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Articles 91 - 120 of 1083
Full-Text Articles in Physical Sciences and Mathematics
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical problems, the most effective classification techniques are based on deep learning. In this approach, once the neural network generates values corresponding to different classes, these values are transformed into probabilities by using the softmax formula. Researchers tried other transformation, but they did not work as well as softmax. A natural question is: why is softmax so effective? In this paper, we provide a possible explanation for this effectiveness: namely, we prove that softmax is the only consistent approach to probability-based classification. In precise terms, it is the only approach for which two reasonable probability-based ideas -- Least …
Why Inverse Layers In Pavement? Why Zipper Fracking? Why Interleaving In Education? A General Explanation, Edgar Daniel Rodriguez Velasquez, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Why Inverse Layers In Pavement? Why Zipper Fracking? Why Interleaving In Education? A General Explanation, Edgar Daniel Rodriguez Velasquez, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, if we split our efforts into two disconnected chunks, we get better results: a pavement is stronger if instead of a single strengthening layer, we place two parts of this layer separated by no-so-strong layers; teaching is more effective if instead of concentrating a topic in a single time interval, we split it into two parts separated in time, etc. In this paper, we provide a general explanation for all these phenomena.
Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich
Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In machine learning -- and in data processing in general -- it is very important to select the proper number of features. If we select too few, we miss important information and do not get good results, but if we select too many, this will include many irrelevant ones that only bring noise and thus again worsen the results. The usual method of selecting the proper number of features is to add features one by one until the quality stops improving and starts deteriorating again. This method works, but it often takes too much time. In this paper, we propose …
Everything Is A Matter Of Degree: The Main Idea Behind Fuzzy Logic Is Useful In Geosciences And In Authorship, Christian Servin, Aaron Velasco, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Everything Is A Matter Of Degree: The Main Idea Behind Fuzzy Logic Is Useful In Geosciences And In Authorship, Christian Servin, Aaron Velasco, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Departmental Technical Reports (CS)
This paper presents two applications of the general principle -- the everything is a matter of degree -- the principle that underlies fuzzy techniques. The first -- qualitative -- application helps explain the fact that while most earthquakes occur close to faults (borders between tectonic plates or terranes), earthquakes have also been observed in areas which are far away from the known faults. The second -- more quantitative -- application is to the problem of which of the collaborators should be listed as authors and which should be simply thanked in the paper. We argue that the best answer to …
Foundations Of Neural Networks Explain The Empirical Success Of The "Surrogate" Approach To Ordinal Regression -- And Recommend What Next, Salvador Robles, Martine Ceberio, Vladik Kreinovich
Foundations Of Neural Networks Explain The Empirical Success Of The "Surrogate" Approach To Ordinal Regression -- And Recommend What Next, Salvador Robles, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Recently, a new efficient semi-heuristic statistical method -- called Surrogate Approach -- has been proposed for dealing with regression problems. How can we explain this empirical success? And since this method is only an approximation to reality, what can we recommend if there is a need for a more accurate approximation? In this paper, we show that this empirical success can be explained by the same arguments that explain the empirical success of neural networks -- and these arguments can also provide us with possible more general techniques (that will hopefully lead to more accurate approximation to real-life phenomena).
Integrity First, Service Before Self, And Excellence: Core Values Of Us Air Force Naturally Follow From Decision Theory, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Integrity First, Service Before Self, And Excellence: Core Values Of Us Air Force Naturally Follow From Decision Theory, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
By analyzing data both from peace time and from war time, the US Air Force came with three principles that determine success: integrity, service before self, and excellent. We show that these three principles naturally follow from decision theory, a theory that describes how a rational person should make decisions.
Wormholes, Superfast Computations, And Selivanov's Theorem, Olga Kosheleva, Vladik Kreinovich
Wormholes, Superfast Computations, And Selivanov's Theorem, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While modern computers are fast, there are still many practical problems that require even faster computers. It turns out that on the fundamental level, one of the main factors limiting computation speed is the fact that, according to modern physics, the speed of all processes is limited by the speed of light. Good news is that while the corresponding limitation is very severe in Euclidean geometry, it can be more relaxed in (at least some) non-Euclidean spaces, and, according to modern physics, the physical space is not Euclidean. The differences from Euclidean character are especially large on micro-level, where quantum …
What Do Goedel's Theorem And Arrow's Theorem Have In Common: A Possible Answer To Arrow's Question, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
What Do Goedel's Theorem And Arrow's Theorem Have In Common: A Possible Answer To Arrow's Question, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Kenneth Arrow, the renowned author of the Impossibility Theorem that explains the difficulty of group decision making, noticed that there is some commonsense similarity between his result and Goedel's theorem about incompleteness of axiomatic systems. Arrow asked if it is possible to describe this similarity in more precise terms. In this paper, we make the first step towards this description. We show that in both cases, the impossibility result disappears if we take into account probabilities. Namely, we take into account that we can consider probabilistic situations, that we can make probabilistic conclusions, and that we can make probabilistic decisions …
Causality: Hypergraphs, Matter Of Degree, Foundations Of Cosmology, Cliff Joslyn, Andres Ortiz-Muñoz, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Causality: Hypergraphs, Matter Of Degree, Foundations Of Cosmology, Cliff Joslyn, Andres Ortiz-Muñoz, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
The notion of causality is very important in many applications areas. Because of this importance, there are several formalizations of this notion in physics and in AI. Most of these definitions describe causality as a crisp ("yes"-"no") relation between two events or two processes -- cause and effect. However, such descriptions do not fully capture the intuitive idea of causality: first, often, several conditions are needed to be present for an effect to occur, and, second, the effect is often a matter of degree. In this paper, we show how to modify the current description of causality so as to …
Towards Decision Making Under Interval Uncertainty, Juan A. Lopez, Vladik Kreinovich
Towards Decision Making Under Interval Uncertainty, Juan A. Lopez, Vladik Kreinovich
Departmental Technical Reports (CS)
In many real-life situations, we need to make a decision. In many cases, we know the optimal decision in situations when we know the exact value of the corresponding quantity x. However, often, we do not know the exact value of this quantity, we only know the bounds on the value x -- i.e., we know the interval containing $x$. In this case, we need to select a decision corresponding to some value from this interval. The selected value will, in general, be different from the actual (unknown) value of this quantity. As a result, the quality of our decision …
Conflict Situations Are Inevitable When There Are Many Participants: A Proof Based On The Analysis Of Aumann-Shapley Value, Sofia Holguin, Vladik Kreinovich
Conflict Situations Are Inevitable When There Are Many Participants: A Proof Based On The Analysis Of Aumann-Shapley Value, Sofia Holguin, Vladik Kreinovich
Departmental Technical Reports (CS)
When collaboration of several people results in a business success, an important issue is how to fairly divide the gain between the participants. In principle, the solution to this problem is known since the 1950s: natural fairness requirements lead to the so-called Shapley value. However, the computation of Shapley value requires that we can estimate, for each subset of the set of all participants, how much gain they would have gained if they worked together without others. It is possible to perform such estimates when we have a small group of participants, but for a big company with thousands of …
People Prefer More Information About Uncertainty, But Perform Worse When Given This Information: An Explanation Of The Paradoxical Phenomenon, Jieqiong Zhao, Olga Kosheleva, Vladik Kreinovich
People Prefer More Information About Uncertainty, But Perform Worse When Given This Information: An Explanation Of The Paradoxical Phenomenon, Jieqiong Zhao, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In a recent experiment, decision makers were asked whether they would prefer having more information about the corresponding situation. They confirmed this preference, and such information was provided to them. However, strangely, the decisions of those who received this information were worse than the decisions of the control group -- that did not get this information. In this paper, we provide an explanation for this paradoxical situation.
Low-Probability High-Impact Events Are Even More Important Than It Is Usually Assumed, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Low-Probability High-Impact Events Are Even More Important Than It Is Usually Assumed, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A large proportion of undesirable events like earthquakes, floods, tornados occur in zones where these events are frequent. However, a significant number of such events occur in other zones, where such events are rare. For example, while most major earthquakes occur in a vicinity of major faults, i.e., on the border between two tectonic plates, some strong earthquakes also occur inside plates. We want to mitigate all undesirable events, but our resources are limited. So, to allocate these resources, we need to decide which ones are more important. For this decision, a natural idea is to use the product of …
How People Make Decisions Based On Prior Experience: Formulas Of Instance-Based Learning Theory (Ilbt) Follow From Scale Invariance, Palvi Aggarwal, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
How People Make Decisions Based On Prior Experience: Formulas Of Instance-Based Learning Theory (Ilbt) Follow From Scale Invariance, Palvi Aggarwal, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To better understand human behavior, we need to understand how people make decisions, how people select one of possible actions. This selection is usually based on predicting consequences of different actions, and these predictions are, in their turn, based on the past experience. For example, consequences that occur more frequently in the past are viewed as more probable. However, this is not just about frequency: recent observations are usually given more weight that past ones. Researchers have discovered semi-empirical formulas that describe our predictions reasonably well; these formulas form the basis of the Instance-Based Learning Theory (ILBT). In this paper, …
Why Gliding Symmetry Used To Be Prevalent In Biology But Practically Disappeared, Julio C. Urenda, Vladik Kreinovich
Why Gliding Symmetry Used To Be Prevalent In Biology But Practically Disappeared, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
At present, many living creatures have symmetries; in particular, the left-right symmetry is ubiquitous. Interestingly, 600 million years ago, very fee living creatures had the left-right symmetry: most of them had a gliding symmetry, symmetry with respect to shift along a line followed by reflection in this line. This symmetry is really seen in living creatures today. In this paper, we provide a physical-based geometric explanation for this symmetry change: we explain both why gliding symmetry was ubiquitous, and why at present, it is rarely observed, while the left-right symmetry is prevalent.
The World Is Cognizable: An Argument Based On Hoermander's Theorem, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
The World Is Cognizable: An Argument Based On Hoermander's Theorem, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Is the world cognizable? Is it, in principle, possible to predict the future state of the world based on the measurements and observations performed in a local area -- e.g., in the Solar system? In this paper, we use general physicists' principles and a mathematical theorem about partial differential equations to show that such prediction is indeed, theoretically possible.
Success (Studying Underlying Characteristics Of Computing And Engineering Student Success) Survey: Non-Cognitive And Affective Profiles In Engineering And Computing Students At Utep (2018-2022), Sanga Kim, Christian Teran Lopez, Andres Segura, Gabriel Miki
Success (Studying Underlying Characteristics Of Computing And Engineering Student Success) Survey: Non-Cognitive And Affective Profiles In Engineering And Computing Students At Utep (2018-2022), Sanga Kim, Christian Teran Lopez, Andres Segura, Gabriel Miki
Departmental Technical Reports (CS)
No abstract provided.
Interval-Valued And Set-Valued Extensions Of Discrete Fuzzy Logics, Belnap Logic, And Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Interval-Valued And Set-Valued Extensions Of Discrete Fuzzy Logics, Belnap Logic, And Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich
Departmental Technical Reports (CS)
It has been recently shown that in some applications, e.g., in ship navigation near a harbor, it is convenient to use combinations of basic colors -- red, green, and blue -- to represent different fuzzy degrees. In this paper, we provide a natural explanation for the efficiency of this empirical fact: namely, we show that it is reasonable to consider discrete fuzzy logics, it is reasonable to consider their interval-valued and set-valued extensions, and that a set-valued extension of the 3-values logic is naturally equivalent to the use of color combinations.
Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, Vladik Kreinovich
Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situation, control experts can only formulate their experience by using imprecise ("fuzzy") words from natural language. To incorporate this knowledge in automatic controllers, Lotfi Zadeh came up with a methodology that translate the informal expert statements into a precise control strategy. This methodology -- and its following modifications -- is known as fuzzy control. Fuzzy control often leads to a reasonable control -- and we can get an even better control results by tuning the resulting control strategy on the actual system. There are many parameters that can be changes during tuning, so tuning usually is rather …
Designing An Optimal Medicine Cocktail Is Np-Hard, Luc Longpre, Vladik Kreinovich
Designing An Optimal Medicine Cocktail Is Np-Hard, Luc Longpre, Vladik Kreinovich
Departmental Technical Reports (CS)
In many cases, a combination of different drugs -- known as a medicine cocktail -- is more effective against a disease than each individual drug. It is desirable to find the most effective cocktail. This problem can be naturally formulated as a problem of maximizing a quadratic expression under the condition that all the unknowns (concentrations of different medicines) are non-negative. At first glance, it may seem that this problem is feasible -- since a similar economic problem of finding the optimal investment portfolio is known to be feasible. However, it turns out that the cocktail problem is different: it …
Why In Mond -- Alternative Gravitation Theory -- A Specific Formula Works The Best: Complexity-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Why In Mond -- Alternative Gravitation Theory -- A Specific Formula Works The Best: Complexity-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Based on the rotation of the stars around a galaxy center, one can estimate the corresponding gravitational acceleration -- which turns out to be much larger than what Newton's theory predicts based on the masses of all visible objects. The majority of physicists believe that this discrepancy indicates the presence of "dark" matter, but this idea has some unsolved problems. An alternative idea -- known as Modified Newtonian Dynamics (MOND, for short) is that for galaxy-size distances, Newton's gravitation theory needs to be modified. One of the most effective versions of this idea uses so-called simple interpolating function. In this …
Non-Localized Physical Processes Can Help Speed Up Computations, Be It Hidden Variables In Quantum Physics Or Non-Localized Energy In General Relativity, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich
Non-Localized Physical Processes Can Help Speed Up Computations, Be It Hidden Variables In Quantum Physics Or Non-Localized Energy In General Relativity, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While most physical processes are localized -- in the sense that each event can only affect events in its close vicinity -- many physicists believe that some processes are non-local. These beliefs range from more heretic -- such as hidden variables in quantum physics -- to more widely accepted, such as the non-local character of energy in General Relativity. In this paper, we attract attention to the fact that non-local processes bring in the possibility of drastically speeding up computations.
Systems Approach Explains Why Low Heart Rate Variability Is Correlated With Depression (And Suicidal Thoughts), Francisco Zapata, Eric Smith, Vladik Kreinovich
Systems Approach Explains Why Low Heart Rate Variability Is Correlated With Depression (And Suicidal Thoughts), Francisco Zapata, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Depression is a serious medical problem. If diagnosed early, it can usually be cured, but if left undetected, it can lead to suicidal thoughts and behavior. The early stages of depression are difficult to diagnose. Recently, researchers found a promising approach to such diagnosis -- it turns out that depression is correlated with low heart rate variability. In this paper, we show that the general systems approach can explain this empirical relation.
Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, for each alternative i, we do not know the corresponding gain xi, we only know the interval [li,ui] of possible gains. In such situations, a reasonable way to select an alternative is to choose some value α from the interval [0,1] and select the alternative i for which the Hurwicz combination α*ui + (1 − α)*li is the largest possible. In situations when we do not know the user's α, a reasonable idea is to select all alternatives that are optimal for some α. In this paper, we describe a feasible algorithm for such a selection.
Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When we usually process data, we, in effect, implicitly assume that we know the exact values of all the inputs. In practice, these values comes from measurements, and measurements are never absolutely accurate. In many cases, the only information about the actual (unknown) values of each input is that this value belongs to an appropriate interval. Under this interval uncertainty, we need to compute the range of all possible results of applying the data processing algorithm when the inputs are in these intervals. In general, the problem of exactly computing this range is NP-hard, which means that in feasible time, …
Data Processing Under Fuzzy Uncertainty: Towards More Accurate Algorithms, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Data Processing Under Fuzzy Uncertainty: Towards More Accurate Algorithms, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Data that we process comes either from measurements or from experts -- or from the results of previous data processing that were also based on measurements and/or expert estimates. In both cases, the data is imprecise. To gauge the accuracy of the results of data processing, we need to take the corresponding data uncertainty into account. In this paper, we describe a new algorithm for taking fuzzy uncertainty into account, an algorithm that, for small number of inputs, leads to the same or even better accuracy than the previously proposed methods.
How Viscosity Of An Asphalt Binder Depends On Temperature: Theoretical Explanation Of An Empirical Dependence, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
How Viscosity Of An Asphalt Binder Depends On Temperature: Theoretical Explanation Of An Empirical Dependence, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Departmental Technical Reports (CS)
Pavement must be adequate for all the temperatures, ranging from the winter cold to the summer heat. In particular, this means that for all possible temperatures, the viscosity of the asphalt binder must stay within the desired bounds. To predict how the designed pavement will behave under different temperatures, it is desirable to have a general idea of how viscosity changes with temperature. Pavement engineers have come up with an empirical approximate formula describing this change. However, since this formula is purely empirical, with no theoretical justification, practitioners are often somewhat reluctant to depend on this formula. In this paper, …
Graph Approach To Uncertainty Quantification, Hector A. Reyes, Cliff Joslyn, Vladik Kreinovich
Graph Approach To Uncertainty Quantification, Hector A. Reyes, Cliff Joslyn, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional analysis of uncertainty of the result of data processing assumes that all measurement errors are independent. In reality, there may be common factor affecting these errors, so these errors may be dependent. In such cases, the independence assumption may lead to underestimation of uncertainty. In such cases, a guaranteed way to be on the safe side is to make no assumption about independence at all. In practice, however, we may have information that a few pairs of measurement errors are indeed independent -- while we still have no information about all other pairs. Alternatively, we may suspect that for …
Will Nanotechnology Bring In The Judgement Day?, Olga Kosheleva, Vladik Kreinovich
Will Nanotechnology Bring In The Judgement Day?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
There are many current and prospective positive aspects of nanotechnology. However, while we look forward to its future successes, we need to keep our eyes open and be prepared for what will really be a future shock: that quantum computing – an inevitable part of nanotechnology – will enable the future folks to read all our encrypted messages and thus, learn everything that we wanted to keep secret. This will be really the Judgement Day, when all our sins will be open to everyone. How we will react to it? Will this destroy our civilization? Let us hope that the …
An Argument In Favor Of Piecewise-Constant Membership Functions, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
An Argument In Favor Of Piecewise-Constant Membership Functions, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Theoretically, we can have membership functions of arbitrary shape. However, in practice, at any given moment of time, we can only represent finitely many parameters in a computer. As a result, we usually restrict ourselves to finite-parametric families of membership functions. The most widely used families are piecewise linear ones, e.g., triangular and trapezoid membership functions. The problem with these families is that if we know a nonlinear relation y = f(x) between quantities, the corresponding relation between membership functions is only approximate -- since for piecewise linear membership functions for x, the resulting membership function for y is not …