Computer Sciences Commons^™

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.

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 …

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 …

How Interval Measurement Uncertainty Affects The Results Of Data Processing: A Calculus-Based Approach To Computing The Range Of A Box, Andrew Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical applications, we are interested in the values of the quantities y₁, ..., y_m which are difficult (or even impossible) to measure directly. A natural idea to estimate these values is to find easier-to-measure related quantities x₁, ..., x_n and to use the known relation to estimate the desired values y_i. Measurements come with uncertainty, and often, the only thing we know about the actual value of each auxiliary quantity x_i is that it belongs to the interval [X_i − Δ_i, X_i + Δ_{i …}

Analysis Of Prosody Around Turn Starts, Gerardo Cervantes, Nigel Ward

Departmental Technical Reports (CS)

We are interested in enabling a robot to communicate with more natural timings: to take turns more appropriately. LSTM models have sometime been effective for this, but we found that this to be not helpful for some tasks. This technical report we look for factors that may explain this difference, by examining statistically the prosodic feature values in the vicinity of turn shift in the data. We observe that the apparent informativeness of prosodic features varies greatly from one dataset to another.

Why Asset-Based Approach To Teaching Is More Effective Than The Usual Deficit-Based Approach, And Why The New Approach Is Not Easy To Implement: A Simple Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional approach to teaching is based on uncovering deficiencies in student's knowledge and working on these deficiencies. Lately, it has been shown that a more efficient approach to education is instead when we start with the student's strengths (assets), and use these strengths to teach the students; however, this asset-based approach is not easy to implement. In this paper, we provide a simple geometric explanation of why the asset-based approach to teaching is more efficient and why it is not easy to implement.

Why Under Stress Positive Reinforcement Is More Effective? Why Optimists Study Better? Why People Become Restless? Simple Utility-Based Explanations, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we use the utility-based approach to decision making to provide simple answers to the following three questions: Why under stress positive reinforcement is more effective? Why optimists study better? Why people become restless?

Towards Foundations Of Interval And Fuzzy Uncertainty, Mahdokhat Afravi, Kehinde Akinola, Fredrick Ayivor, Ramon Bustamante, Erick Duarte, Ahnaf Farhan, Martha Garcia, Govinda K. C., Jeffrey Hope, Olga Kosheleva, Vladik Kreinovich, Jose Perez, Francisco Rodriguez, Christian Servin, Eric Torres, Jesus Tovar

Departmental Technical Reports (CS)

In this paper, we provide a theoretical explanation for many aspects of interval and fuzzy uncertainty: Why boxes for multi-D uncertainty? What if we only know Hurwicz's optimism-pessimism parameter with interval uncertainty? Why swarms of agents are better than clouds? Which confidence set is the most robust? Why μ^p in fuzzy clustering? How do degrees of confidence change with time? What is a natural interpretation of Pythagorean and fuzzy degrees of confidence?

Why Encubation?, Vladik Kreinovich, Rohan Baingolkar, Swapnil S. Chauhan, Ishtjot S. Kamboj

Departmental Technical Reports (CS)

It is known that some algorithms are feasible, and some take too long to be practical/ For example, if the running time of an algorithm is 2ⁿ, where n = len(x) is the bit size of the input x, then already for n = 500, the computation time exceeds the lifetime of the Universe. In computer science, it is usually assumed that an algorithm A is feasible if and only if it is polynomial-time, i.e., if its number of computational steps t_A(x) on any input x is bounded by a polynomial P(n) of the input …

How To Gauge Repair Risk?, Francisco Zapata, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, there exist several automatic tools that, given a software, find locations of possible defects. A general tool does not take into account a specificity of a given program. As a result, while many defects discovered by this tool can be truly harmful, many uncovered alleged defects are, for this particular software, reasonably (or even fully) harmless. A natural reaction is to repair all the alleged defects, but the problem is that every time we correct a program, we risk introducing new faults. From this viewpoint, it is desirable to be able to gauge the repair risk. This will …

How Intelligence Community Interprets Imprecise (Fuzzy) Words, And How To Justify This Empirical-Based Interpretation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To provide a more precise meaning to imprecise (fuzzy) words like "probable" or "almost certain", researchers analyzed how often intelligence predictions hedged by each corresponding word turned out to be true. In this paper, we provide a theoretical explanation for the resulting empirical frequencies.

How To Explain Empirical Distribution Of Software Defects By Severity, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the last decades, several tools have appeared that, given a software package, mark possible defects of different potential severity. Our empirical analysis has shown that in most situations, we observe the same distribution or software defects by severity. In this paper, we present this empirical distribution, and we use interval-related ideas to provide an explanation for this empirical distribution.

Virtual Agent Interaction Framework (Vaif): A Tool For Rapid Development Of Social Agents, Ivan Gris, David G. Novick

Departmental Technical Reports (CS)

Creating an embodied virtual agent is often a complex process. It involves 3D modeling and animation skills, advanced programming knowledge, and in some cases artificial intelligence or the integration of complex interaction models. Features like lip-syncing to an audio file, recognizing the users’ speech, or having the character move at certain times in certain ways, are inaccessible to researchers that want to build and use these agents for education, research, or industrial uses. VAIF, the Virtual Agent Interaction Framework, is an extensively documented system that attempts to bridge that gap and provide inexperienced researchers the tools and means to develop …

Why Zipf's Law: A Symmetry-Based Explanation, Daniel Cervantes, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have probability distributions for which, for large values of the corresponding quantity x, the probability density has the form ρ(x) ~ x^−αfor some α > 0. While, in principle, we have laws corresponding to different α, most frequently, we encounter situations -- first described by Zipf for linguistics -- when α is close to 1. The fact that Zipf's has appeared frequently in many different situations seems to indicate that there must be some fundamental reason behind this law. In this paper, we provide a possible explanation.

Gartner's Hype Cycle: A Simple Explanation, Jose Perez, Vladik Kreinovich

Departmental Technical Reports (CS)

In the ideal world, any innovation should be gradually accepted. It is natural that initially some people are reluctant to adopt a new largely un-tested idea, but as more and more evidence appears that this new idea works, we should see a gradual increase in number of adoptees -- until the idea becomes universally accepted.

In real life, the adoption process is not that smooth. Usually, after the few first successes, the idea is over-hyped, it is adopted in situations way beyond the inventors' intent. In these remote areas, the new idea does not work well, so we have a …

Working On One Part At A Time Is The Best Strategy For Software Production A Proof, Francisco Zapata, Maliheh Zargaran, Vladik Kreinovich

Departmental Technical Reports (CS)

When a company works on a large software project, it can often start recouping its investments by selling intermediate products with partial functionality. With this possibility in mind, it is important to schedule work on different software parts so as to maximize the profit. These exist several algorithms for solving the corresponding optimization problem, and in all the resulting plans, at each moment of time, we work on one part of software at a time. In this paper, we prove that this one-part-at-a-time property holds for all optimal plans.

Why Superforecasters Change Their Estimates On Average By 3.5%: A Possible Theoretical Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent large-scale study of people's forecasting ability has shown that there is a small group of superforecasters, whose forecasts are significantly more accurate than the forecasts of an average person. Since forecasting is important in many application areas, researchers have studied what exactly the supreforecasters do differently -- and how we can learn from them, so that we will be able to forecast better. One empirical fact that came from this study is that, in contrast to most people, superforecasters make much smaller adjustments to their probability estimates. On average, their average probability change is 3.5%. In this …

How To Monitor Possible Side Effects Of Enhanced Oil Recovery Process, Jose Manuel Dominguez Esquivel, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

To extract all the oil from a well, petroleum engineers pump hot reactive chemicals into the well. This enhanced oil recovery process needs to be thoroughly monitored, since the aggressively hot liquid can seep out and, if unchecked, eventually pollute the sources of drinking water. At present, to monitor this process, engineers measure the seismic waves generated when the liquid fractures the minerals. However, the resulting seismic waves are weak in comparison with the background noise. Thus, the accuracy with which we can locate the spreading liquid based on these weak signals is low, and we get only a very …

Reverse Mathematics Is Computable For Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

For systems of equations and/or inequalities under interval uncertainty, interval computations usually provide us with a box whose all points satisfy this system. Reverse mathematics means finding necessary and sufficient conditions, i.e., in this case, describing the set of {\it all} the points that satisfy the given system. In this paper, we show that while we cannot always exactly describe this set, it is possible to have a general algorithm that, given ε > 0, provides an ε-approximation to the desired solution set.

Optimization Of Quadratic Forms And T-Norm Forms On Interval Domain And Computational Complexity, Milan Hladik, Michal Čerńy, Vladik Kreinovich

Departmental Technical Reports (CS)

We consider the problem of maximization of a quadratic form over a box. We identify the NP-hardness boundary for sparse quadratic forms: the problem is polynomially solvable for O(log n) nonzero entries, but it is NP-hard if the number of nonzero entries is of the order n^ε for an arbitrarily small ε > 0. Then we inspect further polynomially solvable cases. We define a sunflower graph over the quadratic form and study efficiently solvable cases according to the shape of this graph (e.g. the case with small sunflower leaves or the case with a restricted number of negative entries). Finally, …

Which T-Norm Is Most Appropriate For Bellman-Zadeh Optimization, Vladik Kreinovich, Olga Kosheleva, Shahnaz Shahbazova

Departmental Technical Reports (CS)

In 1970, Richard Bellman and Lotfi Zadeh proposed a method for finding the maximum of a function under fuzzy constraints. The problem with this method is that it requires the knowledge of the minimum and the maximum of the objective function over the corresponding crisp set, and minor changes in this crisp set can lead to a drastic change in the resulting maximum. It is known that if we use a product "and"-operation (t-norm), the dependence on the maximum disappears. Natural questions are: what if we use other t-norms? Can we eliminate the dependence on the minimum? What if we …

When Is Data Processing Under Interval And Fuzzy Uncertainty Feasible: What If Few Inputs Interact? Does Feasibility Depend On How We Describe Interaction?, Milan Hladík, Michal Čerńy, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in general, data processing under interval and fuzzy uncertainty is NP-hard -- which means that, unless P = NP, no feasible algorithm is possible for computing the accuracy of the result of data processing. It is also known that the corresponding problem becomes feasible if the inputs do not interact with each other, i.e., if the data processing algorithm computes the sum of n functions, each depending on only one of the $n$ inputs. In general, inputs x_i and x_j interact. If we take into account all possible interactions, and we use bilinear functions …