Physical Sciences and Mathematics Commons^™

Preliminaries To A Study Of Stance In News Broadcasts, Nigel Ward

Departmental Technical Reports (CS)

Aspects of stance have significant potential for information retrieval and filtering. This technical report is about stance in radio news broadcast, and is intended primarily to motivate and document details of the data and annotations used in the work reported in Inferring Stance from Prosody (Ward et al., 2016). It describes the process of identifying 14 important aspects of stance, describes two corpora for investigating stance, describes the annotation of those corpora, presents some preliminary observations, and lists a set of useful prosodic features.

Why Pairwise Testing Works So Well: A Possible Theoretical Explanation Of An Empirical Phenomenon, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

Some software defects can be detected only if we consider all possible combinations of three, four, or more inputs. However, empirical data shows that the overwhelming majority of software defects are detected during pairwise testing, when we only test the software on combinations of pairs of different inputs. In this paper, we provide a possible theoretical explanation for the corresponding empirical data.

Metric Spaces Under Interval Uncertainty: Towards An Adequate Definition, Mahdokhat Afravi, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

In many practical situations, we only know the bounds on the distances. A natural question is: knowing these bounds, can we check whether there exists a metric whose distance always lie within these bounds -- or such a metric is not possible and thus, the bounds are inconsistent. In this paper, we provide an answer to this question. We also describe possible applications of this result to a description of opposite notions in commonsense reasoning.

For Multi-Interval-Valued Fuzzy Sets, Centroid Defuzzification Is Equivalent To Defuzzifying Its Interval Hull: A Theorem, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In the traditional fuzzy logic, the expert's degree of certainty in a statement is described either by a number from the interval [0,1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets -- which is, in general, more complex than an interval. In this paper, we prove that for such set-valued fuzzy sets, centroid defuzzification is equivalent to defuzzifying its interval hull.

As a consequence of this result, we prove that the centroid defuzzification of a general type-2 fuzzy set can be reduced …

One Needs To Be Careful When Dismissing Outliers: A Realistic Example, Carlos Fajardo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional approach to eliminating outliers is that we compute the sample mean μ and the sample standard deviation σ, and then, for an appropriate value k₀ = 2, 3, 6, etc., we eliminate all data points outside the interval [μ − k₀ * σ, μ + k₀ * σ] as outliers. Then, we repeat this procedure with the remaining data, eliminate new outliers, etc., until on some iteration, no new outliers are eliminated. In many applications, this procedure works well. However, in this paper, we provide a realistic example in which this procedure, instead of eliminating all …

Avoiding Fake Boundaries In Set Interval Computing, Anthony Welte, Luc Jaulin, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Set intervals techniques are an efficient way of dealing with uncertainty in spatial localization problems. In these techniques, the desired set (e.g., set of possible locations) is represented by an expression that uses intersection, union, and complement of input sets -- which are usually only known with interval uncertainty. To find the desired set, we can, in principle, perform the corresponding set-interval computations one-by-one. However, the estimates obtained by such straightforward computations often contain extra elements -- e.g., fake boundaries. In this paper, we show that we can eliminate these fake boundaries (and other extra elements) if we first transform …

A Classification Of Representable T-Norm Operators For Picture Fuzzy Sets, Bui Cong Cuong, Vladik Kreinovich, Roan Thi Ngan

Departmental Technical Reports (CS)

T-norms and t-conorms are basic operators of fuzzy logics. The classifications of these operators are significant problems. Some results of the classifications of fuzzy logics operators for fuzzy sets are known. In 2013, we defined the picture fuzzy sets, and in 2015 some representable t-norms operators and t-conorms operators were defined. In this paper, we investigate the classification of representable picture t-norms and picture t-conorms operators for picture fuzzy sets.

Concepts Of Solutions Of Uncertain Equations With Intervals, Probabilities And Fuzzy Sets For Applied Tasks, Boris Kovalerchuk, Vladik Kreinovich

Departmental Technical Reports (CS)

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in terms of Moore interval analysis can be completely irrelevant for solving a real world task. We show that formal definitions must follow a meaningful concept of the solution in the real world. The paper proposed several formalized definitions of the …

Robust Data Processing In The Presence Of Uncertainty And Outliers: Case Of Localization Problems, Anthony Welte, Luc Jaulin, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

To properly process data, we need to take into account both the measurement errors and the fact that some of the observations may be outliers. This is especially important in radar-based localization problems, where some signals may reflect not from the analyzed object, but from some nearby object. There are known methods for dealing with both measurement errors and outliers in situations in which we have full information about the corresponding probability distributions. There are also known statistics-based methods for dealing with measurement errors in situations when we only have partial information about the corresponding probabilities. In this paper, we …

How To Determine The Stiffness Of The Pavement's Upper Layer (Base) Based On The Overall Stiffness And The Stiffness Of The Lower Layer (Subgrade), Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

In road construction, it is important to estimate difficult-measure stiffness of the pavement's upper layer based the easier-to-measure overall stiffness and the stiffness of the lower layer. In situations when the overall stiffness is not yet sufficient, it is also important to estimate how much more we need to add to the upper layer to reach the desired overall stiffness. In this paper, for the cases when a linear approximation is sufficient, we provide analytical formulas for the desired estimations.

Why Hausdorff Distance Is Natural In Interval Computations, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Several different metrics have been proposed to describe distance between intervals and, more generally, between compact sets. In this paper, we show that from the viewpoint of interval computations, the most adequate distance is the Hausdorff distance d_H(A,A') -- the smallest value ε > 0 for which every element a from the set A is ε-close to some element a' from the ser A', and every element a' from the set A' is ε-close to some element a of the set A.

The Range Of A Continuous Functional Under Set-Valued Uncertainty Is Always An Interval, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

One of the main problems of interval computations is computing the range of a given function on a given multi-D interval (box). It is known that the range of a continuous function on a box is always an interval. However, if, instead of a box, we consider the range over a subset of this box, the range is, in general, no longer an interval. In some practical situations, we are interested in computing the range of a functional over a function defined with interval (or, more general, set-valued) uncertainty. At first glance, it may seem that under a non-interval set-valued …

Z-Numbers And Type-2 Fuzzy Sets: A Representation Result, Vladik Kreinovich, Rafik Aliev

Departmental Technical Reports (CS)

Traditional [0,1]-based fuzzy sets were originally invented to describe expert knowledge expressed in terms of imprecise ("fuzzy") words from natural language. To make this description more adequate, several generalizations of the traditional [0,1]-based fuzzy sets have been proposed, among them type-2 fuzzy sets and Z-numbers. The main objective of this paper is to study the relation between these two generalizations. As a result of this study, we show that if we apply data processing to Z-numbers, then we get type-2 sets of special type -- that we call monotonic. We also prove that every monotonic type-2 fuzzy set can be …

Rotation-Invariance Can Further Improve State-Of-The-Art Blind Deconvolution Techniques, Fernando Cervantes, Bryan E. Usevitch, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, we need to reconstruct a blurred image in situations when no information about the blurring is available. This problem is known as the problem of blind deconvolution. There exist techniques for solving this problem, but these techniques are not rotation-invariant. Thus, the result of using this technique may change with rotation. So, if we rotate the image a little bit, the method, in general, leads to a different deconvolution result. Therefore, even when the original reconstruction is optimal, the reconstruction of a rotated image will be different and, thus, not optimal. To improve the quality of …

Why Cannot We Have A Strongly Consistent Family Of Skew Normal (And Higher Order) Distributions, Thongchai Dumrongpokaphan, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the only information that we have about the probability distribution is its first few moments. Since many statistical techniques requires us to select a single distribution, it is therefore desirable to select, out of all possible distributions with these moments, a single "most representative" one. When we know the first two moments, a natural idea is to select a normal distribution. This selection is strongly consistent in the sense that if a random variable is a sum of several independent ones, then selecting normal distribution for all of the terms in the sum leads to a …

Econometric Models Of Probabilistic Choice: Beyond Mcfadden's Formulas, Olga Kosheleva, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Traditional decision theory assumes that for every two alternatives, people always make the same (deterministic) choice. In practice, people's choices are often probabilistic, especially for similar alternatives: the same decision maker can sometimes select one of them and sometimes the other one. In many practical situations, an adequate description of this probabilistic choice can be provided by a logit model proposed by 2001 Nobelist D. McFadden. In this model, the probability of selecting an alternative a is proportional to exp(β * u(a)), where u(a) is the alternative's utility. Recently, however, empirical evidence appeared that shows that in some situations, we …

Geometric Symmetries Partially Explain Why Some Paleolithic Signs Are More Frequent, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent analysis of Paleolithic signs have described which signs are more frequent and which are less frequent. In this paper, we show that this relative frequency can be (at least partially) explained by the symmetries of the signs: in general, the more symmetries, the more frequent the sign.

How Neural Networks (Nn) Can (Hopefully) Learn Faster By Taking Into Account Known Constraints, Chitta Baral, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Neural networks are a very successful machine learning technique. At present, deep (multi-layer) neural networks are the most successful among the known machine learning techniques. However, they still have some limitations, One of their main limitations is that their learning process still too slow. The major reason why learning in neural networks is slow is that neural networks are currently unable to take prior knowledge into account. As a result, they simple ignore this knowledge and simulate learning "from scratch". In this paper, we show how neural networks can take prior knowledge into account and thus, hopefully, learn faster.

When We Know The Number Of Local Maxima, Then We Can Compute All Of Them, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to compute local maxima. In general, it is not algorithmically possible, given a computable function, to compute the locations of all its local maxima. We show, however, that if we know the number of local maxima, then such an algorithm is already possible. Interestingly, for global maxima, the situation is different: even if we only know the number of locations where the global maximum is attained, then, in general, it is not algorithmically possible to find all these locations. A similar impossibility result holds for local maxima if instead of knowing their exact number, …

How To Explain Ubiquity Of Constant Elasticity Of Substitution (Ces) Production And Utility Functions Without Explicitly Postulating Ces, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

In many situations, the dependence of the production or utility on the corresponding factors is described by the CES (Constant Elasticity of Substitution) functions. These functions are usually explained by postulating two requirements: an economically reasonable postulate of homogeneity (that the formulas should not change if we change a measuring unit) and a less convincing CSE requirement. In this paper, we show that the CES requirement can be replaced by a more convincing requirement -- that the combined effect of all the factors should not depend on the order in which we combine these factors.

Why Ragin's Fuzzy Techniques Lead To Successful Social Science Applications: An Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To find the relation between two concepts, social scientists traditionally look for correlations between the numerical quantities describing these concepts. Sometimes this help, but sometimes, while we are clear that there is a relation, statistical analysis does not show any correlation. Charles Ragin has shown that often, in such situations, we can find statistically significant correlation between the degrees to which experts estimate the corresponding concepts to be applicable to given situations. In this paper, we provide a simple explanation for this empirical success.

How To Make Plausibility-Based Forecasting More Accurate, Kongliang Zhu, Nantiworn Thianpaen, Vladik Kreinovich

Departmental Technical Reports (CS)

In recent papers, a new plausibility-based forecasting method was proposed. While this method has been empirically successful, one of its steps -- selecting a uniform probability distribution for the plausibility level -- is heuristic. It is therefore desirable to check whether this selection is optimal or whether a modified selection would like to a more accurate forecast. In this paper, we show that the uniform distribution does not always lead to (asymptotically) optimal estimates, and we show how to modify the uniform-distribution step so that the resulting estimates become asymptotically optimal.

Why 3-D Space? Why 10-D Space? A Possible Simple Geometric Explanation, Vladik Kreinovich

Departmental Technical Reports (CS)

In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact, without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is known that for some physical quantities, the 3-D space model with point-wise particles leads to meaningless infinities. To avoid these infinities, physicists have proposed that particles are more adequately described not as 0-D points, but rather as 1-D strings …

Interpolation Sometimes Enhances And Sometimes Impedes Spatial Correlation: Simple Pedagogical Examples, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A natural way to check whether there is a dependence between two quantities is to estimate their correlation. For spatial quantities, such an estimation is complicated by the fact that, in general, we measure the values of the two quantities of interest in somewhat different locations. In this case, one possibility is to correlate each value of the first quantity with the value of the second quantity measured at a nearby point. An alternative idea is to first apply an appropriate interpolation to each of the quantities, and then look for the correlation between the resulting spatial maps. Empirical results …

Report On The Roundtable At The Computing Alliance For Hispanic-Serving Institutions (Cahsi) Summit, San Juan, Puerto Rico, September 12, 2015, Ann Q. Gates, Claudia Casas, Andrea Tirres

Departmental Technical Reports (CS)

No abstract provided.

Which Interval Is The Closest To A Given Set?, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In some practical situations, we know a set of possible values of a physical quantity -- a set which is not an interval. Since computing with sets is often complicated, it is desirable to approximate this set by an easier-to-process set: namely, with an interval. In this paper, we describe intervals which are the closest approximations to a given set.

Fuzzy-Inspired Hierarchical Version Of The Von~Neumann-Morgenstern Solutions As A Natural Way To Resolve Collaboration-Related Conflicts, Olga Kosheleva, Vladik Kreinovich, Martha Osegueda Escobar

Departmental Technical Reports (CS)

In situations when several participants collaborate with each other, it is desirable to come up with a fair way to divide the resulting gain between the participants. Such a fair way was proposed by John von Neumann and Oscar Morgenstern, fathers of the modern game theory. However, in some situations, the von Neumann-Morgenstern solution does not exist. To cover such situations, we propose to use a fuzzy-inspired hierarchical version of the von Neumann-Morgenstern (NM) solution. We prove that, in contrast to the original NM solution, the hierarchical version always exists.

Similarity Beyond Correlation: Symmetry-Based Approach, Ildar Batyrshin, Thongchai Dumrongpokaphan, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

When practitioners analyze the similarity between time series, they often use correlation to gauge this similarity. Sometimes this works, but sometimes, this leads to counter-intuitive results. In this paper, we use natural symmetries -- scaling and shift -- to explain this discrepancy between correlation and common sense, and then use the same symmetries to come up with more adequate measures of similarity.

Towards The Most Robust Way Of Assigning Numerical Degrees To Ordered Labels, With Possible Applications To Dark Matter And Dark Energy, Olga Kosheleva, Vladik Kreinovich, Martha Osegueda Escobar, Kimberly Kato

Departmental Technical Reports (CS)

Experts often describe their estimates by using words from natural language, i.e., in effect, sorted labels. To efficiently represent the corresponding expert knowledge in a computer-based system, we need to translate these labels into a computer-understandable language, i.e., into numbers. There are many ways to translate labels into numbers. In this paper, we propose to select a translation which is the most robust, i.e., which preserves the order between the corresponding numbers under the largest possible deviations from the original translation. The resulting formulas are in good accordance with the translation coming from the Laplace's principle of sufficient reason, and …

Analysis Of The Execution Time Variation Of Openmp-Based Applications On The Intel Xeon Phi, Roberto Camacho Barranco, Patricia J. Teller

Departmental Technical Reports (CS)

The Intel Xeon Phi accelerator is currently being used in several large-scale computer clusters and supercomputers to enhance the execution-time performance of computation-intensive applications. While performing a comprehensive profiling of the Intel Xeon Phi execution-time behavior of different applications included in the Rodinia Benchmark suite, we observed large variations in application execution times. In this report we present the average execution times for different runs of each application. In addition, we describe the different steps taken to try to solve this problem.

For example, a brief study was performed using one of these applications, i.e., a matrix-multiply kernel. By improving …