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# Résumé

(2013-01-01)

By "résumé" I mean "a document representing my background and skillsets."

## Background

I had my formal education from kindergarten, elementary school, junior high school, secondary high school, to universities, and I had formally worked for several institutions and companies in several countries.

I had majored in mathematics as an undergraduate, and hold a BA degree in mathematics and its applications from Vytautas Magnus University in Lithuania. Currently, I was a PhD student of an interdisciplinary program at Purdue University (from 2011 to 2013).

I had been an employee of the Institute of Physics in Lithuania, Santoku Inc. and Unoh Inc. (now Zynga Japan K.K.) in Japan, and the most recently I was working as a teaching assistant at Purdue University in the U.S.

During my undergraduate studies, I had participated in a one year student exchange program with Waseda Univeristy in Tokyo, where I had focused on learning Japanese language and communication in this language.

During various periods of my life, I had learned to also communicate in Russian, Chinese, and German.

### Mathematical background

#### Topics of Classes Taken

Calculus I and II: set of real nubers, set operations, bounds for sets of real numbers, sequences of numbers and their limits, real function and its limit, continuous functions, derivatives, Taylor formula, function graphing. Indefinite integral, integration of indefinite integral, definite integral, Newton-Leibniz formula, application of definite integral in geometry, physics and mechanics, infinite series. Convergence tests for series, functional series, power series, Taylor series.

Multivariable Calculus: Multivariable functions, limits and continuity of multivariable functions, partial derivatives of multivariable functions, extreme values of multivariable functions, least square method, double integrals, triple integrals, line integrals, Green’s formula, surface integrals.

Geometry: vectors, operations with vectors, linear dependence of vectors in plane and space, basis in plane and space, scalar product, vector product, parallelepipedal product, equation of a plane, equation of a line in space, equation of a line in plane, circle, ellipse, hyperbola, parabola, cone, cylinder, tangent plane and normal of the curve.

Complex Analysis: operations with complex numbers, sequences and series of complex numbers, functions of a complex variable, limits and continuity, derivatives, Cauchy-Riemann equations, integrals, Cauchy’s theorem, Cauchy’s integral formulas, Taylor’s series, Laurent’s series, residues, residue theorem, Fourier series and integrals.

Algebra: theory of linear algebraic equations, sets and mappings, relations, permutations, integer numbers, linear vector space, linear transformations, matrices, determinants and their properties, algebraic structures, semi groups and monoids, groups, isomorphism, rings, fields, complex numbers, polynomials, closure of complex numbers field.

Differential Equations: the first order differential equations, the Cauchy problem, general, particular and special solutions, phase space, vector and direction fields, examples of differential equations, systems of ODE, Existence and Uniqueness theorems, higher order ODE, fundamental system, linear differential equations, equations with constant coefficients, a qualitative approach in the plane, first integrals, Lyapunov stability definition.

Measure and Integral Theory: basic operations on sets, the power of a set, countable sets, the power of the continuum, algebras of sets, step functions, continuous functions, monotone functions, bounded variation functions, absolutely continuous functions, measurable functions, measurable set, Lebesgue integral, Fubini’s theorem, multiple integrals, fundamentals of set theory, measurable spaces, Lebesgue–Stieltjes measure on a line, distribution function, convergence almost everywhere, convergence in measure. [*]

Discrete Mathematics: countable sets, principle of mathematical induction, arrangements, permutations and combinations, binomial coefficient identity, principle of sieve, Stirling numbers, degree generating function, exponential generating function, recurrence relations, continued fractions, propositional logic, basic concept of graph.

Partial Differential Equations: first order partial differential equations, classification of partial differential equations, main types of equations and problems of mathematical physics, the wave equation, initial and initial-boundary value problems, the heat conduction equation, initial and initial-boundary value problems, the existence and uniqueness of a solution, solving methods, boundary value problems for the Laplace equation in simple regions. (Taught according to: An Introduction to Partial Differential Equations by Y. Pinchover and J. Rubinstein.)

Numerical Methods: function interpolation, cubical splines, numerical integration, solution of nonlinear equations and linear algebraic equation systems, matrix proper value problem.

Functional Analysis: sets, metric spaces, contracting mappings, topological spaces, compactness in the topological and metric spaces, linear spaces, Hahn-Banach theorem, normal spaces, spaces with inner product, Hilbert spaces, Continues linear operators, conjugate spaces and conjugate operators, compact operators, spectral theorem, Fredholm equations. (Taught according to: Functional Analysis, K. Yosida, with some topics taken from Elements of the Theory of Functions and Functional Analysis by A.N. Kolmogorov and S.V. Fomin.)

Numerical Methods for Differential Equations: interpolation by algebraic polynomials, interpolation by splines, numeric integration, Monte Carlo integration, solving non-linear equations, solving system of linear algebraic equations by iterative methods, solving system of linear algebraic equations by direct methods, convergence of iterative methods, eigenvectors and eigenvalues problem, eigenvectors and eigenvalues problem solving by orthogonal transformations, one variable function optimization.

Probability Theory: random events, probability space, conditional probability, random variables, distribution functions, density functions, multivariate random variables, independent random variables, moments and cumulants, binomial distribution, Poisson distribution, normal distribution, convergence of infinite sequences of random variables, the law of large numbers, the central – limit theorem.

### Statistical Background

#### Topics of the Classes Taken

Mathematical Statistics: notion of sample and sample space, numerical characteristics of distribution and their estimates, main parametric distributions, point estimates of parameters, parametric estimation methods (method of moments and maximum likelihood estimate), confidence intervals for parameters, basic concepts of hypothesis testing, testing hypotheses on mean and variance, nonparametric hypotheses, linear regression model.

Correlation Analysis: problem examples and solution stages, types of dependencies, rank correlation, generalized correlation coefficient, partial and multivariate correlation, hypothesis testing on independence, regression analysis, types of regression functions, parameters estimation on linear models, least-square method, accuracy of estimations in regression analysis.

Multivariate Statistics: distributional characteristics of multivariate random variables, statistical estimation, multivariate normal distribution, analysis of variance, logistic regression, basic concepts of classification, discriminant analysis, cluster analysis, introduction to factor analysis and survival analysis. Notions of multivariate distributions and numerical characteristics and their properties, marginal distributions, covariance matrix, covariance and correlation coefficient, multivariate Gaussian distribution, conditional distributions, conditional expectations and variations, Walld's identity, iterated expectation, conditional variance, estimates of mean and correlation matrix and its maximum likelihood parameter estimation. ANOVA, Two-Way ANOVA, ANOVA for blocked data, regression, multiple regression, logistic regression, hypothesis testing for parameters of regressions, cluster analysis (hierarchical/non-hierarchical, K-means method), discriminant analysis, factor analysis, survival analysis.

Stochastic Processes: notion of stochastic process, distribution and numerical characteristics, classification of stochastic processes, conditional probability and mathematical expectations, random walk, ( reflection principle, arcsine law, ) the classifications of states of Markov chains, branching processes, Lévy processes and their properties. Properties of Gaussian and Poisson processes, birth and death processes, elements of queuing theory, stationary processes, classification of random processes, Wiener and Markov processes, Kolmogorov–Chapmen equations.

Statistical Methods For Biology: Descriptive statistics, binomial and normal distributions, confidence interval estimation, hypothesis testing, analysis of variance, introduction to nonparametric testing, linear regression and correlation, goodness-of-fit tests, and contingency tables.

### Computer Science Background

#### Topics of the Classes Taken

Mathematical logic: Validity of formulas, the resolution principle for the prepositional logic, interpretations of formulas in the predicate logic, prenex normal forms, a set of clauses, semantic trees, Herbrand's theorem, substitution and unification, the resolution principle for the predicate logic, search trees, space and heuristics, logic programs, declarative semantics of logic programs, procedural semantics of logic programs, negation - negative information and failure, closed world assumption, negation as failure rule, SLDNF - resolution, Closed world databases.

Programming in Python: Variables, expressions, and statements, functions, conditionals, fruitful functions, iteration, strings, lists, modules and files, recursion and exceptions, dictionaries, classes and objects, classes and functions, classes and methods, sets of objects, inheritance, linked lists, stacks, queues, trees, debugging.

Computing For Life Sciences: Unix system, programming in Python, basic background about proteins, DNA, and RNA biological databases, algorithms for biological sequence (DNA, protein) sequence alignment and database search, algorithms for sequence motif search, protein tertiary (3D) structure comparison, protein 3D strucure prediction from amino acid sequence, protein-protein interaction, biological network analysis, systems biology, drug protein interaction.

Process Analysis and Recognition: Determinate and random processes in continuous and discrete spaces, phenomena of signal discretization and quantization, synthesis of signals, processes of dynamic systems; time and frequency characteristics of signals, cepstral parameters of signals, filtering, processes recognition.

Data Structures (C++): abstract types, their implementation and application in design of object-oriented software models, class description methods, class internal structure hiding, external interface description, feature inheritance in class families and their polimorfism, class compositions, critical situation management and template programming.

Programming in C: basic terminology of structural programming, notion of algorithm, linear cyclic and branching algorithms, structure of C programming language, data types and variables, control structures, recursive computation, input/output control, subroutines, two dimmentional arrays (search, insertion, deletion, sorting), elementary strings and file processing. Programming style and guidelines.

Programming in Java: objects and classes, OOP principles, the Object class, reflection, garbage collection, java project structure, assert conditions, Java I/O system, text processing, collections framework, generics, threads, JFC/Swing, applets, processing XML with Java, networking (client-server applications).

Stanford - Introduction to Databases (by Jennifer Widom): Relational Databases, XML Data, JSON Data, Relational Algebra, SQL, Relational Design Theory, Querying XML, UML, Indexes, Constraints and Triggers, Transactions, Views, Authorization, Recursion, On-Line Analytical Processing, NoSQL Systems.

Stanford - Introduction to Artificial Intelligence: Overview of AI, Search, Statistics, Uncertainty, and Bayes networks, Machine Learning, Logic and Planning, Markov Decision Processes and Reinforcement Learning, Hidden Markov Models and Filters, Adversarial and Advanced Planning, Image Processing and Computer Vision, Robotics and robot motion planning, Natural Language Processing and Information Retrieval.

Stanford - Machine Learning (by Andrew Ng): Supervised learning setup, LMS, logistic regression, perceptron, exponential family, generative learning algorithms, gaussian discriminant analysis, naive bayes, support vector machines, model selection and feature selection, ensemble methods: bagging, boosting, evaluating and debugging learning algorithms, bias-variance tradeoff, union and Chernoff-Hoeffding bounds, VC dimension, worst case (online) learning, clustering, k-means, EM, mixture of gaussians, factor analysis, PCA (principal components analysis), ICA (independent components analysis), MDPs, Bellman equations, value iteration and policy iteration, linear quadratic regulation (LQR), LQG, Q-learning, value function approximation, policy search, reinforce, POMDPs.

Stanford - Probabilistic Graphical Models (by Daphne Koller): The Bayesian network and Markov network representation, including extensions for reasoning over domains that change over time and over domains with a variable number of entities, Reasoning and inference methods, including exact inference (variable elimination, clique trees) and approximate inference (belief propagation message passing, Markov chain Monte Carlo methods), Learning parameters and structure in PGMs, Using a PGM for decision making under uncertainty.