polystyrene. An experimental protocol was defined such that the full creep compliance function could be obtained while minimizing morphological changes. Dynamic experiments were performed to characterize the shorter time relaxation processes, and creep and recovery measurements were used to detect the longer time portions of the relaxation spectra. Extended retardation and relaxation spectra were constructed by combining these data. It was found that using this technique, very long-time relaxation peaks which were inaccessible with dynamic experiments alone could be detected. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4720081]

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies' growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Development of enzymic time-temperature integrators with rapid detection for evaluation of continuous HTST pasteurization processes

The assessment of the thermal process impact in terms of food safety and quality is of great importance for process evaluation and design. This can be accomplished from the analysis of the residence time and temperature distributions coupled with the kinetics of thermal change, or from the use of a proper time-temperature integrator (TTI) as indicator of safety and quality. The objective of this work was to develop and test enzymic TTIs with rapid detection for the evaluation of continuous HTST pasteurization processes (70-85 degrees C, 10-60 s) of low-viscosity liquid foods, such as milk and juices. Enzymes peroxidase, lactoperoxidase and alkaline phosphatase in phosphate buffer were tested and activity was determined with commercial reflectometric strips. Discontinuous thermal treatments at various time-temperature combinations were performed in order to adjust a first order kinetic model of a two-component system. The measured time-temperature history was considered instead of assuming isothermal conditions. Experiments with slow heating and cooling were used to validate the adjusted model. Only the alkaline phosphatase TTI showed potential to be used for the evaluation of pasteurization processes. The choice was based on the obtained z-values of the thermostable and thermolabile fractions, on the cost and on the validation tests. (C) 2012 Elsevier Ltd. All rights reserved.

Mangrove Forests and Sedimentary Processes on the South of Coast of Sao Paulo State (Brazil)

Mangrove structure and distribution is conditioned by geomorphic processes. This paper describes the response of mangroves to sedimentary processes at the Cananeia-Iguape Coastal System on the south coast of Sao Paulo State (Brazil), between latitudes 24 degrees 40`S and 25 degrees 20`S. Within six study areas 41 plots were established along 14 transects. Plot size varied according to stem density from 2mx2m to 20mx20m. Here mangroves are strongly coupled to sedimentary processes, forming discrete architectural elements within particular depositional environments or topographic settings. These sedimentary structures and progradation environments are colonized by Laguncularia racemosa, associated with the smooth cordgrass Spartina alterniflora. Rhizophora mangle occurs typically near creeklets where tidal flooding is more frequent. Where tidal influence is restricted Avicennia schaueriana becomes dominant. Erosive margins are dominated by A. schaueriana or R. mangle. Single linkage cluster analysis yields three groups (A, B and C), with high levels of similarity, providing support to the classification of the data into two broad landform categories: depositional and erosive. Group A includes plots with the least structural development (nominal stem diameter d(n) between 1.05 and 4.61cm). Group B is composed of stems of intermediate diameter (4.99 cm <= d(n) <= 5.63cm). Group C plots have the largest structural development (5.50 cm <= d(n) <= 11.10cm). The structure of mangroves (dominance and structural development) reflects responses to geomorphology and habitat change.

Patterns and processes of diversification in a widespread and ecologically diverse avian group, the buteonine hawks (Aves, Accipitridae)

Buteonine hawks represent one of the most diverse groups in the Accipitridae, with 58 species distributed in a variety of habitats on almost all continents. Variations in migratory behavior, remarkable dispersal capability, and unusual diversity in Central and South America make buteonine hawks an excellent model for studies in avian evolution. To evaluate the history of their global radiation, we used an integrative approach that coupled estimation of the phylogeny using a large sequence database (based on 6411 bp of mitochondrial markers and one nuclear intron from 54 species), divergence time estimates, and ancestral state reconstructions. Our findings suggest that Neotropical buteonines resulted from a long evolutionary process that began in the Miocene and extended to the Pleistocene. Colonization of the Nearctic, and eventually the Old World, occurred from South America, promoted by the evolution of seasonal movements and development of land bridges. Migratory behavior evolved several times and may have contributed not only to colonization of the Holarctic, but also derivation of insular species. In the Neotropics, diversification of the buteonines included four disjunction events across the Andes. Adaptation of monophyletic taxa to wet environments occurred more than once, and some relationships indicate an evolutionary connection among mangroves, coastal and varzea environments. On the other hand, groups occupying the same biome, forest, or open vegetation habitats are not monophyletic. Refuges or sea-level changes or a combination of both was responsible for recent speciation in Amazonian taxa. In view of the lack of concordance between phylogeny and classification, we propose numerous taxonomic changes. (C) 2009 Elsevier Inc. All rights reserved.

A peculiar Maxwell's Demon observed in a time-dependent stadium-like billiard

The dynamics of a driven stadium-like billiard is considered using the formalism of discrete mappings. The model presents a resonant velocity that depends on the rotation number around fixed points and external boundary perturbation which plays an important separation rule in the model. We show that particles exhibiting Fermi acceleration (initial velocity is above the resonant one) are scaling invariant with respect to the initial velocity and external perturbation. However, initial velocities below the resonant one lead the particles to decelerate therefore unlimited energy growth is not observed. This phenomenon may be interpreted as a specific Maxwell's Demon which may separate fast and slow billiard particles. (C) 2012 Elsevier B.V. All rights reserved.

Exploration time of static images implying different body movements causes time distortions

Studies of subjective time have adopted different methods to understand different processes of time perception. Four sculptures, with implied movement ranked as 1.5-, 3.0-, 4.5-, and 6.0-point stimuli on the Body Movement Ranking Scale, were randomly presented to 42 university students untrained in visual arts and ballet. Participants were allowed to observe the images for any length of time (exploration time) and, immediately after each image was observed, recorded the duration as they perceived it. The results of temporal ratio (exploration time/time estimation) showed that exploration time of images also affected perception of time, i.e., the subjective time for sculptures representing implied movement were overestimated.\