Herr Dr. Dimitry Volchenkov: Kontakt
|1. Fakultät für Physik|
|2. Center of Excellence - Cognitive Interaction Technology CITEC|
|3. Fakultät für Physik / AG Mathematische Physik|
<a href="http://www.physik.uni-bielefeld.de/~volchenk/Resume_Volchenkov.pdf">My CV</a>
<a href="http://www.physik.uni-bielefeld.de/~volchenk/PUBLICATIONS.pdf">My Publication List</a>
My multidisciplinary research agenda is focused on the development and application of mathematical tools for
• Model fitting and data analysis (with particular research highlights on (Algebraic) Graph theory, database and networks geometrization (visualization), discrete Fourier and wavelet transforms, fractal and multifractal analysis of time series, statistical modeling and regression analysis, data cross-validation and sensitivity analysis);
• Mathematical optimization (with particular research highlights on Machine learning, multi-objective convex optimization, shape/topology/geodesics optimization, probabilistic based design optimization, stochastic approximation and optimization, entropy and energy minimization);
• Stochastic non-linear dynamics and Control (with particular research highlights on non-perturbative methods of Quantum Field theory, Self-organized criticality, (stochastic) Navier-Stocks turbulence, combustion and flame front dynamics, Magneto-hydrodynamics and plasma turbulence, vorticity confinement);
• Uncertainty, Randomness and Simulations (with particular research highlights on theory of Markov chains, Markov decision processes, probabilistic geometry, random search algorithms, evolutionary algorithms, Markov Chain Monte Carlo, numerical methods for ODE and PDE, Spectral methods).
in Applications to the various real-world complex systems, stochastic nonlinear dynamical systems of many degrees of freedom, complex urban and transportation networks, living and social systems, economic and political systems:
Probability Models of Survival, Evolution and Communication in Complex Social and Economic Systems
Probability models of subsistence and survival in precarious environments. Socio-economic models in different ecologies that would mark their inhabitants via cues to the ’faster’ versus ’slower’ behavioral strategies (the problems of HIV- and other decease prevention policy efficiency, adaptive management under uncertainty, etc.). The analysis of the historical data trends (UN Statistics Division, the Madisson Historical GDP database, the Top World Income database, Political Regime Characteristics and Transitions). The developed mathematical methods can be used for the development of optimal monitoring tools for ecological and social systems, for the analysis of biomedical data.
Volchenkov, D., "Survival under Uncertainty. An Introduction to Probability Models of Social Structure and Evolution", Springer Series in Understanding Complex Systems , ISBN 978-3-319-39419-0, Berlin / Heidelberg © 2016.
Non-perturbative methods of Quantum Field Theory in Stochastic Nonlinear Dynamics
I have studied the stochastic counterparts of nonlinear dynamical systems, in which deterministic trajectories are replaced by random trial trajectories of some well-defined stochastic processes. The proposed approach is closely related to the Nelson stochastic mechanics, the probabilistic interpretation of dynamical equations, and the critical phenomena theory. I use the non-perturbative techniques developed in the framework of quantum-field theory (renormalization group and instantons) for obtaining asymptotic solutions in the problems of stochastic non-linear dynamics. In particular, I have applied the developed methods in the theory of turbulence, for the study of tsunami waves, in magneto-hydrodynamics, and in self-organized criticality.
Volchenkov, D., “Renormalization group and instantons in stochastic nonlinear dynamics: From self-organized criticality to thermonuclear reactors.” The European Physical Journal - Special Topics 1951-6355 (Print) 1951-6401 (Online) 170(1), pp.1-142 DOI: 10.1140/epjst/e2009-01001-3 © Springer Berlin / Heidelberg (2009)
From Mathematics of Automated Data Interpretation to Mathematics of Big Data
There is currently a common dream of automated extracting generic laws of nature in economics, sociology, neuroscience, by focalizing the description of phenomena to a minimal set of variables and parameters, linked together by causal equations of evolution whose structure may reveal hidden principles. This requires a huge reduction of dimensionality (number of degrees of freedom) and a change in the level of description. The paradigmatic mathematical problem of data analysis is aggregation of individual cases/events/states in a separable metric (Polish) space into the probability distributions and lifting an empirical metric to another metric defined on distributions rather than on the events. The lifting of the empirical metric to the metric defined on distributions is known as the Monge-Kantorovich (MK) optimal transportation problem searching for minimizing the transportation costs over all available transportation plans. Many metrics known in measure theory, ergodic theory, functional analysis, land use (land prices), music (tonality scale) are the special cases of the MK- transportation metric.
Volchenkov, Dimitri, Blanchard, Philippe, "Random Walks and Diffusions on Graphs and Databases. An Introduction", Springer Series in Complexity ISBN 978-3-642-19592-1, Berlin / Heidelberg © 2011.
Mathematical analysis of urban spatial networks
Cities can be considered to be among the largest and most complex artificial networks created by human beings. At the same time the city is the ever biggest communication editor that determines not only our present social and economic wellbeing but for those generations to come, as providing an interface for our everyday mutual interactions. Sociologists think that isolation worsens an area's economic prospects by reducing opportunities for commerce, and engenders a sense of isolation in inhabitants, both of which can fuel poverty and crime. Unfortunately, urban planners and governments have often failed to take such isolation into account when shaping the city landscape, not least because isolation can sometimes be difficult to quantify in the complex fabric of a major city. Many neighborhoods are cut off from other parts of the city by poor transport links and haphazard urban planning, which can often lead to social ills. By spatial organization of urban space, we can create new rules for how the neighborhoods where people can move and meet other people face-to face by chance are fit together on a large scale in public places (such as office buildings, shops, hospitals, etc.).
Volchenkov, Dimitri, Blanchard, Philippe, "Mathematical Analysis of Urban Spatial Networks", Springer Series in Understanding Complex Systems, ISBN 978-3-540-87829-2, © 2009.
Ongoing research on Mathematics of Big Data
The proposed methodology of data analysis can be naturally generalized to the immense and heterogeneous Big Data arrays within the concept of scalable probabilistic data networks. Within the proposed approach, past and/or current data/streams are split into smaller data patches, each data patch is approximated by picking a random portion of the data patch, the probability of co-occurrence of patch fragments between the various patches is estimated. This action will order data according to probability of cross-relevance and facilitate asynchronous cross stream processing between unstructured, multimodal and diverse text streams. The same concept can be applied to diverse and multimodal streams: audio-, video- and text data streams. The key observation here is that this is a highly scalable and hierarchical concept which takes into account cross-relevance. The irrelevant patches are also grouped together and therefore, if needed, can be ignored. The proposed methodology is the key element for real-time cross processing of diverse unstructured data streams of any origin.