Reduced order feedback control equations for linear time and frequency domain analysis

An algorithm was developed which can be used to obtain the equations. In a more general context, the algorithm computes a real nonsingular similarity transformation matrix which reduces a real nonsymmetric matrix to block diagonal form, each block of which is a real quasi upper triangular matrix. The algorithm works with both defective and derogatory matrices and when and if it fails, the resultant output can be used as a guide for the reformulation of the mathematical equations that lead up to the ill conditioned matrix which could not be block diagonalized

Constellation Queries over Big Data

A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation contexts. For example, a particularly interesting geometric pattern in astronomy is the Einstein cross, which is an astronomical phenomenon in which a single quasar is observed as four distinct sky objects (due to gravitational lensing) when captured by earth telescopes. Finding such crosses, as well as other geometric patterns, is a challenging problem as the potential number of sets of elements that compose shapes is exponentially large in the size of the dataset and the pattern. In this paper, we denote geometric patterns as constellation queries and propose algorithms to find them in large data applications. Our methods combine quadtrees, matrix multiplication, and unindexed join processing to discover sets of points that match a geometric pattern within some additive factor on the pairwise distances. Our distributed experiments show that the choice of composition algorithm (matrix multiplication or nested loops) depends on the freedom introduced in the query geometry through the distance additive factor. Three clearly identified blocks of threshold values guide the choice of the best composition algorithm. Finally, solving the problem for relative distances requires a novel continuous-to-discrete transformation. To the best of our knowledge this paper is the first to investigate constellation queries at scale

Oblivious Median Slope Selection

We study the median slope selection problem in the oblivious RAM model. In this model memory accesses have to be independent of the data processed, i.e., an adversary cannot use observed access patterns to derive additional information about the input. We show how to modify the randomized algorithm of Matou\v{s}ek (1991) to obtain an oblivious version with O(n log^2 n) expected time for n points in R^2. This complexity matches a theoretical upper bound that can be obtained through general oblivious transformation. In addition, results from a proof-of-concept implementation show that our algorithm is also practically efficient.Comment: 14 pages, to appear in Proceedings of CCCG 202

User Preference Web Search -- Experiments with a System Connecting Web and User

We present models, methods, implementations and experiments with a system enabling personalized web search for many users with different preferences. The system consists of a web information extraction part, a text search engine, a middleware supporting top-k answers and a user interface for querying and evaluation of search results. We integrate several tools (implementing our models and methods) into one framework connecting user with the web. The model represents user preferences with fuzzy sets and fuzzy logic, here understood as a scoring describing user satisfaction. This model can be acquired with explicit or implicit methods. Model-theoretic semantics is based on fuzzy description logic f-EL. User preference learning is based on our model of fuzzy inductive logic programming. Our system works both for English and Slovak resources. The primary application domain are job offers and job search, however we show extension to mutual investment funds search and a possibility of extension into other application domains. Our top-k search is optimized with own heuristics and repository with special indexes. Our model was experimentally implemented, the integration was tested and is web accessible. We focus on experiments with several users and measure their satisfaction according to correlation coefficients