Computer Engineering Commons^™

Computing The Range Of Variance-To-Mean Ratio Under Interval And Fuzzy Uncertainty, Sio-Long Lo, Gang Xiang

Departmental Technical Reports (CS)

In many practical problems such as radar imaging, it is useful to compute the variance-to-mean ratio. The need is important because for the sum of k identical independent signal components, both the variance and the mean are multiplied by k, so this ratio is independent on k and thus, provides useful information about the components. In practice, we only know the samples values with uncertainty. It is therefore necessary to compute the variance-to-mean ratio under this uncertainty. In this paper, we present efficient algorithms for computing this ratio under interval and fuzzy uncertainty.

Mamdani Approach To Fuzzy Control, Logical Approach, What Else?, Samuel Bravo, Jaime Nava

Departmental Technical Reports (CS)

In fuzzy control, two approaches are mainly used: Mamdani's approach, in which we represent the knowledge base as a disjunction of statements Ai(x) & Bi(u) corresponding to individual rules, and logical approach, in which the knowledge base is represented as a conjunction of the rules themselves Ai(x) --> Bi(u). Both approaches are known not to be perfect, so a natural question arises: what other approaches are possible? In this paper, we describe all possible approaches; alternative approaches use an "exclusive or" operation and correspond, e.g., to the fuzzy transform idea.

Least Sensitive (Most Robust) Fuzzy "Exclusive Or" Operations, Jesus E. Hernandez, Jaime Nava

Departmental Technical Reports (CS)

In natural language, "or" sometimes means "inclusive or" and sometimes means "exclusive or". To adequately describe commonsense and expert knowledge, it is therefore important to have not only t-conorms describing fuzzy "inclusive or" operations, but also fuzzy "exclusive or" operations f(a,b). Since the degrees of certainty are only approximately defined, it is reasonable to require that the corresponding operation be the least sensitive to small changes in the inputs. In this paper, we show that the least sensitive fuzzy "exclusive or" operation has the form f(a,b)=min(max(a,b),max(1-a,1-b)).

Estimating Mean Under Interval Uncertainty And Variance Constraint, Ali Jalal-Kamali, Luc Longpre, Misha Kosheleva

Departmental Technical Reports (CS)

Towards Chemical Applications Of Dempster-Shafer-Type Approach: Case Of Variant Ligands, Jaime Nava

Departmental Technical Reports (CS)

Towards Optimal Sensor Placement In Multi-Zone Measurements, Octavio Lerma, Craig Tweedie, Vladik Kreinovich

Departmental Technical Reports (CS)

In multi-zone areas, where the boundaries change with time, it is desirable to place sensors in such a way that the boundary is covered at all times. In this paper, we describe the optimal sensor placement with this property. In this optimal placement, sensors are placed along a see-saw trajectory going between the current location of the boundary and its farthest future location.

Reducing Over-Conservative Expert Failure Rate Estimates In The Presence Of Limited Data: A New Probabilistic/Fuzzy Approach, Carlos M. Ferregut, F. Joshua Campos, Vladik Kreinovich

Departmental Technical Reports (CS)

Unique highly reliable components are typical for aerospace industry. For such components, due to their high reliability and uniqueness, we do not have enough empirical data to make statistically reliable estimates about their failure rate. To overcome this limitation, the empirical data is usually supplemented with expert estimates for the failure rate. The problem is that experts tend to be -- especially in aerospace industry -- over-cautious, over-conservative; their estimates for the failure rate are usually much higher than the actual observed failure rate. In this paper, we provide a new fuzzy-related statistically justified approach for reducing this over-estimation.

From Single To Double Use Expressions, With Applications To Parametric Interval Linear Systems: On Computational Complexity Of Fuzzy And Interval Computations, Joseph A Lorkowski

Departmental Technical Reports (CS)

In many practical problems, we need to estimate the range of a given expression f(x1, ..., xn) when each input xi belongs to a known interval [xi] -- or when each input xi is described by a known fuzzy set. It is known that this problem is easy to solve when we have a Single Use Expression, i.e., an expression in which each variable xi occurs only once. In this paper, we show that for similarly defined Double Use Expressions, the corresponding range estimation problem is NP-hard. Similar problems are analyzed for the problem of solving linear systems under interval …

How To Tell When A Product Of Two Partially Ordered Spaces Has A Certain Property: General Results With Application To Fuzzy Logic, Francisco Zapata, Olga Kosheleva, Karen Villaverde

Departmental Technical Reports (CS)

Fundamental Physical Equations Can Be Derived By Applying Fuzzy Methodology To Informal Physical Ideas, Eric Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy methodology transforms expert ideas -- formulated in terms of words from natural language -- into precise rules and formulas. In this paper, we show that by applying this methodology to intuitive physical ideas, we can get fundamental physical equations. This fact provides an additional justification for the fuzzy methodology.

Towards Optimal Placement Of Bio-Weapon Detectors, Chris Kiekintveld, Octavio Lerma

Departmental Technical Reports (CS)

Biological weapons are difficult and expensive to detect. Within a limited budget, we can afford a limited number of bio-weapon detector stations. It is therefore important to find the optimal locations for such stations. A natural idea is to place more detectors in the areas with more population -- and fewer in desert areas, with fewer people. However, such a commonsense analysis does not tell us how many detectors to place where. To decide on the exact placement of bio-weapon detectors, we formulate the placement problem in precise terms, and come up with an (almost) explicit solution to the resulting …

Fusing Continuous And Discrete Data, On The Example Of Merging Seismic And Gravity Models In Geophysics, Omar Ochoa, Aaron Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

From Program Synthesis To Optimal Program Synthesis, Joaquin Reyna

Departmental Technical Reports (CS)

Adding Constraints -- A (Seemingly Counterintuitive But) Useful Heuristic In Solving Difficult Problems, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Intuitively, the more constraints we impose on a problem, the more difficult it is to solve it. However, in practice, difficult-to-solve problems sometimes get solved when we impose additional constraints and thus, make the problems seemingly more complex. In this methodological paper, we explain this seemingly counter-intuitive phenomenon, and we show that, dues to this explanation, additional constraints can serve as a useful heuristic in solving difficult problems.

How To Bargain: An Interval Approach, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Why Curvature In L-Curve: Combining Soft Constraints, Uram Anibal Sosa Aguirre, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In solving inverse problems, one of the successful methods of determining the appropriate value of the regularization parameter is the L-curve method of combining the corresponding soft constraints, when we plot the curve describing the dependence of the logarithm $x$ of the mean square difference on the logarithm $y$ of the mean square non-smoothness, and select a point on this curve at which the curvature is the largest. This method is empirically successful, but from the theoretical viewpoint, it is not clear why we should use curvature and not some other criterion. In this paper, we show that reasonable scale-invariance …

Universal Approximation With Uninorm-Based Fuzzy Neural Networks, Andre Lemos, Vladik Kreinovich, Walmir Caminhas, Fernando Gomide

Departmental Technical Reports (CS)

Fuzzy neural networks are hybrid models capable to approximate functions with high precision and to generate transparent models, enabling the extraction of valuable information from the resulting topology. In this paper we will show that the recently proposed fuzzy neural network based on weighted uninorms aggregations uniformly approximates any real functions on any compact set. We will describe the network topology and inference mechanism and show that the universal approximation property of this network is valid for a given choice of operators.

Testing Shock Absorbers: Towards A Faster Parallelizable Algorithm, Christian Servin

Departmental Technical Reports (CS)

Cars are equipped with shock absorbers, which are designed to smooth out the shocks on the road. In practice, there is a need to test them. To test the shock absorbers, we need to estimate the values of the shock absorber's parameters. If we did not have any measurement errors, then two measurements would be sufficient to determine the parameters. However, in reality, there are measurement errors. Usually, in engineering practice, it is assumed that the errors are normally distributed with 0 mean, so we can use least squares method to test it. In practice, we often only know the …

Cleanjava: A Formal Notation For Functional Program Verification, Yoonsik Cheon, Cesar Yeep, Melisa Vela

Departmental Technical Reports (CS)

Unlike a Hoare-style program verification, a functional program verification supports forward reasoning by viewing a program as a mathematical function from one program state to another and proving its correctness by essentially comparing two mathematical functions, the function computed by the program and its specification. Since it requires a minimal mathematical background and reflects the way programmers reason about the correctness of a program informally, it can be taught and practiced effectively. However, there is no formal notation supporting the functional program verification. In this paper, we propose a formal notation for writing functional program specifications for Java programs. The …

Power Vs. Performance Evaluation Of Synthetic Aperture Radar Image-Formation Algorithms And Implementations For Embedded Hec Environments (Ongoing Study), Ricardo Portillo, Sarala Arunagiri, Patricia J. Teller

Departmental Technical Reports (CS)

The continuing miniaturization and parallelization of processing hardware has facilitated the development of mobile and field-deployable systems that can accommodate terascale processing within once prohibitively small size and weight constraints. Unfortunately, the added computational capability of these small systems often comes at the cost of larger power demands, an already strained resource in these embedded systems. This study explores the power issues in a specific type of field-deployable system, Mobile Radar. Specifically, we focus on a computationally intensive phase of Synthetic Aperture Radar, Image Formation (IF), and evaluate performance tradeoffs in terms of time-to-solution, output image quality, and power consumption …

Why L2 Topology In Quantum Physics, Chris Culellar, Evan Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that in quantum mechanics, the set S of all possible states coincides with the set of all the complex-valued functions f(x) for which the integral of |f(x)|² is 1. From the mathematical viewpoint, this set is a unit sphere in the space L² of all the functions for which this integralis finite. Because of this mathematical fact, usually the set S is considered with the topology induced by L², i.e., topology in which the basis of open neighborhood of a state f is formed by the open balls. This topology seem to work …

A New Answer To Pauli's Question: Almost All Quantum States Can Be Uniquely Determined By Measuring Location And Momentum, Don Jackson, Olga Kosheleva

Departmental Technical Reports (CS)

In classical mechanics, we can uniquely reconstruct the state of each particle by measuring its spatial location and momentum. In his 1958 paper, W. Pauli, one of the founders of quantum mechanics, conjectured that the same should be true in the quantum case as well: that every quantum state can be uniquely determined by measuring spatial location and momentum. This conjecture was disproven: there are pairs of physically different states that cannot be distinguished if we only measure special location and momentum. A natural question is: how frequent are such pairs? In this paper, we show that almost all quantum …

Visualization Queries, Nicholas Del Rio, Paulo Pinheiro Da Silva

Departmental Technical Reports (CS)

This paper introduces the notion of a query that describes a visualization request in terms of a universe of concepts, which includes but is not limited to Views, Operators, and Parameters. In the presence of specifications based on these concepts, users may be able to request for what properties they want to see in their visualizations (i.e., the graphical analogues of some dataset) without having to specify how to generate them, and more importantly, without being fully aware of a wide range of toolkit specific implementation details. The result of a query is a visualization that satisfies declarative user-defined criteria …

A Use Case-Guided Comparison Of Opm And Pml, Paulo Pinheiro Da Silva, Steve Roach

Departmental Technical Reports (CS)

The World Wide Web Consortium (W3C) Provenance Incubator Group has the goal of providing "a state-of-the art understanding ... in the area of provenance for Semantic Web technologies." To enhance the mutual understanding of language capabilities, the group is attempting to map several of the existing provenance languages such as Provenir, PREMIS, and the Proof Markup Language (PML) into the provenance language the Open Provenance Model (OPM). OPM is intended to be a precise inter-lingua for exchanging provenance information. This article contributes to the understanding of the capabilities of OPM and PML by establishing a set of six common and …

Strings Lead To Lattice-Type Causality, Francisco Zapata, Essau Ramirez, Joel A. Lopez, Olga Kosheleva

Departmental Technical Reports (CS)

Traditional causality relation of special relativity is a lattice in the simplest case of 1-D space (2-D space-time), but it is no longer a lattice in the actual 3-D space (and 4-D space-time). We show that if we take into account effects of string theory, then we get a lattice-type causality relation even for the 4-D space-time.

Towards A Fast, Practical Alternative To Joint Inversion Of Multiple Datasets: Model Fusion, Omar Ochoa, Aaron A. Velasco, Christian Servin

Departmental Technical Reports (CS)

In many areas of science and engineering, we have different sources of data. For example, in geophysics, there are many sources of data for Earth models: first-arrival passive seismic data (from the actual earthquakes), first-arrival controlled-source seismic data (from the seismic experiments), gravity data, etc.

Equivalence Of Gian-Carlo Rota Poset Approach And Taylor Series Approach Extended To Variant Ligands, Jaime Nava, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, molecules can be obtained from a "template" molecule like benzene by replacing some of its hydrogen atoms with ligands (other atoms or atom groups). There can be many possible replacements of this type. To avoid time-consuming testing of all possible replacements, it is desirable to test some of the replacements and then extrapolate to others -- so that only the promising molecules, for which the extrapolated values are desirable, will have to be synthesized and tested.

Towards Simpler Description Of Properties Like Commutativity And Associativity: Using Expression Fragments, Shubhra Datta, Valeria Fierro, Krasen Petrov, Jessica Romo, Gesuri Ramirez, Cesar Valenzuela

Departmental Technical Reports (CS)

Properties like commutativity and associativity are very important in many applications. To make detecting these properties easier, it is desirable to reformulate them in the simplest possible way. A known way to simplify these descriptions is to use postfix notations, in which there is no need to use parentheses. We show that some of these properties can be further simplified if we represent them as equalities not between well-defined expressions, but as equalities between expression fragments.

Why Feynman Path Integration?, Jaime Nava, Juan Ferret, Vladik Kreinovich, Gloria Berumen, Sandra Griffin, Edgar Padilla

Departmental Technical Reports (CS)

To describe physics properly, we need to take into account quantum effects. Thus, for every non-quantum physical theory, we must come up with an appropriate quantum theory. A traditional approach is to replace all the scalars in the classical description of this theory by the corresponding operators. The problem with the above approach is that due to non-commutativity of the quantum operators, two mathematically equivalent formulations of the classical theory can lead to different (non-equivalent) quantum theories. An alternative quantization approach that directly transforms the non-quantum action functional into the appropriate quantum theory, was indeed proposed by the Nobelist Richard …

Uncertainty In Partially Ordered Sets As A Natural Generalization Of Intervals: Negative Information Is Sufficient, Positive Is Not, David Mireles, Olga Kosheleva

Departmental Technical Reports (CS)

In many real-life applications, we have an ordered set: a set of all space-time events, a set of all alternatives, a set of all degrees of confidence. In practice, we usually only have a partial information about an element x of this set. This partial information includes positive knowledge: that a <= x or x <= a for some known a, and negative knowledge: that it is not true that a <= x or x <= a for some known a. In the case of a total order, the set of all elements satisfying this partial information is an interval. We show that in the general case of a partial order, the corresponding analogue of an interval is a convex set. We also show that in general, to describe partial knowledge, it is sufficient to have only negative information about x but it is not sufficient to have only positive information.