Target Search Problems

This book presents cutting-edge research addressing the mathematical models used to tackle the "Target problem" as it manifests itself in a wide range of disciplines. Leading international experts from around the world describe a variety of different approaches to this truly multidisciplinary topic. 

Recent years have witnessed a substantial and still growing interest in understanding the general "Target problem". This encompasses a wide range of different situations in which some "agents" perform a deterministic or stochastic motion to search for a certain immobile or mobile "target". Such problems arise in many disciplines: to name but a few, computer science, the evolution of stock markets, biochemistry, bio-medicine, evolutionary games, as well as diverse areas of physics. This book with its up-to-date collection of chapters authored by leading experts in these and other fields, provides a comprehensive and complete picture in broadlyaccessible language.

The book will naturally serve as a source of inspiration for further research, as well as facilitating a cross-fertilization of approaches, ideas, and research directions.

Denis Grebenkov studied physics at the Department of Statistical Physics in Saint Petersburg State University (1995-1999). After receiving his Bachelor of Science in Physics with honors, Denis Grebenkov moved to Ecole Polytechnique in Paris, France, for the master program in theoretical physics (1999-2001), where he later obtained the PhD degree on theoretical physics specialized in Laplacian transport towards irregular interfaces under supervision by Professors Bernard Sapoval and Marcel Filoche (2001-2004). In parallel, he continued scientific research on a thermodynamic theory of relaxations in micellar solutions and obtained another PhD degree on statistical physics from Saint Petersburg State University under supervision of Professor Alexander Grinin (2001-2003). From 2004 to 2005 Denis Grebenkov was a post-doc in the experimental group of Dr. Geneviève Guillot at the University of Orsay (France) and studied confined diffusion of hyperpolarized helium-3 in the human pulmonary acinus for improving emphysema diagnostic. Then he got a Marie Curie postdoc position at the University of Naples (Italy) and worked on complex systems exhibiting a structural arrest in the field of soft and colloidal matter in the group of Professor Antonio Coniglio (2005-2006). In 2006, Denis Grebenkov obtained a permanent research position at CNRS (France) in the laboratory of Condensed Matter Physics. He received several prices and distinctions such as the Best PhD award from Ecole Polytechnique (2004), Giulio Cesare Borgia Prize for fundamental contributions to diffusion nuclear magnetic resonance (2010), Bronze Medal CNRS (2012), and Friedrich Wilhelm Bessel Research Award from the Alexander von Humboldt Foundation (2019). Denis Grebenkov authored 183 publications.
Denis Grebenkov investigates various diffusion-mediated phenomena in complex media, e.g., intracellular transport and cell signaling, transport in human organs, diffusion-controlled reactions in industrial devices. Two related fundamental questions are at the heart of this research: how the geometric complexity of a system affects its transport properties and functions, and what the observed diffusion characteristics can tell us about the geometric structure. To solve these forward and inverse problems, Denis Grebenkov employs various theoretical tools from statistical physics, probability, spectral theory, mathematical physics, theory of differential equations, etc. In parallel, he develops advanced numerical techniques (Monte Carlo simulations, finite-element methods, spectral methods, etc.) to incorporate the geometric complexity of natural and industrial systems and to bridge the gap between theory and applications.

Ralf Metzler studied physics at the University of Ulm (1989-1994) where he also obtained his PhD degree on anomalous dynamical phenomena with Theo Nonnenmacher. From 1998 to 2000 Ralf was a postdoc at Tel Aviv University, working with Yossi Klafter, and from 2000 to 2002 he was at MIT with Mehran Kardar. In 2002 Ralf was appointed as assistant professor (non tenure-track) at NORDITA (Nordic Institute for Theoretical Physics) in Copenhagen. In 2006 he became associate professor and Canada Research Chair in Biological Physics at the University of Ottawa. From 2007 Ralf was professor at Technical University of Munich, and since 2011 he is full professor for Theoretical Physics at the University of Potsdam. During 2010-2015 Ralf was also Finland Distinguished Professor (Academy of Finland) at Tampere University of Technology. From 2019-2022 Ralf was Alexander von Humboldt Honorary Research Scholar at Wroclaw University of Science and Technology, and in 2023 he was Heilbronn Distinguished Visiting Fellow in ISAAC Cambridge and University of Bristol, as well as Distinguished Visiting Professor at the Indian Institute of Technology Bombay. Currently is APCTP distinguished fellow at the Asia Pacific Center for Theoretical Physics, Pohang, Korea.
The Metzler group mainly focuses on the modelling of diffusive transport in complex environments. These range from multi-scale molecular reaction time distributions relevant for biochemical signalling in cells and cellular colonies, to passive and active stochastic motion in heterogeneous systems such as cells or membranes, and up to large-scale systems such as groundwater aquifers or animal motion. General themes are anomalous diffusion based on different physical mechanisms, non-Gaussianity, and trajectory-to-trajectory fluctuations. Technically, we use probabilistic approaches and simulations. We also actively collaborate with a number of experimental single-particle tracking groups. To analyse data we are developing classical statistical observables as well as Bayesian and deep learning techniques. On top of these research lines we also study passive and active soft matter systems with respect to crowding effects and heterogeneity of the environment.
Ralf Metzler has published more than 400 journal papers which have garnered more than 35,000 citations; his Hirsch index is 85 (Scopus).

Dr Gleb Oshanin studied physics at Moscow State University (1980-1986) and obtained his Ph. D. degree in 1989 from the Institute of Chemical Physics for the Thesis entitled "Kinetics of many-body diffusion controlled processes". He was an associated researcher at French CNRS in 1992 - 1993 affiliated at the Laboratory for Theoretical Physics of Liquids at the University Pierre and Marie Curie, and subsequently in 1993-1994 was a Humboldt research fellow at the University of Freiburg. In 1995 - 1996 he was an invited Professor at the University of Mons-Hainaut in Belgium. In 1997 he obtained a staff position at CNRS and is currently a CNRS research director affiliated at the Theoretical Condensed Matter Laboratory at Sorbonne University.
Dr. Gleb Oshanin is an author of more than 200 scientific publications. His fields of expertise cover quite diverse subjects, such as, e.g. wetting phenomena, systems with reaction-diffusion processes, systems of interacting particles, first-passage phenomena and extreme events in stochastic processes, algorithms of efficient search processes, and etc.