Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Optimization of Tapered Composite Beams

A study on the optimization of tapered composite beams for vibration is conducted. Designers of tapered rotating structural components such as wind mill, helicopter or turbine blades are increasingly considering composite materials as an option to create lighter structures without compromising structural stiffness and to significantly increase their efficiency. In the design of composite material structures, a challenge arises due to a large number of design variables, therefore numerical optimization is required for a better design. Given this, the purpose of this study is to propose an optimization methodology for the design of a tapered beam, considering the vibration constrains present in rotating components. This is achieved by coupling a numerical model which considers the bending modes of vibration, with an optimization algorithm, both coded in MATLAB. Five optimization algorithms, heuristic and deterministic, are coded and compared and the most efficient method is selected. Because the ply orientation angles can assume an infinite number of possible angles, or follow the regular 0 / ±45 / 90 degrees approach, four possible tuning approaches are defined. The beam is optimized for the following design cases of boundary conditions and design requirements: the presence or absence of a tensile axial force, the presence or absence of a taper, three taper configurations, four proposed structural tuning approaches and four boundary conditions. Two of these structural tuning approaches are compared for its influence in the dynamic behavior of the structural component and in achieving better values of in-plane and out-of-plane stresses. The results demonstrate the Genetic Algorithm is an efficient method for optimization, a design analysis is an important step in optimization, and an appropriate tuning approach can improve the overall efficiency of the optimized structure

Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function

Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications---for which proper functionality depends sensitively on the extent of synchronization---there remains a lack of understanding for how systems evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system's ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments.Comment: 25 pages, 6 figure

A Genetic Search in Frequency Space for Stabilizing Atoms by High-Intensity Laser Fields

The goal of this paper is to explore the power of stochastic search methods, in particular genetic algorithms, to solve a challenging problem in experimental physics. The problem is to find an optimum frequency to stabilize atoms by high-intensity laser fields. The standard approach to search for optimal laser parameters has been by trial and error. This is the first known application of a genetic algorithm technique to model atomic stabilization. Genetic algorithms worked well for this problem as a way to automate the search in a time efficient manner. A parallel platform is used to perform the genetic search efficiently. Locating the best frequency to achieve a suppression of ionization, which is predicted to occur at high intensities, can help design a laboratory experiment and tune to that frequency in order to identify a stabilization effect. The genetic algorithms did successfully identify this optimum frequency. It is indeed possible to extend the number of unknown tunable laser parameters, beyond searching merely over frequency space. For instance, optimal pulse shape and pulse duration can also be included. While conducting such a search in multi-dimensional parameter space, parallel genetic algorithms can offer an advantage to the tedious trial and error procedures

Simulated Annealing

The book contains 15 chapters presenting recent contributions of top researchers working with Simulated Annealing (SA). Although it represents a small sample of the research activity on SA, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. In fact, one of the salient features is that the book is highly multidisciplinary in terms of application areas since it assembles experts from the fields of Biology, Telecommunications, Geology, Electronics and Medicine

Readiness of Quantum Optimization Machines for Industrial Applications

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number of problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for testing near-term quantum annealers and other quantum algorithmic strategies for optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied versio

Optimizing Omega

"The original publication is available at www.springerlink.com " Copyright Springer. DOI: 10.1007/s10898-008-9396-5This paper considers the Omega function, proposed by Cascon, Keating & Shadwick as a performance measure for comparing financial assets. We discuss the use of Omega as a basis for portfolio selection. We show that the problem of choosing portfolio weights in order to maximize Omega typically has many local solutions and we describe some preliminary computational experience of finding the global optimum using a NAG library implementation of the Huyer & Neumaier MCS method.Peer reviewe

An Evolutionary Computational Approach for the Problem of Unit Commitment and Economic Dispatch in Microgrids under Several Operation Modes

In the last decades, new types of generation technologies have emerged and have been gradually integrated into the existing power systems, moving their classical architectures to distributed systems. Despite the positive features associated to this paradigm, new problems arise such as coordination and uncertainty. In this framework, microgrids constitute an effective solution to deal with the coordination and operation of these distributed energy resources. This paper proposes a Genetic Algorithm (GA) to address the combined problem of Unit Commitment (UC) and Economic Dispatch (ED). With this end, a model of a microgrid is introduced together with all the control variables and physical constraints. To optimally operate the microgrid, three operation modes are introduced. The first two attend to optimize economical and environmental factors, while the last operation mode considers the errors induced by the uncertainties in the demand forecasting. Therefore, it achieves a robust design that guarantees the power supply for different confidence levels. Finally, the algorithm was applied to an example scenario to illustrate its performance. The achieved simulation results demonstrate the validity of the proposed approach.Ministerio de Ciencia, Innovación y Universidades TEC2016-80242-PMinisterio de Economía y Competitividad PCIN-2015-043Universidad de Sevilla Programa propio de I+D+