Physical Sciences and Mathematics Commons^™

Hierarchial Multiclass Classification Works Better Than Direct Classification: An Explanation Of The Empirical Fact, Julio Urenda, Nancy Avila, Nelly Gordillo, Vladik Kreinovich

Departmental Technical Reports (CS)

Machine learning techniques have been very efficient in many applications, in particular, when learning to classify a given object to one of the given classes. Such classification problems are ubiquitous: e.g., in medicine, such a classification corresponds to diagnosing a disease, and the resulting tools help medical doctors come up with the correct diagnosis. There are many possible ways to set up the corresponding neural network (or another machine learning technique). A direct way is to design a single neural network with as many outputs as there are classes -- so that for each class i, the system would …

Geometric Aspects Of Wound Healing, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that many aspects of complex biological processes related to wound healing can be explained in terms of the corresponding geometric symmetries.

Why H-Index, Vladik Kreinovich, Olga Kosheleva, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

At present, one of the main ways to gauge the quality of a researcher is to use his or her h-index, which is defined as the largest integer n such that the researcher has at least n publications each of which has at least n citations. The fact that this quantity is widely used indicates that h-index indeed reasonably adequately describes the researcher's quality. So, this notion must capture some intuitive idea. However, the above definition is not intuitive at all, it sound like a somewhat convoluted mathematical exercise. So why is h-index so efficient? In this paper, we …

Accuracy Of Data Fusion: Interval (And Fuzzy) Case, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The more information we have about a quantity, the more accurately we can estimate this quantity. In particular, if we have several estimates of the same quantity, we can fuse them into a single more accurate estimate. What is the accuracy of this estimate? The corresponding formulas are known for the case of probabilistic uncertainty. In this paper, we provide similar formulas for the cases of interval and fuzzy uncertainty.

Optimization Under Uncertainty Explains Empirical Success Of Deep Learning Heuristics, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

One of the main objectives of science and engineering is to predict the future state of the world -- and to come up with devices and strategies that would make this future state better. In some practical situations, we know how the state changes with time -- e.g., in meteorology, we know the partial differential equations that describes the atmospheric processes. In such situations, prediction becomes a purely computational problem. In many other situations, however, we do not know the equation describing the system's dynamics. In such situations, we need to learn this dynamics from data. At present, the most …

Code Reuse Between Java And Android Applications, Yoonsik Cheon, Carlos V. Chavez, Ubaldo Castro

Departmental Technical Reports (CS)

Java and Android applications can be written in the same programming language. Thus, it is natural to ask how much code can be shared between them. In this paper, we perform a case study to measure quantitatively the amount of code that can be shared and reused for a multiplatform application running on the Java platform and the Android platform. We first configure a development environment consisting of platform-specific tools and supporting continuous integration. We then propose a general architecture for a multiplatform application under a guiding design principle of having clearly defined interfaces and employing loose coupling to accommodate …

Contrast Similarity Measures Of Fuzzy Sets, Ildar Batyrshin, Olga Kosheleva, Vladik Kreinovich, Nailya Kubysheva, Raouf Akhtiamov

Departmental Technical Reports (CS)

The paper proposes a new class of fuzzy set similarity measures taking into account the proximity of membership values to the border values 0 and 1. These similarity measures take values in [0,1] and generalize the crisp weak equality relation of fuzzy sets considered in the theory of fuzzy sets. The method of construction of a contrast similarity measure using a bipolar function symmetric with respect to 0.5 is presented. The similarity measure defined by the contrast intensification operation considered by Lotfi Zadeh is discussed.

Why A Is Usually 90, B Is 80, Etc.: A Possible Explanation, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the US education system, instructors typically use 90/100, 80/100, 70/100, and 60/100 thresholds to gauge students' knowledge: students who get 90 or more points out of 100 get the highest grade of A, students whose grades are in between 80 and 90 get a B, followed by C, D, and F (fail). In this paper, we show that these seemingly arbitrary threshold have a natural explanation: A means that a student can solve almost all problems; C means that two students with this level of knowledge can solve almost all problems when working together; D means that we need …

Why Liquids? A Symmetry-Based Solution To Weisskopf's Challenge, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In 1977, the renowned physicist Victor Weisskopf challenged the physics community to provide a fundamental explanation for the existence of the liquid phase of matter. A recent essay confirms that Weisskopf's 1977 question remains a challenge. In this paper, we use natural symmetry ideas to show that liquids are actually a natural state between solids and gases.

The Heresy Of Unheard-Of Simplicity: Comment On "The Unreasonable Effectiveness Of Small Neural Ensembles In High-Dimensional Brain" By A. N. Gorban, V. A. Makarov, And I. Y. Tyukin, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Geometric Reformulation Of Learning Models Can Help Prepare Better Teachers, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Many researchers have been analyzing how to further improve teacher preparation -- and thus, how to improve teaching. Many of their results are based on complex models and/or on complex data analysis. Because of this complexity, future teachers often view the resulting recommendations as black boxes, without understanding the motivations for these recommendations -- and thus, without much willingness to follow these recommendations. One of the natural ways to make these recommendations clearer is to reformulate them in geometric terms, since geometric models are usually easier to understand than algebraic more abstract ones. In this paper, on the example of …

Global Independence, Possible Local Dependence: Towards More Realistic Error Estimates For Indirect Measurements, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, it is not realistically possible to directly measure the desired physical quantity. In such situations, we have to measure this quantity indirectly, i.e., measure related quantities and use the known relation to estimate the value of the desired quantity. How accurate it the resulting estimate? The traditional approach assumes that the measurement errors of all direct measurements are independent. In many practical situations, this assumption works well, but in many other practical situations, it leads to a drastic underestimation of the resulting estimation error: e.g., when we base our estimate on measurements performed at nearby moments …

Why Fuzzy Partition In F-Transform?, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be …

Why Patients Do Not Always Follow Doctor's Advice: Systems Approach Explains Empirical Observation, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical studies show that when a medical doctor prescribes a medicine, only two third of the patients fill the prescription, and of this filling-prescription group, only half follow the doctor's instructions when taking the medicine. In this paper, we show that a general systems approach -- namely, abstracting from the specifics of this situation -- helps explain these empirical observations. We also mention that systems approach can not only explains this problem, it can also help solve it -- i.e., it can help increase the patients' adherence to the doctors' recommendations.

Why Triangular Membership Functions Are So Efficient In F-Transform Applications: A Global Explanation To Supplement The Existing Local One, Olga Kosheleva, Vladik Kreinovich, Thach N. Nguyen

Departmental Technical Reports (CS)

The main ideas of F-transform came from representing expert rules. It would be therefore re reasonable to expect that the more accurately the membership functions describe human reasoning, the more efficient will be the corresponding F-transform formulas. We know that an adequate description of our reasoning corresponds to complicated membership functions -- however, somewhat surprisingly, most efficient applications of F-transform use the simplest possible triangular membership functions. There exist some explanations for this phenomenon which are based on local behavior of the signal. In this paper, we supplement this local explanation by a global one: namely, we prove that triangular …

Multiplatform Application Development For Android And Java, Yoonsik Cheon

Departmental Technical Reports (CS)

Software developers of today are under increasing pressure to support multiple platforms, in particular mobile platforms. However, developing a multiplatform application is difficult and challenging due to a variety of platform differences. We propose a native approach for developing a multiplatform application running on two similar but different platforms, Java and Android. We address practical software engineering concerns attributed to native multiplatform application development, from configuration of tools to software design and development process. Our approach allows one to share 37%~40% of application code between the two platforms as well as improving the quality of the application. We believe our …

Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the important steps in deep learning is softmax, when we select one of the alternatives with a probability depending on its expected gain. A similar formula describes human decision making: somewhat surprisingly, when presented with several choices with different expected equivalent monetary gain, we do not just select the alternative with the largest gain; instead, we make a random choice, with probability decreasing with the gain -- so that it is possible that we will select second highest and even third highest value. Both formulas assume that we know the exact value of the expected gain for each …

Decision Theory Can Explain Why Buying And Selling Prices Are Different, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

According to a naive understanding of economic behavior, for each object, we should have an internal estimate of how much this object is worth for us. If anyone offers us to buy this object at a smaller amount, we should agree, and if anyone offers to buy it from us for a larger amount, we should agree as well. In practice, however, contrary to this understanding, the price for which we are willing to buy and the price at which we are willing to sell are often different. In this paper, we show that this seemingly counterintuitive phenomenon can be …

For Quantum And Reversible Computing, Intervals Are More Appropriate Than General Sets, And Fuzzy Numbers Than General Fuzzy Sets, Oscar Galindo, Vladik Kreinovich

Departmental Technical Reports (CS)

Need for faster and faster computing necessitates going down to quantum level -- which means involving quantum computing. One of the important features of quantum computing is that it is reversible. Reversibility is also important as a way to decrease processor heating and thus, enable us to place more computing units in the same volume. In this paper, we argue that from this viewpoint, interval uncertainty is more appropriate than the more general set uncertainty -- and, similarly, that fuzzy numbers (for which all alpha-cuts are intervals) are more appropriate than more general fuzzy sets. We also explain why intervals …

Why High-Level Attention Constantly Oscillates: System-Based Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

In many situations like driving, it is important that a person concentrates all his/her attention at a certain critical task -- e.g., watching the road for possible problems. Because of this need to maintain high level of attention, it was assumed, until recently, that in such situations, the person maintains a constantly high level of attention (of course, until he or she gets tired). Interestingly, recent experiments showed that in reality, from the very beginning, attention level oscillates. In this paper, we show that such an oscillation is indeed helpful -- and thus, it is necessary to emulate such an …

How To Define "And"- And "Or"-Operations For Intuitionistic And Picture Fuzzy Sets, Christian Servin, Reynaldo Martinez, Peter Hanson, Leonel Lopez, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional fuzzy logic does not distinguish between the cases when we know nothing about a statement S and the cases when we have equally convincing arguments for S and for its negation ~S: in both cases, we assign the degree 0.5 to such a statement S. This distinction is provided by intuitionistic fuzzy logic, when to describe our degree of confidence in a statement S, we use two numbers a₊ and a₋ that characterize our degree of confidence in S and in ~S. An even more detailed distinction is provided …

Decision Making Under General Set Uncertainty: Additivity Approach, Srialekya Edupalli, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a decision under interval or set uncertainty: e.g., we need to decide how much we are willing to pay for an option that will bring us between $10 and $40, i.e., for which the set of possible gains is the interval S = [10,40]. To make such decisions, researcher have used the idea of additivity: that if have two independent options, then the price we pay for both should be equal to the sum of the prices that we pay for each of these options. It is known that this requirement enables …

Which Fourier Components Are Most Informative: General Idea And Case Studies, Julio Urenda, Nancy Avila, Nelly Gordillo, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, the information comes not in terms of the original image or signal, but in terms of its Fourier transform. To detect complex features based on this information, it is often necessary to use machine learning. In the Fourier transform, usually, there are many components, and it is not easy to use all of them in machine learning. So, we need to select the most informative components. In this paper, we provide general recommendations on how to select such components. We also show that these recommendations are in good accordance with two examples: the structure of the …

Scale-Invariance-Based Pre-Processing Drastically Improves Neural Network Learning: Case Study Of Diagnosing Lung Dysfunction In Children, Nancy Avila, Julio Urenda, Nelly Gordillo, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately treat different types of lung dysfunctions in children, it is important to properly diagnose the corresponding dysfunction, and this is not an easy task. Neural networks have been trained to perform this diagnosis, but they are not perfect in diagnostics: their success rate is 60%. In this paper, we show that by selecting an appropriate invariance-based pre-processing, we can drastically improve the diagnostic success, to 100% for diagnosing the presence of a lung dysfunction.

Perfect Reproducibility Is Not Always Algorithmically Possible: A Pedagogical Observation, Jake Lasley, Salamah Salamah, Vladik Kreinovich

Departmental Technical Reports (CS)

Uses of computer-based based systems often want perfect reproducibility: when encountering the same situation twice, the system should exhibit the same behavior. For real-life systems that include sensors, this is not always possible: due to inevitable measurement uncertainty, for the same actual value of the corresponding quantity, we may get somewhat different measurement results, and thus, show somewhat different behavior. In this paper, we show that the above-described ideal reproducibility is not possible even in the idealized situation, when we assume that a sensor can perform its measurement with any given accuracy.

Computational Complexity Of Experiment Design In Civil Engineering, Olga Kosheleva, Yan Wang, Vladik Kreinovich

Departmental Technical Reports (CS)

To guarantee reliability and safety of engineering structures, we need to regularly measure their mechanical properties. Such measurements are often expensive and time-consuming. It is therefore necessary to carefully plan the corresponding measurement experiments, to minimize the corresponding expenses.

It is known that, in general, experiment design is NP-hard. However, the previous proofs dealt either with nonlinear systems, or with situations with low measurement accuracy. In civil engineering, however, most systems are well-described by linear systems, and measurements are reasonably accurate. In this paper, we show that experiment design is NP-hard even for civil engineering problems. We show that even …

A Theoretical Explanation For The Efficiency Of Generalized Harmonic Wavelets In Engineering And Seismic Spectral Analysis, Michael Beer, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

Wavelets of different shapes are known to be very efficient in many data processing problems. In many engineering applications, the most efficient shapes are shapes of a generalized harmonic wavelet, i.e., a wavelet of the shape w(t) = t^a * exp(b * t) for complex b. Similar functions are empirically the most successful in the seismic analysis -- namely, in simulating the earthquake-related high-frequency ground motion. In this paper, we provide a theoretical explanation for the empirical success of these models.

How To Estimate Pavement Roughness: Beyond International Roughness Index, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich

Departmental Technical Reports (CS)

The standard way to describing the road's roughness it to use a single numerical characteristics called International Roughness Index (IRI). This characteristic describes the effect of the road roughness on a vehicle of standard size. To estimate IRI, practitioners tried to use easily available vehicles (whose size may be somewhat different) and then estimate IRI based on these different-size measurements. The problem is that the resulting estimates of IRI are very inaccurate -- which means that a single numerical characteristic like IRI is not sufficient to properly describe road roughness. In this paper, we show that the road roughness can …

How Quantum Computing Can Help With (Continuous) Optimization, Christian Ayub, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the use of quantum computing can reduced the time needed for a search in an unsorted array: from the original non-quantum time T to a much smaller quantum computation time T_q proportional to the square root √(T) of T. In this paper, we show that for a continuous optimization problem, with quantum computing, we can reach almost the same speed-up: namely, we can reduce the non-quantum time T to a much shorter quantum computation time √(T) * ln(T).

Planning For A Corpus Of Continuous Ratings Of Spoken Dialog Quality, Nigel G. Ward

Departmental Technical Reports (CS)

While many aspects of speech processing, including speech recognition and speech synthesis, have seen enormous advances over the past few years, advances in dialog have been more modest. This difference is largely attributable to the lack of resources that can support machine learning of dialog models and dialog phenomena. The research community accordingly needs a corpus of spoken dialogs with quality annotations every 100 milliseconds or so. We envisage a large and diverse collection: on the order of fifty hours of data, representing hundreds of speakers and many genres, with every instant labeled for interaction quality by one or more …