With the advent of advances in Geospatial Information Systems (GIS); there is a need to determine the areas of research and new tools available for GIS systems. GIS consists of the collection, integration, storage, exploitation, and visualization of geographic and contextual data and spatial information. Future GIS needs, techniques, models, and standards should be shared openly among developers for future instantiation of products. The summary of selected areas include (1) support for large-data formats including meta-data transparency, (2) adherence to open standards, (3) generation of extensible architectures, and (4) development of a consistent set of metrics for analysis. The future of GIS products will include non-spatial as well as spatial data which requires information fusion, management functions from machine-processed data to user-defined actionable information, and use-case challenge problems for comparison.
Psoriasis is an autoimmune disorder with the symptom of chronic inflammation of the skin. Psoriasis makes skin cells build up quickly on the skin surface which causes the skin to appear red, dry, and with scaly patches. Adequate treatment for psoriasis is very challenging and a total cure of the disease still does not exit. Mathematical models have long been effective means to predict cellular behaviors of skin regulation under normal or pathological circumstances. In this paper, a proposed control model of psoriasis is described on a given time interval by a nonlinear control system of three differential equations involving the concentrations of dendritic cells (tissues macrophages), T-lymphocytes, and keratinocytes with medication intake as a control function. An optimal control problem of minimizing the release of keratinocytes at the end of the time interval is stated and studied using the Pontryagin maximum principle. Different types of optimal control dependent on model parameters are obtained analytically. Possible applications to an optimal drug therapy are discussed.
A Susceptible, Exposed, Infectious, and Recovered (SEIR) type control model describing the Ebola epidemic in a population of constant size is considered over a fixed time interval. This model is an extension of the well-known SEIR model and is more suitable to the study of the control mechanism of Ebola epidemics. Along with the traditional SEIR compartments, this model contains an isolated infectious compartment representing the number of infected and exposed individuals that have been isolated from the susceptible individuals. The model has two intervention controls reflecting efforts to protect susceptible individuals from infected and exposed individuals. Additionally, there are two control functions that define efforts for the detection and isolation of infected and exposed individuals. The minimization problem of the sum of total fractions of infected and exposed individuals and total weighted costs of control constraints over a given time interval is stated. For the analysis of the corresponding optimal controls, the Pontryagin maximum principle is used. Accordingly, the controls are bang-bang functions determined by the corresponding switching functions. In order to estimate the number of zeros of the switching functions, a new approach is proposed based on the analysis of the Cauchy problems for the derivatives of these functions. It is found that the optimal controls of the original problem have at most one switching. This allows the reduction of the original complex optimal control problem to the solution of a much simpler problem of conditional minimization of a function of three variables. Results of the numerical solution to this problem and their analysis are provided. Keywords: SEIR model; nonlinear control system; optimal control; Pontryagin maximum principle; switching function. ResumenSe considera un modelo de tipo Susceptible, Expuesto, Infeccioso y Recuperado (SEIR) que describe la epidemia del ébola en una población de tamaño constante sobre un intervalo de tiempo fijo. Este modelo es una extensión del bien conocido modelo SEIR y es más adecuado para el estudio del mecanismo de control de la epidemia del ébola. Además de los compartimientos tradicionales del SEIR, este modelo contiene un compartimiento aislado infeccioso que representa el número de individuos infectados y expuestos que han sido aislados de los individuos susceptibles. El modelo tiene dos controles de intervención que reflejan los esfuerzos para proteger a los individuos susceptibles de los individuos infectados y expuestos. Adicionalmente, hay dos funciones de control que definen los esfuerzos para la detección y aislamiento de individuos infectados y expuestos. Se plantea el problema de minimización de la suma del OPTIMAL CONTROL PROBLEM FOR A SEIR TYPE MODEL 81 total de cocientes de individuos infectados y expuestos y el total de costos ponderados de restricciones de control sobre un intervalo de tiempo. Para el análisis de los correspondientes controles óptimos, se usa el principio del máximo de Pontryanguin. En ...
In this paper we propose a novel method of fault detection based on a clustering algorithm developed in the information theoretic framework. A mathematical formulation for a multi-input multi-output (MIMO) system is developed to identify the most informative signals for the fault detection using mutual information (MI) as the measure of correlation among various measurements on the system. This is a modelindependent approach for the fault detection. The effectiveness of the proposed method is successfully demonstrated by employing MI-based algorithm to isolate various faults in 16-cylinder diesel engine in the form of distinct clusters.
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