Computer Sciences Commons^™

Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the important steps in deep learning is softmax, when we select one of the alternatives with a probability depending on its expected gain. A similar formula describes human decision making: somewhat surprisingly, when presented with several choices with different expected equivalent monetary gain, we do not just select the alternative with the largest gain; instead, we make a random choice, with probability decreasing with the gain -- so that it is possible that we will select second highest and even third highest value. Both formulas assume that we know the exact value of the expected gain for each …

Why Liquids? A Symmetry-Based Solution To Weisskopf's Challenge, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In 1977, the renowned physicist Victor Weisskopf challenged the physics community to provide a fundamental explanation for the existence of the liquid phase of matter. A recent essay confirms that Weisskopf's 1977 question remains a challenge. In this paper, we use natural symmetry ideas to show that liquids are actually a natural state between solids and gases.

Why A Is Usually 90, B Is 80, Etc.: A Possible Explanation, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the US education system, instructors typically use 90/100, 80/100, 70/100, and 60/100 thresholds to gauge students' knowledge: students who get 90 or more points out of 100 get the highest grade of A, students whose grades are in between 80 and 90 get a B, followed by C, D, and F (fail). In this paper, we show that these seemingly arbitrary threshold have a natural explanation: A means that a student can solve almost all problems; C means that two students with this level of knowledge can solve almost all problems when working together; D means that we need …

The Heresy Of Unheard-Of Simplicity: Comment On "The Unreasonable Effectiveness Of Small Neural Ensembles In High-Dimensional Brain" By A. N. Gorban, V. A. Makarov, And I. Y. Tyukin, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Contrast Similarity Measures Of Fuzzy Sets, Ildar Batyrshin, Olga Kosheleva, Vladik Kreinovich, Nailya Kubysheva, Raouf Akhtiamov

Departmental Technical Reports (CS)

The paper proposes a new class of fuzzy set similarity measures taking into account the proximity of membership values to the border values 0 and 1. These similarity measures take values in [0,1] and generalize the crisp weak equality relation of fuzzy sets considered in the theory of fuzzy sets. The method of construction of a contrast similarity measure using a bipolar function symmetric with respect to 0.5 is presented. The similarity measure defined by the contrast intensification operation considered by Lotfi Zadeh is discussed.

Multiplatform Application Development For Android And Java, Yoonsik Cheon

Departmental Technical Reports (CS)

Software developers of today are under increasing pressure to support multiple platforms, in particular mobile platforms. However, developing a multiplatform application is difficult and challenging due to a variety of platform differences. We propose a native approach for developing a multiplatform application running on two similar but different platforms, Java and Android. We address practical software engineering concerns attributed to native multiplatform application development, from configuration of tools to software design and development process. Our approach allows one to share 37%~40% of application code between the two platforms as well as improving the quality of the application. We believe our …

Global Independence, Possible Local Dependence: Towards More Realistic Error Estimates For Indirect Measurements, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, it is not realistically possible to directly measure the desired physical quantity. In such situations, we have to measure this quantity indirectly, i.e., measure related quantities and use the known relation to estimate the value of the desired quantity. How accurate it the resulting estimate? The traditional approach assumes that the measurement errors of all direct measurements are independent. In many practical situations, this assumption works well, but in many other practical situations, it leads to a drastic underestimation of the resulting estimation error: e.g., when we base our estimate on measurements performed at nearby moments …

Why Patients Do Not Always Follow Doctor's Advice: Systems Approach Explains Empirical Observation, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical studies show that when a medical doctor prescribes a medicine, only two third of the patients fill the prescription, and of this filling-prescription group, only half follow the doctor's instructions when taking the medicine. In this paper, we show that a general systems approach -- namely, abstracting from the specifics of this situation -- helps explain these empirical observations. We also mention that systems approach can not only explains this problem, it can also help solve it -- i.e., it can help increase the patients' adherence to the doctors' recommendations.

Why Triangular Membership Functions Are So Efficient In F-Transform Applications: A Global Explanation To Supplement The Existing Local One, Olga Kosheleva, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

The main ideas of F-transform came from representing expert rules. It would be therefore re reasonable to expect that the more accurately the membership functions describe human reasoning, the more efficient will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions -- however, somewhat surprisingly, most efficient applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon which are based on local behavior of the signal. In this paper, we supplement this local explanation by a global one: namely, we prove that triangular …

Geometric Reformulation Of Learning Models Can Help Prepare Better Teachers, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Many researchers have been analyzing how to further improve teacher preparation -- and thus, how to improve teaching. Many of their results are based on complex models and/or on complex data analysis. Because of this complexity, future teachers often view the resulting recommendations as black boxes, without understanding the motivations for these recommendations -- and thus, without much willingness to follow these recommendations. One of the natural ways to make these recommendations clearer is to reformulate them in geometric terms, since geometric models are usually easier to understand than algebraic more abstract ones. In this paper, on the example of …

Decision Theory Can Explain Why Buying And Selling Prices Are Different, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

According to a naive understanding of economic behavior, for each object, we should have an internal estimate of how much this object is worth for us. If anyone offers us to buy this object at a smaller amount, we should agree, and if anyone offers to buy it from us for a larger amount, we should agree as well. In practice, however, contrary to this understanding, the price for which we are willing to buy and the price at which we are willing to sell are often different. In this paper, we show that this seemingly counterintuitive phenomenon can be …

How To Estimate Pavement Roughness: Beyond International Roughness Index, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich

Departmental Technical Reports (CS)

The standard way to describing the road's roughness it to use a single numerical characteristics called International Roughness Index (IRI). This characteristic describes the effect of the road roughness on a vehicle of standard size. To estimate IRI, practitioners tried to use easily available vehicles (whose size may be somewhat different) and then estimate IRI based on these different-size measurements. The problem is that the resulting estimates of IRI are very inaccurate -- which means that a single numerical characteristic like IRI is not sufficient to properly describe road roughness. In this paper, we show that the road roughness can …

For Quantum And Reversible Computing, Intervals Are More Appropriate Than General Sets, And Fuzzy Numbers Than General Fuzzy Sets, Oscar Galindo, Vladik Kreinovich

Departmental Technical Reports (CS)

Need for faster and faster computing necessitates going down to quantum level -- which means involving quantum computing. One of the important features of quantum computing is that it is reversible. Reversibility is also important as a way to decrease processor heating and thus, enable us to place more computing units in the same volume. In this paper, we argue that from this viewpoint, interval uncertainty is more appropriate than the more general set uncertainty -- and, similarly, that fuzzy numbers (for which all alpha-cuts are intervals) are more appropriate than more general fuzzy sets. We also explain why intervals …

Which Fourier Components Are Most Informative: General Idea And Case Studies, Julio Urenda, Nancy Avila, Nelly Gordillo, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the information comes not in terms of the original image or signal, but in terms of its Fourier transform. To detect complex features based on this information, it is often necessary to use machine learning. In the Fourier transform, usually, there are many components, and it is not easy to use all of them in machine learning. So, we need to select the most informative components. In this paper, we provide general recommendations on how to select such components. We also show that these recommendations are in good accordance with two examples: the structure of the …

Decision Making Under General Set Uncertainty: Additivity Approach, Srialekya Edupalli, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a decision under interval or set uncertainty: e.g., we need to decide how much we are willing to pay for an option that will bring us between $10 and $40, i.e., for which the set of possible gains is the interval S = [10,40]. To make such decisions, researcher have used the idea of additivity: that if have two independent options, then the price we pay for both should be equal to the sum of the prices that we pay for each of these options. It is known that this requirement enables …

Planning For A Corpus Of Continuous Ratings Of Spoken Dialog Quality, Nigel G. Ward

Departmental Technical Reports (CS)

While many aspects of speech processing, including speech recognition and speech synthesis, have seen enormous advances over the past few years, advances in dialog have been more modest. This difference is largely attributable to the lack of resources that can support machine learning of dialog models and dialog phenomena. The research community accordingly needs a corpus of spoken dialogs with quality annotations every 100 milliseconds or so. We envisage a large and diverse collection: on the order of fifty hours of data, representing hundreds of speakers and many genres, with every instant labeled for interaction quality by one or more …

Is "No Trade Theorem" Really A Paradox: Analysis Based On Decision Theory, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the challenges in foundations of finance is the so-called "no trade theorem" paradox: if an expert trader wants to sell some stock, that means that this trader believes that this stock will go down; however, the very fact that another expert trader is willing to buy it means that this other expert believes that the stock will go up. The fact that equally good experts have different beliefs should dissuade the first expert from selling -- and thus, trades should be very rare. However, in reality, trades are ubiquitous. In this paper, we show that a detailed application …

How Quantum Computing Can Help With (Continuous) Optimization, Christian Ayub, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the use of quantum computing can reduced the time needed for a search in an unsorted array: from the original non-quantum time T to a much smaller quantum computation time T_q proportional to the square root √(T) of T. In this paper, we show that for a continuous optimization problem, with quantum computing, we can reach almost the same speed-up: namely, we can reduce the non-quantum time T to a much shorter quantum computation time √(T) * ln(T).

A Theoretical Explanation For The Efficiency Of Generalized Harmonic Wavelets In Engineering And Seismic Spectral Analysis, Michael Beer, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

Wavelets of different shapes are known to be very efficient in many data processing problems. In many engineering applications, the most efficient shapes are shapes of a generalized harmonic wavelet, i.e., a wavelet of the shape w(t) = t^a * exp(b * t) for complex b. Similar functions are empirically the most successful in the seismic analysis -- namely, in simulating the earthquake-related high-frequency ground motion. In this paper, we provide a theoretical explanation for the empirical success of these models.

Computational Complexity Of Experiment Design In Civil Engineering, Olga Kosheleva, Yan Wang, Vladik Kreinovich

Departmental Technical Reports (CS)

To guarantee reliability and safety of engineering structures, we need to regularly measure their mechanical properties. Such measurements are often expensive and time-consuming. It is therefore necessary to carefully plan the corresponding measurement experiments, to minimize the corresponding expenses.

It is known that, in general, experiment design is NP-hard. However, the previous proofs dealt either with nonlinear systems, or with situations with low measurement accuracy. In civil engineering, however, most systems are well-described by linear systems, and measurements are reasonably accurate. In this paper, we show that experiment design is NP-hard even for civil engineering problems. We show that even …

Perfect Reproducibility Is Not Always Algorithmically Possible: A Pedagogical Observation, Jake Lasley, Salamah Salamah, Vladik Kreinovich

Departmental Technical Reports (CS)

Uses of computer-based based systems often want perfect reproducibility: when encountering the same situation twice, the system should exhibit the same behavior. For real-life systems that include sensors, this is not always possible: due to inevitable measurement uncertainty, for the same actual value of the corresponding quantity, we may get somewhat different measurement results, and thus, show somewhat different behavior. In this paper, we show that the above-described ideal reproducibility is not possible even in the idealized situation, when we assume that a sensor can perform its measurement with any given accuracy.

How To Define "And"- And "Or"-Operations For Intuitionistic And Picture Fuzzy Sets, Christian Servin, Reynaldo Martinez, Peter Hanson, Leonel Lopez, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional fuzzy logic does not distinguish between the cases when we know nothing about a statement S and the cases when we have equally convincing arguments for S and for its negation ~S: in both cases, we assign the degree 0.5 to such a statement S. This distinction is provided by intuitionistic fuzzy logic, when to describe our degree of confidence in a statement S, we use two numbers a₊ and a₋ that characterize our degree of confidence in S and in ~S. An even more detailed distinction is provided …

Why High-Level Attention Constantly Oscillates: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

In many situations like driving, it is important that a person concentrates all his/her attention at a certain critical task -- e.g., watching the road for possible problems. Because of this need to maintain high level of attention, it was assumed, until recently, that in such situations, the person maintains a constantly high level of attention (of course, until he or she gets tired). Interestingly, recent experiments showed that in reality, from the very beginning, attention level oscillates. In this paper, we show that such an oscillation is indeed helpful -- and thus, it is necessary to emulate such an …

Logarithms Are Not Infinity: A Rational Physics-Related Explanation Of The Mysterious Statement By Lev Landau, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Nobel-prize winning physicist Lev Landau liked to emphasize that logarithms are not infinity -- meaning that from the physical viewpoint, logarithms of infinite values are not really infinite. Of course, from a literally mathematical viewpoint, this statement does not make sense: one can easily prove that logarithm of infinity is infinite. However, when a Nobel-prizing physicist makes a statement, you do not want to dismiss it, you want to interpret it. In this paper, we propose a possible physical explanation of this statement. Namely, in physics, nothing is really infinite: according to modern physics, even the Universe is finite in …

How To Fuse Expert Knowledge: Not Always "And" But A Fuzzy Combination Of "And" And "Or", Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the non-fuzzy (e.g., interval) case, if two expert's opinions are consistent, then, as the result of fusing the knowledge of these two experts, we take the intersection of the two sets (e.g., intervals) describing the expert's opinions. In the experts are inconsistent, i.e., if the intersection is empty, then a reasonable idea is to assume that at least of these experts is right, and thus, to take the union of the two corresponding sets. In practice, expert opinions are often imprecise; this imprecision can be naturally described in terms of fuzzy logic -- a technique specifically designed to describe …

Optimal Distribution Of Testing Resources Between Different System Levels, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

When designing a system, we need to perform testing and checking on all levels of the system hierarchy, from the most general system level to the most detailed level. Our resources are limited, so we need to find the best way to allocate these resources, i.e., we need to decide how much efforts to use of each of the levels. In this paper, we formulate this problem in precise terms, and provide a solution to the resulting optimization problem.

Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

People usually underestimate time passed since distant events, and overestimate time passed since recent events. There are several explanations for this "telescoping effect", but most current explanations utilize specific features of human memory and/or human perception. We show that the telescoping effect can be explained on a much basic level of decision theory, without the need to invoke any specific ways we perceive and process time.

A Simple Quantitative Model Of Cognitive Tradeoff Phenomenon, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent study of chimpanzees has shown that on the individual basis, they are, surprisingly, much better than humans in simple tasks requiring intelligence and memory. A usual explanation -- called cognitive tradeoff -- is that a human brain has sacrificed some of its data processing (computation) abilities in favor of enhancing the ability to communicate; as a result, while individual humans may not be as smart as possible, jointly, we can solve complex problems. A similar cognitive tradeoff phenomenon can be observed in computer clusters: the most efficient computer clusters are not formed from the fastest, most efficient computers, …

Why Grade Distribution Is Often Multi-Modal: An Uncertainty-Based Explanation, Olga Kosheleva, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

There are many different independent factors that affect student grades. There are many physical situations like this, in which many different independent factors affect a phenomenon, and in most such situations, we encounter normal distribution -- in full accordance with the Central Limit Theorem, which explains that in such situations, distribution should be close to normal. However, the grade distribution is definitely not normal -- it is multi-modal. In this paper, we explain this strange phenomenon, and, moreover, we explain several observed features of this multi-modal distribution.

Derivation Of Louisville-Bratu-Gelfand Equation From Shift- Or Scale-Invariance, Leobardo Valera, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Louisville-Bratu-Gelfand equation appear in many different physical situations ranging from combustion to explosions to astrophysics. The fact that the same equation appears in many different situations seems to indicate that this equation should not depend on any specific physical process, that it should be possible to derive it from general principles. This is indeed what we show in this paper: that this equation can be naturally derived from basic symmetry requirements.