Minimal Committee Problem for Inconsistent Systems of Linear Inequalities on the Plane

A representation of an arbitrary system of strict linear inequalities in R^n as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a committee solution of an inconsistent plane system of linear inequalities is given. A solution of two problems on minimal committee of a plane system is proposed. The obtained solutions to these problems can be found by means of the proposed algorithm.Comment: 29 pages, 2 figure

Graphs for Pattern Recognition

This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition. Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important special subclass of infeasible systems of constraints with a monotonicity property – systems whose multi-indices of feasible subsystems form abstract simplicial complexes (independence systems), which are fundamental objects of combinatorial topology. The methods of data mining and machine learning discussed in this monograph form the foundation of technologies like big data and deep learning, which play a growing role in many areas of human-technology interaction and help to find solutions, better solutions and excellent solutions

Dynamical Systems; Proceedings of an IIASA Workshop, Sopron, Hungary, September 9-13, 1985

The investigation of special topics in systems dynamics -- uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory -- has become a major issue at the System and Decision Sciences Research Program of IIASA. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under variations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of nonlinear dynamic systems theory to biomathematics and ecology. The proceedings of a workshop on the "Mathematics of Dynamic Processes", dealing with these topics is presented in this volume

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

Instructor perceptions of student learning in secondary and postsecondary algebra classes.

The purpose of this study was to investigate various secondary to postsecondary mathematics transition issues for students. Making successful transitions from high school to postsecondary study has become necessary if our nation\u27s young people are to obtain and hold good-paying jobs in the workplace. Knowledge of algebra is the critical gatekeeper for success in completing high school and postsecondary training. Nationwide 22% of entering freshmen at degree-granting institutions are under-prepared for college mathematics and must enroll in developmental mathematics classes that repeat the content of high school mathematics courses. Researchers have documented disconnects between secondary and postsecondary mathematics\u27 expectations and assessments. Reform initiatives, many of which are working in isolation from each other, have been undertaken at both the secondary and postsecondary level, but little research has been conducted to determine whether there are differences in instructor beliefs at the secondary and postsecondary level that may impact the transitions for students in mathematics. A researcher-developed survey was administered to a random sample of high school, two-year community and technical college, and four-year college and university mathematics instructors in Kentucky to determine how well they believed students were mastering American Diploma Project algebra benchmarks in high school, non-creditbearing, and credit-bearing college algebra classes. Findings indicated there are differences in high school and four-year college and university and high school and two-year community college instructors\u27 perceptions of perceived algebra learning in high school classes and in credit-bearing college algebra classes, with high school teachers consistently rating mastery of algebra topics higher than the college instructors. Research indicates that instructor perceptions have an impact on instruction and on student learning. Differences in instructor perceptions of student learning in key transition algebra classes may affect the quality of instruction, and consequently equity for all students may be in jeopardy. Significant three-way dialogue between high school, community college, and four-year college and university instructors is needed in order to mediate differences in instructor beliefs and find ways to enable students to make successful transitions from high school to college mathematics

Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods

Ankara : Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1998.Thesis (Ph.D.) -- Bilkent University, 1998.Includes bibliographical references leaves 86-93.Several algorithms for the feasibility problem are investigated. For linear systems, a number of different block projections approaches have been implemented and compared. The parallel algorithm of Yang and Murty is observed to be much slower than its sequential counterpart. Modification of the step size has allowed us to obtain a much better algorithm, exhibiting considerable speedup when compared to the sequential algorithm. For the convex feasibility problem an approach combining rectangular cutting planes and subgradients is developed. Theoretical convergence results are established for both ca^es. Two broad classes of image recovery problems are formulated as linear feasibility problems and successfully solved with the algorithms developed.Özaktaş, HakanPh.D