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Why Most Bright Stars Are Binary But Most Dim Stars Are Single: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that most visible stars are binary: they have a nearby companion star, and these two stars orbit around each other. Based on this fact, until recently, astronomers believed that, in general, most stars are binary. A few years ago, a surprising paper showed that while most bright stars are indeed binary, most dim stars are single. In this paper, we provide a simple qualitative explanation for this empirical fact.

When Invading, Cancer Cells Do Not Divide: A Geometric (Symmetry-Based) Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, malignant tumors are known to grow fast, cancer cells that form these tumors divide and spread around. Tumors also experience the process of metastasis, when cancer cells invade neighboring organs. A recent experiment has shown that, contrary to the previous assumptions, when cancer cells are invading, they stop dividing. In this paper, we provide a geometric explanation for this empirical phenomenon.

Structure Of Filled Functions: Why Gaussian And Cauchy Templates Are Most Efficient, Vyacheslav Kalashnikov, Vladik Kreinovich, José Guadalupe Flores Muñiz, Nataliya Kalashnykova

Departmental Technical Reports (CS)

One of the main problems of optimization algorithms is that they often end up in a local optimum. It is, therefore, necessary to make sure that the algorithm gets out of the local optimum and eventually reaches the global optimum. One of the promising ways guiding one from the local optimum is prompted by the filled function method. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and Cauchy functions. In this paper, we provide a possible theoretical explanation of this empirical effect.

Fuzzy Pareto Solution In Multi-Criteria Group Decision Making With Intuitionistic Linguistic Preference Relation, Bui Cong Cuong, Vladik Kreinovich, Le Hoang Son, Nilanjan Dey

Departmental Technical Reports (CS)

In this paper, we investigate the multi criteria group decision making with intuitionistic linguistic preference relation. The concept of Fuzzy Collective Solution (FCS) is used to evaluate and rank the candidate solution sets for modeling under linguistic assessments. Intuitionistic linguistic preference relation and associated aggregation procedures are then defined in a new concept of Fuzzy Pareto Solution. Numerical examples are presented to demonstrate computing procedures. The results affirm efficiency of the proposed method.

Towards An Algebraic Description Of Set Arithmetic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To describe the state of the world, we need to describe the values of all physical quantities. In practice, due to inevitable measurement inaccuracy, we do not know the exact values of these quantities, we only know the sets of possible values for these quantities. On the class of such uncertainty-related sets, we can naturally define arithmetic operations that transform, e.g., uncertainty in a and b into uncertainty with which we know the sum a + b.

In many applications, it has been useful to reformulate the problem in purely algebraic terms, i.e., in terms of axioms that the basic …

A Heuristic Solution Of The Toll Optimal Problem With Congestion Affected Costs, Vyacheslav Kalashnikov, José Guadalupe Flores Muñiz, Nataliya Kalashnykova

Departmental Technical Reports (CS)

An important problem concerning the toll roads is the setting of appropriate costs for driving along paid arcs of a transportation network. Our paper treats this problem as a bilevel programming model. At the upper level, decisions are made by a public regulator/private company that administers the toll roads endeavoring to elevate their benefits. At the lower level, several transportation companies/individual users appease the existing demand for transportation of goods or passengers while selecting the routes that would minimize their total travel costs. In contrast to the previous models, here the lower level problem assumes quadratic costs implied by the …

Yes- And No-Gestures Explained By Symmetry, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most cultures, "yes" is indicate by a vertical head movement (nod), while "no" is indicated by a left-right movement (shake). In this paper, we show that basic symmetries can explain this cultural phenomenon.

What Is The Best Way To Add Large Number Of Integers: Number-By-Number As Computers Do Or Lowest-Digits-Than-Next-Digits-Etc As We Humans Do?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we need to add several integers, computers add them one by one, while we usually add them digit by digit: first, we add all the lowest digits, then we add all next lowest digits, etc. Which way is faster? Should we learn from computers or should we teach computers to add several integers our way?

In this paper, we show that the computer way is faster. This adds one more example to the list of cases when computer-based arithmetic algorithms are much more efficient than the algorithms that we humans normally use.

Why Product "And"-Operation Is Often Efficient: One More Argument, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is an empirical fact that the algebraic product is one the most efficient "and"-operations in fuzzy logic. In this paper, we provide one of the possible explanations of this empirical phenomenon.

Towards Decision Making Under Interval Uncertainty, Andrzej Pownuk, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we know the exact form of the objective function, and we know the optimal decision corresponding to each values of the corresponding parameters x_i. What should we do if we do not know the exact values of x_i, and instead, we only know each x_i with uncertainty -- e.g., with interval uncertainty? In this case, one of the most widely used approaches is to select, for each i, one value from the corresponding interval -- usually, a midpoint -- and to use the exact-case optimal decision corresponding to the selected values. …

For Fuzzy Logic, Occam's Principle Explains The Ubiquity Of The Golden Ratio And Of The 80-20 Rule, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that for fuzzy logic, the Occam's principle -- that we should always select the simplest possible explanation -- explains the ubiquity of the golden ratio and of the 80-20 rule.

How To Make Machine Learning Robust Against Adversarial Inputs, Gerardo Muela, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been recently shown that it is possible to "cheat" many machine learning algorithms -- i.e., to perform minor modifications of the inputs that would lead to a wrong classification. This feature can be used by adversaries to avoid spam detection, to create a wrong identification allowing access to classified information, etc. In this paper, we propose a solution to this problem: namely, instead of applying the original machine learning algorithm to the original inputs, we should first perform a random modification of these inputs. Since machine learning algorithms perform well on random data, such a random modification ensures …

Why Rsa? A Pedagogical Comment, Pedro Barragan Olague, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most widely used cryptographic algorithms is the RSA algorithm in which a message m encoded as the remainder c of m^e modulo n, where n and e are given numbers -- forming a public code. A similar transformation c^d mod n$, for an appropriate secret code d, enables us to reconstruct the original message. In this paper, we provide a pedagogical explanation for this algorithm.

A Simple Geometric Explanation Of Occam's Razor, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Occam's razor states that out of possible explanations, plans, and designs, we should select the simplest one. It turns out that in many practical situations, the simplest explanation indeed turns out to be the correct one, the simplest plan is often the most successful, etc. But why this happens is not very clear. In this paper, we provide a simple geometric explanation of Occam's razor.

Fuzzy Data Processing Beyond Min T-Norm, Andrzej Pownuk, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Usual algorithms for fuzzy data processing -- based on the usual form of Zadeh's extension principle -- implicitly assume that we use the min "and"-operation (t-norm). It is known, however, that in many practical situations, other t-norms more adequately describe human reasoning. It is therefore desirable to extend the usual algorithms to situations when we use t-norms different from min. Such an extension is provided in this paper.

Specifying A Global Optimization Solver In Z, Angel F. Garcia Contreras, Yoonsik Cheon

Departmental Technical Reports (CS)

NumConSol is an interval-based numerical constraint and optimization solver to find a global optimum of a function. It is written in Python. In this document, we specify the NumConSol solver in Z, a formal specification language based on sets and predicates. The aim is to provide a solid foundation for restructuring and refactoring the current implementation of the NumConSol solver as well as facilitating its future improvements. The formal specification also allows us to design more effective testing for the solver, e.g., generating test cases from the specification.

A Modification Of Backpropagation Enables Neural Networks To Learn Preferences, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

To help a person make proper decisions, we must first understand the person's preferences. A natural way to determine these preferences is to learn them from the person's choices. In principle, we can use the traditional machine learning techniques: we start with all the pairs (x,y) of options for which we know the person's choices, and we train, e.g., the neural network to recognize these choices. However, this process does not take into account that a rational person's choices are consistent: e.g., if a person prefers a to b and b to c, this person should also prefer a and …

Why Growth Of Cancerous Tumors Is Gompertzian: A Symmetry-Based Explanation, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the growth of a cancerous tumor is well described by the Gompertz's equation. The existing explanations for this equation rely on specifics of cell dynamics. However, the fact that for many different types of tumors, with different cell dynamics, we observe the same growth pattern, make us believe that there should be a more fundamental explanation for this equation. In this paper, we show that a symmetry-based approach indeed leads to such an explanation: indeed, out of all scale-invariant growth dynamics, the Gompertzian growth is the closest to the linear-approximation exponential growth model.

Grading That Takes Into Account The Need To Learn From Mistakes, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known that the best way to learn the new material is to try it, to make mistakes, and to learn from these mistakes. However, the current grading scheme, in which the overall grade is a weighted average of the grades for all the assignments, exams, etc., does not encourage mistakes: any mistake decreases the grade on the corresponding assignment and thus, decreases the overall grade for the class. It is therefore desirable to modify the usual grading scheme, so that it will take into account -- and encourage -- learning by mistakes. Such a modification is proposed …

Optimal Group Decision Making Criterion And How It Can Help To Decrease Poverty, Inequality, And Discrimination, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Traditional approach to group decision making in economics is to maximize the GDP, i.e., the overall gain. The hope behind this approach is that the increased wealth will trickle down to everyone. Sometimes, this happens, but often, in spite of an increase in overall GDP, inequality remains: some people remain poor, some groups continue to face economic discrimination, etc. This shows that maximizing the overall gain is probably not always the best criterion in group decision making. In this chapter, we find a group decision making criterion which is optimal (in some reasonable sense), and we show that using this …

Why The Presence Of Point-Wise ("Punctate") Calcifications Or Linear Configurations Of Calcifications Makes Breast Cancer More Probable: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When a specialist analyzes a mammogram for signs of possible breast cancer, he or she pays special attention to point-wise and linear-shaped calcifications and point-wise and linear configurations of calcification -- since empirically, such calcifications and combinations of calcifications are indeed most frequently associated with cancer. In this paper, we provide a geometric explanation for this empirical phenomenon.

A Simplified Derivation Of Confidence Regions Based On Inferential Models, Vladik Kreinovich

Departmental Technical Reports (CS)

Recently, a new inferential models approach has been proposed for statistics. Specifically, this approach provides a new random-set-based way to come up with confidence regions. In this paper, we show that the confidence regions obtained by using the main version of this new methodology can also be naturally obtained directly, without invoking random sets.

Scaling-Invariant Description Of Dependence Between Fuzzy Variables: Towards A Fuzzy Version Of Copulas, Gerardo Muela, Vladik Kreinovich, Christian Servin

Departmental Technical Reports (CS)

To get a general description of dependence between n fuzzy variables x₁, ..., x_n, we can use the membership function μ(x₁, ..., x_n) that describes, for each possible tuple of values (x₁, ..., x_n) to which extent this tuple is possible.

There are, however, many ways to elicit these degrees. Different elicitations lead, in general, to different numerical values of these degrees -- although, ideally, tuples which have a higher degree of possibility in one scale should have a higher degree in other scales as well. It is …

Why Multiplication Has Higher Priority Than Addition: A Pedagogical Remark, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, multiplication has higher priority over addition; this means that there is no need to add parentheses if we want to perform multiplication first, and we need to explicitly add parentheses if we want addition to be performed first. Why not use an alternative arrangement, in which addition has higher priority? In this paper, we explain the traditional priority arrangement by showing that in the general case, the traditional arrangement allows us to use fewer parentheses than the alternative one.

It Is Advantageous To Make A Syllabus As Precise As Possible: Decision-Theoretic Analysis, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Should a syllabus be precise? Shall we indicate exactly how many points we should assign for each test and for each assignment? On the one hand, many students like such certainty. On the other hand, instructors would like to have some flexibility: if an assignment turns out to be more complex than expected, we should be able to increase the number of points for this assignment, and, vice versa, it it turns out to be simpler than expected, we should be able to decrease the number of points.

In this paper, we analyze this problem from a decision-theoretic viewpoint. Our …

Gaussian And Cauchy Functions In The Filled Function Method -- Why And What Next: On The Example Of Optimizing Road Tolls, José Guadalupe Flores Muñiz, Vyacheslav V. Kalashnikov, Nataliya Kalashnykova, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical problems, we need to find the values of the parameters that optimize the desired objective function. For example, for the toll roads, it is important to set the toll values that lead to the fastest return on investment.

There exist many optimization algorithms, the problem is that these algorithms often end up in a local optimum. One of the promising methods to avoid the local optima is the filled function method, in which we, in effect, first optimize a smoothed version of the objective function, and then use the resulting optimum to look for the optimum of …

Use Of Machine Learning To Analyze And -- Hopefully -- Predict Volcano Activity, Justin Parra, Olac Fuentes, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Volcanic eruptions cause significant loss of lives and property around the world each year. Their importance is highlighted by the sheer number of volcanoes for which eruptive activity is probable. These volcanoes are classified as in a state of unrest. The Global Volcano Project maintained by the Smithsonian Institution estimates that approximately 600 volcanoes, many proximal to major urban areas, are currently in this state of unrest. A spectrum of phenomena serve as precursors to eruption, including ground deformation, emission of gases, and seismic activity. The precursors are caused by magma upwelling from the Moho to the shallow (2-5 km) …

Writing Jml Specifications Using Java 8 Streams, Yoonsik Cheon, Zejing Cao, Khandoker Rahad

Departmental Technical Reports (CS)

JML is a formal behavioral interface specification language for Java to document Java program modules such as classes and interfaces. When composing JML specifications, one frequently writes assertions involving a collection of values. In this paper we propose to use Java 8 streams for writing more concise and cleaner assertions on a collection. The use of streams in JML can be minimal and non-invasive in the conventional style of writing assertions. It can also be holistic to write all assertions in the abstract state defined by streams. We perform a small case study to illustrate our approach and show its …

Preliminary Investigation Of Mobile System Features Potentially Relevant To Hpc, David Pruitt, Eric Freudenthal

Departmental Technical Reports (CS)

Energy consumption's increasing importance in scientific computing has driven an interest in developing energy efficient high performance systems. Energy constraints of mobile computing has motivated the design and evolution of low-power computing systems capable of supporting a variety of compute-intensive user interfaces and applications. Others have observed the evolution of mobile devices to also provide high performance. Their work has primarily examined the performance and efficiency of compute-intensive scientific programs executed either on mobile systems or hybrids of mobile CPUs grafted into non-mobile (sometimes HPC) systems.

This report describes an investigation of performance and energy consumption of a single scientific …

Why Half-Frequency In Intelligent Compaction, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

To gauge how well vibrating rollers have compacted the road segment, it is reasonable to process the acceleration measured by the attached sensors. Theoretically, we expect the resulting signal to be periodic with the same frequency f with which the roller vibrates -- and thus, after a Fourier transform, we expect to observe only frequencies which are multiples of the vibration frequency f.

Surprisingly, often, we also observe a peak at half-frequency f/2.

In this paper, we explain this empirical phenomenon: we show that it is a particular case of a spontaneous symmetry violation, and that the general physical theory …