Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

An adaptive behavioral immune system: a model of population health behavior

The understanding that immunity could be strengthened in the general population (e.g., through vaccine interventions) supported global advances upon acute infectious disease epidemics in the eighteenth, nineteenth, and twentieth centuries. However, in the twenty-first century, global populations face chronic disease epidemics. Research demonstrates that diseases largely emerge from health risk behavior. The understanding of how health behavior, like the biological immune system, can be strengthened in the general population, could support advances in the twenty-first century. To consider how health behavior can be strengthened in the general population, the authors present a theoretical model of population health behavior. The model operationalizes health behavior as a system of functions that, like the biological immune system, exists in each member of the population. Constructs are presented that operationalize the specific decisions and habits that drive health behavior and behavior change in the general population. The constructs allow the authors to present parallels (1) among existing behavior change theories and (2) between the proposed system and the biological immune system. Through these parallels, the authors introduce a model and a logic of population-level health behavior change. The Adaptive Behavioral Immune System is an integrative model of population health behavior

A philosophy of health: life as reality, health as a universal value

Emphases on biomarkers (e.g. when making diagnoses) and pharmaceutical/drug methods (e.g. when researching/disseminating population level interventions) in primary care evidence philosophies of health (and healthcare) that reduce health to the biological level. However, with chronic diseases being responsible for the majority of all cause deaths and being strongly linked to health behavior and lifestyle; predominantly biological views are becoming increasingly insufficient when discussing this health crisis. A philosophy that integrates biological, behavioral, and social determinants of health could benefit multidisciplinary discussions of healthy publics. This manuscript introduces a Philosophy of Health by presenting its first five principles of health. The philosophy creates parallels among biological immunity, health behavior change, social change by proposing that two general functions—precision and variation—impact population health at biological, behavioral, and social levels. This higher-level of abstraction is used to conclude that integrating functions, rather than separated (biological) structures drive healthy publics. A Philosophy of Health provides a framework that can integrate existing theories, models, concepts, and constructs

Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

Bank risk and performance in the MENA region: The importance of capital requirements

This paper benefits from various risk-and non-risk-based regulatory capital ratios and examines their impact on bank risk and performance in the Middle East and North Africa (MENA) region. Our findings suggest that compliance with Basel capital requirements enhances bank protection against risk, and improves efficiency and profitability. The impact of capital requirements on bank performance is more pronounced for too-big-to-fail banks, banks in periods of crises and banks in countries with good governance. The results are also robust when controlling for the Arab Spring transition period. Finally, endogeneity checks, alternative risk and performance measures, a principal component analysis and other estimation techniques confirm findings. JEL classification: G21, G28, G32, P5

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface