The understanding of disease outbreaks, as well the prevalence and lifetime of contagious diseases have become a challenge in biomedical sciences. The unavoidable difficulties in poorest populations to access valuable medical triages together with the lack of policies to inspect the reported cases in controlled populations, drive to a shortage of the quality of the recorded datasets. Although different interdisciplinary perspectives have been proposed to understand the dynamics of different diseases, recent advances in the understanding of complex systems dynamics suggest alternative viewpoints that may enhance our understanding of the problem. Under this framework, we propose an aggregated-data-based model that shows how the persistence of events in disease outbreaks follows specific progressions that can be identified and characterized thanks to the analysis of the temporal patterns encoded in the number of infected individuals. Our methodology considers aggregated data as the seminal information to extract either the level of complexity and entropy (local and global) of the evolution of a disease, as well as the distribution of hidden temporal patterns. Beyond focusing on a single disease and, with the aim of gaining general intuition about the results of the proposed methodology, we consider different diseases and track their similarities and divergences. Additionally, we build up directed weighted networks associated to the disease dynamics, in which the nodes (edges) represent specific temporal events (progressions between consecutive events). This way, we can study the role of each node (pattern) in the diseases considered, as well as the structure of the complex network related to the disease temporal patterns and find, for instance, the existence of common persistent events (hubs). In this scenario, we identify similarities in the structure of networks associated to different outbreaks and make a dynamical and topological characterization of such networks. These results lead to the primary conclusion that, in general, disease outbreaks maintain specific ordinal patterns, which is translated to specific values of statistical complexity and permutation entropy, when the whole symbolic network is analyzed. Furthermore, there are particular nodes that have an important role in the system which depend on the particular disease considered. Lastly, we consider the possible relations between dynamical-topological-prevalence variables.

Most chimera states to date require global coupling to produce co-stable solutions. We present here a system that can lead to up to 4 different co-existing solutions  in a system composed of identical oscillators only coupled by diffusion. The single oscillatory system is based on the saline oscillator. In this talk, we first demonstrate the bi-stability of this system experimental as a function of initial conditions and perturbations with a given strength and phase. Then create a mathematical model for this system that when coupled in 1 and 2D by just diffusion allows the existence of up to 4 different solutions co-existing in space at the same time.

Neuronal cultures offer a unique platform to study collective
phenomena in neuronal networks. The ability of experimentalists to
modify the connectivity among neurons and their dynamics offer a
unique scenario to investigate key open questions in neuroscience,
including the emergence of spontaneous activity patterns, the
importance of spatial embedding, network connectivity, and the
resilience of the networks to damage. Here I will present
different experiments and theoretic-numerical resources to shed light
on these questions. In particular, I will pinpoint the potential of
effective connectivity inference to characterize the behavior of
neuronal networks affected by Sanfilippo, Alzheimer’s and other
diseases.

Synchrotron radiation facilities are sources using the light
emitted by relativistic electron bunches and dedicated to various
users of THz, VUV and X-ray radiation. The power delivered generally
depends of the electron-bunch charge, and synchrotron radiation
facilities tend to use electron bunches with the highest possible
charge density.

However, at high charge density, a spatio-temporal instability affects
the electron-bunches in most facilities \cite{1} (e.g. ALS in Berkeley,
BESSY in Berlin, DIAMOND in UK, SOLEIL in France \cite{2} , etc). This
instability has a fondamental origin: it comes from the interaction of
the electron bunch with its own radiated electric field. As a
consequence, microstructures appear in the longitudinal direction of
the bunch with a complex temporal evolution.

Here, we present the first results on the control of those
instabilities using a feedback method. The strategy is directly
inspired from chaos control method (In particular from the OGY and Pyragas
methods). The idea is to stabilized a pre-existing unstable periodic
solution. A feedback system continuously applies small perturbations
on one of accelerator parameters in function of the deviation between
the unstable solution and the system state. After numerical studies on
the system model (Fokker-Planck-Vlasov equations), we succeeded to
experimentally control this instability at synchrotron SOLEIL
(France). To this purpose, we used a rather simple elecronic feedback
system (base on a FPGA board). We will present the results as well as
the open questions (from the dynamical point of view) raised by this
study.

\begin{thebibliography}{10}
\bibitem{1} Beam instability and microbunching due to coherent synchrotron radiation, G. Stupakov and S. Heifets, Phys. Rev. ST Accel. Beams, 5, 054402 (2002)
\bibitem{2} Direct observation of spatiotemporal dynamics of short electron bunches in storage rings, C Evain, E Roussel, M Le Parquier, C Szwaj, M-A Tordeux, J-B Brubach, L Manceron, P Roy, S Bielawski, Phys. Rev. Lett. 118, 054801 (2017).
\end{thebibliography}

I describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.