Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Computer Networks Security Models - A New Approach for Denial-of-Services Attacks Mitigation

Computer networks are a critical factor for the performance of a modern company. Managing networks is as important as managing any other aspect of the company’s performance and security. There are many tools and appliances for monitoring the traffic and analyzing the network flow security. They use different approaches and rely on a variety of characteristics of the network flows. Network researchers are still working on a common approach for security baselining that might enable early watch alerts. This research focuses on the network security models, particularly the Denial-of-Services (DoS) attacks mitigation, based on a network flow analysis using the flows measurements and the theory of Markov models. The content of the paper comprises the essentials of the author’s doctoral thesis.

Education in Computer Science and the Role of the Teacher in the Environment of Open Educational Resources

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Interactive Visualization of the Building of University of Economics – Varna via 3D Modeling

The object of this paper is presenting the University of Economics – Varna, using a 3D model with 3Ds MAX. Created in 1920, May 14, University of Economics - Varna is a cultural institution with a place and style of its own. With the emergence of the three-dimensional modeling we entered a new stage of the evolution of computer graphics. The main target is to preserve the historical vision, to demonstrate forward-thinking and using of future-oriented approaches.

Content-Based Image Retrieval for Computer Tomography Images Using Wavelet Descriptors

An approach to building a CBIR-system for searching computer tomography images using the methods of wavelet-analysis is presented in this work. The index vectors are constructed on the basis of the local features of the image and on their positions. The purpose of the proposed system is to extract visually similar data from the individual personal records and from analogous analysis of other patients.

Five Turning Points in the Historical Progress of Statistics - My Personal Vision

Statistics has penetrated almost all branches of science and all areas of human endeavor. At the same time, statistics is not only misunderstood, misused and abused to a frightening extent, but it is also often much disliked by students in colleges and universities. This lecture discusses/covers/addresses the historical development of statistics, aiming at identifying the most important turning points that led to the present state of statistics and at answering the questions “What went wrong with statistics?” and “What to do next?”. ACM Computing Classification System (1998): A.0, A.m, G.3, K.3.2.

Computer aided licence selection

A model of multiple criteria decision making is presented for selecting the “best” of a finite number of alternatives. Techniques of scoring the alternatives and weighting the criteria are combined with different evaluating procedures and amalgamated in an interactive algorithm. Application of this method for choosing the best tender in a competitive bidding is discussed and a case is presented in some detail.

Effects of cooperative and individual integrated learning system on attitudes and achievement in mathematics

This study compares the effects of cooperative delivery (CD) and individual delivery (ID) of integrated learning system (ILS) instruction in mathematics on achievement, attitudes and behaviors in adult (16-21 yrs.) high school students (grades 9-13). The study was conducted in an urban adult high school in Miami-Dade County Public Schools using a pre-test/post-test design. Achievement was measured using the Test of Adult Basic Education (TABE) by CTB MC-Graw-Hill and Compass Learning. An attitudinal survey measured attitudes towards mathematics, the computer-related lessons, and attitudes toward group activities. Behavior was assessed using computer lab observations. ^ Two-way analyses of variance (ANOVA) were conducted on achievement (TABE and Compass) by group and time (pre and post). A one-way ANOVA was conducted on the overall attitude by group on the five components (i.e., content mathematics, delivery/computers, cooperative, partners, and self efficacy) and a one-way ANOVA was conducted on the on-task behavior by group. ^ The results of the study revealed that CD and ID students working on mathematics activities delivered by the ILS performed similarly on achievement tests of the TABE. The CD-ILS students had significantly better overall mathematics attitudes than the ID-ILS students and the ID-ILS group was on-task significantly more than the CD-ILS group. This study concludes that regularity and period of time over which the ILS is used may prove to be important variables although there were insufficient data to fully investigate the impact of models of use. Additionally, a minimum amount of time-on-system is necessary before gains can become apparent in innumeracy and increasing exposure to the system may have beneficial effects on learning. ^

A method for enhancing digital information displayed to computer users with visual refractive errors via spatial and spectral processing

This research pursued the conceptualization, implementation, and verification of a system that enhances digital information displayed on an LCD panel to users with visual refractive errors. The target user groups for this system are individuals who have moderate to severe visual aberrations for which conventional means of compensation, such as glasses or contact lenses, does not improve their vision. This research is based on a priori knowledge of the user's visual aberration, as measured by a wavefront analyzer. With this information it is possible to generate images that, when displayed to this user, will counteract his/her visual aberration. The method described in this dissertation advances the development of techniques for providing such compensation by integrating spatial information in the image as a means to eliminate some of the shortcomings inherent in using display devices such as monitors or LCD panels. Additionally, physiological considerations are discussed and integrated into the method for providing said compensation. In order to provide a realistic sense of the performance of the methods described, they were tested by mathematical simulation in software, as well as by using a single-lens high resolution CCD camera that models an aberrated eye, and finally with human subjects having various forms of visual aberrations. Experiments were conducted on these systems and the data collected from these experiments was evaluated using statistical analysis. The experimental results revealed that the pre-compensation method resulted in a statistically significant improvement in vision for all of the systems. Although significant, the improvement was not as large as expected for the human subject tests. Further analysis suggest that even under the controlled conditions employed for testing with human subjects, the characterization of the eye may be changing. This would require real-time monitoring of relevant variables (e.g. pupil diameter) and continuous adjustment in the pre-compensation process to yield maximum viewing enhancement.

An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

Effects of Cooperative and Individual Integrated Learning System on Attitudes and Achievement in Mathematics

The purpose of this study was to determine the effects of a computer-based Integrated Learning Systems (ILS) model used with adult high school students engaging mathematics activities. This study examined achievement, attitudinal and behavior differences between students completing ILS activities in a traditional, individualized format compared to cooperative learning groups.

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

A method for enhancing digital information displayed to computer users with visual refractive errors via spatial and spectral processing

This research pursued the conceptualization, implementation, and verification of a system that enhances digital information displayed on an LCD panel to users with visual refractive errors. The target user groups for this system are individuals who have moderate to severe visual aberrations for which conventional means of compensation, such as glasses or contact lenses, does not improve their vision. This research is based on a priori knowledge of the user's visual aberration, as measured by a wavefront analyzer. With this information it is possible to generate images that, when displayed to this user, will counteract his/her visual aberration. The method described in this dissertation advances the development of techniques for providing such compensation by integrating spatial information in the image as a means to eliminate some of the shortcomings inherent in using display devices such as monitors or LCD panels. Additionally, physiological considerations are discussed and integrated into the method for providing said compensation. In order to provide a realistic sense of the performance of the methods described, they were tested by mathematical simulation in software, as well as by using a single-lens high resolution CCD camera that models an aberrated eye, and finally with human subjects having various forms of visual aberrations. Experiments were conducted on these systems and the data collected from these experiments was evaluated using statistical analysis. The experimental results revealed that the pre-compensation method resulted in a statistically significant improvement in vision for all of the systems. Although significant, the improvement was not as large as expected for the human subject tests. Further analysis suggest that even under the controlled conditions employed for testing with human subjects, the characterization of the eye may be changing. This would require real-time monitoring of relevant variables (e.g. pupil diameter) and continuous adjustment in the pre-compensation process to yield maximum viewing enhancement.

The impact of standards-based practices in mathematics on the achievement of low-performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

CASIMIRO: a robot head for human-computer interaction

The physical appearance and behavior of a robot is an important asset in terms of Human-Computer Interaction. Multimodality is also fundamental, as we humans usually expect to interact in a natural way with voice, gestures, etc. People approach complex interaction devices with stances similar to those used in their interaction with other people. In this paper we describe a robot head, currently under development, that aims to be a multimodal (vision, voice, gestures,...) perceptual user interface.