Computer Engineering Commons^™

Locating Local Extrema Under Interval Uncertainty: Multi-D Case, Karen Villaverde, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to locate local maxima and/or local minima of a function which is only know with interval uncertainty. For example, in radioastronomy, components of a radiosource are usually identified by locations at which the observed brightness reaches a local maximum. In clustering, different clusters are usually identified with local maxima of the probability density function (describing the relative frequency of different combinations of values). In the 1-D case, a feasible (polynomial-time) algorithm is known for locating local extrema under interval (and fuzzy) uncertainty. In this paper, we extend this result to the general multi-dimensional case.

Optimizing Computer Representation And Computer Processing Of Epistemic Uncertainty For Risk-Informed Decision Making: Finances Etc., Vladik Kreinovich, Nitaya Buntao, Olga Kosheleva

Departmental Technical Reports (CS)

Uncertainty is usually gauged by using standard statistical characteristics: mean, variance, correlation, etc. Then, we use the known values of these characteristics (or the known bounds on these values) to select a decision. Sometimes, it becomes clear that the selected characteristics do not always describe a situation well; then other known (or new) characteristics are proposed. A good example is description of volatility in finance: it started with variance, and now many descriptions are competing, all with their own advantages and limitations.

In such situations, a natural idea is to come up with characteristics tailored to specific application areas: e.g., …

How To Describe And Propagate Uncertainty When Processing Time Series: Metrological And Computational Challenges, With Potential Applications To Environmental Studies, Christian Servin, Martine Ceberio, Aline Jaimes, Craig Tweedie, Vladik Kreinovich

Departmental Technical Reports (CS)

Time series comes from measurements, and measurements are never absolutely accurate. Traditionally, when we deal with an individual measurement or with a sample of measurement results, we subdivide a measurement error into random and systematic components: systematic error does not change from measurement to measurement which random errors corresponding to different measurements are independent. In time series, when we measure the same quantity at different times, we can also have correlation between measurement errors corresponding to nearby moments of time. To capture this correlation, environmental science researchers proposed to consider the third type of measurement errors: periodic. This extended classification …

Research-Related Projects For Graduate Students As A Tool To Motivate Graduate Students In Classes Outside Their Direct Interest Areas, Vladik Kreinovich

Departmental Technical Reports (CS)

In most graduate programs, students are required to take both "depth" classes -- classes in the areas of the student's direct interest -- and "breadth" classes, classes outside their direct interest areas. Naturally, the student's interest in "breadth" classes is often naturally lower than their interest in the "depth" classes. To enhance the students' interest in the "breadth" classes, a natural idea is to make research-related project an important part of the class, a project in which the student can apply the skills that he or she learns in the class to the research area of direct interest to this …

Towards Formalizing Non-Monotonic Reasoning In Physics: Logical Approach Based On Physical Induction And Its Relation To Kolmogorov Complexity, Vladik Kreinovich

Departmental Technical Reports (CS)

To formalize some types of non-monotonic reasoning in physics, researchers have proposed an approach based on Kolmogorov complexity. Inspired by Vladimir Lifschitz's belief that many features of reasoning can be described on a purely logical level, we show that an equivalent formalization can be described in purely logical terms: namely, in terms of physical induction.

One of the consequences of this formalization is that the set of not-abnormal states is (pre-)compact. We can therefore use Lifschitz's result that when there is only one state that satisfies a given equation (or system of equations), then we can algorithmically find this state. …

Negative Results Of Computable Analysis Disappear If We Restrict Ourselves To Random (Or, More Generally, Typical) Inputs, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known that many computational problems are, in general, not algorithmically solvable: e.g., it is not possible to algorithmically decide whether two computable real numbers are equal, and it is not possible to compute the roots of a computable function. We propose to constraint such operations to certain "sets of typical elements" or "sets of random elements".

In our previous papers, we proposed (and analyzed) physics-motivated definitions for these notions. In short, a set T is a set of typical elements if for every definable sequences of sets A_n for which each A_n is a subset …

Towards Optimizing Cloud Computing: An Example Of Optimization Under Uncertainty, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most efficient way to store and process data is cloud computing. In cloud computing, instead of storing the data at the user-defined location (e.g., at the user's computer or at the centralized server), the computer system ("cloud") selects the location of the data storage that speeds up computations -- by minimizing the (average) communication time. In this chapter, we provide an analytical solution to the corresponding optimization problem.

The demand for cloud computing is growing fast, and we expect that this demand -- and thus, the size of the resulting cloud -- will continue to grow. …

Do Constraints Facilitate Or Inhibit Creative Problem Solving: A Theoretical Explanation Of Two Seemingly Contradictory Experimental Studies, Karen Villaverde, Olga Kosheleva, Martine Ceberio

Departmental Technical Reports (CS)

Do constraints facilitate or inhibit creative problem solving? Recently, two experimental studies appeared, one showing that removing constraints may enhance creativity, another showing that adding constraints can facilitate creative problem solving. In this paper, we provide a theoretical explanation of these two seemingly contradictory experimental results.

Validated Templates For Specification Of Complex Ltl Formulas, Salamah Salamah, Ann Q. Gates, Vladik Kreinovich

Departmental Technical Reports (CS)

Formal verification approaches that check software correctness against formal specifications have been shown to improve program dependability. Tools such as Specification Pattern System (SPS) and Property Specification (Prospec) support the generation of formal specifications. SPS has defined a set of patterns (common recurring properties) and scopes (system states over which a pattern must hold) that allows a user to generate formal specifications by using direct substitution of propositions into parameters of selected patterns and scopes. Prospec extended SPS to support the definition of patterns and scopes that include the ability to specify parameters with multiple propositions (referred to as composite …

Towards Symmetry-Based Explanation Of (Approximate) Shapes Of Alpha-Helices And Beta-Sheets (And Beta-Barrels) In Protein Structure, Jaime Nava, Vladik Kreinovich

Departmental Technical Reports (CS)

Protein structure is invariably connected to protein function. There are two important secondary structure elements: alpha helices and beta-sheets (which sometimes come in a shape of beta-barrels). The actual shapes of these structures can be complicated, but in the first approximation, they are usually approximated by, correspondingly, cylindrical spirals and planes (and cylinders, for beta-barrels). In this paper, following the ideas pioneered by a renowned mathematician M. Gromov, we use natural symmetries to show that, under reasonable assumptions, these geometric shapes are indeed the best approximating families for secondary structures.

Estimating Statistical Characteristics Of Lognormal And Delta-Lognormal Distributions Under Interval Uncertainty: Algorithms And Computational Complexity, Nitaya Buntao, Sa-Aat Niwitpong, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional statistical estimates S(x₁, ..., x_n) for different statistical characteristics S (such as mean, variance, etc.) implicitly assume that we know the sample values x₁, ..., x_n exactly. In practice, the sample values Xi come from measurements and are, therefore, in general, different from the actual (unknown) values x_i of the corresponding quantities. Sometimes, we know the probabilities of different values of the measurement error d_i = X_i - x_i, but often, the only information that we have about the measurement error is the upper bound D_{i …}

A Framework To Create Ontologies For Scientific Data Management, Leonardo Salayandia, Paulo Pinheiro Da Silva, Ann Q. Gates

Departmental Technical Reports (CS)

Scientists often build and use highly customized systems to support observation and analysis efforts. Creating effective ontologies to manage and share data products created from those systems is a difficult task that requires collaboration among domain experts, e.g., scientists and knowledge representation experts. A framework is presented that scientists can use to create ontologies that describe how customized systems capture and transform data into products that support scientific findings. The framework establishes an abstraction that leverages knowledge representation expertise to describe data transformation processes in a consistent way that highlights properties relevant to data users. The intention is to create …