Algorithms for computing Fibonacci numbers quickly

A study of the running time of several known algorithms and several new algorithms to compute the n[superscript th] element of the Fibonacci sequence is presented. Since the size of the n[superscript th] Fibonacci number grows exponentially with n, the number of bit operations, instead of the number of integer operations, was used as the unit of time. The number of bit operations used to compute f[subscript n] is reduced to less than 1/2 of the number of bit operations used to multiply two n bit numbers. The algorithms were programmed in Ibuki Common Lisp and timing runs were made on a Sequent Balance 21000. Multiplication was implemented using the standard n² algorithm. Times for the various algorithms are reported as various constants times n². An algorithm based on generating factors of Fibonacci numbers had the smallest constant. The Fibonacci sequence, arranged in various ways, is searched for redundant information that could be eliminated to reduce the number of operations. Cycles in the b[superscript th] bit of f[subscript n] were discovered but are not yet completely understood

Air Force Institute of Technology Research Report 2012

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

Algebraic curves and applications to coding theory.

by Yan Cho Hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 122-124).Abstract also in Chinese.Chapter 1 --- Complex algebraic curves --- p.6Chapter 1.1 --- Foundations --- p.6Chapter 1.1.1 --- Hilbert Nullstellensatz --- p.6Chapter 1.1.2 --- Complex algebraic curves in C2 --- p.9Chapter 1.1.3 --- Complex projective curves in P2 --- p.11Chapter 1.1.4 --- Affine and projective curves --- p.13Chapter 1.2 --- Algebraic properties of complex projective curves in P2 --- p.16Chapter 1.2.1 --- Intersection multiplicity --- p.16Chapter 1.2.2 --- Bezout's theorem and its applications --- p.18Chapter 1.2.3 --- Cubic curves --- p.21Chapter 1.3 --- Topological properties of complex projective curves in P2 --- p.23Chapter 1.4 --- Riemann surfaces --- p.26Chapter 1.4.1 --- Weierstrass &-function --- p.26Chapter 1.4.2 --- Riemann surfaces and examples --- p.27Chapter 1.5 --- Differentials on Riemann surfaces --- p.28Chapter 1.5.1 --- Holomorphic differentials --- p.28Chapter 1.5.2 --- Abel's Theorem for tori --- p.31Chapter 1.5.3 --- The Riemann-Roch theorem --- p.32Chapter 1.6 --- Singular curves --- p.36Chapter 1.6.1 --- Resolution of singularities --- p.37Chapter 1.6.2 --- The topology of singular curves --- p.45Chapter 2 --- Coding theory --- p.48Chapter 2.1 --- An introduction to codes --- p.48Chapter 2.1.1 --- Efficient noiseless coding --- p.51Chapter 2.1.2 --- The main coding theory problem --- p.56Chapter 2.2 --- Linear codes --- p.58Chapter 2.2.1 --- Syndrome decoding --- p.63Chapter 2.2.2 --- Equivalence of codes --- p.65Chapter 2.2.3 --- An introduction to cyclic codes --- p.67Chapter 2.3 --- Special linear codes --- p.71Chapter 2.3.1 --- Hamming codes --- p.71Chapter 2.3.2 --- Simplex codes --- p.72Chapter 2.3.3 --- Reed-Muller codes --- p.73Chapter 2.3.4 --- BCH codes --- p.75Chapter 2.4 --- Bounds on codes --- p.77Chapter 2.4.1 --- Spheres in Zn --- p.77Chapter 2.4.2 --- Perfect codes --- p.78Chapter 2.4.3 --- Famous numbers Ar (n，d) and the sphere-covering and sphere packing bounds --- p.79Chapter 2.4.4 --- The Singleton and Plotkin bounds --- p.81Chapter 2.4.5 --- The Gilbert-Varshamov bound --- p.83Chapter 3 --- Algebraic curves over finite fields and the Goppa codes --- p.85Chapter 3.1 --- Algebraic curves over finite fields --- p.85Chapter 3.1.1 --- Affine varieties --- p.85Chapter 3.1.2 --- Projective varieties --- p.37Chapter 3.1.3 --- Morphisms --- p.89Chapter 3.1.4 --- Rational maps --- p.91Chapter 3.1.5 --- Non-singular varieties --- p.92Chapter 3.1.6 --- Smooth models of algebraic curves --- p.93Chapter 3.2 --- Goppa codes --- p.96Chapter 3.2.1 --- Elementary Goppa codes --- p.96Chapter 3.2.2 --- The affine and projective lines --- p.98Chapter 3.2.3 --- Goppa codes on the projective line --- p.102Chapter 3.2.4 --- Differentials and divisors --- p.105Chapter 3.2.5 --- Algebraic geometric codes --- p.112Chapter 3.2.6 --- Codes with better rates than the Varshamov- Gilbert bound and calculation of parameters --- p.116Bibliograph

Air Force Institute of Technology Research Report 2010

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physic

採餌問題のための確率的探索戦略の設計と最適化

Autonomous robot’s search strategy is the set of rules that it employs while looking for targets in its environment. In this study, the stochastic movement of robots in unknown environments is statistically studied, using a Levy walk method. Biological systems (e.g., foraging animals) provide useful models for designing optimal stochastic search algorithms. Observations of biological systems, ranging from large animals to immune cells, have inspired the design of efficient search strategies that incorporate stochastic movement. In this study, we seek to identify the optimal stochastic strategies for autonomous robots. Given the complexity of interaction between the robot and its environment, optimization must be performed in high-dimensional parameter space. The effect of the explanatory variable on the forger robot movement with the minimum required energy was also studied using experiments done by the response surface methodology (RSM). We analyzed the extent to which search efficiency requires these characteristics, using RSM. Correlation between the involved parameters via a Lévy walk process was examined through designing a setup for the experiments to determine the interaction of the involved variables and the robot movement. The extracted statistical model represents the priority influence of those variables on the robot by developing the statistical model of the mentioned unknown area. The efficiency of a simple strategy was investigated based on Lévy walk search in two-dimensional landscapes with clumped resource distributions. We show how RSM techniques can be used to identify optimal parameter values as well as to describe how sensitive efficiency reacts to the changes in these values. Here, we identified optimal parameter for designing robot by using stochastic search pattern and applying mood-switching criteria on a mixture of speed and sensor and μ to determine how many robots are needed for a solution. Fractal criterion-based robot strategies were more efficient than those based on the resource encounter criterion, and the former was found to be more robust to changes in resource distribution as well.九州工業大学博士学位論文 学位記番号:生工博甲第358号 学位授与年月日:令和元年9月20日1 Introduction|2 Levy Walk|3 Design of Experiment (DOE)|4 Response Surface Methodology|5 Results and Discussions|6 Conclusion九州工業大学令和元年

Feasibility of using citations as document summaries

The purpose of this research is to establish whether it is feasible to use citations as document summaries. People are good at creating and selecting summaries and are generally the standard for evaluating computer generated summaries. Citations can be characterized as concept symbols or short summaries of the document they are citing. Similarity metrics have been used in retrieval and text summarization to determine how alike two documents are. Similarity metrics have never been compared to what human subjects think are similar between two documents. If similarity metrics reflect human judgment, then we can mechanize the selection of citations that act as short summaries of the document they are citing. The research approach was to gather rater data comparing document abstracts to citations about the same document and then to statistically compare those results to several document metrics; frequency count, similarity metric, citation location and type of citation. There were two groups of raters, subject experts and non-experts. Both groups of raters were asked to evaluate seven parameters between abstract and citations: purpose, subject matter, methods, conclusions, findings, implications, readability, andunderstandability. The rater was to identify how strongly the citation represented the content of the abstract, on a five point likert scale. Document metrics were collected for frequency count, cosine, and similarity metric between abstracts and associated citations. In addition, data was collected on the location of the citations and the type of citation. Location was identified and dummy coded for introduction, method, discussion, review of the literature and conclusion. Citations were categorized and dummy coded for whether they refuted, noted, supported, reviewed, or applied information about the cited document. The results show there is a relationship between some similarity metrics and human judgment of similarity.Ph.D., Information Studies -- Drexel University, 200

Programming an interim report on the SETL project. Part I: generalities. Part II: the SETL language and examples of its use

A summary of work during the past several years on SETL, a new programming language drawing its dictions and basic concepts from the mathematical theory of sets, is presented. The work was started with the idea that a programming language modeled after an appropriate version of the formal language of mathematics might allow a programming style with some of the succinctness of mathematics, and that this might ultimately enable one to express and experiment with more complex algorithms than are now within reach. Part I discusses the general approach followed in the work. Part II focuses directly on the details of the SETL language as it is now defined. It describes the facilities of SETL, includes short libraries of miscellaneous and of code optimization algorithms illustrating the use of SETL, and gives a detailed description of the manner in which the set-theoretic primitives provided by SETL are currently implemented. (RWR

Automatic recognition of three dimensional planar objects by Hough transform type operations

This thesis describes an investigation into the recognition from range data of three dimensional objects with plane surfaces. In it a Hough transform type operation is used to identify objects. This is adapted for three dimensions and uses a voting scheme to identify objects. First, all available edges of the object present in the scene are extracted. Then, two edges of the object and two lines of a model are taken at a time. These are pruned and potential matching lines are selected. Next, geometric transformations necessary to take them into a fixed position in space are calculated. Matrices resulting from successful matches are computed and stored. The presence of an object similar to a model results in the generation of the same matrices. Recognition is achieved by choosing the model with the highest occurring matrix. In order to extract edges a vision system is designed and set up. In it a stripe of light generated from the projector together with a camera is employed. A procedure to calibrate the system and extract three dimensional information is devised. Then objects are scanned and from the images taken, coordinates of edge points are computed. Next, edge points are linked and edges of the object are extracted and a recognition algorithm is applied. The system is tested on objects with varying complexity. Recognition is performed in two different categories. First objects are placed on a specific face. Then they are recognised in arbitrary position and orientation. For each object the results and implications of the recognition algorithm, are investigated. A modified version of the recognition algorithm with two and three connected lines is tested and compared with previous experiments

An evaluation of factors affecting students' use of a web-based engineering resource

The purpose of this work was to investigate the relationship between a number of influential factors, including cognitive style and approach to learning, and students’ processing behaviour during their use of a particular Web-based resource for Electronics and Electrical Engineering undergraduates. This was achieved through the development of a learner profile for each student using Riding’s (1991) Revised Study Process Questionnaire (R-SPQ-2F). The quantitative component of the research was then set against a detailed analysis of students’ processing behaviour using verbal protocol data gathered through individual think-aloud sessions and post-intervention interviews. The results of the quantitative component of the research provided no compelling evidence to suggest that cognitive style was a factor that influenced student performance while using the resource or their perceptions of the package. There was however, some evidence to suggest that the package was more positively received by students who profiled as deep learners than their surface counterparts. The analysis of students’ processing behaviour from their verbal protocols highlighted a number of the resource’s shortcomings, which typically promoted a surface, goal-oriented approach to its content. It also identified problems with the design and structure of the resource, which at times had a deleterious effect on learning. The results also raised questions regarding the efficacy and use of psychometric inventories in this kind of research