Computer Engineering Commons^™

Efficient Algorithms For Heavy-Tail Analysis Under Interval Uncertainty, Vladik Kreinovich, Monchaya Chiangpradit, Wararit Panichkitkosolkul

Departmental Technical Reports (CS)

Most applications of statistics to science and engineering are based on the assumption that the corresponding random variables are normally distributed, i.e., distributed according to Gaussian law in which the probability density function d(x) exponentially decreases with x: d(x) ~ exp(-k * x^2). Normal distributions indeed frequently occur in practice. However, there are also many practical situations, including situations from mathematical finance, in which we encounter heavy-tailed distributions, i.e., distributions in which d(x) decreases as d(x) ~ x^(-a). To properly take this uncertainty into account when making decisions, it is necessary to estimate the parameters of such distributions based on …

Metrization Theorem For Space-Times: From Urysohn's Problem Towards Physically Useful Constructive Mathematics, Vladik Kreinovich

Departmental Technical Reports (CS)

In the early 1920s, Pavel Urysohn proved his famous lemma (sometimes referred to as "first non-trivial result of point set topology"). Among other applications, this lemma was instrumental in proving that under reasonable conditions, every topological space can be metrized.

A few years before that, in 1919, a complex mathematical theory was experimentally proven to be extremely useful in the description of real world phenomena: namely, during a solar eclipse, General Relativity theory -- that uses pseudo-Riemann spaces to describe space-time -- has been (spectacularly) experimentally confirmed. Motivated by this success, Urysohn started working on an extension of his lemma …

Extending Maximum Entropy Techniques To Entropy Constraints, Gang Xiang, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have only partial information about the probabilities. In some cases, we have {\em crisp} (interval) bounds on the probabilities and/or on the related statistical characteristics. In other situations, we have {\em fuzzy} bounds, i.e., different interval bounds with different degrees of certainty.

In a situation with uncertainty, we do not know the exact value of the desired characteristic. In such situations, it is desirable to find its worst possible value, its best possible value, and its "typical" value -- corresponding to the "most probable" probability distribution. Usually, as such a "typical" distribution, we select the …

Towards A Natural Proof Of Metrization Theorem For Space-Times, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In the early 1920s, Pavel Urysohn proved his famous lemma (sometimes referred to as "first non-trivial result of point set topology"). Among other applications, this lemma was instrumental in proving that under reasonable conditions, every topological space can be metrized.

A few years before that, in 1919, a complex mathematical theory was experimentally proven to be extremely useful in the description of real world phenomena: namely, during a solar eclipse, General Relativity theory -- that uses pseudo-Riemann spaces to describe space-time -- has been (spectacularly) experimentally confirmed. Motivated by this success, Urysohn started working on an extension of his lemma …

Selecting The Best Location For A Meteorological Tower: A Case Study Of Multi-Objective Constraint Optimization, Aline James, Craig Tweedie, Tanja Magoc, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

Using the problem of selecting the best location for a meteorological tower as an example, we show that in multi-objective optimization under constraints, the traditional weighted average approach is often inadequate. We also show that natural invariance requirements lead to a more adequate approach -- a generalization of Nash's bargaining solution.

How To Relate Spectral Risk Measures And Utilities, Songsak Sriboonchitta, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional decision theory describes human behavior and human preferences in terms of utility functions. In the last decades, it was shown that in many economic situations, a reasonable description of the actual decisions can be found if we use a different approach -- of spectral risk measures. In each of these approaches, we first need to empirically find the corresponding function: utility function in the traditional approach and the weighting function for spectral risk measures. Since both approaches provide a reasonable description of the same actual behavior (in particular, of the same actual economic behavior), it is desirable to be …

Why Polynomial Formulas In Soft Computing, Decision Making, Etc.?, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that in many application areas including soft constraints reasonable requirements of scale-invariance lead to polynomial formulas for combining degrees (of certainty, of preference, etc.)

Towards Improved Trapezoidal Approximation To Intersection (Fusion) Of Trapezoidal Fuzzy Numbers: Specific Procedure And General Non-Associativity Theorem, Gang Xiang, Vladik Kreinovich

Departmental Technical Reports (CS)

In some cases, our uncertainty about a quantity can be described by an interval of its possible values. If we have two or more pieces of interval information about the same quantity, then we can conclude that the actual value belongs to the intersection of these intervals.

In general, we may need a fuzzy number to represent our partial knowledge. A fuzzy number can be viewed as a collection of intervals (alpha-cuts) corresponding to different degrees alpha from [0,1]. In practice, we can only store finitely many alpha-cuts. Usually, we only store the lower and upper alpha-cuts (corresponding to alpha …

Access Control Contracts For Java Program Modules, Carlos E. Rubio-Medrano, Yoonsik Cheon

Departmental Technical Reports (CS)

Application-level security has become an issue in recent years; for example, errors, discrepancies and omissions in the specification of access control constraints of security-sensitive software components are recognized as an important source for security vulnerabilities. We propose to formally specify access control assumptions or constraints of a program module and enforce them at run-time. We call such specifications access control contracts. To realize access control contracts, we extended the JML language, a formal interface specification language for Java, and developed a prototype support tool that translates access control contracts to runtime checks. The access control contract reduces the vulnerability that …

A New Eclipse-Based Jml Compiler Built Using Ast Merging, Amritam Sarcar, Yoonsik Cheon

Departmental Technical Reports (CS)

The Java Modeling Language (JML) is a formal interface specification language to document the behavior of Java program modules and has been used in many research and industrial projects. However, its inability to support Java 5 features such as generics is reducing its user base significantly. Besides, the JML compiler is on average 8.5 times slower than the javac Java compiler. In this paper, we present a new JML compiler built on the Eclipse Java compiler to support Java 5 features. We used a technique called AST merging to implement coarse-grained incremental compilation. In our experiments we observed a significant …

Runtime Constraint Checking Approaches For Ocl, A Critical Comparison, Carmen Avila, Amritam Sarcar, Yoonsik Cheon, Cesar Yeep

Departmental Technical Reports (CS)

There are many benefits of checking design constraints at runtime---for example, automatic detection of design drift or corrosion. However, there is no comparative analysis of different approaches although such an analysis could provide a sound basis for determining the appropriateness of one approach over the others. In this paper we conduct a comparative analysis and evaluation of different constraint checking approaches possible for the Object Constraint Language (OCL). We compare several approaches including (1) direct translation to implementation languages, (2) use of executable assertion languages, and (3) use of aspect-oriented programming languages. Our comparison includes both quantitative metrics such as …

Runtime Assertion Checking For Jml On The Eclipse Platform Using Ast Merging, Amritam Sarcar

Departmental Technical Reports (CS)

The Java Modeling Language (JML) is a formal behavioral interface specification language for Java. It is used for detailed design documentation of Java program modules such as classes and interfaces. JML has been used extensively by many researchers across various projects and has a large and varied spectrum of tool support. It extends from runtime assertion checking (RAC) to theorem proving.

Amongst these tools, RAC and ESC/Java has been used as a common tool for many research projects. RAC for JML is a tool that checks at runtime for possible violations of any specifications. However, lately there has been a …

Estimating Information Amount Under Uncertainty: Algorithmic Solvability And Computational Complexity, Vladik Kreinovich, Gang Xiang

Departmental Technical Reports (CS)

Measurement results (and, more generally, estimates) are never absolutely accurate: there is always an uncertainty, the actual value x is, in general, different from the estimate X. Sometimes, we know the probability of different values of the estimation error dx=X-x, sometimes, we only know the interval of possible values of dx, sometimes, we have interval bounds on the cdf of dx. To compare different measuring instruments, it is desirable to know which of them brings more information - i.e., it is desirable to gauge the amount of information. For probabilistic uncertainty, this amount of information is described by Shannon's entropy; …

A Subthreshold Reconfigurable Architecture For Harsh Environments, Ameet Chavan

Open Access Theses & Dissertations

Energy harvesting and functional reconfigurability are necessary features in order to simultaneously achieve longer operating lifetimes and versatility in application for many next generation electronic systems. The presented research incorporates capabilities that not only enable applications to self-power from ambience but also permit change in functionality based on real-time application requirements. Currently, many applications are battery powered with custom hardware, which severely confines the application platform. Moreover, maintenance and upgrades are prohibitively expensive, particularly in the case of remote locations with limited accessibility. For harsh environments like Space or the battlefield, apart from features such as low power and reconfigurability, …

E-Quality: Using Dimensional Index Values Towards Improving Classification Accuracy, Prashanth Devaram

Open Access Theses & Dissertations

E-quality is a process through which inspection of the process and quality of the part produced is done online resulting in the improvement of the process and reduction in the amount of time consumed for the overall process. Automated quality control involves using a methodology to classify the parts based on the dimensions of the features on a part. However, achieving 100% classification accuracy is not an easy task, especially in area of quality control where small differences in dimensions result in part fall into a different category. In this study, a novel approach for modifying the data before being …

Optimal Sensor Placement In Environmental Research: Designing A Sensor Network Under Uncertainty, Aline James, Craig Tweedie, Tanja Magoc, Vladik Kreinovich, Martine Ceberio

Departmental Technical Reports (CS)

One of our main challenges in meteorology and environment research is that in many important remote areas, sensor coverage is sparse, leaving us with numerous blind spots. Placement and maintenance of sensors in these areas are expensive. It is therefore desirable to find out how, within a given budget, we can design a sensor network are important activities was developing reasonable techniques for sensor that would provide us with the largest amount of useful information while minimizing the size of the "blind spot" areas which is not covered by the sensors.

This problem is very difficult even to formulate in …

Symmetries: A General Approach To Integrated Uncertainty Management, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

We propose to use symmetries as a general approach to maintaining different types of uncertainty, and we show how the symmetry approach can help, especially in in economics-related applications.

Discrete Taylor Series As A Simple Way To Predict Properties Of Chemical Substances Like Benzenes And Cubanes, Jaime Nava, Vladik Kreinovich, Guillermo Restrepo, Douglas J. Klein

Departmental Technical Reports (CS)

In many applications, we have numerous molecules that are obtained from a "template" molecule like benzene C6H6 or cubane C8H8 by replacing some of its hydrogen atoms with other atoms or atom groups (called ligands). Depending on how many original atoms are replaced and which ones are replaced, we obtain a large number of different chemical substances. It is desirable to be able, based on the measurements performed on a small number of such substances, to accurately predict the characteristics (such as energy) of all similar substances.

Such predictions are very important, since, e.g. cubanes, while kinetically stable, are highly …

Towards Optimal Effort Distribution In Process Design Under Uncertainty, With Application To Education, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most application areas, we need to take care of several (reasonably independent) participants. For example, in controlling economics, we must make sure that all the economic regions prosper. In controlling environment, we want to guarantee that all the geographic regions have healthy environment. In education, we want to make sure that all the students learn all the needed knowledge and skills.

In real life, the amount of resources is limited, so we face the problem of "optimally" distributing these resources between different objects.

What is a reasonable way to formalize "optimally"? For each of the participants, preferences can be …

Checking Design Constraints At Run-Time Using Ocl And Aspectj, Yoonsik Cheon, Carmen Avila, Steve Roach, Cuauhtemoc Munoz

Departmental Technical Reports (CS)

Design decisions and constraints of a software system can be specified precisely using a formal notation such as the Object Constraint Language (OCL). However, they are not executable, and assuring the conformance of an implementation to its design is hard. The inability of expressing design constraints in an implementation and checking them at runtime invites, among others, the problem of design drift and corrosion. We propose runtime checks as a solution to mitigate this problem. The key idea of our approach is to translate design constraints written in a formal notation such as OCL into aspects that, when applied to …

Fuzzy Transforms Of Higher Order Approximate Derivatives: A Theorem, Irina Perfilieva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical applications, it is useful to represent a function f(x) by its fuzzy transform, i.e., by the "average" values over different elements of a fuzzy partition A₁(x), ..., _n(x) (for which A_i(x) >= 0 and A₁(x) + ... + A_n(x) = 1). It is known that when we increase the number n of the partition elements A_i(x), the resulting approximation get closer and closer to the original function: for each value x₀, the values F_i corresponding to the function A_i(x) for …

A Broad Prospective On Fuzzy Transforms: From Gauging Accuracy Of Quantity Estimates To Gauging Accuracy And Resolution Of Measuring Physical Fields, Vladik Kreinovich, Irina Perfilieva

Departmental Technical Reports (CS)

Fuzzy transform is a new type of function transforms that has been successfully used in different application. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.

From Gauging Accuracy Of Quantity Estimates To Gauging Accuracy And Resolution Of Measuring Physical Fields, Vladik Kreinovich, Irina Perfilieva

Departmental Technical Reports (CS)

For a numerical physical quantity v, because of the measurement imprecision, the measurement result V is, in general, different from the actual value v of this quantity. Depending on what we know about the measurement uncertainty d = V - v, we can use different techniques for dealing with this imprecision: probabilistic, interval, etc.

When we measure the values v(x) of physical fields at different locations x (and/or different moments of time), then, in addition to the same measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location …

Model Fusion Under Probabilistic And Interval Uncertainty, With Application To Earth Sciences, Omar Ochoa, Aaron A. Velasco, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most important studies of the earth sciences is that of the Earth's interior structure. There are many sources of data for Earth tomography models: first-arrival passive seismic data (from the actual earthquakes), first-arrival active seismic data (from the seismic experiments), gravity data, and surface waves. Currently, each of these datasets is processed separately, resulting in several different Earth models that have specific coverage areas, different spatial resolutions and varying degrees of accuracy. These models often provide complimentary geophysical information on earth structure (P and S wave velocity structure).

Combining the information derived from each requires a joint …

Automating Java Program Testing Using Ocl And Aspectj, Yoonsik Cheon, Carmen Avila

Departmental Technical Reports (CS)

Random testing can eliminate subjectiveness in constructing test data and increase the diversity of test data. However, one difficult problem is to construct test oracles that decide test results---test failures or successes. Assertions can be used as test oracles and are most effective when derived from formal specifications such as OCL constraints. If fully automated, random testing can reduce the cost of testing dramatically. In this paper we propose an approach for automating Java program testing by combining random testing and OCL. The key idea of our approach is to use OCL constraints as test oracles by translating them to …

Astronomical Tests Of Relativity: Beyond Parameterized Post-Newtonian Formalism (Ppn), To Testing Fundamental Principles, Vladik Kreinovich

Departmental Technical Reports (CS)

By the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.

Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. …

Why Tensors?, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

We show that in many application areas including soft constraints reasonable requirements of scale-invariance lead to polynomial (tensor-based) formulas for combining degrees (of certainty, of preference, etc.)

Continuous If-Then Statements Are Computable, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we must compute the value of an if-then expression f(x) defined as "if c(x) >= 0 then f₊(x) else f_-(x)", where f₊(x), f_-(x), and c(x) are computable functions. The value f(x) cannot be computed directly, since in general, it is not possible to check whether a given real number c(x) is non-negative or non-positive. Similarly, it is not possible to compute the value f(x) if the if-then function is discontinuous, i.e., when f₊(x₀) =/= f_-(x₀) for some x₀ for …

Symmetry Between True, False, And Uncertain: An Explanation, Eulalia Szmidt, Vladik Kreinovich

Departmental Technical Reports (CS)

In intuitionistic fuzzy sets, there is a natural symmetry between degrees of truth and falsity. As a result, for such sets, natural similarity measures are symmetric relative to an exchange of true and false values. It has been recently shown that among such measures, the most intuitively reasonable are the ones which are also symmetric relative to an arbitrary permutation of degrees of truth, falsity, and uncertainty. This intuitive reasonableness leads to a conjecture that such permutations are not simply mathematical constructions, that these permutations also have some intuitive sense. In this paper, we show that each such permutation can …

From Interval Computations To Constraint-Related Set Computations: Towards Faster Estimation Of Statistics And Odes Under Interval And P-Box Uncertainty, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.