Speaker
Nicolas Rubido

Description The relation between structure and function is one of the most studied topics in the theory of complex networks. The structure is a topological representation of the interacting elements forming a network and it is rigorously described by the theory of graphs. The function is related to how the network units interact, exchange information, or dynamically evolve. The work I am presenting deals with analytical solutions for flow networks that satisfy conservation laws [1]. The model for the flow network is stated in terms of resistor networks (weighted symmetric graphs), which have a source node s and a sink node t feeding the system, and a linear relationship between loads (voltages) and flows (currents). Its solutions establish a clear relationship between the topological structure of the networks (namely, adjacency matrix and edge weights, assumed known) and the functional flows passing through nodes and edges (that are a consequence of solving the flow model). [1] Nicolás Rubido, Celso Grebogi and Murilo S. Baptista, EPL, 101 (2013) 68001

Speaker
Stefan Thurner

Description In information theory the so-called 4 Shannon-Khinchin (SK) axioms uniquely determine Boltzmann-Gibbs entropy as the one and only possible entropy. Physics (and social systems in particular) are different from information theory in the sense that such systems can be non-ergodic. Many complex systems in fact are. To describe strongly interacting statistical non-ergodic systems (i.e. complex systems) within a thermodynamical framework, it becomes necessary to introduce generalized entropies. A number of such entropies have been proposed in the past. The understanding of the fundamental origin of these entropies and its deeper relations to complex systems has remained unclear. Non-ergodicity explicitly violates the fourth SK axiom. We show that violating this axiom and keeping the other three axioms intact, determines an explicit form of a more general entropy, $S\sim \sum_i \Gamma (d+1,1-c\log p_i)$, uniquely describing a statistical system; $c$ and $d$ are scaling exponents,Gamma is the incomplete Gamma function. All recently proposed entropies appear to be special cases. We prove that each (!) statistical system is uniquely characterized by the pair of the two scaling exponents (c,d), which define equivalence classes for all (!) interacting and non-interacting systems, and that no other possibilities for entropies exist. The corresponding distribution functions are special forms of so-called Lambert-W exponentials, containing as special cases Boltzmann, stretched exponential and Tsallis distributions(power-laws) all abundant in nature. We show how the phasespace volume of a system is related to its(generalized) entropy and illustrate this with physical examples of spin systems on constant-connectency networks and accelerating random walks.

Speaker
Gijs Wuite

Description Homologous recombination is essential for the preservation of genome stability. The core protein in this process, RAD51, drives homology search and DNA strand exchange, processes that requires the nucleation, assembly and disassembly (collapse) of a RAD51 filament on single-stranded (ss) and double-stranded (ds)DNA, coupled to ATP binding and hydrolysis. Here we show that we can characterize all these RAD51 DNA transactions on long individual DNA molecules, in real-time, at the single-protein level using a combination of single-molecule fluorescence microscopy and optical tweezers. These experiments show that the sizes of RAD51 nuclei on ssDNA vary and display a broad Poissonian distribution with an average size of 4 monomers. Filament extension tracked in time with single-protein resolution reveals that nuclei extend by one RAD51 monomer at a time with a rate independent of tension on the ssDNA. This is in contrast to force-dependent monomeric extension on dsDNA. Counting and timing individual RAD51 monomers disassembling from nucleoprotein filament on ssDNA also yields contrasting results compared with dsDNA, reflecting the difference in the underlying mechanical properties ssDNA and dsDNA based nucleoprotein filaments. Together, these results yield unprecedented quantitative insight in the mechanical rearrangement during formation and collapse of RAD51 nucleoprotein filaments.

Description

The structure of this school + workshop will be: 1) School Courses: - Dynamics of Complex Systems (intermittency, stability, etc.). Henrik J. Jensen, Imperial College London. - Critical Phenomena and Percolation Theory. Kim Christensen, Imperial College London. - Percolation in Complex Networks. Marián Boguñá, Universitat de Barcelona - Non-Equilibrium Phase Transitions, Field Theory and Self-Organised Criticality. Gunnar Pruessner, Imperial College London, - Complex Networks and Hidden Metric Spaces: Internet, Metabolic Networks… M. Ángeles Serrano, Universitat de Barcelona. - Multifractal Formalism: from models for turbulent flows to applications in ocean remote sensing. Antonio Turiel, Institut de Ciències del Mar, Barcelona. 2) Problem-solving classes: directly related to the contents of the courses. 3) Plenary lecture, by Stefan Thurner, Medical University of Vienna 4) Contributed Talks 5) Posters Important deadlines: January 27, 2013 (lodging and registration grant application) March 8, 2013 (contributed talks and posters) March 18, 2013 (registration and payment) If you wish to submit a talk or a poster, please send the required information to Ms Núria Hernandez (nhernandez@crm.cat) It is possible to attend the school or the workshop separately

Organizers
Centre de Recerca Matematica

Speaker
Esther Ibáñez

Description There is a complex relationship between genotype and phenotype. One of the outstanding features of this map is that is not a one-to-one map, because many genotypes are compatible with the same phenotype. Whereas genes are the entities passed on from one generation to the next and their frequencies measured over populations (the remit of population genetics), selection acts at the level of phenotypes. Thus, assigning fitness values to genes (mutant variants, di erent alleles, etc.) is not, in general, the valid approach. We are trying to put forward some of new properties we may expect to emerge when the genotype- phenotype di erence is taken into account, both in a general setting and in particular cases related to disease. We have been focused on formulating models of evolutionary dynamical processes with genotype-phenotype map, give a de nition of phenotype based on the attractors of simple models of the dynamics gene regulatory networks, and simulate it in order to ascertain its dynamical properties. We have introduced a bipartite network to study genotype and phenotype together and their structural relationship. Also a way to understand their structure is to study their clustering coeficient, existence of communities, which are related to phenotypic robustness, or connectivity between communities (it means, innovation).