TAAC'2013: Lectures

The analysis of Chain - Like Structures (CLS) has increased in importance over last decades. Studies of such objects as polymers are of primary interest in many branches of science and technology. The complexity of their macromolecular architecture as well as the variability of physical properties make CLS-related problems hardly tractable in a traditional formal-theoretical way. As is often the case, the remedy is to make use of computer simulation which during last years became a fundamental tool for CLS studies.
In our lecture we will introduce new concepts for algorithmization of the CLS movement. The main underlying idea is to sequentialize each move of the CLS in order to reduce the complexity involved in the dynamics of polymer transport as well as to reflect the propagation of the tension through its body.

This talk is intended to find out computer science in modern information technologies. Nowadays developers are using technologies made by vendors. I propose to sink to layer of creating own technologies. Let’s start from mutex algorithms: Dekker’s algorithm, Peterson Lock, Lamport’s Bakery Algorithm.

In my talk, I will survey the development of the theory of branching processes starting from Thomas Robert Malthus' Essay on the Principle of Population in which he established the idea that a population, when unchecked, grows exponentially fast. I will introduce the first probabilistic model of a branching mechanism, the Galton-Watson process, and later come to the theory of general branching processes which includes many other branching processes that have been studied before. The focus of the talk will be on limit theorems in these models that reflect Malthus' idea of exponential population growth.

Graph Search is Facebook's search engine that is capable of answering natural language user queries. It provides personalized results based on Facebook object graph that consists of more than one billion users, 240 billions of photos, 1 trillion posts and trillions of connections between them. In the lecture I will cover query understanding and parsing techniques that are used in the Graph Search, document retrieval and ranking and results blending. I will also talk about software and hardware infrastructure that supports Graph Search.

In my lecture, I will describe a novel method of elliptic featureless discriminant analysis using Petunin's proximity measure and a new method of multivariate ordering using elliptical peeling on the basis of Petunin's ellipsoids. The statistical properties of the Petunin's ellipsoids will be demonstrated. The application of the method for the minimization of uncertainty under elliptic discriminant analysis in breast cancer detection will be described.

Natural Language (NL) addressing is a possibility to access information using natural language words or phrases as addresses of the information stored in the multi-dimensional numbered information spaces. For this purpose the internal encoding of the letters is used to generate corresponded co-ordinates. Several experiments of NL-storing of small, middle-size and large datasets are presented in the lecture. Results from series of experiments for estimating the time of NL-storing of small datasets (dictionaries, thesauruses, and ontologies) as well as middle-size and large RDF-datasets are outlined. From experimental data we concluded that NL-access time: (1) Depends on number of elements in a dataset’s instances; (2) Not depends on number of instances in the dataset. The second is very important for multi-processing because it means linear reverse dependence on number of processors.

The lection will consider partial functions defined on finite sets. The emphasis of the lection will be on sets closed under superposition — hyper-clones and multi-clones. Several completeness criteria and maximal hyper-clones and multi-clones will be considered. Also the lection will concern some applications of clones.

Nowadays mobile technologies extend a set of mathematical apparatus and methods used in algorithms of the signal forming and processing, compression of audio and video data. The lecture deals with methods and sections of applied mathematics, which a software developer should know to work with physical layer of wireless communication standards 3G, LTE and 802.11ac.