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Full-Text Articles in Physical Sciences and Mathematics
Algorithm For Generating Derivative Structures, Gus L. W. Hart, Rodney W. Forcade
Algorithm For Generating Derivative Structures, Gus L. W. Hart, Rodney W. Forcade
Faculty Publications
We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The run time of the algorithm scales linearly with the number of unique structures found.
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We use a new algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d}, on the commuting variables a, b, c, d, with zero autocorrelation function. Then we use these sequences to construct a series of new three and four variable orthogonal designs in order 36. We show that the necessary conditions plus (.s1, s2, s3, s4) not equal to 12816 18 816 221313 26721 36 816 4889 12825 191313 23 424 289 9 381015 8899 14425 22 916 are sufficient for the existence of an OD(36; s1, s2 s3, s4) constructed using four circulant …
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Basel, 1979, by A. V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the existence of many new weighing matrices and orthogonal designs of order 2n where n is odd. We give a number of new constructions for orthogonal designs. Then using number theory, linear algebra and computer searches we find new weighing …
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices: Ii, C. Koukouvinos, E. Lappas, M. Mitrouli, Jennifer Seberry
An Algorithm To Find Formulae And Values Of Minors For Hadamard Matrices: Ii, C. Koukouvinos, E. Lappas, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
An algorithm computing the (n — j) x (n — j ) , j = 1, 2, ... minors of Hadamard matrices of order n is presented. Its implementation is analytically described step by step for several values of n and j. For j = 7 the values of minors are computed for the first time. A formulae estimating all the values of (n — j) x (n — j) minors is predicted.
A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken
A Hike Through The Forest: The Knapsack Problem In Graph Theory, Bridget K. Druken
Senior Honors Projects
Graph theory is a branch of mathematics which studies graphs a collection of a set of edges and vertices used to sometimes model structures. My interest in graph theory began last semester in a math/computer science course entitled “Discrete Structures." One aspect which makes graph theory an appealing area to research is the amount of understanding that comes from a relatively short amount of time spent learning the subject material. The visual appeal of being able to draw a graph along practical applications that surface daily make graph theory a prime candidate for further research. Through research of the history …
Machine Learning And Graph Theory Approaches For Classification And Prediction Of Protein Structure, Gulsah Altun
Machine Learning And Graph Theory Approaches For Classification And Prediction Of Protein Structure, Gulsah Altun
Computer Science Dissertations
Recently, many methods have been proposed for the classification and prediction problems in bioinformatics. One of these problems is the protein structure prediction. Machine learning approaches and new algorithms have been proposed to solve this problem. Among the machine learning approaches, Support Vector Machines (SVM) have attracted a lot of attention due to their high prediction accuracy. Since protein data consists of sequence and structural information, another most widely used approach for modeling this structured data is to use graphs. In computer science, graph theory has been widely studied; however it has only been recently applied to bioinformatics. In this …
Improving Performance Of The Filtered-X Least Mean Square Algorithm For Active Control Of Noise Contatining Multiple Quasi-Stationary Tones, Stephan P. Lovstedt
Improving Performance Of The Filtered-X Least Mean Square Algorithm For Active Control Of Noise Contatining Multiple Quasi-Stationary Tones, Stephan P. Lovstedt
Theses and Dissertations
The Filtered-X Least-Mean-Square (FXLMS) algorithm is widely used in active noise control due to its robustness, simplicity, and ability to be implemented in real time. In a feedforward implementation of the FXLMS algorithm, a reference signal that is highly correlated with the noise to be controlled is filtered with an estimate of the transfer function of the secondary path. The convergence characteristics of the FXLMS algorithm have been well studied. A convergence parameter is used to optimize the convergence of the algorithm. However, the optimal value for the convergence parameter is frequency dependent. Thus for noise containing multiple tones at …
Simulation And Visualization Of Environments With Multidimensional Time, Luther A. Tychonievich
Simulation And Visualization Of Environments With Multidimensional Time, Luther A. Tychonievich
Theses and Dissertations
This work introduces the notion of computational hypertime, or the simulation and visualization of hypothetical environments possessing multidimensional time. An overview of hypertime is provided,including an intuitive visualization paradigm and a discussion of the failure of common simulation techniques when extended to include multidimensional time. A condition for differential equations describing hypertime motion to be amenable to standard time-iterative simulation techniques is provided,but is not satisfied by any known model of physics. An alternate simulation algorithm involving iterative refinement of entire equations of motion is presented,with an example implementation to solve elastic collisions in hypertime. An artificial intelligence algorithm for …
Topological And Categorical Properties Of Binary Trees, Homeira Pajoohesh
Topological And Categorical Properties Of Binary Trees, Homeira Pajoohesh
Publications and Research
Binary trees are very useful tools in computer science for estimating the running time of so-called comparison based algorithms, algorithms in which every action is ultimately based on a prior comparison between two elements. For two given algorithms A and B where the decision tree of A is more balanced than that of B, it is known that the average and worst case times of A will be better than those of B, i.e., ₸A(n) ≤₸B(n) and TWA (n)≤TWB (n). Thus the most balanced and the most imbalanced binary trees play a main role. Here we consider them as semilattices …
An Energy-Aware Multilevel Clustering Algorithm For Wireless Sensor Networks, Xinfang Yan, Jiangtao Xi, Joe F. Chicharo, Yanguang Yu
An Energy-Aware Multilevel Clustering Algorithm For Wireless Sensor Networks, Xinfang Yan, Jiangtao Xi, Joe F. Chicharo, Yanguang Yu
Faculty of Informatics - Papers (Archive)
Clustering sensors nodes as the basic of routing is an efficient mechanism for prolonging the lifetime of wireless sensor networks. In this paper, the high-efficient multilevel clustering is abstracted as a root tree which has the performances of the minimal relay set and the maximal weight according to graph theory. A mathematical model for the clustering virtual backbone is built. Based on the model, an algorithm called energy-aware multilevel clustering (EAMC) is proposed. The EAMC can reduce the number of relays used for data transmission by minimizing the amount of the nodes in the root tree (that is cluster-head). Furthermore, …