Physical Sciences and Mathematics Commons^™

How To Modify Grade Point Average (Gpa) To Make It More Adequate, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, the amounts of knowledge acquired by different graduates of the same program are usually compared by comparing their GPAs. We argue that this is not always the most adequate description: for example, if, after completing all required classes with the highest grade of "excellent" (A), a student takes an additional challenging class and gets a "satisfactory" grade (C), the amount of her knowledge increases, but the GPA goes down. We propose a modification of the GPA which is free of this drawback and is, thus, more adequate for describing the student's knowledge. We also provide a psychological explanation …

Dealing With Uncertainties In Computing: From Probabilistic And Interval Uncertainty To Combination Of Different Types Of Uncertainty, Vladik Kreinovich

Departmental Technical Reports (CS)

To predict values of future quantities, we apply algorithms to the current and past measurement results. Because of the measurement errors and model inaccuracy, the resulting estimates are, in general, different from the desired values of the corresponding quantities. There exist methods for estimating this difference, but these methods have been mainly developed for the two extreme cases: the case when we know the exact probability distributions of all the measurement errors and the interval case, when we only know the bounds on the measurement errors. In practice, we often have some partial information about the probability distributions which goes …

Observable Causality Implies Lorentz Group: Alexandrov-Zeeman-Type Theorem For Space-Time Regions, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The famous Alexandrov-Zeeman theorem proves that causality implies Lorentz group. The physical meaning of this result is that once we observe which event can causally affect which other events, then, using only this information, we can reconstruct the linear structure of the Minkowski space-time. The original Alexandrov-Zeeman theorem is based on the causality relation between events represented by points in space-time. Knowing such a point means that we know the exact moment of time and the exact location of the corresponding event - and that this event actually occurred at a single moment of time and at a single spatial …

How To Estimate Relative Spatial Resolution Of Different Maps Or Images Of The Same Area?, Christian Servin, A A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we describe how to estimate relative spatial resolution of different maps or images of the same area under uncertainty. We consider probabilistic and fuzzy approaches and we show that both approaches lead to the same estimates -- which makes us more confident that this joint result is reasonable.

Interval And Symmetry Approaches To Uncertainty -- Pioneered By Wiener -- Helps Explain Many Seemingly Irrational Human Behaviors: A Case Study, Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been observed that in many cases, when we present a user with three selections od different price (and, correspondingly, different quality), then the user selects the middle selection. This empirical fact -- known as a compromise effect -- seems to contradicts common sense. Indeed, when a rational decision-maker selects one of the two alternatives, and then we add an additional option, then the user will either keep the previous selection or switch to a new option, but he/she will not select a previously rejected option. However, this is exactly what happens under the compromise effect. If we present …

A Simple Probabilistic Explanation Of Term Frequency-Inverse Document Frequency (Tf-Idf) Heuristic (And Variations Motivated By This Explanation), Lukas Havrlant, Vladik Kreinovich

Departmental Technical Reports (CS)

In document analysis, an important task is to automatically find keywords which best describe the subject of the document. One of the most widely used techniques for keyword detection is a technique based on the term frequency-inverse document frequency (tf-idf) heuristic. This techniques has some explanations, but these explanations are somewhat too complex to be fully convincing. In this paper, we provide a simple probabilistic explanation for the tf-idf heuristic. We also show that the ideas behind explanation can help us come up with more complex formulas which will hopefully lead to a more adequate detection of keywords.

Towards Efficient Algorithms For Approximating A Fuzzy Relation By Fuzzy Rules: Case When "And"- And "Or"-Operation Are Distributive, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

A generic fuzzy relation often requires too many parameters to represent -- especially when we have a relation between many different quantities x1, ..., xn. There is, however, a class of relations which require much fewer parameters to describe - namely, relations which come from fuzzy rules. It is therefore reasonable to approximate a given relation by fuzzy rules. In this paper, we explain how this can be done in an important case when "and"- and "or"-operation are distributive -- and we also explain why this case is important.

Wiener's Conjecture About Transformation Groups Helps Predict Which Fuzzy Techniques Work Better, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, application success only comes when we select specific fuzzy techniques (t-norm, membership function, etc.) -- and in different applications, different techniques are the best. How to find the best technique? Exhaustive search of all techniques is not an option: there are too many of them. We need to come up with a narrow class of promising techniques, so that trying them all is realistic. In this paper, we show that such a narrowing can be obtained from transformation groups techniques motivated by N. Wiener's conjecture -- which was, in its turn, motivated by observations about human vision.

Writing Self-Testing Java Classes With Selftest, Yoonsik Cheon

Departmental Technical Reports (CS)

This document provides a tutorial introduction to Java annotations called SelfTest. The SelfTest annotations allow one to annotate Java classes with test data, and the SelfTest annotation processor generates executable JUnit test classes from annotated Java classes by translating test cases to executable JUnit tests. The SelfTest annotations not only automate unit testing of Java classes significantly but also provides a step toward writing self-testing Java classes by embedding test data in source code for both compile and runtime processing.

In Category Of Sets And Relations, It Is Possible To Describe Functions In Purely Category Terms, Vladik Kreinovich, Martine Ceberio, Quentin Brefort

Departmental Technical Reports (CS)

We prove that in the category of sets and relations, it is possible to describe functions in purely category terms.

Towards Decision Making Under Interval, Set-Valued, Fuzzy, And Z-Number Uncertainty: A Fair Price Approach, Joe Lorkowski, Vladik Kreinovich, Rafik Aliev

Departmental Technical Reports (CS)

In this paper, we explore one of the possible ways to make decisions under uncertainty: namely, we explain how to define a fair price for a participation in such a decision, and then select an alternative for which the corresponding fair price is the largest. This idea is explained on the examples of interval uncertainty, set-valued, fuzzy, and Z-number uncertainty.

Simpler-To-Describe Cases Are Often More Difficult To Prove: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many areas of mathematics, simpler-to-describe cases are often more difficult to prove. In this paper, we provide examples of such phenomena (Bieberbach's Conjecture, Poincar\'e Conjecture, Fermat's Last Theorem), and we provide a possible explanation for this empirical fact.

Decision Making Under Interval Uncertainty: What Can And What Cannot Be Computed In Linear Time And In Real Time, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering, we constantly need to make decisions: which design to select, which parameters to select for this design, etc.

The traditional approach to decision making is based on the assumption that we know all possible consequences of each alternative, and we know the probability of each such consequence. Under this assumption, we can describe a rational decision-making process: to each possible consequence, we assign a numerical values called its utility, and we select the alternative for which the expected value of the utility is the largest.

An important advantage of this approach is that it can be performed in …

Extending Ocl To Better Express Uml Qualified Associations, Alla Dove, Aditi Barua, Yoonsik Cheon

Departmental Technical Reports (CS)

A qualified association in the Unified Modeling Language (UML) is an association that allows one to restrict the objects referred in an association using a key called a qualifier. A qualified association can appear in a constraint written in the Object Constraint Language (OCL) to specify a precise UML model. However, the OCL notation fails to provide appropriate support for expressing certain types of constraints written using qualified associations. In this paper we first describe a deficiency of OCL in expressing qualified associations and then propose a small extension to OCL to make it more expressive. The key idea of …

For Each Mathematical Statement, Only Finitely Many Of Its Generalizations Are Useful: A Formal Proof Of E. Bishop's Idea, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Generalization is one of the main mathematical activities. Some generalizations turn out to be useful for working mathematics, while many other generalizations have so far been not very useful. E. Bishop believed that most fruitless-so-far generalizations are hopeless, that every mathematical statement has only a few useful generalizations. In this paper, we show that, under a natural definition of the notion of useful generalization, Bishop's belief can be proven -- moreover, it turns out that for each mathematical statement, only finitely many of its generalizations are useful.

Fuzzy Logic Ideas Can Help In Explaining Kahneman And Tversky's Empirical Decision Weights, Joe Lorkowski, Vladik Kreinovich

Departmental Technical Reports (CS)

Analyzing how people actually make decisions, the Nobelist Daniel Kahneman and his co-author Amos Tversky found out that instead of maximizing the expected gain, people maximize a weighted gain, with weights determined by the corresponding probabilities. The corresponding empirical weights can be explained qualitatively, but quantitatively, these weights remains largely unexplained. In this paper, we show that with a surprisingly high accuracy, these weights can be explained by fuzzy logic ideas.

How To Understand Connections Based On Big Data: From Cliques To Flexible Granules, Ali Jalal-Kamali, M. Shahriar Hossain, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of science and engineering is to predict the future state of the world -- and to come up with actions which will lead to the most favorable outcome. To be able to do that, we need to have a quantitative model describing how the values of the desired quantities change -- and for that, we need to know which factors influence this change. Usually, these factors are selected by using traditional statistical techniques, but with the current drastic increase in the amount of available data -- known as the advent of {\it big data} -- …

From Interval-Valued Probabilities To Interval-Valued Possibilities: Case Studies Of Interval Computation Under Constraints, Luis C. Gutierrez, Martine Ceberio, Vladik Kreinovich, Rebekah L. Gruver, Mariana Peña, Mathew J. Rister, Abraham Saldaña, John Vasquez, Janelle Ybarra, Salem Benferhat

Departmental Technical Reports (CS)

In many engineering situations, we need to make decisions under uncertainty. In some cases, we know the probabilities p_i of different situations i; these probabilities should add up to 1. In other cases, we only have expert estimates of the degree of possibility μ_ii of different situations; in accordance with the possibility theories, the largest of these degrees should be equal to 1.

In practice, we often only know these degrees p_i and μ_ii with uncertainty. Usually, we know the upper bound and the lower bound on each of these values. In other words, …

Deep Mathematical Results Are The Ones That Connect Seemingly Unrelated Areas: Towards A Formal Proof Of Gian-Carlo Rota's Thesis, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When is a mathematical result deep? At first glance, the answer to this question is subjective: what is deep for one mathematician may not sound that deep for another. A renowned mathematician Gian-Carlo Rota expressed an opinion that the notion of deepness is more objective that we may think: namely, that a mathematical statement is deep if and only if it connects two seemingly unrelated areas of mathematics. In this paper, we formalize this thesis, and show that in this formalization, Gian Carlo Rota's thesis becomes a provable mathematical result.

Roadmap For Graduating Students With Expertise In The Analysis And Development Of Secure Cyber-Systems, Ann Q. Gates, Salamah Salamah, Luc Longpre

Departmental Technical Reports (CS)

Modern society is intensely and irreversibly dependent on software systems of extraordinary size and complexity. This includes software systems in domain areas such as defense, energy, communication, transportation, and manufacturing. Due to the rapid expansion and reliance on the global Internet for day-to-day functions of individuals, organizations, governments, and industry around the world, cyber-security has emerged as an essential component of computing curricula. To address regional and national needs, the Computer Science Department has defined a roadmap for educating and preparing students who have expertise in the analysis and development of secure cyber-systems. Toward that vision, the department has set …

Logic Of Scientific Discovery: How Physical Induction Affects What Is Computable, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Most of our knowledge about a physical world comes from physical induction: if a hypothesis is confirmed by a sufficient number of observations, we conclude that this hypothesis is universally true. We show that a natural formalization of this property affects what is computable when processing measurement and observation results, and we explain how this formalization is related to Kolmogorov complexity and randomness. We also consider computational consequences of an alternative idea also coming form physics: that no physical law is absolutely true, that every physical law will sooner or later need to be corrected. It turns out that this …

How To Compare Different Range Estimations: A Symmetry-Based Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

How to compare different range estimators for multivariate functions under uncertainty? To answer this question, we analyze which utility functions can be used for this task. Specifically, we: (1) introduce various invariance assumptions, (2) describe the class of all utility functions which satisfy these assumptions, and (3) show how the resulting utility functions can be used to compare different range estimators.

Range Estimation Under Constraints Is Computable Unless There Is A Discontinuity, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems of interval computations is computing the range of a given function over given intervals. It is known that there is a general algorithm for computing the range of computable functions over computable intervals. However, if we take into account that often in practice, not all possible combinations of the inputs are possible (i.e., that there are constraints), then it becomes impossible to have an algorithm which would always compute this range. In this paper, we explain that the main reason why range estimation under constraints is not always computable is that constraints may introduce discontinuity …

Interleaving Enhances Learning: A Possible Geometric Explanation, Octavio Lerma, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the traditional approach to learning, if we want students to learn how to solve different types of problems, we first teach them how to solve problems of the first type, then how to solve problems of the second type, etc. It turns out that we can speed up learning if we interleave problems of different types. In particular, it has bene empirically shown that interleaving problems of four different types leads to a double speed-up. In this paper, we provide a possible geometric explanation for this empirical fact.

Fitts's Law: Towards A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich, Octavio Lerma

Departmental Technical Reports (CS)

In designing human-computer interfaces, designers use an empirical Fitts's Law, according to which the average time T of accessing an icon of size w at a distance d from the center of the screen is proportional to the logarithm of the ratio w/d. There exist explanations for this law, but these explanations have gaps. In this paper, we show that these gaps can be explained if we analyze this problem from the geometric viewpoint. Thus, we get a geometric explanation of the Fitts's Law.

A Simple Geometric Model Provides A Possible Quantitative Explanation Of The Advantages Of Immediate Feedback In Student Learning, Octavio Lerma, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Calculus is a known bottleneck for many students studying science and engineering. Various techniques have been developed to enhance the students' success. A recent study published in the Notices of American Mathematical Society showed that only one factor determines the success of a technique: the presence of immediate feedback. On average, students who receive immediate feedback learn twice faster than students who are taught in a more traditional way, with a serious feedback only once or twice a semester (after a test).

The very fact that immediate feedback is helpful is not surprising: it helps the student clear misconceptions and …

Zipf's Law And 7 Plus Minus 2 Principle Lead To A Possible Explanation Of Daniel's Law, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In 1961, D. R. Daniel observed that the success of a company is usually determined by three to six major factors. This observation has led to many successful management ideas, but they leave one puzzled: why three to six? why not two or seven? In this paper, we provide a possible explanation to this puzzle; namely, we show that these numbers of factors can be derived from Zipf's Law and from the 7 plus minus 2 principle.

Diversity Is Beneficial For A Research Group: One More Quantitative Argument, Komsan Suriya, Tatcha Sudtasan, Tonghui Wang, Octavio Lerma, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we propose a natural model describing competition between two research groups of the same average research strength. The analysis of this model enables us to conclude that a more diverse group has an advantage: namely, the more diverse the group, the higher the average quality of its publications.

From Global To Local Constraints: A Constructive Version Of Bloch's Principle, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Generalizing several results from complex analysis, A. Bloch formulated an informal principle -- that for every global implication there is a stronger local implication. This principle has been formalized for complex analysis, but is has been successfully used in other areas as well. In this paper, we propose a new formalization of Bloch's Principle, and we show that in general, the corresponding localized version can be obtained algorithmically.

Biochemical Characterization Of Four Distinct Proteins, Gustavo A. Avila

Open Access Theses & Dissertations

Proteins are ubiquitous in all living organisms, executing the majority of cellular functions in distinct ways. Understanding a protein's role necessitates investigating its structure and function, which are closely related. My research couples these two aspects by delving into the biochemical and structural characterization of proteins in four distinct systems, all playing central roles in numerous significant disease progressions. These four original research endeavors were all targeted for structural studies with a unifying relationship to establish our new structural biochemistry lab. These four systems are: (1) Gam1, an early adenovirus protein globally inhibiting host SUMOylation; (2) Anthrax toxin complexed with …