Many aquatic microorganisms are motile and typically swim in a moving, sometimes turbulent, fluid environment. The interaction between swimming (self-propulsion) and flow advection gives rise to interesting phenomenology, especially concerning the spatial distribution of microbes. Many aspects of such interaction can be understood by using ideas and tools from dynamical systems theory. Here we shall discuss some of these aspects mostly focusing on the case study of gyrotactic phytoplankton, which swims by means of two flagella opposite to the center of mass, which is displaced with respect to the center of symmetry --- bottom heavy cells.

The aim of our study is to develop an original approach to the modeling of battle dynamics among social animals. We focus on ant behavior, for a variety of reasons. Ants represent an important environmental actor, exhibit extraordinary strategies used to achieve their ecological success, and are individually "simple" to be studied in laboratory. Moreover, modeling ant warfare has a direct application to the monitoring of invasive species. An invasive ant species become dominant through an extraordinary cooperative behavior, an aspect of which is represented by the strategies adopted during the wars against other species. Our studies focused on two species with different fighting strategies: the invasive Lasius neglectus and the autochthonous Lasius paralienus. We performed several in vitro experiments, with a small number of ants in a limited environment (Petri dish) due to observational limits. These experiments represent the validating framework of the models developed. We started by assuming the absence of any cognitive strategy, applying the classical "chemical modeling", where all the interactions among members of the system are represented following the formalism used to represent chemical reactions. The proposed chemical model considers the ant individuals and fighting groups equivalent to atoms and molecules. We identified a system of differential non-linear equations, taking into consideration the observed groups. To reproduce the stochastic fluctuations of the observed data and to generate realistic trajectories, we considered two agent-based stochastic models, with and without a spatial distribution. With respect to other war models, our chemical model considers all phases of the battle and not only casualties. One more advantage of this approach is that all possible interactions can be outlined using a simple but biologically meaningful formalism, which provide a "microscopic" (i.e., at the individual level) description of the system, in contrast with the "macroscopic" population level description provided by classical models like Lanchester's ones. Finally, assuming that our model is a good description of the real interspecies interactions, and studying battles among more species, we can address the problem of deriving the chemical parameters from a smaller number of species-specific parameters (like aggressiveness, strength, cooperation, resistance, etc.). The possibility to have a scalable way of investigating animal fights (that may involve thousands of individuals) may have deep consequences in predicting the outcome of real combats and an important tool in predicting the successfulness of invasive species.

The Kuramoto model of coupled oscillators serves as a prototype to study spontaneous synchronization in biological and physical systems. The model involves overdamped motion of globally coupled oscillators of distributed natural frequencies. We study the model by including inertial terms and thermal noise in the dynamics. For unimodal frequency distributions, we show that the system exhibits a nonequilibrium first-order transition from a synchronized phase at low parameter values to an unsynchronized phase at high values. By interpreting the model as a system of particles interacting through long-range interaction and driven out of equilibrium by quenched external forces, we suggest how one may adopt a statistical physics perspective to study the dynamics.

TBA

I'll review some forms of collective behaviour that may emerge in various setups of neural networks, ranging from globally coupled to sparse systems, and including the possible presence of quenched disorder. Most of the attention will be devoted to the case of "simple" phase oscillators, each described by a single phase-like variable.
Analogies and differences among different classes of models will be also briefly reviewed.

In voltage driven translocation experiments (Kasianowicz et al. 1996), an applied voltage across two electrolytic cells connected through a nanopore induces the migration of macromolecules across the hole. The macromolecule engaging the pore produces detectable ion current variations that can be very informative on the physical and chemical properties of the passing species. While this experimental technique is announced to work for fast and cheap sequencing of nucleic acids, its applicability to protein molecules is still under intensive research.

An increasing accumulation of experimental data supports the view that large proteins translocate across narrow pores via a multistep process involving a sequence of dynamical bottlenecks (stall events) that, to some extent, can be considered as the fingerprint of the passing molecule. Our computer simulations on a coarse-grained model of the protein-pore system confirm the multistep scenario which results from the tight coupling between the unfolding process and the translocation dynamics. Moreover our results strongly indicate a correlation between: i) stall events of the transport dynamics, ii) ascending ramps in the free-energy profile G(Q) of a translocation reaction coordinate Q, and iii) regions of the protein richer in "backward native-contacts" (i.e. native non-bonded interactions among those aminoacids that have not yet entered the pore).

We thus can argue that the sequence and nature of such bottlenecks might have a simple and univocal interpretation in terms of the structural properties of the protein native-state. Therefore, inference on the presence of a multistep translocation dynamics of proteins can be done from the knowledge of their native-state topology. In a possible inverse scenario, we guess that the correlation between stalls and protein structural elements would allow to distinguish protein motives and domains from the detection of stalls during the translocation dynamics.

The process of pattern formation for reaction-diffusion systems defined on complex networks is discussed. According to the deterministic picture, partial differential equations are assumed to govern the evolution of the concentrations of the interacting species that populate the nodes of the network. A small perturbation of a homogeneous fixed point can spontaneously amplify as follow a symmetry breaking instability and eventually yield to asymptotically stable non homogeneous patterns, the celebrated Turing patterns. Traveling waves can also manifest as a byproduct of the instability. Beyond the deterministic scenario, single individual effects, stemming from the intimate discreteness of the analyzed medium, prove crucial by significantly modifying the mean-field predictions. The stochastic component of the microscopic dynamics can in particular induce the emergence of regular macroscopic patterns, in time and space, outside the region of deterministic instability. To gain insight into the role of fluctuations and eventually work out the conditions for the emergence of stochastic patterns, one can operate under the linear noise approximations scheme adapted to network based applications, as I shall discuss. Furthermore, I will also consider reaction-diffusion models defined on a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts, at variance with the conventional case for a symmetric network. It is found that the homogeneous fixed point can become unstable due to the topology of the network, resulting in a new class of instabilities which cannot be induced on undirected graphs.

Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. I will show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology I will discuss in this seminar