String Theory and the Fuzzy Torus

We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.Comment: Invited review for IJMPA rev1: an imprecision corrected and a reference adde

Almost automorphic delayed differential equations and Lasota-Wazewska model

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.Comment: 16 page

Symmetry Breaking and Order in the Age of Quasicrystals

The discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation symmetries of the liquid-phase into a discrete lattice of translations, and a finite group of rotations. Quasicrystals, on the other hand, possess no such symmetries-there are no translations, nor, in general, are there any rotations, leaving them invariant. Does this imply that no symmetry is left, or that the meaning of symmetry should be revised? We review this and other questions related to the liquid-to-crystal symmetry-breaking transition using the notion of indistinguishability. We characterize the order-parameter space, describe the different elementary excitations, phonons and phasons, and discuss the nature of dislocations-keeping in mind that we are now living in the age of quasicrystals.Comment: To appear in a special issue on quasicrystals of The Israel Journal of Chemistry, in celebration of the 2011 Nobel Prize in Chemistr

Fuzzy Feedback Scheduling of Resource-Constrained Embedded Control Systems

The quality of control (QoC) of a resource-constrained embedded control system may be jeopardized in dynamic environments with variable workload. This gives rise to the increasing demand of co-design of control and scheduling. To deal with uncertainties in resource availability, a fuzzy feedback scheduling (FFS) scheme is proposed in this paper. Within the framework of feedback scheduling, the sampling periods of control loops are dynamically adjusted using the fuzzy control technique. The feedback scheduler provides QoC guarantees in dynamic environments through maintaining the CPU utilization at a desired level. The framework and design methodology of the proposed FFS scheme are described in detail. A simplified mobile robot target tracking system is investigated as a case study to demonstrate the effectiveness of the proposed FFS scheme. The scheme is independent of task execution times, robust to measurement noises, and easy to implement, while incurring only a small overhead.Comment: To appear in International Journal of Innovative Computing, Information and Contro

Chaos in the BMN matrix model

We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.Comment: 23 pages, 15 figures, v2: further clarifications and references adde

Discrete and fuzzy dynamical genetic programming in the XCSF learning classifier system

A number of representation schemes have been presented for use within learning classifier systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF learning classifier system. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous fuzzy logic networks in the continuous-valued case. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such dynamical systems within XCSF to solve a number of well-known test problems