PhD research topics

• Mathematical modeling
• Mathematical statistics
• Intelligent data analysis
• Geometrical and statistical methods in data analysis
• Manifold Learning
• Machine Learning
• Analysis of neuroimaging and biomedical data

• Improvement, Development, and Application of Proteomics and Metabolomics Quantitative Technologies for Clinical Diagnostics
• Development of Precision Medicine Based on Coupling of Big Data and Multi-Omics Studies
• Correlating Patterns in Proteogenomics Data to Improve Precision Oncology
• Integrating Structural Proteomics Experimental Mass Spectrometry Data for Solving Protein Structures for Biomedical Research

• Polyelectrolyte-based Nano-actuators, Nano-tribology
• Mathematical Modeling of Complex Fluids, Polyelectrolyte, and Colloidal Solutions, and their biological applications
• Mathematical Modeling of Granular Matter, Granular Hydrodynamics and Kinetics
• Mathematical Modeling of Astrophysical Systems
• Theory of far-from-equilibrium processes and pattern formation
• Mathematical Modeling of systems of active particles and traffic modeling

• Generative modeling
• Manifold learning
• Deep learning for approximation of physical models
• Deep learning for 3D computer vision and neurovisualization

• Application of AI for early diagnosis and detection of some mental diseases
• Tensor Networks and Tensor Decomposition for Machine Learning and Deep Learning
• EEG Brain-Computer Interfaces, Human-Computer Interactions, and Human Cooperation
• Signal/Image Processing and Machine Learning Algorithms
• Portfolio Optimization and Time Series Analysis
• Time Series Forecasting Using Deep Neural Networks and Machine Learning
• Humanoid Robotics and Human-Robot Interactions

• Computational imaging
• Computer Vision
• Medical Vision
• Fundamental Aspects of Imaging

• Robotics
• Path Planning
• Perception
• Human Motion Prediction
• Dynamic Environments
• Localization
• Mapping
• Sensor Fusion

• Information theory for deep learning
• Machine learning in communications
• Coded Distributed Computing
• LDPC and Polar codes and their applications to future 5G wireless networks
• Non-orthogonal multiple access (NOMA) schemes for massive Internet of Things
• Random access protocols (coded slotted ALOHA)
• Coding for distributed and cloud storage systems
• Coding for fiber optic lines
• Post-quantum (code and lattice-based) cryptography

• Inverse and ill-posed problems of mathematical physics
• Differential equations
• Integral equations
• Mathematical modeling
• Magneto- and electroencephalography (MEG/EEG)
• Microscopy
• Tomography
• Signal and Image processing

• High-resolution mass spectrometry
• Analysis of complex natural mixtures, proteomics, metabolomics
• Gas-phase ion chemistry
• Instrumentation development and supercomputer simulation of ion optic

• Wireless Technologies
• Internet of Things
• Telecommunication systems

• Computer vision
• Visual recognition
• Biomedical image analysis

• Supercomputer modeling of ion clouds behavior in accumulation and transport mass spectrometer devices
• Further development of Particle in Cell Algorithm and Code for FT ICR signals simulation
• Development of analytical solution for the dynamically harmonized FT ICR cell
• Quantitative mass spectrometry for personalized medicine
• Investigation of microgravity influence on astronaut’s body liquid proteome and metabolome by quantitative mass spectrometry
• Omics technologies
• Development and application of on fly H/D exchange methods
• Classification analysis of organic carbon natural storages using ultrahigh accuracy mass spectrometry (Fourier Transform Ion Cyclotron Resonance Mass Spectrometry)

• Solution of multidimensional integral and differential equations discretized on fine grids
• Ab initio computations in quantum chemistry and computational material design
• Construction of reduced-order models for multiparametric systems in engineering
• Uncertainty quantification in engineering sciences
• Data mining and compression

• Reinforcement learning (RL)
• Safe AI

Topics in RL:

• Deep RL and its convergence
• Stability and safety of RL
• Predictive RL
• Fusion of image recognition and RL
• Applications of RL: robots (wheeled, legged, manipulators), economic optimization agriculture, etc.

Topic in safe AI:

• Adversarial robustness, in particular via control theory and Lyapunov methods
• Verified computation and formal verification
• Stability and safety of dynamical AI systems

• Stochastic processes and phenomena
• Target search optimization
• Machine learning applications in statistical physics
• Reinforcement learning for search optimization
• Mathematical modeling of soft matter
• Mathematical modeling of traffic problems

• Lexical semantics (especially word sense induction and disambiguation, frame induction and disambiguation, semantic similarity and relatedness, sense embeddings, automated construction and completion of lexical resources such as WordNet and FrameNet)
• Argument mining (especially comparative argument mining, and argument retrieval)
• Learning representations of linguistic symbolic structures (graphs) such as knowledge bases and lexical resource
• NLP for a better society: recognition of fake news, hate speech, and related phenomena
• Textual style transfer

• Bayesian methods in machine learning and statistics
• Uncertainty estimation for machine learning models
• Algorithms and statistical analysis of complex networks
• Gaussian processes regression
• Statistical inference, semiparametric inference

• Tensor decomposition and tensor networks for ML applications
• Deep convolutional tensor network
• Intelligent signal processing
• Tensor fusion network and multimodality analysis
• Blind Sources Separation
• Brain-Computer Interface

• Intelligent sensing and data analysis in the scope of eSports, biomedical, and precision agriculture applications.
• Power management, energy harvesting for wireless sensor networks, and wearables.

• Image analysis and its applications to medicine,
• Adaptive nonparametric smoothing and hypothesis testing,
• High dimensional data analysis,
• Statistical methods in finance and nonlinear nonstationary time series

• protein-protein interaction (PPI) inhibitors (applicable in breast and prostate cancers) and activators (Alzheimer disease);
• novel scaffolds for inhibition of evaluated target enzymes (infectious diseases);
• prediction of drug metabolism by cytochrome P450 enzymes.

• Advancing of mathematical modeling methodology & simulation techniques
• Physics-informed machine learning
• Porous structures & interfaces: characterization, thermodynamics, and transport
• Structure-property relationships in soft matter
• Statistical mechanics, especially in application to complex media and molecules

• Theoretical methods of deep learning
• Applications of machine learning to wireless communication and bioinformatics

• Neuromorphic computing with a focus on both algorithm development and hardware
• Variational quantum algorithms and quantum computing
• Computational materials science and atomistic-scale modeling

• Advanced algorithms for Bayesian optimization
• Embeddings for weakly structured data
• Adversarial attacks for categorical data
• Anomaly detection approaches

• Theory and practical algorithms for subdivision surfaces, surface deformation, and mapping
• Efficient computational methods for integral equations
• Geometric modeling
• Geometry processing
• Scientific computing