Computer Engineering Commons^™

Coincidences Are Not Accidental: A Theorem, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we formalize and prove the statement that coincidences cannot be accidental, a statement that underlies many useful heuristics in mathematics and physics.

Our proof uses a version of Kolmogorov complexity, a technique originally developed to describe randomness and "accidentalness".

Why Kolmogorov Complexity In Physical Equations, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

Several researchers, including M. Gell-Mann, argue that the notion of Kolmogorov complexity, developed in the algorithmic information theory, is useful in physics (i.e., in the description of the physical world). Their arguments are rather convincing, but there seems to be a gap between traditional physical equations and Kolmogorov complexity: namely, it is not clear how the standard equations of physics can lead to algorithmic notions underlying Kolmogorov complexity. In this paper, this "gap" is bridged: we explain how Kolmogorov complexity naturally appear in physical equation.

Spinal Cord Stimulation For Chronic Pain Management: Towards An Expert System, Kenneth M. Alo, Richard Alo, Andre De Korvin, Vladik Kreinovich

Departmental Technical Reports (CS)

Chronic pain is a serious health problem affecting millions of people worldwide. Currently, spinal cord simulation is one of the most effective methods of easing the chronic pain. For most patients, a careful selection of weak electric currents enables to drastically decrease the pain level. The first devices offered only a few possible regimes, and it was possible to choose an appropriate regime simply by exhaustive search. Continuous engineering progress leads to more and more flexible devices that offer a wide variety of millions of possible simulation regimes. With this variety, it is no longer possible to test all of …

From Fuzzification And Intervalization To Anglification: A New 5d Geometric Formalism For Physics And Data Processing, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

From Expert Words Directly To Numerical Simulations: Group-Theoretic Approach To Computing With Words In Information/Intelligent Systems, Vladik Kreinovich, Brian Penn, Scott A. Starks

Departmental Technical Reports (CS)

In many real-life situations, e.g., when making an environmental decision, it is important to be able to predict long-term consequences of different decisions. Very often, these predictions must be done in the situation where the only available information consists of expert rules, which are formulated by words from natural language. One possible way to transform these expert words into numerical simulation (leading to prediction) is to use the fuzzy control methodology. However, there is a problem with using this methodology: it invokes replacing each word by a membership function, and this replacement drastically increases the required computer space (and thus, …

Strict Achimedean T-Norms And T-Conorms As Universal Approximators, Hung T. Nguyen, Vladik Kreinovich, Piotr Wojciechowski

Departmental Technical Reports (CS)

In knowledge representation, when we have to use logical connectives, various continuous t-norms and t-conorms are used. In this paper, we show that every continuous t-norm and t-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm (t-conorm).

Computational Geometry And Artifical Neural Networks: A Hybrid Approach To Optimal Sensor Placement For Aerospace Nde, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault locations. However, there are two obstacles to this ideal formulation:

--First, this ideal formulation requires that we know the probabilities of different fault locations etc., and there are usually not enough statistics to determine these probabilities.

--Second, even …

Identification And Classification Of Inconsistency In Relationship To Software Maintenance, Daniel Cooke, Luqi, Vladik Kreinovich

Departmental Technical Reports (CS)

This paper provides an overview of the relationship between recent work in logic programming and recent developments in software engineering. The relationship to software engineering is more specifically concerned with how formal specifications can be used to explain and represent the basis of software maintenance and evolution. Some of the results reviewed here have appeared in our previous papers. These previous results are summarized, extended, and made more general in this paper.

The Challenge Of Hyper-Spectral Satellite Imaging And Integer-Valued Fuzzy Sets, Maria Beltran, Vladik Kreinovich, Scott A. Starks

Departmental Technical Reports (CS)

Satellite images already produce huge amounts of data, which makes their processing a serious computational challenge. This problem will become even more complicated with the launch of multi-spectral Earth-imaging satellites that will increase the amount of information by at least two orders of magnitude. With such a huge amount of information, it is necessary to come up with data processing methods that are as fast as possible. In particular, we show that for fuzzy processing techniques, this leads to the necessity to use integer-valued fuzzy sets.

Sensor Placement For Aerospace Non-Destructive Evaluation (Nde): Optimization Under Fuzzy Uncertainty, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

Environmentally-Oriented Processing Of Multi-Spectral Satellite Images: New Challenges For Bayesian Methods, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

Remotely sensed images from new generation satellites present an opportunity for scientists to investigate problems in environmental and earth science which have been previously intractable. The magnitude of data that will arise from these hyperspectral instruments create the need for innovative techniques to accomplish data reduction. This paper presents an algorithm which shows promise as a tool for reducing the dimensionality of data resulting from remote sensing. The optimality criteria for the algorithm is the Bayes Risk in the reduced dimension space.

We Must Choose The Simplest Physical Theory: Levin-Li-Vitanyi Theorem And Its Potential Physical Applications, Dirk Fox, Martin Schmidt, Misha Kosheleva, Vladik Kreinovich, Luc Longpre, Jeff Kuhn

Departmental Technical Reports (CS)

If several physical theories are consistent with the same experimental data, which theory should we choose? Physicists often choose the simplest theory; this principle (explicitly formulated by Occam) is one of the basic principles of physical reasoning. However, until recently, this principle was mainly a heuristic because it uses the informal notion of simplicity.

With the explicit notion of simplicity coming from the Algorithmic Information theory, it is possible not only to formalize this principle in a way that is consistent with its traditional usage in physics, but also to prove this principle, or, to be more precise, deduce it …

Which Algorithms Are Feasible? Maxent Approach, Daniel E. Cooke, Vladik Kreinovich, Luc Longpre

Departmental Technical Reports (CS)

It is well known that not all algorithms are feasible; whether an algorithm is feasible or not depends on how many computational steps this algorithm requires. The problem with the existing definitions of feasibility is that they are rather ad hoc. Our goal is to use the maximum entropy (MaxEnt) approach and get more motivated definitions.

If an algorithm is feasible, then, intuitively, we would expect the following to be true:

If we have a flow of problems with finite average length L, then we expect the average time T to be finite as well.

Thus, we can say …

Maximum Entropy Approach To Optimal Sensor Placement For Aerospace Non-Destructive Testing, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault locations. However, there are two obstacles to this ideal formulation:

--First, this ideal formulation requires that we know the probabilities of different fault locations and the probabilities of different aircraft exploitation regimes. In reality, especially for a …

Soft Computing Explains Heuristic Numerical Methods In Data Processing And In Logic Programming, Hung T. Nguyen, Vladik Kreinovich, Bernadette Bouchon-Meuiner

Departmental Technical Reports (CS)

We show that fuzzy logic and other soft computing approaches explain and justify heuristic numerical methods used in data processing and in logic programming, in particular, M-methods in robust statistics, regularization techniques, metric fixed point theorems, etc.

Non-Equilibrium Thermodynamics Explains Semiotic Shapes: Applications To Astronomy And To Non-Destructive Testing Of Aerospace Systems, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

Proceedings of the International Conference on Intelligent Systems and Semiotics (ISAS'97), National Institute of Standards and Technology Publ., Gaithersburg, MD, 1997, pp. 378-382.

Celestial bodies such as galaxies, stellar clusters, planetary systems, etc., have different geometric shapes (e.g., galaxies can be spiral or circular, etc.). Usually, complicated physical theories are used to explain these shapes; for example, several dozen different theories explain why many galaxies are of spiral shape. Some rare shapes are still difficult to explain.

It turns out that to explain these "astroshapes", we do not need to know the details of physical equations: practically all the shapes …

Multi-Resolution Data Processing: It Is Necessary, It Is Possible, It Is Fundamental, Scott A. Starks, Vladik Kreinovich, Alex Meystel

Departmental Technical Reports (CS)

Experience shows that many data processing problems are difficult to solve, and some of these problems have even been proven to be computationally intractable. Human experts successfully solve many such problems by using a hierarchical, multi-resolution approach. These multi-resolution methods are, in several cases, provably optimal. However, due to the computational intractability of the problem itself, the multi-resolution approach can only work if the systems that we are analyzing are themselves hierarchical. We show that, first, due to (inevitable) measurement inaccuracies, an arbitrary input data is consistent with the hierarchical model, and second, that in many cases, the actual physical …

Towards Computers Of Generation Omega - Non-Equilibrium Thermodynamics, Granularity, And Acausal Processes: A Brief Survey, Misha Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Proceedings of the International Conference on Intelligent Systems and Semiotics (ISAS'97), National Institute of Standards and Technology Publ., Gaithersburg, MD, 1997, pp. 383-388.

Nowadays, we are using mainly computer of fourth generation, and we are designing fifth-generation computers. It is reasonable to ask: what is the perspective? What will the computers of generation omega look like?

--As the speed of data processing increases, we face a natural limitation of causality, according to which the speed of all processes is limited by the speed of light.

--Lately, a new area of acausal (causality violating) processes has entered mainstream physics.

This …

How To Make World Wide Web Sites Faster And Easier To Use, Misha Kosheleva

Departmental Technical Reports (CS)

Working Notes of the AAAI Symposium on Frontiers in Soft Computing and Decision Systems, Boston, MA, November 8-10, 1997.

We propose a new idea of organizing Web sites so that the Web will be easier and faster to use.

Soft Computing: Frontiers? A Case Study Of Hyper-Spectral Satellite Imaging, Scott A. Starks, Vladik Kreinovich

Departmental Technical Reports (CS)

Soft computing methods such as fuzzy control, neural networks, etc., often require lots of computations even for small amounts of data. It is, therefore, sometimes believed that for larger amounts of data, the required amount of computations will be so large that we will reach the frontiers of soft computing.

In this paper, we show, on the example of hyper-spectral satellite imaging, that this belief is often too pessimistic. We should not be afraid to use (or at least to try to use) soft computing methods even for large amounts of data.

Multi-Criteria Optimization - An Important Foundation Of Fuzzy System Design, Hung T. Nguyen, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life design situations, there are several different criteria that we want to optimize, and these criteria are often in conflict with each other. Traditionally, such multi-criteria optimization situations are handled in an ad hoc manner, when different conflicting criteria are artificially combined into a single combination objective that is then optimized. The use of unnatural ad hoc tools is clearly not the best way of describing a very natural aspect of human reasoning. Fuzzy logic describes a much more natural way of handling multi-criterion optimization problems: when we cannot maximize each of the original conflicting criteria 100%, we …

Computers Of Generation Omega, Vladik Kreinovich

Departmental Technical Reports (CS)

To make computers faster, we must take smaller and smaller processing elements, and to analyze these elements, we need to take into consideration more and more subtle quantum effects. A. Stern has shown a natural way to use quantum field theory for computing. It turns out that if we take into consideration all quantum effects, then this idea leads to an even faster performance.