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Articles 91 - 105 of 105
Full-Text Articles in Physical Sciences and Mathematics
Is "No Trade Theorem" Really A Paradox: Analysis Based On Decision Theory, Laxman Bokati, Vladik Kreinovich
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 …
Derivation Of Louisville-Bratu-Gelfand Equation From Shift- Or Scale-Invariance, Leobardo Valera, Martine Ceberio, Vladik Kreinovich
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.
Optimal Distribution Of Testing Resources Between Different System Levels, Griselda Acosta, Eric Smith, Vladik Kreinovich
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.
Why Grade Distribution Is Often Multi-Modal: An Uncertainty-Based Explanation, Olga Kosheleva, Christian Servin, Vladik Kreinovich
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.
How To Fuse Expert Knowledge: Not Always "And" But A Fuzzy Combination Of "And" And "Or", Christian Servin, Olga Kosheleva, Vladik Kreinovich
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 …
Logarithms Are Not Infinity: A Rational Physics-Related Explanation Of The Mysterious Statement By Lev Landau, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
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 …
When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich
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, …
Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich
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.
How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
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.
A Simple Quantitative Model Of Cognitive Tradeoff Phenomenon, Griselda Acosta, Eric Smith, Vladik Kreinovich
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 Bilingualism Helps Autistic Children Function: A Symmetry-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Why Bilingualism Helps Autistic Children Function: A Symmetry-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main problems of autistic children is that it is very difficult for them to switch to a different state, to a different activity -- and such switches are often needed. Researchers have recently shown that bilingualism helps autistic children function: namely, it is somewhat easier for bilingual children to switch to a new activity. In this paper, we provide a possible explanation for this empirical phenomenon. Namely, we show that, in general terms, autism means difficulty with breaking symmetries of a state, and we describe how this general reformulation indeed explains the above recently discovered phenomenon.
High Concentrations Naturally Lead To Fuzzy-Type Interactions And To Gravitational Wave Bursts, Oscar Galindo, Olga Kosheleva, Vladik Kreinovich
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.
Use Of Symmetries In Economics: An Overview, Vladik Kreinovich, Olga Kosheleva, Nguyen N. Thach, Nguyen Duc Trung
Use Of Symmetries In Economics: An Overview, Vladik Kreinovich, Olga Kosheleva, Nguyen N. Thach, Nguyen Duc Trung
Departmental Technical Reports (CS)
In this paper, we show that many semi-heuristic econometric formulas can be derived from the natural symmetry requirements. The list of such formulas includes many famous formulas provided by Nobel-prize winners, such as Hurwicz optimism-pessimism criterion for decision making under uncertainty, McFadden's formula for probabilistic decision making, Nash's formula for bargaining solution -- as well as Cobb-Douglas formula for production, gravity model for trade, etc.
Physics's Need For Interval Uncertainty And How It Explains Why Physical Space Is (At Least) 3-Dimensional, Olga Kosheleva, Vladik Kreinovich
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 …
Towards A More Efficient Representation Of Functions In Quantum And Reversible Computing, Oscar Galindo, Laxman Bokati, Vladik Kreinovich
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 …