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Articles 1 - 30 of 69
Full-Text Articles in Physical Sciences and Mathematics
Finitely Generated Sets Of Fuzzy Values: If "And" Is Exact, Then "Or" Is Almost Always Approximate, And Vice Versa -- A Theorem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Finitely Generated Sets Of Fuzzy Values: If "And" Is Exact, Then "Or" Is Almost Always Approximate, And Vice Versa -- A Theorem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the traditional fuzzy logic, experts' degrees of confidence are described by numbers from the interval [0,1]. Clearly, not all the numbers from this interval are needed: in the whole history of the Universe, there will be only countably many statements and thus, only countably many possible degree, while the interval [0,1] is uncountable. It is therefore interesting to analyze what is the set S of actually used values. The answer depends on the choice of "and"-operations (t-norms) and "or"-operations (t-conorms). For the simplest pair of min and max, any finite set will do -- as long as it is …
Fuzzy Logic Explains The Usual Choice Of Logical Operations In 2-Valued Logic, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Fuzzy Logic Explains The Usual Choice Of Logical Operations In 2-Valued Logic, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the usual 2-valued logic, from the purely mathematical viewpoint, there are many possible binary operations. However, in commonsense reasoning, we only use a few of them: why? In this paper, we show that fuzzy logic can explain the usual choice of logical operations in 2-valued logic.
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is …
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Which Distributions (Or Families Of Distributions) Best Represent Interval Uncertainty: Case Of Permutation-Invariant Criteria, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probability of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult -- crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we …
Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that the distribution of seismic inter-event times is well described by the Gamma distribution. Recently, this fact has been used to successfully predict major seismic events. In this paper, we explain that the Gamma distribution of seismic inter-event times can be naturally derived from the first principles.
Why Spiking Neural Networks Are Efficient: A Theorem, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Why Spiking Neural Networks Are Efficient: A Theorem, Michael Beer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Current artificial neural networks are very successful in many machine learning applications, but in some cases they still lag behind human abilities. To improve their performance, a natural idea is to simulate features of biological neurons which are not yet implemented in machine learning. One of such features is the fact that in biological neural networks, signals are represented by a train of spikes. Researchers have tried adding this spikiness to machine learning and indeed got very good results, especially when processing time series (and, more generally, spatio-temporal data). In this paper, we provide a theoretical explanation for this empirical …
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Why A Classification Based On Linear Approximation To Dynamical Systems Often Works Well In Nonlinear Cases, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
It can be proven that linear dynamical systems exhibit either stable behavior, or unstable behavior, or oscillatory behavior, or transitional behavior. Interesting, the same classification often applies to nonlinear dynamical systems as well. In this paper, we provide a possible explanation for this phenomenon, i.e., we explain why a classification based on linear approximation to dynamical systems often works well in nonlinear cases.
Confirmation Bias In Systems Engineering: A Pedagogical Example, Griselda Acosta, Eric Smith, Vladik Kreinovich
Confirmation Bias In Systems Engineering: A Pedagogical Example, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the biases potentially affecting systems engineers is the confirmation bias, when instead of selecting the best hypothesis based on the data, people stick to the previously-selected hypothesis until it is disproved. In this paper, on a simple example, we show how important is to take care of this bias: namely, that because of this bias, we need twice as many experiments to switch to a better hypothesis.
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main motivations for designing computer models of complex systems is to come up with recommendations on how to best control these systems. Many complex real-life systems are so complicated that it is not computationally possible to use realistic nonlinear models to find the corresponding optimal control. Instead, researchers make recommendations based on simplified -- e.g., linearized -- models. The recommendations based on these simplified models are often not realistic but, interestingly, they can be made more realistic if we "tone them down" -- i.e., consider predictions and recommendations which are close to the current status quo state. …
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich
Departmental Technical Reports (CS)
Numerical experiments show that for classifying neural networks, it is beneficial to select a smaller deviation for initial weights that what is usually recommended. In this paper, we provide a theoretical explanation for these unexpected simulation results.
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
It is well known that, according to the second law of thermodynamics, the entropy of a closed system increases (or at least stays the same). In many situations, this increase is the smallest possible. The corresponding minimum entropy production principle was first formulated and explained by a future Nobelist Ilya Prigogine. Since then, many possible explanations of this principle appeared, but all of them are very technical, based on complex analysis of differential equations describing the system's dynamics. Since this phenomenon is ubiquitous for many systems, it is desirable to look for a general system-based explanation, explanation that would not …
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Many computer-based services use recommender systems that predict our preferences based on our degree of satisfaction with the past selections. One of the most efficient techniques making recommender systems successful is matrix factorization. While this technique works well, until now, there was no general explanation of why it works. In this paper, we provide such an explanation.
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
In many practical situations, observations and measurement results are consistent with many different models -- i.e., the corresponding problem is ill-posed. In such situations, a reasonable idea is to take into account that the values of the corresponding parameters should not be too large; this idea is known as regularization. Several different regularization techniques have been proposed; empirically the most successful are LASSO method, when we bound the sum of absolute values of the parameters, and EN and CLOT methods in which this sum is combined with the sum of the squares. In this paper, we explain the empirical success …
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Departmental Technical Reports (CS)
In the Bayesian approach, to describe a prior distribution on the set [0,1] of all possible probability values, typically, a Beta distribution is used. The fact that there have been many successful applications of this idea seems to indicate that there must be a fundamental reason for selecting this particular family of distributions. In this paper, we show that the selection of this family can indeed be explained if we make reasonable invariance requirements.
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
Departmental Technical Reports (CS)
In many practical situations, for some components of the uncertainty (e.g., of the measurement error) we know the corresponding probability distribution, while for other components, we know only upper bound on the corresponding values. To decide which of the algorithms or techniques leads to less uncertainty, we need to be able to gauge the combined uncertainty by a single numerical value -- so that we can select the algorithm for which this values is the best. There exist several techniques for gauging the combination of interval and probabilistic uncertainty. In this paper, we consider the problem of gauging the combination …
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
In many graph-related problems, an obvious necessary condition is often also sufficient. This phenomenon is so ubiquitous that it was even named TONCAS, after the first letters of the phrase describing this phenomenon. In this paper, we provide a possible explanation for this phenomenon.
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To make an adequate decision, we need to know the probabilities of different consequences of different actions. In practice, we only have partial information about these probabilities -- this situation is known as imprecise probabilities. A general description of all possible imprecise probabilities requires using infinitely many parameters. In practice, the two most widely used few-parametric approximate descriptions are p-boxes (bounds on the values of the cumulative distribution function) and interval-valued moments (i.e., bounds on moments). In some situations, these approximations are not sufficiently accurate. So, we need more accurate more-parametric approximations. In this paper, we explain what are the …
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
Departmental Technical Reports (CS)
In many practical situations, we only have partial information about the probabilities; this means that there are several different probability distributions which are consistent with our knowledge. In such cases, if we want to select one of these distributions, it makes sense not to pretend that we have a small amount of uncertainty -- and thus, it makes sense to select a distribution with the largest possible value of uncertainty. A natural measure of uncertainty of a probability distribution is its entropy. So, this means that out of all probability distributions consistent with our knowledge, we select the one whose …
How To Apply Software Engineering Testing Methodologies To Education, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
How To Apply Software Engineering Testing Methodologies To Education, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Testing is a very important part of quality control in education. To decide how to best test, it makes sense to use experience of other areas where testing is important, where there is a large amount of experimental data comparing the efficiency of different testing strategies. One such area is software engineering. The experience of software engineering shows that the most efficient approach to testing is to test thoroughly on every single stage of the project. In regards to teaching, the resulting recommendation means making testing as frequent as possible, preferably giving weekly quizzes. At first glance, this may seem …
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
Departmental Technical Reports (CS)
In their 1983 paper, C. Alsina, E. Trillas, and L. Valverde proved that distributivity, monotonicity, and boundary conditions imply that the "and"-operation is min and the "or"-operation is max. In this paper, we show that all these conditions are necessary for Alsina et al. result to be true.
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
When people have several possible investment instruments, people often invest equally into these instruments: in the case of n instruments, they invest 1/n of their money into each of these instruments. Of course, if additional information about each instrument is available, this 1/n investment strategy is not optimal. We show, however, that in the absence of reliable information, 1/n investment is indeed the best strategy.
Faster Quantum Alternative To Softmax Selection In Deep Learning And Deep Reinforcement Learning, Oscar Galindo, Christian Ayub, Martine Ceberio, Vladik Kreinovich
Faster Quantum Alternative To Softmax Selection In Deep Learning And Deep Reinforcement Learning, Oscar Galindo, Christian Ayub, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Deep learning and deep reinforcement learning are, at present, the best available machine learning tools for use in engineering problems. However, at present, the use of these tools is limited by the fact that they are very time-consuming, usually requiring the use of a high performance computer. It is therefore desirable to look for possible ways to speed up the corresponding computations. One of the time-consuming parts of these algorithms is softmax selection, when instead of selecting the alternative with the largest possible value of the corresponding objective function, we select all possible values, with probabilities increasing with the value …
How To Use Quantum Computing To Check Which Inputs Are Relevant: A Proof That Deutsch-Jozsa Algorithm Is, In Effect, The Only Possibility, Vladik Kreinovich, Martine Ceberio, Ricardo Alvarez
How To Use Quantum Computing To Check Which Inputs Are Relevant: A Proof That Deutsch-Jozsa Algorithm Is, In Effect, The Only Possibility, Vladik Kreinovich, Martine Ceberio, Ricardo Alvarez
Departmental Technical Reports (CS)
One of the main reasons why computations -- in particular, engineering computations -- take long is that, to be on the safe side, models take into account all possible affecting features, most of which turn out to be not really relevant for the corresponding physical problem. From this viewpoint, it is desirable to find out which inputs are relevant. In general, the problem of checking the input's relevancy is itself NP-hard, which means, crudely speaking, that no feasible algorithm can always solve it. Thus, it is desirable to speed up this checking as much as possible. One possible way to …
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Formal implication does not capture the intuitive idea of "if A then B", since in formal implication, every two true statements -- even completely unrelated ones -- imply each other. A more adequate description of intuitive implication happens if we consider how much the use of A can shorten a derivation of B. At first glance, it may seem that the number of bits by which we shorten this derivation is a reasonable degree of implication, but we show that this number is not in good accordance with our intuition, and that a natural formalization of this intuition leads to …
How Earthquake Risk Depends On The Closeness To A Fault: Symmetry-Based Geometric Analysis, Aaron A. Velasco, Solymar Ayala Cortez, Olga Kosheleva, Vladik Kreinovich
How Earthquake Risk Depends On The Closeness To A Fault: Symmetry-Based Geometric Analysis, Aaron A. Velasco, Solymar Ayala Cortez, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Earthquakes can lead to a huge damage -- and the big problem is that they are very difficult to predict. To be more precise, it is very difficult to predict the time of a future earthquake. However, we can estimate which earthquake locations are probable. In general, earthquakes are mostly concentrated around the corresponding faults. For some faults, all the earthquakes occur in a narrow vicinity of the fault, while for other faults, areas more distant from the fault are risky as well. To properly estimate the earthquake's risk, it is important to understand when this risk is limited to …
Relationship Between Measurement Results And Expert Estimates Of Cumulative Quantities, On The Example Of Pavement Roughness, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich
Relationship Between Measurement Results And Expert Estimates Of Cumulative Quantities, On The Example Of Pavement Roughness, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situation, we are interesting in values of cumulative quantities -- e.g., quantities that describe the overall quality of a long road segment. Some of these quantities we can measure, but measuring such quantities requiring measuring many local values and is, thus, expensive and time-consuming. As a result, in many cases, instead of the measurement, we reply on expert estimating such cumulative quantities on a scale, e.g., from 0 to 5. Researchers have come up with an empirical formula that provides a relation between the measurement result and a 0-to-5 expert estimate. In this paper, we provide a …
Why Some Non-Classical Logics Are More Studied?, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Why Some Non-Classical Logics Are More Studied?, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
It is well known that the traditional 2-valued logic is only an approximation to how we actually reason. To provide a more adequate description of how we actually reason, researchers proposed and studied many generalizations and modifications of the traditional logic, generalizations and modifications in which some rules of the traditional logic are no longer valid. Interestingly, for some of such rules (e.g., for law of excluded middle), we have a century of research in logics that violate this rule, while for others (e.g., commutativity of ``and''), practically no research has been done. In this paper, we show that fuzzy …
Hierarchial Multiclass Classification Works Better Than Direct Classification: An Explanation Of The Empirical Fact, Julio Urenda, Nancy Avila, Nelly Gordillo, Vladik Kreinovich
Hierarchial Multiclass Classification Works Better Than Direct Classification: An Explanation Of The Empirical Fact, Julio Urenda, Nancy Avila, Nelly Gordillo, Vladik Kreinovich
Departmental Technical Reports (CS)
Machine learning techniques have been very efficient in many applications, in particular, when learning to classify a given object to one of the given classes. Such classification problems are ubiquitous: e.g., in medicine, such a classification corresponds to diagnosing a disease, and the resulting tools help medical doctors come up with the correct diagnosis. There are many possible ways to set up the corresponding neural network (or another machine learning technique). A direct way is to design a single neural network with as many outputs as there are classes -- so that for each class i, the system would …
Geometric Aspects Of Wound Healing, Julio Urenda, Vladik Kreinovich
Geometric Aspects Of Wound Healing, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that many aspects of complex biological processes related to wound healing can be explained in terms of the corresponding geometric symmetries.
Why H-Index, Vladik Kreinovich, Olga Kosheleva, Nguyen Hoang Phuong
Why H-Index, Vladik Kreinovich, Olga Kosheleva, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
At present, one of the main ways to gauge the quality of a researcher is to use his or her h-index, which is defined as the largest integer n such that the researcher has at least n publications each of which has at least n citations. The fact that this quantity is widely used indicates that h-index indeed reasonably adequately describes the researcher's quality. So, this notion must capture some intuitive idea. However, the above definition is not intuitive at all, it sound like a somewhat convoluted mathematical exercise. So why is h-index so efficient? In this paper, we …