Non stationary operator selection with island models

The purpose of adaptive operator selection is to choose dynamically the most suitable variation operator of an evolutionary algorithm at each iteration of the search process. These variation operators are applied on individuals of a population which evolves, according to an evolutionary process, in order to find an optimal solution. Of course the efficiency of an operator may change during the search and therefore its application should be precisely controlled. In this paper, we use dynamic island models as operator selection mechanisms. A sub-population is associated to each operators and individuals are allowed to migrate from one sub-population to another one. In order to evaluate the performance of this adaptive selection mechanism, we propose an abstract operator representation using fitness improvement distributions that allow us to define non stationary operators with mutual interactions. Our purpose is to show that the adaptive selection is able to identify not only good operators but also suitable sequences of operators

Mass concentration in a nonlocal model of clonal selection

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model describing dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling, which describes regulatory feedback loops in cell proliferation and differentiation process. We show that such coupling leads to mass concentration in points corresponding to maximum of the self-renewal potential and the model solutions tend asymptotically to a linear combination of Dirac measures. Furthermore, using a Lyapunov function constructed for a finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in space of positive Radon measures equipped with flat metric. The analytical results are illustrated by numerical simulations

Utterance Selection Model of Language Change

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.Comment: 21 pages, 17 figure

Is the Size Distribution of Income in Canada a Random Walk?

Several recent studies have investigated whether the size distribution of income in the United States follows a random walk meaning that it has a unit root, with mixed results. In this paper, we investigate the same issue using Canadian national and provincial income inequality data. The investigation is conducted using three different unit root tests. The results suggest modeling the Gini coefficients for Canada and for most provinces as an I(1) is quite reasonable.

Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).Comment: 49 pages, 16 figure

Unit Root Tests of Canadian Poverty Measures

This note examines the non-stationarity property of a most widely used Canadian poverty measure, low income cut-off, for Canada and for each of its ten provinces using various unit root tests which started gaining popularity since the early 1980s. Most test results indicate that the Canadian poverty rates for the period of 1980 to 2003 are non-stationary. Therefore it is quite reasonable and appropriate to model the Canadian poverty rates as an I(1) process in the empirical studies on poverty issues in Canada.

Fog Computing in Medical Internet-of-Things: Architecture, Implementation, and Applications

In the era when the market segment of Internet of Things (IoT) tops the chart in various business reports, it is apparently envisioned that the field of medicine expects to gain a large benefit from the explosion of wearables and internet-connected sensors that surround us to acquire and communicate unprecedented data on symptoms, medication, food intake, and daily-life activities impacting one's health and wellness. However, IoT-driven healthcare would have to overcome many barriers, such as: 1) There is an increasing demand for data storage on cloud servers where the analysis of the medical big data becomes increasingly complex, 2) The data, when communicated, are vulnerable to security and privacy issues, 3) The communication of the continuously collected data is not only costly but also energy hungry, 4) Operating and maintaining the sensors directly from the cloud servers are non-trial tasks. This book chapter defined Fog Computing in the context of medical IoT. Conceptually, Fog Computing is a service-oriented intermediate layer in IoT, providing the interfaces between the sensors and cloud servers for facilitating connectivity, data transfer, and queryable local database. The centerpiece of Fog computing is a low-power, intelligent, wireless, embedded computing node that carries out signal conditioning and data analytics on raw data collected from wearables or other medical sensors and offers efficient means to serve telehealth interventions. We implemented and tested an fog computing system using the Intel Edison and Raspberry Pi that allows acquisition, computing, storage and communication of the various medical data such as pathological speech data of individuals with speech disorders, Phonocardiogram (PCG) signal for heart rate estimation, and Electrocardiogram (ECG)-based Q, R, S detection.Comment: 29 pages, 30 figures, 5 tables. Keywords: Big Data, Body Area Network, Body Sensor Network, Edge Computing, Fog Computing, Medical Cyberphysical Systems, Medical Internet-of-Things, Telecare, Tele-treatment, Wearable Devices, Chapter in Handbook of Large-Scale Distributed Computing in Smart Healthcare (2017), Springe