Computer Sciences Commons^™

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 …

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 …

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 …

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.

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 …

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 …

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 …

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.

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 …

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.

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 …

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.

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.

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.

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 …

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.

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 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.

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 …

How Resilient Modulus Of A Pavement Depends On Moisture Level: Towards A Theoretical Justification Of A Practically Important Empirical Formula, Pedro Barragan Olague, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Resilient modulus is a mechanical characteristic describing the stiffness of a pavement. Its value depends on the moisture level. In pavement construction, it is important to be able, knowing the resilient modulus corresponding to one moisture level, to predict resilient modulus corresponding to other moisture levels. There exists an empirical formula for this prediction. In this paper, we provide a possible theoretical explanation for this empirical formula.

Computers Of Generation Omega And The Future Of Computing, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

George Klir And The Great Chain Of Ideas, Vladik Kreinovich

Departmental Technical Reports (CS)

Earlier this year, I received sad news that my good friend and dear colleague George Klir is no more. George was a great scientist -- and, in my opinion, a greatly underestimated one. I therefore believe that it will be beneficial to explain his true role in science.

Why Compaction Meter Value (Cmv) Is A Good Measure Of Pavement Stiffness: Towards A Possible Theoretical Explanation, Andrzej Pownuk, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

To measure stiffness of the compacted pavement, practitioners use the Compaction Meter Value (CMV); a ratio between the amplitude for the first harmonic of the compactor's acceleration and the amplitude corresponding to the vibration frequency. Numerous experiments show that CMV is highly correlated with the pavement stiffness, but as of now, there is no convincing theoretical explanation for this correlation. In this paper, we provide a possible theoretical explanation for the empirical correlation. This explanation also explains why, the stiffer the material, the more higher-order harmonics we observe.

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.

Which Point From An Interval Should We Choose?, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we know the exact form of the objective function, and we know the optimal decision corresponding to each value of the corresponding parameter x. What should we do if we do not know the exact value of x, and instead, we only know x with uncertainty -- e.g., with interval uncertainty? In this case, a reasonable idea is to select one value from the given interval, and to use the optimal decision corresponding to the selected value. But which value should we choose? In this paper, we provide a solution to this problem for …

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 …

What If We Use Different "And"-Operations In The Same Expert System, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

In expert systems, we often face a problem of estimating the expert's degree of confidence in a composite statement A & B based on the known expert's degrees of confidence a = d(A) and b = d(B) in individual statements A and B. The corresponding estimate f_&(a,b) is sometimes called an "and"-operation. Traditional fuzzy logic assumes that the same "and"-operation is applied to all pairs of statements. In this case, it is reasonable to justify that the "and"-operation be associative; such "and"-operations are known as t-norms. In practice, however, in different areas, different "and"-operations provide a good description …

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 …

What Will Make Computers Faster: An Approach Based On Computational Complexity, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.