Engineering Commons^™

Processing Educational Data: From Traditional Statistical Techniques To An Appropriate Combination Of Probabilistic, Interval, And Fuzzy Approaches, Olga Kosheleva, Martine Ceberio

Departmental Technical Reports (CS)

There are many papers that experimentally compare effectiveness of different teaching techniques. Most of these papers use traditional statistical approach to process the experimental results. The traditional statistical approach is well suited to numerical data but often, what we are processing is either intervals (e.g., A means anything from 90 to 100) or fuzzy-type perceptions, words from the natural language like "understood well" or "understood reasonably well". We show that the use of intervals and fuzzy techniques leads to more adequate processing of educational data.

Interval Versions Of Statistical Techniques With Applications To Environmental Analysis, Bioinformatics, And Privacy In Statistical Databases, Vladik Kreinovich, Luc Longpre, Scott A. Starks, Gang Xiang, Jan Beck, Raj Kandathi, Asis Nayak, Scott Ferson, Janos Hajagos

Departmental Technical Reports (CS)

In many areas of science and engineering, it is desirable to estimate statistical characteristics (mean, variance, covariance, etc.) under interval uncertainty. For example, we may want to use the measured values x(t) of a pollution level in a lake at different moments of time to estimate the average pollution level; however, we do not know the exact values x(t) -- e.g., if one of the measurement results is 0, this simply means that the actual (unknown) value of x(t) can be anywhere between 0 and the detection limit DL. We must therefore modify the existing statistical algorithms to process such …

Towards Combining Probabilistic And Interval Uncertainty In Engineering Calculations: Algorithms For Computing Statistics Under Interval Uncertainty, And Their Computational Complexity, Vladik Kreinovich, Gang Xiang, Scott A. Starks, Luc Longpre, Martine Ceberio, Roberto Araiza, J. Beck, R. Kandathi, A. Nayak, R. Torres, J. Hajagos

Departmental Technical Reports (CS)

In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.

In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known …

Which Fuzzy Logic Is The Best: Pragmatic Approach (And Its Theoretical Analysis), Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

In this position paper, we argue that when we are looking for the best fuzzy logic, we should specify in what sense the best, and that we get different fuzzy logics as ``the best'' depending on what optimality criterion we use.

Kolmogorov Complexity Leads To A Representation Theorem For Idempotent Probabilities (Sigma-Maxitive Measures), Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

In many application areas, it is important to consider maxitive measures (idempotent probabilities), i.e., mappings m for which m(A U B)=max(m(A),m(B)). In his papers, J. H. Lutz has used Kolmogorov complexity to show that for constructively defined sets A, one maxitive measure - fractal dimension - can be represented as m(A)= sup{f(x): x in A}. We show that a similar representation is possible for an arbitrary maxitive measure.

If An Exact Interval Computation Problem Is Np-Hard, Then The Approximate Problem Is Also Np-Hard: A Meta-Result, Aline B. Loreto, Laira V. Toscani, Leila Robeiro, Dalcidio M. Claudio, Liara S. Leal, Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

In interval computations, usually, once we prove that a problem of computing the exact range is NP-hard, then it later turns out that the problem of computing this range with a given accuracy is also NP-hard. In this paper, we provide a general explanation for this phenomenon.

Consortium Of Cise-Mii Funded Institutions: Initial Recommendations On Broadening Participation Of Hispanics, Ann Q. Gates

Departmental Technical Reports (CS)

No abstract provided.

Kaluza-Klein 5d Ideas Made Fully Geometric, Scott A. Starks, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

After the 1916 success of General relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (dg_{ij}/dx^5=0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approach is that while the model itself is geometric, conditions like cylindricity are not geometric. This problem was partly solved by Einstein and Bergman who proposed, in their 1938 paper, that the 5th dimension is compactified into a small circle S^1 …

Some Usability Issues And Research Priorities In Spoken Dialog Applications, Nigel Ward, Anais G. Rivera, Karen Ward, David G. Novick

Departmental Technical Reports (CS)

As a priority-setting exercise, we examined interactions between users and a simple spoken dialog system in comparison to interactions with a human operator. Based on analysis of the observed usability differences and their root causes we propose seven priority issues for spoken dialog systems research.

Computing Best-Possible Bounds For The Distribution Of A Sum Of Several Variables Is Np-Hard, Vladik Kreinovich, Scott Ferson

Departmental Technical Reports (CS)

In many real-life situations, we know the probability distribution of two random variables x1 and x2, but we have no information about the correlation between x1 and x2; what are the possible probability distributions for the sum x1+x2? This question was originally raised by A. N. Kolmogorov. Algorithms exist that provide best-possible bounds for the distribution of x1+x2; these algorithms have been implemented as a part of the efficient software for handling probabilistic uncertainty. A natural question is: what if we have several (n>2) variables with known distribution, we have no information about their correlation, and we are interested …

Why Product Of Probabilities (Masses) For Independent Events? A Remark, Vladik Kreinovich, Scott Ferson

Departmental Technical Reports (CS)

For independent events A and B, the probability P(A&B) is equal to the product of the corresponding probabilities: P(A&B)=P(A)*P(B). It is well known that the product f(a,b)=a*b has the following property: once P(A1)+...+P(An)=1 and P(B1)+...+P(Bm)=1, the probabilities P(Ai&Bj)=f(P(Ai),P(Bj)) also add to 1: f(P(A1),P(B1))+...+f(P(An),P(Bm))=1. We prove that the product is the only function that satisfies this property, i.e., that if, vice versa, this property holds for some function f(a,b), then this function f is the product. This result provided an additional explanation of why for independent events, we multiply probabilities (or, in the Dempster-Shafer case, masses).

In this paper, we strengthen …

New Algorithms For Statistical Analysis Of Interval Data, Gang Xiang, Scott A. Starks, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

It is known that in general, statistical analysis of interval data is an NP-hard problem: even computing the variance of interval data is, in general, NP-hard. Until now, only one case was known for which a feasible algorithm can compute the variance of interval data: the case when all the measurements are accurate enough -- so that even after the measurement, we can distinguish between different measured values Xi. In this paper, we describe several new cases in which feasible algorithms are possible -- e.g., the case when all the measurements are done by using the same (not necessarily very …

Use Of Maxitive (Possibility) Measures In Foundations Of Physics And Description Of Randomness: Case Study, A. M. Finkelstein, Olga Kosheleva, Vladik Kreinovich, Scott A. Starks, Hung T. Nguyen

Departmental Technical Reports (CS)

According to the traditional probability theory, events with a positive but very small probability can occur (although very rarely). For example, from the purely mathematical viewpoint, it is possible that the thermal motion of all the molecules in a coffee cup goes in the same direction, so this cup will start lifting up.

In contrast, physicists believe that events with extremely small probability cannot occur. In this paper, we show that to get a consistent formalization of this belief, we need, in addition to the original probability measure, to also consider a maxitive (possibility) measure.

From Fuzzification And Intervalization To Anglification: A New 5d Geometric Formalism For Physics And Data Processing, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that in understanding foundations of modern physics, with its 10-dimensional (and higher-dimensional) space-time models, it is very helpful to use the main ideas behind fuzzification -- extension of arithmetic operations and elementary functions from exact numbers to fuzzy numbers. The resulting formalism is, from the mathematical viewpoint, somewhat more complex than the traditional fuzzy arithmetic, but it is still much simpler than the quantum field theory -- and thus, it helps to make several important ideas from foundations of modern physics much more intuitively clear.

The Interval Categorizer Tesselation-Based Model For High Perfomance Computing, Marilton S. De Aguiar, Gracaliz P. Dimuro, Antonio C. Da Rocha Costa, Rafael K.S. Silva

Departmental Technical Reports (CS)

The paper presents the results obtained by an implementation of the interval tessellation-based model for categorization of geographic regions according the analysis of the relief function declivity, called ICTM. The analysis of the relief declivity, which is embedded in the rules of the model ICTM, categorizes each tessellation cell, with respect to the whole considered region, according to the (positive, negative, null) signal of the declivity of the cell. Such information is represented in the states assumed by the cells of the model. The overall configuration of such cells allows the division of the region into sub-regions of cells belonging …

Random Interval Arithmetic Is Closer To Common Sense: An Observation, Rene Alt, Jean-Luc Lamotte, Vladik Kreinovich

Departmental Technical Reports (CS)

From the commonsense viewpoint, if on a bridge whose weight we know with an accuracy of 1 ton, we place a car whose weight we know with an accuracy of 5 kg, then the accuracy with which we know the overall weight of a bridge with a car on it should still be 1 ton. This is what an engineer or a physicist would say. Alas, this is not so in traditional interval arithmetic. In this paper, we show that, in contrast to traditional interval arithmetic, the random interval arithmetic (proposed by the first two authors) actually has this important …

How The Concept Of Information As Average Number Of "Yes"-"No" Questions (Bits) Can Be Extended To Intervals, P-Boxes, And More General Uncertainty, Vladik Kreinovich, Gang Xiang, Scott Ferson

Departmental Technical Reports (CS)

We explain how the concept of information as average number of "yes"-"no" questions (bits) can be extended to intervals, p-boxes, and more general uncertainty.

Interval Methods: An Introduction, Luke Achenie, Vladik Kreinovich, Kaj Madsen

Departmental Technical Reports (CS)

The ongoing development of ever more advanced computers provides the potential for solving increasingly difficult computational problems. However, given the complexity of modern computer architectures, the task of realizing this potential needs careful attention. A main concern of High Performance Computing is the development of software that optimizes the performance of a given computer.

An important characteristic of the computer performance in scientific computing is the accuracy of the computation results. Often, we can estimate this accuracy by using traditional statistical techniques. However, in many practical situations, we do not know the probability distributions of different measurement, estimation, and/or roundoff …

Supporting Documentation For The Sps-Prospec Case Study, Salamah I. Salamah, Ann Q. Gates

Departmental Technical Reports (CS)

In this work, we report on the results of a case study comparing the correctness of Linear Temporal Logic (LTL)formulas generated by the Property Specification Tool Prospec and the Specification Pattern System (SPS). The report includes all the components used in the case study. In addition, this report provides a description of the use of the SPIN model checker to verify correctness of LTL specifications. Particularly, the report provides screenshots of XSPIN (SPIN�s graphical interface) and how properties (i.e., LTL formulas) can be specified and verified.

How To Reconstruct The Original Shape Of A Radar Signal?, Matthew G. Averill, Gang Xiang, Vladik Kreinovich, George R. Keller, Scott A. Starks, Patrick S. Debroux, James Boehm

Departmental Technical Reports (CS)

The shape of the radar signal can provide us with the additional information about the reflecting surface. However, to decrease the noise, radars use filtering, and filtering changes the shapes of the radar signal. It is therefore necessary to reconstruct the original shape of the radar signal.

Towards An Optimal Approach To Soft Constraint Problems, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In traditional constraint satisfaction, constraints are ``hard'' in the sense that we need to satisfy them all. In many practical situations, however, constraints are "soft" in the sense that if we are unable to satisfy some of them, the corresponding solution is still practically useful. In such situations, it is desirable to satisfy as many high-priority constraints as possible. In this paper, we describe an optimal algorithm for solving the corresponding soft constraint problem.

Nsf Advance: Institutional Transformation For Faculty Diversity - Faculty Worklife Survey Results, Manuela Romero, Ann Q. Gates

Departmental Technical Reports (CS)

The The University of Texas at El Paso (UTEP) received an NSF ADVANCE grant in October 2003 to create an initiative for institutional change with the goal of serving as a model for other institutions that desire to increase the representation and advancement of women, including underrepresented minorities, in academic science and engineering careers. In the first year of the grant, co-PI's Ann Gates and Patricia Witherspoon worked with the ADVANCE Program Evaluator, Manuela Romero, to create an instrument to survey faculty work life at UTEP. The instrument is based on the "Study of Faculty Work Life" survey instrument that …

Supporting Documentation For The 2003 Sps-Prospec Experiment, Oscar Mondragon, Salamah Salamah

Departmental Technical Reports (CS)

In spring of 2003 an empirical study was conducted to compare the effectiveness of the Prospec tool with the Specification Pattern System (SPS). The objective of the experiment was to determine the effect that Prospec and SPS have over the completeness and correctness of the generated software property specifications. The purpose of this document is to present the material that was used during the experiment, and to document how the classification of the patterns and scopes of each trial was validated.

A Contextual Interpretation Of Undefinedness For Runtime Assertion Checking, Yoonsik Cheon, Gary T. Leavens

Departmental Technical Reports (CS)

Runtime assertion checkers and static checking and verification tools must all cope with the well-known undefinedness problem of logic. This problem is particularly severe for runtime assertion checkers, since, in addition to the possibility of exceptions and errors, runtime assertion checkers must cope with non-executable expressions (such as certain quantified expressions). This paper describes how the runtime assertion checker of the Java Modeling Language (JML) copes with undefinedness. JML is interesting because it attempts to satisfy the needs of a wide range of tools; besides runtime assertion checking, these include static checking tools (like ESC/Java) and static verification tools. These …

Fast Algorithm For Computing The Upper Endpoint Of Sample Variance For Interval Data: Case Of Sufficiently Accurate Measurements, Gang Xiang

Departmental Technical Reports (CS)

When we have n results x1,...,xn of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals [xi] of possible values of xi. In such situations, for different possible values xi from [xi], we get different values of the variance. We must therefore find the range [V] of possible values of V. It is known that in general, this problem is NP-hard. For the case …

Specifying And Checking Method Call Sequences In Jml, Yoonsik Cheon, Ashaveena Perumandla

Departmental Technical Reports (CS)

In a pre- and post-conditions style specification, it is difficult to specify allowed sequences of method calls, often called protocols. However, the protocols are essential properties of reusable object-oriented classes and application frameworks, and the approaches based on the pre- and post-conditions, such as design by contracts (DBC) and formal behavioral interface specification languages (BISL), are being accepted as a practical and effective way of describing precise interfaces of (reusable) program modules. We propose a simple extension to JML, a BISL for Java, to specify protocol properties in an intuitive and concise manner. We also define a formal semantics of …

A Complete Automation Of Unit Testing For Java Programs, Yoonsik Cheon, Myoung Yee Kim, Ashaveena Perumandla

Departmental Technical Reports (CS)

Program testing is expensive and labor-intensive, often consuming more than half of the total development costs, and yet it is frequently not done well and the results are not always satisfactory. However, testing is the primary method to ensure that programs comply with requirements. We describe our on-going project that attempts to completely automate unit testing of object-oriented programs. Our project investigates the use of an evolutionary approach, called genetic algorithms, for the test data generation and the use of program specifications, written in JML, for the test result determination. A proof-of-concept tool has been implemented and shows that a …

On Inverse Halftoning: Computational Complexity And Interval Computations, Sergio D. Cabrera, K. Iyer, Gang Xiang, Vladik Kreinovich

Departmental Technical Reports (CS)

We analyze the problem of inverse half-toning. This problem is a particular case of a class of difficult-to-solve problems: inverse problems for reconstructing piece-wise smooth images. We show that this general problem is NP-hard. We also propose a new idea for solving problems of this type, including the inverse halftoning problem.

Exact Bounds For Interval And Fuzzy Functions Under Monotonicity Constraints, With Potential Applications To Biostratigraphy, Emil Platon, Kavitha Tupelly, Vladik Kreinovich, Scott A. Starks, Karen Villaverde

Departmental Technical Reports (CS)

The age of fossil species in samples recovered from a well that penetrates an undisturbed sequence of sedimentary rocks increases with depth. The results of biostratigraphic analysis of such a sequence consist of several age-depth values -- both known with interval (or fuzzy) uncertainty -- and we would like to find, for each possible depth, the interval of the possible values of the corresponding age. A similar problem of bounding an intervally (fuzzily) defined function under monotonicity constraint occurs in many other application areas. In this paper, we provide an efficient algorithm for solving this problem.

To Properly Reflect Physicists' Reasoning About Randomness, We Also Need A Maxitive (Possibility) Measure, Andrei M. Finkelstein, Olga Kosheleva, Vladik Kreinovich, Scott A. Starks, Hung T. Nguyen

Departmental Technical Reports (CS)

According to the traditional probability theory, events with a positive but very small probability can occur (although very rarely). For example, from the purely mathematical viewpoint, it is possible that the thermal motion of all the molecules in a coffee cup goes in the same direction, so this cup will start lifting up.

In contrast, physicists believe that events with extremely small probability cannot occur. In this paper, we show that to get a consistent formalization of this belief, we need, in addition to the original probability measure, to also consider a maxitive (possibility) measure.