Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.

Complex dynamics of financial indices

This paper presents a novel method for the analysis of nonlinear financial and economic systems. The modeling approach integrates the classical concepts of state space representation and time series regression. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the dynamical behavior. The results reveal that business cycles can be clearly revealed, while the noise effects common in financial indices can elegantly be filtered out of the results.

Using attractor dynamics to generate decentralized motion control of two mobile robots transporting a long object in coordination

Dynamical systems theory is used here as a theoretical language and tool to design a distributed control architecture for a team of two mobile robots that must transport a long object and simultaneously avoid obstacles. In this approach the level of modeling is at the level of behaviors. A “dynamics” of behavior is defined over a state space of behavioral variables (heading direction and path velocity). The environment is also modeled in these terms by representing task constraints as attractors (i.e. asymptotically stable states) or reppelers (i.e. unstable states) of behavioral dynamics. For each robot attractors and repellers are combined into a vector field that governs the behavior. The resulting dynamical systems that generate the behavior of the robots may be nonlinear. By design the systems are tuned so that the behavioral variables are always very close to one attractor. Thus the behavior of each robot is controled by a time series of asymptotically stable states. Computer simulations support the validity of our dynamic model architectures.

Evaluating the combination of relaxation and argumentation in ontology matching negotiation

No decorrer dos últimos anos, os agentes (inteligentes) de software foram empregues como um método para colmatar as dificuldades associadas com a gestão, partilha e reutilização de um crescente volume de informação, enquanto as ontologias foram utilizadas para modelar essa mesma informação num formato semanticamente explícito e rico. À medida que a popularidade da Web Semântica aumenta e cada vez informação é partilhada sob a forma de ontologias, o problema de integração desta informação amplifica-se. Em semelhante contexto, não é expectável que dois agentes que pretendam cooperar utilizem a mesma ontologia para descrever a sua conceptualização do mundo. Inclusive pode revelar-se necessário que agentes interajam sem terem conhecimento prévio das ontologias utilizadas pelos restantes, sendo necessário que as conciliem em tempo de execução num processo comummente designado por Mapeamento de Ontologias [1]. O processo de mapeamento de ontologias é normalmente oferecido como um serviço aos agentes de negócio, podendo ser requisitado sempre que seja necessário produzir um alinhamento. No entanto, tendo em conta que cada agente tem as suas próprias necessidades e objetivos, assim como a própria natureza subjetiva das ontologias que utilizam, é possível que tenham diferentes interesses relativamente ao processo de alinhamento e que, inclusive, recorram aos serviços de mapeamento que considerem mais convenientes [1]. Diferentes matchers podem produzir resultados distintos e até mesmo contraditórios, criando-se assim conflitos entre os agentes. É necessário que se proceda então a uma tentativa de resolução dos conflitos existentes através de um processo de negociação, de tal forma que os agentes possam chegar a um consenso relativamente às correspondências que devem ser utilizadas na tradução de mensagens a trocar. A resolução de conflitos é considerada uma métrica de grande importância no que diz respeito ao processo de negociação [2]: considera-se que existe uma maior confiança associada a um alinhamento quanto menor o número de conflitos por resolver no processo de negociação que o gerou. Desta forma, um alinhamento com um número elevado de conflitos por resolver apresenta uma confiança menor que o mesmo alinhamento associado a um número elevado de conflitos resolvidos. O processo de negociação para que dois ou mais agentes gerem e concordem com um alinhamento é denominado de Negociação de Mapeamentos de Ontologias. À data existem duas abordagens propostas na literatura: (i) baseadas em Argumentação (e.g. [3] [4]) e (ii) baseadas em Relaxamento [5] [6]. Cada uma das propostas expostas apresenta um número de vantagens e limitações. Foram propostas várias formas de combinação das duas técnicas [2], com o objetivo de beneficiar das vantagens oferecidas e colmatar as suas limitações. No entanto, à data, não são conhecidas experiências documentadas que possam provar tal afirmação e, como tal, não é possível atestar que tais combinações tragam, de facto, o benefício que pretendem. O trabalho aqui apresentado pretende providenciar tais experiências e verificar se a afirmação de melhorias em relação aos resultados das técnicas individuais se mantém. Com o objetivo de permitir a combinação e de colmatar as falhas identificadas, foi proposta uma nova abordagem baseada em Relaxamento, que é posteriormente combinada com as abordagens baseadas em Argumentação. Os seus resultados, juntamente com os da combinação, são aqui apresentados e discutidos, sendo possível identificar diferenças nos resultados gerados por combinações diferentes e possíveis contextos de utilização.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.