Analysis Commons^™

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

The Summer Undergraduate Research Fellowship (SURF) Symposium

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model) …

An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, Fei Wang, Hector-Hugo Franco-Penya, John D. Kelleher, John Pugh, Robert J. Ross

Conference papers

Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that …

Inverse Laplace Transform And Post Inversion Formula, Qinmao Zhang

Mathematical Sciences Technical Reports (MSTR)

This paper is dedicated to a general numerical approach to inverse Laplace transforms based on the Post Inversion Formula, which is a theoretical equivalent to the inverse Laplace transform. Though most approaches are too computationally intensive to be of practical use, we introduce an efficient algorithm to compute it based on the Parker-Sochacki method (PSM). This paper also contains some example MATLAB code and algorithm analysis.

An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R³, but also to the general case of finding minimal functionals on hypersurfaces in Rⁿ associated with an arbitrary metric.

Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert

The Summer Undergraduate Research Fellowship (SURF) Symposium

There has been a rise in the use of visual analytic techniques to create interactive predictive environments in a range of different applications. These tools help the user sift through massive amounts of data, presenting most useful results in a visual context and enabling the person to rapidly form proactive strategies. In this paper, we present one such visual analytic environment that uses historical crime data to predict future occurrences of crimes, both geographically and temporally. Due to the complexity of this analysis, it is necessary to find an appropriate statistical method for correlative analysis of spatiotemporal data, as well …

Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed

Applications and Applied Mathematics: An International Journal (AAM)

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

Image Processing Algorithms For Improving Planetary Exploration And Understanding, Ali Pouryazdanpanah

College of Engineering: Graduate Celebration Programs

• To design a fully automated tool-set that allows to detect and extract the sky region in planetary images.

• To develop the new method for rock segmentation in planetary stereo images.
• To develop the new method for shadow detection in planetary images

Coding Theorems On A Non-Additive Generalized Entropy Of Havrda-Charvat And Tsallis, Satish Kumar, Arun Choudhary

Applications and Applied Mathematics: An International Journal (AAM)

A new measure L^β_α, called average code word length of order α and type β is defined and its relationship with a generalized information measure of order α and type β is discussed. Using L^β_α , some coding theorems are proved.

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …

Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.

Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia

Applications and Applied Mathematics: An International Journal (AAM)

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

The Evolution Of Cell Colonies In Volvocacean Algae : Investigation By Theoretical Analysis And Computer Simulation., Frank Noe

Theses

This thesis presents a mathematical analysis and computational simulation which is used to investigate the evolution of cell colonies. The evolutionary transition from unicellular to cell colony form is a prerequesite for multicellular life as it exists abundantly on earth. This transition has occured numerous times independently so that we expect a high selective advantage to be associated with it. The photosynthetic green algae order Volvocaceae is an appropriate set of model organisms for the study of the evolution of cell colonies since it comprises living unicellular organisms, cell colonies, and multicellular organisms of different shapes, sizes and levels of …