Physical Sciences and Mathematics Commons^™

Studying Volatility And Dependency Of Chinese Outbound Tourism Demand In Singapore, Malaysia, And Thailand: A Vine Copula Approach, Jianxu Liu, Songsak Sriboonchitta, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

This paper investigates the volatility and dependence of Chinese tourism demand for Singapore, Malaysia, and Thailand (SMT) destinations, using the vine copula based auto regression moving average-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. It is found that a jolt to the tourist flow can have long-standing ramifications for the SMT countries. The estimation of the vine copulas among SMT show that the Survival Gumbel, Frank, and Gaussian copulas are the best copulas for Canonical vine (C-vine) or Drawable vine (D-vine) among the possible pair-copulas. In addition, this paper illustrates the making of time-varying Frank copulas for vine copulas. Finally, there is …

A Vine Copula Approach For Analyzing Financial Risk And Co-Movement Of The Indonesian, Philippine And Thailand Stock Markets, Songsak Sriboonchitta, Jianxu Liu, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

This paper aims at analyzing the financial risk and co-movement of stock markets in three countries: Indonesia, Philippine and Thailand. It consists of analyzing the conditional volatility and test the leverage effect in the stock markets of the three countries. To capture the pairwise and conditional dependence between the variables, we use the method of vine copulas. In addition, we illustrate the computations of the value at risk and the expected shortfall using Monte Carlo simulation with copula based GJR-GARCH model. The empirical evidence shows that all the leverage effects add much to the capacity for explanation of the three …

Picture Fuzzy Sets - A New Concept For Computational Intelligence Problems, Bui Cong Cuong, Vladik Kreinovich

Departmental Technical Reports (CS)

Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov). Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.

Data Collection For The Similar Segments In Social Speech Task, Nigel G. Ward, Steven D. Werner

Departmental Technical Reports (CS)

Information retrieval systems rely heavily on models of similarity, but for spoken dialog such models currently use mostly standard textual-content similarity. As part of the MediaEval Benchmarking Initiative, we have created a new corpus to support development of similarity models for spoken dialog. This corpus includes 26 casual dialogs among members of two semi-cohesive groups, totaling about 5 hours, with 1889 labeled regions associated into 227 sets which annotators judged to be similar enough to share a tag. This technical report brings together information about this corpus and its intended uses.

Why In Mayan Mathematics, Zero And Infinity Are The Same: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In Mayan mathematics, zero is supposed to be, in some sense, equal to infinity. At first glance, while this statement may have a deep philosophical meaning, it does not seem to make much mathematical sense. In this paper, we show, that this statement may be made mathematically reasonable. Specifically, on a real line, it is often useful to consider both −∞ and +∞ as a single infinity. When we deal with very small and very large numbers, it makes sense to use floating point representation, i.e., in effect, consider logarithms of the original values. In terms of logarithms, the original …

Similarity Approach To Defining Basic Level Of Concepts Explained From The Utility Viewpoint, Joe Lorkowski, Martin Trnecka

Departmental Technical Reports (CS)

In many practical situations, it is necessary to describe an image in words. From the purely logical viewpoint, to describe the same object, we can use concepts of different levels of abstraction: e.g., when the image includes a dog, we can say that it is a dog, or that it is a mammal, or that it is a German Shepherd. In such situations, humans usually select a concept which, to them, in the most natural; this concept is called the basic level concept. However, the notion of a basic level concept is difficult to describe in precise terms; as a …

Why Rozenzweig-Style Midrashic Approach Makes Rational Sense: A Logical (Spinoza-Like) Explanation Of A Seemingly Non-Logical Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A 20 century German Jewish philosopher Franz Rosenzweig promoted a new approach to knowledge, an approach in which in addition to logical reasoning, coming up with stories with imagined additional details is also important. This approach is known as midrashic since it is similar to the use of similar stories -- known as midrashes -- in Judaism. While stories can make the material interesting, traditionally, such stories are not viewed as a serious part of scientific discovery. In this paper, we show that this seemingly non-logical approach can actually be explained in logical terms and thus, makes perfect rational sense.

Fuzzy Sets Can Be Interpreted As Limits Of Crisp Sets, And This Can Help To Fuzzify Crisp Notions, Olga Kosheleva, Vladik Kreinovich, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

Fuzzy sets have been originally introduced as generalizations of crisp sets, and this is how they are usually considered. From the mathematical viewpoint, the problem with this approach is that most notions allow many different generalizations, so every time we try to generalize some notions to fuzzy sets, we have numerous alternatives. In this paper, we show that fuzzy sets can be alternatively viewed as limits of crisp sets. As a result, for some notions, we can come up with a unique generalization -- as the limit of the results of applying this notion to the corresponding crisp sets.

Computing Covariance And Correlation In Optimally Privacy-Protected Statistical Databases: Feasible Algorithms, Joshua Day, Ali Jalal-Kamali, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, e.g., in medicine, it is necessary to process data while preserving the patients' confidentiality. One of the most efficient methods of preserving privacy is to replace the exact values with intervals that contain these values. For example, instead of an exact age, a privacy-protected database only contains the information that the age is, e.g., between 10 and 20, or between 20 and 30, etc. Based on this data, it is important to compute correlation and covariance between different quantities. For privacy-protected data, different values from the intervals lead, in general, to different estimates for the desired …

Note On Fair Price Under Interval Uncertainty, Joshua Mckee, Joe Lorkowski, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

Often, in decision making situations, we do not know the exact value of a gain resulting from making each decision, we only know the bounds on this gain. To make a reasonable decision under such interval uncertainty, it makes sense to estimate the fair price of each alternative, and then to select the alternative with the highest price. In this paper, we show that the value of the fair price can be uniquely determined from some reasonable requirements: e.g., the additivity requirement, that the fair price of two objects together should be equal to the sum of the fair prices …

Vine Copulas As A Way To Describe And Analyze Multi-Variate Dependence In Econometrics: Computational Motivation And Comparison With Bayesian Networks And Fuzzy Approaches, Songsak Sriboonchitta, Jianxu Liu, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

In the last decade, vine copulas emerged as a new efficient techniques for describing and analyzing multi-variate dependence in econometrics. Our experience has shown, however, that while these techniques have been successfully applied to many practical problems of econometrics, there is still a lot of confusion and misunderstanding related to vine copulas. In this paper, we provide a motivation for this new technique from the computational viewpoint. We show that other techniques used to described dependence -- Bayesian networks and fuzzy techniques -- can be viewed as a particular case of vine copulas.

Complete Description Of Idempotent Hedges In Fuzzy Logic, Jaime Nava

Departmental Technical Reports (CS)

In describing expert knowledge, it is often important to properly take into account hedges} like "very", "somewhat", etc. In particular, fuzzy logic provides a consistent way of describing hedges. For some of the hedges, a repetition changes the meaning: e.g., "very very small" is smaller than "very small". However, other hedges -- like "somewhat" -- are idempotent, in the sense that repeating this hedge twice does not change the meaning. In this paper, we provide a complete description of such idempotent hedges.

How To Distinguish True Dependence From Varying Independence?, Marketa Krmelova, Martin Trnecka, Vladik Kreinovich, Berlin Wu

Departmental Technical Reports (CS)

A usual statistical criterion for the quantities X and Y to be independent is that the corresponding distribution function F(x,y) is equal to the product of the corresponding marginal distribution functions. If this equality is violated, this is usually taken to mean that X and Y are dependent. In practice, however, the inequality may be caused by the fact that we have a mixture of several populations, in each of which X and Y are independent. In this paper, we show how we can distinguish true dependence from such varying independence. This can also lead to new measures to degree …

Why Trapezoidal And Triangular Membership Functions Work So Well: Towards A Theoretical Explanation, Aditi Barua, Lalitha Snigdha Mudunuri, Olga Kosheleva

Departmental Technical Reports (CS)

In fuzzy logic, an imprecise ("fuzzy") property is described by its membership function μ(x), i.e., by a function which describes, for each real number x, to what degree this real number satisfies the desired property. In principle, membership functions can be of different shape, but in practice, trapezoidal and triangular membership functions are most frequently used. In this paper, we provide an interval-based theoretical explanation for this empirical fact.

How To Faster Test A Device For Different Combinations Of Parameters, Francisco Zapata, Luis C. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

A device has to function properly under all possible conditions: e.g., for all temperatures within a given range, for all possible humidity values within a given range, etc. Ideally, it would be nice to be able to test a device for all possible combinations of these parameters, but the number of such combinations is often so huge that such an exhaustive testing is not possible. Instead, it is reasonable to check the device for all possible values of each parameter, for each possible pairs of values of two parameters, and, in general, for all possible combinations of values of k …

On Early Stages Of Idea Propagation, The Number Of Adopters Grows As N(T) ~ C * Ta: Theoretical Explanation Of The Empirical Observation, L. Octavio Lerma, Deana Pennington, Vladik Kreinovich

Departmental Technical Reports (CS)

New good ideas sometimes propagate too slowly. To speed up their propagation, we need to have a quantitative understanding of how ideas propagate. An intuitive understanding of ideas propagation has led to several reasonable first-approximation mathematical models. These models provide a good description of idea propagation on the later stages, when the ideas have already been adopted by a reasonably large number of people. However, at the critically important early stages, these models are not perfect: these models predict a linear growth with time, while empirical growth data is often better described by a power law. In this paper, we …

Conservation Of Energy Implies Conservation Of Momentum: How We Can Explain Conservation Of Momentum To Before-Calculus Students, Eric Freudenthal, Eric Hagedorn, Olga Kosheleva

Departmental Technical Reports (CS)

In solving physics problems, it is often important to use the laws of conservation of energy and momentum. While most people have intuitive understanding of energy and of its conservation, there is usually no intuition behind momentum, and known textbook derivations of conservation of momentum use calculus -- which is usually taught after momentum. In this paper, we show how the law of conservation of momentum can be explained to before-calculus student: by using the fact that this law can be derived from the more intuitive conservation of energy if we consider energy in different coordinate systems.

Lexical And Prosodic Indicators Of Importance In Spoken Dialog, Nigel G. Ward, Karen A. Richart-Ruiz

Departmental Technical Reports (CS)

This technical report complements the paper, Patterns of Importance Variation in Spoken Dialog (Ward and Richart-Ruiz, 2013), providing additional evidence for the claims, additional findings, and more analysis. In particular, we report more on inter-annotator disagreement, on words that correlate with importance, on prosodic features and patterns that correlate with importance, and on how our predictive model of importance might be improved.

Solving Interval Linear Systems Is Np-Hard Even When All Inputs Are Known With The Same Accuracy, Ralph Kelsey, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that in general, solving interval linear systems is NP-hard. There exist several proofs of this NP-hardness, and all these proofs use examples with intervals of different width -- corresponding to different accuracy in measuring different coefficients. For some classes of interval linear systems with the same accuracy, feasible algorithms are known. We show, however, that in general, solving interval linear systems is NP-hard even when all inputs are known with the same accuracy.

How To Explain (And Overcome) 2% Barrier In Teaching Computer Science: Fuzzy Ideas Can Help, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Computer science educators observed that in the present way of teaching computing, only 2% of students can easily handle computational concepts -- and, as a result, only 2% of the students specialize in computer science. With the increasing role of computers in the modern world, and the increasing need for computer-related jobs, this 2% barrier creates a shortage of computer scientists. We notice that the current way of teaching computer science is based on easiness of using two-valued logic, on easiness of dividing all situations, with respect to each property, into three classes: yes, no, and unknown. The fact that …

Computing With Words: Towards A New Tuple-Based Formalization, Olga Kosheleva, Vladik Kreinovich, Ariel Garcia, Felipe Jovel, Luis A. Torres Escobedo, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

An expert opinion describes his or her opinion about a quantity by using imprecise ("fuzzy") words from a natural language, such as "small", "medium", "large", etc. Each of these words provides a rather crude description of the corresponding quantity. A natural way to refine this description is to assign degrees to which the observed quantity fits each of the selected words. For example, an expert can say that the value is reasonable small, but to some extent it is medium. In this refined description, we represent each quantity by a tuple of the corresponding degrees.

Once we have such a …

Stochastic Causality Is Inconsistent With The Lorentz Group, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to modern physics, all physical processes are described by quantum theory. In particular, due to quantum fluctuations, even in the empty space, the causal relation is, in general, slightly different from the usual Minkowski one. Since quantum effects are probabilistic, to properly represent the corresponding stochastic causality, we need to describe, for every two events e and e', the probability p(e,e') that e can causally influence e'. Surprisingly, it turns out that such a probability functions cannot be Lorentz-invariant. In other words, once we take into account quantum effects in causality, Lorentz-invariance is violated -- similarly to the fact …

Is Langrangian Formalism Adequately Describing Energy Conservation?, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In most physical theories, total energy is conserved. For example, when the kinetic energy of a particle decreases, the potential energy increase accordingly. For some physical systems, energy is not conserved. For example, if we consider a particle moving with friction, the energy of the particle itself is not conserved: it is transformed into thermal energy of the surrounding medium. For simple systems, energy is easy to define. For more complex physical systems, such a definition is not easy. To describe energy of generic systems, physicists came up with a general notion of energy based on the Lagrangian formalism -- …

Towards A Localized Version Of Pearson's Correlation Coefficient, Vladik Kreinovich, Hung T. Nguyen, Berlin Wu

Departmental Technical Reports (CS)

Pearson's correlation coefficient is used to describe dependence between random variables X and Y. In some practical situations, however, we have strong correlation for some values X and/or Y and no correlation for other values of X and Y. To describe such a local dependence, we come up with a natural localized version of Pearson's correlation coefficient. We also study the properties of the newly defined localized coefficient.

How To Gauge Accuracy Of Measurements And Of Expert Estimates: Beyond Normal Distributions, Christian Servin, Aline Jaimes, Craig Tweedie, Aaron A. Velasco, Omar Ochoa, Vladik Kreinovich

Departmental Technical Reports (CS)

To properly process data, we need to know the accuracy of different data points, i.e., accuracy of different measurement results and expert estimates. Often, this accuracy is not given. For such situations, we describe how this accuracy can be estimated based on the available data.

How To Detect Linear Dependence On The Copula Level?, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In many practical situations, the dependence between the quantities is linear or approximately linear. Knowing that the dependence is linear simplifies computations; so, is is desirable to detect linear dependencies. If we know the joint probability distribution, we can detect linear dependence by computing Pearson's correlation coefficient. In practice, we often have a copula instead of a full distribution; in this case, we face a problem of detecting linear dependence based on the copula. Also, distributions are often heavy-tailed, with infinite variances, in which case Pearson's formulas cannot be applied. In this paper, we show how to modify Pearson's formula …

Minimization Of Average Sensitivity As A Method Of Selecting Fuzzy Functions And Operations: Successes And Limitations, Riya George, Suresh Subramanian, Alejandro Vega, Olga Kosheleva

Departmental Technical Reports (CS)

Fuzzy logic is an extension of the standard 2-valued logic -- with two possible truth values 0 ("false") and ("true") -- to values (degrees of certainty) represented by arbitrary numbers from the interval [0,1]. One of the main challenges in fuzzy logic is that we need to extend the usual logical operations from the set {0,1} to the entire interval, and there are many possible extensions. One promising technique for selecting a reasonable extension is to take into account that the fuzzy degrees of certainty are themselves only known with uncertainty; so, it makes sense to select an operation which …

Towards Discrete Interval, Set, And Fuzzy Computations, Enrique Portillo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many applications, we know the function f(x1,...,xn), we know the intervals [xi] of possible values of each quantity xi, and we are interested in the range of possible values of y=f(x1,...,xn); this problem is known as the problem of interval computations. In other applications, we know the function f(x1,...,xn), we know the fuzzy sets Xi that describe what we know about each quantity xi, and we are interested in finding the fuzzy set Y corresponding to the quantity y=f(x1,...,xn); this problem is known as the problem of fuzzy computations. There are many efficient algorithms for solving these problems; however, …

Images Are Easier To Restore Than 1-D Signals: A Theoretical Explanation Of A Surprising Empirical Phenomenon, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

Similar techniques are often used to restore 1-D signals and 2-D images from distorted ("blurred") observations. From the purely mathematical viewpoint, 1-D signals are simpler, so it should be easier to restore signals than images. However, in practice, it is often easier to restore a 2-D image than to restore a 1-D signal. In this paper, we provide a theoretical explanation for this surprising empirical phenomenon.

Enhancing The Expressiveness Of The Cleanjava Language, Melisa Vela, Yoonsik Cheon

Departmental Technical Reports (CS)

The CleanJava language is a formal annotation language for Java to support Cleanroom-style functional program verification that views a program as a mathematical function from one program state to another. The CleanJava notation is based on the Java expression syntax with a few extensions, and thus its vocabulary is somewhat limited to that of Java. This often makes it difficult to specify the rich semantics of a Java program in a succinct and natural way that is easy to manipulate for formal correctness reasoning. In this paper we propose to make the CleanJava language more expressive by supporting user-defined mathematical …