Computer Sciences Commons^™

Why Max And Average Poolings Are Optimal In Convolutional Neural Networks, Ahnaf Farhan, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we do not know the exact relation between different quantities; this relation needs to be determined based on the empirical data. This determination is not easy -- especially in the presence of different types of uncertainty. When the data comes in the form of time series and images, many efficient techniques for such determination use algorithms for training convolutional neural network. As part of this training, such networks "pool" several values corresponding to nearby temporal or spatial points into a single value. Empirically, the most efficient pooling algorithm consists of taking the maximum of the pooled …

A Symmetry-Based Explanation Of The Main Idea Behind Chubanov's Linear Programming Algorithm, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Many important real-life optimization problems can be described as optimizing a linear objective function under linear constraints -- i.e., as a linear programming problem. This problem is known to be not easy to solve. Reasonably natural algorithms -- such as iterative constraint satisfaction or simplex method -- often require exponential time. There exist efficient polynomial-time algorithms, but these algorithms are complicated and not very intuitive. Also, in contrast to many practical problems which can be computed faster by using parallel computers, linear programming has been proven to be the most difficult to parallelize. Recently, Sergei Chubanov proposed a modification of …

Need To Combine Interval And Probabilistic Uncertainty: What Needs To Be Computed, What Can Be Computed, What Can Be Feasibly Computed, And How Physics Can Help, Songsak Sriboonchitta, Thach N. Nguyen, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

In many practical situations, the quantity of interest is difficult to measure directly. In such situations, to estimate this quantity, we measure easier-to-measure quantities which are related to the desired one by a known relation, and we use the results of these measurement to estimate the desired quantity. How accurate is this estimate?

Traditional engineering approach assumes that we know the probability distributions of measurement errors; however, in practice, we often only have partial information about these distributions. In some cases, we only know the upper bounds on the measurement errors; in such cases, the only thing we know about …

Which Fuzzy Logic Operations Are Most Appropriate For Ontological Semantics: Theoretical Explanation Of Empirical Observations, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In several of their papers, Victor Raskin and coauthors proposed to use fuzzy techniques to make ontological semantics techniques more adequate in dealing with natural language. Specifically, they showed that the most adequate results appear when we use min as an "and"-operation and max as an "or"-operation. It is interesting that in other applications of fuzzy techniques, such as intelligent control, other versions of fuzzy techniques are the most adequate. In this chapter, we explain why the above techniques are empirically the best in the semantics case.

Why Bohmian Approach To Quantum Econometrics: An Algebraic Explanation, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and time-consuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas -- equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics -- namely, from quantum physics. The resulting approach for solving economic equations is known as quantum econometrics. In quantum physics, …

How To Select The Best Paper: Towards Justification (And Possible Enhancement) Of Current Semi-Heuristic Procedures, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To select the best paper at a conference or in a journal, people use reasonably standard semi-heuristic procedures like averaging scores. These procedures usually work well, but sometimes, new situations appear for which the existing procedures are not automatically applicable. Since the existing procedures are heuristic, it is often not clear how to extend them to new situations. In this paper, we provide a possible explanation for the existing procedures. This explanations enables us to naturally generalize these procedures to possible new situations.

Why Triangular And Trapezoid Membership Functions: A Simple Explanation, Vladik Kreinovich, Olga Kosheleva, Shahnaz Shahbazova

Departmental Technical Reports (CS)

In principle, in applications of fuzzy techniques, we can have different complex membership functions. In many practical applications, however, it turns out that to get a good quality result -- e.g., a good quality control -- it is sufficient to consider simple triangular and trapezoid membership functions. There exist explanations for this empirical phenomenon, but the existing explanations are rather mathematically sophisticated and are, thus, not very intuitively clear. In this paper, we provide a simple -- and thus, more intuitive -- explanation for the ubiquity of triangular and trapezoid membership functions.

Decision Making Under Interval Uncertainty: Beyond Hurwicz Pessimism-Optimism Criterion, Tran Anh Tuan, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

In many practical situations, we do not know the exact value of the quantities characterizing the consequences of different possible actions. Instead, we often only known lower and upper bounds on these values, i.e., we only know intervals containing these values. To make decisions under such interval uncertainty, the Nobelist Leo Hurwicz proposed his optimism-pessimism criterion. It is known, however, that this criterion is not perfect: there are examples of actions which this criterion considers to be equivalent but which for which common sense indicates that one of them is preferable. These examples mean that Hurwicz criterion must be extended, …

Why Stem?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Is the idea of combining science, technology, engineering, and mathematics into a single STEM complex a fashionable tendency, as some educator think - or is there a deep reason behind this combination? In this paper, we show that the latest developments in Theory of Computation make such a union necessary and desirable.

Summation Of Divergent Infinite Series: How Natural Are The Current Tricks, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Infinities are usually an interesting topic for students, especially when they lead to what seems like paradoxes, when we have two different seemingly correct answers to the same question. One of such cases is summation of divergent infinite sums: on the one hand, the sum is clearly infinite, on the other hand, reasonable ideas lead to a finite value for this same sum. A usual way to come up with a finite sum for a divergent infinite series is to find a 1-parametric family of series that includes the given series for a specific value p = p0 of the …

Composing A Cross-Platform Development Environment Using Maven, Terry J. Speicher, Yoonsik Cheon

Departmental Technical Reports (CS)

It is challenging to develop a cross-platform application, that is, an application that runs on multiple platforms. It requires not only code reuse but also an individual building or compilation for each platform, possibly with different development tools. In this paper, we show a simple approach for creating a cross-platform application using Maven, a build tool. We configure a cross-platform development environment by composing a set of platform-specific tools or integrated development environments (IDE's). The key idea of our approach is to use Maven to immediately propagate changes made using one platform tool, or IDE, to other platforms. For this, …

Why Triangular And Trapezoid Membership Functions Are Efficient In Design Applications, Afshin Gholamy, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many design problems, it is important to take into account expert knowledge. Expert often describe their knowledge by using imprecise ("fuzzy") natural-language words like "small". To describe this imprecise knowledge in computer-understandable terms, Zadeh came up with special fuzzy methodology -- techniques that have been successful in many applications. This methodology starts with eliciting, from the expert, a membership function corresponding to each imprecise term -- a function that assigns, to each possible value of the corresponding quantity, a degree to which this value satisfies the relevant property (e.g., a degree to which, in the expert's opinion, this value …

Optimization Under Fuzzy Constraints: From A Heuristic Algorithm To An Algorithm That Always Converges, Vladik Kreinovich, Juan Carlos Figueroa-Garcia

Departmental Technical Reports (CS)

An efficient iterative heuristic algorithm has been used to implement Bellman-Zadeh solution to the problem of optimization under fuzzy constraints. In this paper, we analyze this algorithm, explain why it works, show that there are cases when this algorithm does not converge, and propose a modification that always converges.

A Turing Machine Is Just A Finite Automaton With Two Stacks: A Comment On Teaching Theory Of Computation, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Traditionally, when we teach Theory of Computation, we start with finite automata, we show that they are not sufficient, then we switch to pushdown automata (i.e., automata-with-stacks). Automata-with-stacks are also not sufficient, so we introduce Turing machines. The problem is that while the transition from finite automata to automata-with-stacks is reasonably natural, Turing machine are drastically different, and as a result, transition to Turing machines is difficult for some students. In this paper, we propose to solve this pedagogical problem by emphasizing that a Turing machine is, in effect, nothing else but a finite automaton with two stacks. This representation …

Soft Computing Ideas Can Help Earthquake Geophysics, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Earthquakes can be devastating, thus it is important to gain a good understanding of the corresponding geophysical processing. One of the challenges in geophysics is that we cannot directly measure the corresponding deep-earth quantities, we have to rely on expert knowledge, knowledge which often comes in terms of imprecise ("fuzzy") words from natural language. To formalize this knowledge, it is reasonable to use techniques that were specifically designed for such a formalization -- namely, fuzzy techniques, In this paper, we formulate the problem of optimally representing such knowledge. By solving the corresponding optimization problem, we conclude that the optimal representation …

Fuzzy Ideas Explain A Complex Heuristic Algorithm For Gauging Pavement Conditions, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To gauge pavement conditions, researchers have come up with a complex heuristic algorithm that combines several expert estimates of pavement characteristics into a single index -- which is well correlated with the pavement's durability and other physical characteristics. While empirically, this algorithm works well, it lacks physical or mathematical justification beyond being a good fit for the available data. This lack of justification decreases our confidence in the algorithm's results -- since it is known that often, empirically successful heuristic algorithms need change when the conditions change. To increase the practitioners' confidence in the resulting pavement condition estimates, it is …

When Is Propagation Of Interval And Fuzzy Uncertainty Feasible?, Vladik Kreinovich, Andrzej Pownuk, Olga Kosheleva, Aleksandra Belina

Departmental Technical Reports (CS)

In many engineering problems, to estimate the desired quantity, we process measurement results and expert estimates. Uncertainty in inputs leads to the uncertainty in the result of data processing. In this paper, we show how the existing feasible methods for propagating the corresponding interval and fuzzy uncertainty can be extended to new cases of potential practical importance.

What Is The Economically Optimal Way To Guarantee Interval Bounds On Control?, Alfredo Vaccaro, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

For control under uncertainty, interval methods enable us to find a box B=[u⁻₁,u⁺₁] X ... X [u⁻_n,u⁺_n] for which any control u from B has the desired properties -- such as stability. Thus, in real-life control, we need to make sure that u_i is in [u⁻_i,u⁺_i] for all parameters u_i describing control. In this paper, we describe the economically optimal way of guaranteeing these bounds.

Computer Vision Evidence Supporting Craniometric Alignment Of Rat Brain Atlases To Streamline Expert-Guided, First-Order Migration Of Hypothalamic Spatial Datasets Related To Behavioral Control, Arshad Khan, Jose Perez, Claire Wells, Olac Fuentes

Selected Works Temporary Series

The rat has arguably the most widely studied brain among all animals, with numerous reference atlases for rat brain having been published since 1946. For example, many neuroscientists have used the atlases of Paxinos and Watson (PW, first published in 1982) or Swanson (S, first published in 1992) as guides to probe or map specific rat brain structures and their connections. Despite nearly three decades of contemporaneous publication, no independent attempt has been made to establish a basic framework that allows data mapped in PW to be placed in register with S, or vice versa. Such data migration would allow …

Algorithmic Need For Subcopulas, Thach N. Nguyen, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

One of the efficient ways to describe the dependence between random variables is by describing the corresponding copula. For continuous distributions, the copula is uniquely determined by the corresponding distribution. However, when the distributions are not continuous, the copula is no longer unique, what is unique is a subcopula, a function C(u,v) that has values only for some pairs (u,v). From the purely mathematical viewpoint, it may seem like subcopulas are not needed, since every subcopula can be extended to a copula. In this paper, we prove, however, that from the algorithmic viewpoint, it is, in general, not possible …

Blockchains Beyond Bitcoin: Towards Optimal Level Of Decentralization In Storing Financial Data, Thach N. Nguyen, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In most current financial transactions, the record of each transaction is stored in three places: with the seller, with the buyer, and with the bank. This currently used scheme is not always reliable. It is therefore desirable to introduce duplication to increase the reliability of financial records. A known absolutely reliable scheme is blockchain -- originally invented to deal with bitcoin transactions -- in which the record of each financial transaction is stored at every single node of the network. The problem with this scheme is that, due to the enormous duplication level, if we extend this scheme to all …

Quantum Approach Explains The Need For Expert Knowledge: On The Example Of Econometrics, Songsak Sriboonchitta, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

The main purposes of econometrics are: to describe economic phenomena, and to find out how to regulate these phenomena to get the best possible results. There have been many successes in both purposes. Companies and countries actively use econometric models in making economic decisions. However, in spite of all the successes of econometrics, most economically important decisions are not based only on the econometric models -- they also take into account expert opinions, and it has been shown that these opinions often drastically improve the resulting decisions. Experts -- and not econometricians -- are still largely in charge of the …

Why Quantum (Wave Probability) Models Are A Good Description Of Many Non-Quantum Complex Systems, And How To Go Beyond Quantum Models, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

In many practical situations, it turns out to be beneficial to use techniques from quantum physics in describing non-quantum complex systems. For example, quantum techniques have been very successful in econometrics and, more generally, in describing phenomena related to human decision making. In this paper, we provide a possible explanation for this empirical success. We also show how to modify quantum formulas to come up with an even more accurate descriptions of the corresponding phenomena.

Why Hammerstein-Type Block Models Are So Efficient: Case Study Of Financial Econometrics, Thongchai Dumrongpokaphan, Afshin Gholamy, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In the first approximation, many economic phenomena can be described by linear systems. However, many economic processes are non-linear. So, to get a more accurate description of economic phenomena, it is necessary to take this non-linearity into account. In many economic problems, among many different ways to describe non-linear dynamics, the most efficient turned out to be Hammerstein-type block models, in which the transition from one moment of time to the next consists of several consequent blocks: linear dynamic blocks and blocks describing static non-linear transformations. In this paper, we explain why such models are so efficient in econometrics.

How To Take Expert Uncertainty Into Account: Economic Approach Illustrated By Pavement Engineering Applications, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Thach N. Nguyen, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many application areas, we rely on expert estimates. For example, in pavement engineering, we often rely on expert graders to gauge the condition of road segments and to see which repairs are needed. Expert estimates are imprecise; it is desirable to take the resulting uncertainty into account when making the corresponding decisions. The traditional approach is: to first apply the traditional statistical methods to get the most accurate estimate, and then to take the corresponding uncertainty into account when estimating the economic consequences of the resulting decision. On the example of pavement engineering applications, we show that it is …

Why The Best Predictive Models Are Often Different From The Best Explanatory Models: A Theoretical Explanation, Songsak Sriboonchitta, Luc Longpre, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Traditionally, in statistics, it was implicitly assumed that models which are the best predictors also have the best explanatory power. Lately, many examples have been provided that show that the best predictive models are often different from the best explanatory models. In this paper, we provide a theoretical explanation for this difference.

Why Threshold Models: A Theoretical Explanation, Thongchai Dumrongpokaphan, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many economic phenomena are well described by linear models. In such models, the predicted value of the desired quantity -- e.g., the future value of an economic characteristic -- linearly depends on the current values of this and related economic characteristic and on the numerical values of external effects. Linear models have a clear economic interpretation: they correspond to situations when the overall effect does not depend, e.g., on whether we consider a loose federation as a single country or as several countries. While linear models are often reasonably accurate, to get more accurate predictions, we need to take into …

Computer Vision Evidence Supporting Craniometric Alignment Of Rat Brain Atlases To Streamline Expert-Guided, First-Order Migration Of Hypothalamic Spatial Datasets Related To Behavioral Control, Khan, Jose Perez, Claire Wells, Olac Fuentes

Departmental Papers (Biology)

The rat has arguably the most widely studied brain among all animals, with numerous reference atlases for rat brain having been published since 1946. For example, many neuroscientists have used the atlases of Paxinos and Watson (PW, first published in 1982) or Swanson (S, first published in 1992) as guides to probe or map specific rat brain structures and their connections. Despite nearly three decades of contemporaneous publication, no independent attempt has been made to establish a basic framework that allows data mapped in PW to be placed in register with S, or vice versa. …

Economics Of Commitment: Why Giving Away Some Freedom Makes Sense, Vladik Kreinovich, Olga Kosheleva, Mahdokhat Afravi, Genesis Bejarano, Marisol Chacon

Departmental Technical Reports (CS)

In general, the more freedom we have, the better choices we can make, and thus, the better possible economic outcomes. However, in practice, people often artificially restrict their future options by making a commitment. At first glance, commitments make no economic sense, and so their ubiquity seems puzzling. Our more detailed analysis shows that commitment often makes perfect economic sense: namely, it is related to the way we take future gains and losses into account. With the traditionally assumed exponential discounting, commitment indeed makes no economic sense, but with the practically observed hyperbolic discounting, commitment is indeed often economically beneficial.

Why Bellman-Zadeh Approach To Fuzzy Optimization, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many cases, we need to select the best of the possible alternatives, but we do not know for sure which alternatives are possible and which are not possible. Instead, for each alternative x, we have a subjective probability p(x) that this alternative is possible. In 1970, Richard Bellman and Lotfi Zadeh proposed a heuristic method for selecting an alternative under such uncertainty. Interestingly, this method works very well in many practical applications, while similarly motivated alternative formulas do not work so well. In this paper, we explain the empirical success of the Bellman-Zadeh approach by showing that its formulas …