Description Advection is a transport mechanism where substances are passively conveyed by bulk flows. It plays important roles in a wide range of research fields. The flow pattern is generally given and not influenced by variations in particles' concentration. Note that there are also many situations where flows are passing over connections between discrete nodes constituting a network. An obvious example is provided by pipelines, which is used for delivery of gas, oil, or pollutant to a set of destinations. Another example should be given by the transportation. Traffic flows are established by trains, ships or aircraft on a regular scheduled service between rail stations, ocean harbours or airports. It is however remarkable that advection equation for networks have not been so far mathematically formulated. In this talk, we present a mathematical formulation of the advection equation for network-organized systems. The network-advection equation is derived under two assumptions: (i) The flow pattern is stationary and, for each node, total incoming and outgoing flows are equal. (ii) The particles can be only transported together with a flow, so that the transition probability from one node to another is proportional to the intensity of the flow passing through the respective link.

Speaker
Antoni Luque

Description Abstract.- In humans, each cell condenses two meters of genomic DNA in the nucleus, using a cohort of proteins like core histones and linker histones. This forms chromatin, a macromolecular complex present in all eukaryotes. Chromatin is composed of nucleosomes, nanometric beads made of DNA and eight core histones. Consecutive nucleosomes are connected by DNA linkers and form chromatin fibers that fold into hierarchical structures, constituting the chromosomes. Experimental techniques have characterized at great detail the structure of chromatin at the nucleosome and chromosome level. But the intermediate scales of chromatin remain elusive. Here, I will present a computational model that has been developed for more than a decade and captures the mesoscale properties of chromatin fibers. In particular, I will discuss a physical mechanism promoted by linker histones that regulate the coexistence of two controversial chromatin structures: 30-nm fibers and 10-nm interdigitated fibers. I will also introduce a refined linker histone model that captures the spontaneous condensation of the linker histone C-terminal domainupon nucleosome binding and explains the impact of linker histone on chromatin structure. Our findings are in excellent agreement with independent experiments and provide a framework to understand local and global mechanisms regulating chromatin organization, like post-translational modifications and the interplay between linker histones and linker DNA length.

Description Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of discrete equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton. The presentation will emphasize mathematical structure and properties of the model. References: Bia?ecki M. (2012) Motzkin numbers out of Random Domino Automaton Phys. Lett. A 376 (2012) 3098-3100. Bia?ecki M. and Z. Czechowski (2013) On one-to-one dependence of rebound parameters on statistics of clusters: exponential and inverse-power distributions out of Random Domino Automaton J. Phys. Soc. Jpn. 82 (2013) 014003.

Speaker
Julia Poncela

Description Adoption of innovations, whether new ideas, technologies, or products, is crucially important in knowledge societies. Studies of adoption of innovations have generally focused on products with little societal impact (such as online apps) and, even if large-scale and real-world based, on heterogeneous populations. These limitations have so far hindered the development and testing of a mechanistic understanding of the adoption process. In this work, we experimentally study the adoption by critical care physicians of a medical innovation that complements current protocols for the diagnosis of life-threatening bacterial infections. We show through computational modeling of the experiment that infection spreading models – which have been formalized as generalized contagion processes – are not consistent with the experimental data. Instead, we find that a “persuasion” model inspired by opinion models is better able to reproduce the empirical data, providing insight into the mechanism of innovation adoption within this homogeneous population of highly-trained professionals. Using our model, we also propose an intervention scheme and show its possible impact on increasing the rate and robustness of innovation adoption in the real-world.