Computer Sciences Commons^™

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.

How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Students feel more comfortable with rational numbers than with irrational ones. Thus, when teaching the beginning of calculus, it is desirable to have examples of simple problems for which both zeros and extrema point are rational. Recently, an algorithm was proposed for generating cubic polynomials with this property. However, from the computational viewpoint, the existing algorithm is not the most efficient one: in addition to applying explicit formulas, it also uses trial-and-error exhaustive search. In this paper, we propose a computationally efficient algorithm for generating all such polynomials: namely, an algorithm that uses only explicit formulas.

When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, it may seem that revolutions happen when life becomes really intolerable. However, historical analysis shows a different story: that revolutions happen not when life becomes intolerable, but when a reasonably prosperous level of living suddenly worsens. This empirical observation seems to contradict traditional decision theory ideas, according to which, in general, people's happiness monotonically depends on their level of living. A more detailed model of human behavior, however, takes into account not only the current level of living, but also future expectations. In this paper, we show that if we properly take these future expectations into account, …

Towards A More Efficient Representation Of Functions In Quantum And Reversible Computing, Oscar Galindo, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

Many practical problem necessitate faster computations. Simple physical estimates show that the only way to achieve a drastic computation speedup is to use quantum -- or, more generally, reversible -- computing. Thus, we need to be able to transform the existing algorithms into reversible form. Such transformation schemes exist. However, such schemes are not very efficient. Indeed, in general, when we write an algorithm, we composed it of several pre-existing modules. It would be nice to be able to similarly compose a reversible version of our algorithm from reversible version of these moduli -- but the existing transformation schemes cannot …

Physics's Need For Interval Uncertainty And How It Explains Why Physical Space Is (At Least) 3-Dimensional, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the fundamental problems of modern physics is the problem of divergence: e.g., when we try to compute the overall energy of the electric field generated by a charged elementary particle, we get a physically meaningless infinite value. In this paper, we show that one way to avoid these infinities is to take into account that measurements are always imprecise -- and thus, we never get the exact values of the physical quantities, only intervals of possible values. We also show that 3-dimensional space is the simplest one in which such interval uncertainty is inevitable. This may explain why …

High Concentrations Naturally Lead To Fuzzy-Type Interactions And To Gravitational Wave Bursts, Oscar Galindo, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy logic is normally used to describe the uncertainty of human knowledge and human reasoning. Physical phenomena are usually described by probabilistic models. In this paper, we show that in extremal conditions, when the concentrations are very large, some formulas describing physical interactions become fuzzy-type. We also show the observable consequences of such fuzzy-type formulas: they lead to bursts of gravitational waves.

Towards Optimal Implementation Of Decentralized Currencies: How To Best Select Probabilities In An Ethereum-Type Proof-Of-Stake Protocol, Thach N. Nguyen, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

Nowadays, most financial transactions are based on a centralized system, when all the transaction records are stored in a central location. This centralization makes the financial system vulnerable to cyber-attacks. A natural way to make the financial system more robust and less vulnerable is to switch to decentralized currencies. Such a transition will also make financial system more transparent. Historically first currency of this type -- bitcoin -- use a large amount of electric energy to mine new coins and is, thus, not scalable to the level of financial system as a whole. A more realistic and less energy-consuming scheme …

Relativistic Effects Can Be Used To Achieve A Universal Square-Root (Or Even Faster) Computation Speedup, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that special relativity phenomenon can be used to reduce computation time of any algorithm from T to square root of T. For this purpose, we keep computers where they are, but the whole civilization starts moving around the computer -- at an increasing speed, reaching speeds close to the speed of light. A similar square-root speedup can be achieved if we place ourselves near a growing black hole. Combining the two schemes can lead to an even faster speedup: from time T to the 4-th order root of T.

Secure Multi-Agent Quantum Communication: Towards The Most Efficient Scheme (A Pedagogical Remark), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many economic and financial applications, it is important to have secure communications. At present, communication security is provided mostly by RSA coding, but the emergent quantum computing can break this encoding, thus making it not secure. One way to make communications absolutely secure is to use quantum encryption. The existing schemes for quantum encryption are aimed at agent-to-agent communications; however, in practice, we often need secure multi-agent communications, where each of the agents has the ability to securely send messages to everyone else. In principle, we can repeat the agent-to-agent scheme for each pair of agents, but this requires …

Computing With Words -- When Results Do Not Depend On The Selection Of The Membership Function, Christopher W. Tovar, Carlos Cervantes, Mario Delgado, Stephanie Figueroa, Caleb Gillis, Daniel Gomez, Andres Llausas, Julio C. Lopez Molinar, Mariana Rogriguez, Alexander Wieczkowski, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, we need to transform natural-language expert knowledge into computer-understandable numerical form. One of the most successful ways to do it is to use fuzzy logic and membership functions. The problem is that membership functions are subjective. It is therefore desirable to look for cases when the results do not depend on this subjective choice. In this paper, after describing a known example of such a situation, we list several other examples where the results do not depend on the subjective choice of a membership function.

Should School Feel Like A Family: Lessons From Business Controversy As Interpreted By Decision Making Theory, Olga Kosheleva, Julian Viera Jr., Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional business theory promoted the ideal of business as a family: everyone should feel good about each other, all employees should feel good working together towards a joint goal. Recently, however, researchers claim that the well-promoted ideal is unattainable, it is a ruse causing everyone to overwork. Instead, these researchers propose a non-emotional collaboration of adults working temporarily on a joint project. In this paper, we show that this new trend is not just based on anecdotal evidence, it actually has a solid foundation in decision theory. So maybe we should apply this new trend to teaching too - and …