Dengue is a mosquito-borne viral infection that is a leading cause of serious illness and death among children and adults in many countries across the world. In Paraguay, dengue incidence has been increasing especially in urban areas, becoming endemic and epidemic in the last few years.

This work seeks to understand what factors are responsible for the epidemic and hemorrhagic varieties of dengue. Considering that collected data are of mixed nature (nominal and continuous), Categorical Principal Components Analysis (CatPCA) is adopted as a first tool. However, interpretation of CatPCA output can be challenging, partly because the same variable may appear throughout several of the principal components.

Multivariate Symmetrical Uncertainty (MSU), an entropy-based similarity measure, allows quantifying correlations in a multivariate environment and detecting both linear and nonlinear associations. In this work, the MSU measure is used in combination with CatPCA to obtain greater insight regarding the relevance of each variable.

We apply the two techniques combined in stages, using nation-wide data collected by the country's Sanitary Surveillance Department from nearly 200,000 suspected and confirmed cases throughout 5 years. The first few runs of CatPCA help to discard the less relevant attributes. A subsequent run of CatPCA provides principal components that account for a high percentage of the total variance. Working with the attribute sets identified by CatPCA, MSU finds $n$-way interactions and correlations, and groups those attributes for further selection. Segregation of attributes in disjoint groups can be done at this stage; this allows for an easier interpretation of groupings including those containing the key linear and nonlinear correlations.

The outcomes from this combined approach are better than the CatPCA alone, identifying individual and grouped variables that contribute to the behavior of the class.

In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that has been shown to exhibit several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system's many unstable periodic orbits (generally located densely around an associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero during each system’s collapse to the given period orbit. In this talk, we further discuss the role that entropy plays in chaotic entanglement. We also discuss the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. The talk will conclude with a discussion of future research directions.

Given a group of individuals inside a fluid flow (e.g., air or water) that behaves as a collective to some degree, factors like the shape of a group or the distance between its individuals can affect the forces that each individual inside the group may notice, such as drag or lift forces. Bird flocks , swarms or cycling riders are just some group behavior examples where the topology of fluid flow and information exchange affects the aerodynamics of the whole group, and may also interact with other groups or external individuals.

This group dynamics and interaction can be numerically correlated by entropy. The fundamental basis of the most of Computational Fluid Dynamics (CFD) problems is the Navier–Stokes (NS) equations, which define many single-phase fluid flows with some multi-phase flow extensions. NS equations are written as a function of the fluid velocity and pressure (in addition to other variables that describe the fluid properties), but they can also be re-written as a function of entropy . However, it is not easy to find a direct methodology that relates the entropy of a system, the fluid dynamics and the collective behavior of a system inside this fluid.

In this work we propose a method to easily calculate the entropy of a CFD solution by computing the pixels of its image based on Shannon entropy . Using the results obtained, we study the relation between information mechanics, fluid dynamics and fluid forces.

An important but difficult problem in the analysis of dynamical systems consists in determining the system's complexity, analytically and on the basis of given data. As a new approach to this problem, in 2002, Bandt and Pompe introduced the permutation entropy. Their method depends on the distribution of so called "ordinal patterns", which are based on the relative ordering between different values. Since this approach has many theoretical and practical advantages over alternative methods, it has been successfully applied to various real-world problems. However, it is still not completely understood on a theoretical level.
In this presentation we will investigate conditional variants of the permutation entropy that were first mentioned in 2014. Two closely related types of conditional permutation entropy will be considered and compared mathematically. Additionally, we will show how this conditional permutation entropy is related to the non-conditional variant. Finally, we will demonstrate why the conditional permutation entropy can be a more efficient measure for complexity than the original permutation entropy.

The orientational phase transitions occurring in a system of long straight rigid rods of length k (k-mers) on square lattices are studied by combining Monte Carlo simulations and theoretical analysis. The phenomenology of this model was examined in Refs. [1-5]. A nematic (N) phase, characterized by a big domain of parallel k-mers, is separated from a disordered-isotropic (D) state, by a continuous transition occurring at intermediate density. A second phase transition, from an N order to an ordered-isotropic (O) state, occurs near saturation density values. In the present work, the process is analyzed by following the number of accessible adsorption states along the vertical[horizontal] direction as a function of the surface coverage W_v(q)[W_h(q)], which allows us to define a vertical[horizontal] configurational entropy. These quantities show strong variations with coverage (eventually leading to ergodicity breakdown), allowing to identify the different phases (N, D and O) characterizing the critical behavior of the system. Comparisons between Monte Carlo simulations and analytical calculations were performed in order to evaluate the reaches and limitations of the theoretical model.

[1] A. Ghosh and D. Dhar, Eur. Phys. Lett. 78, 20003 (2007).

[2] D. A. Matoz-Fernandez, D. H. Linares and A. J. Ramirez-Pastor, Eur. Phys. Lett. 82, 50007 (2008).

[3] J. Kundu, R. Rajesh, D. Dhar, and J. F. Stilck, Phys. Rev. E 87, 032103 (2013).

[4] E. E. Vogel, G. Saravia, and A. J. Ramirez-Pastor, Phys. Rev E 96, 062133 (2017).

[5] E. E. Vogel, G. Saravia, A. J. Ramirez-Pastor, and P. M. Pasinetti, Phys. Rev E, in press.

Biological materials are biodegradable in nature. Consequently, it is harder to preserve their material value. Recycling these materials to its original form is difficult. Hence the material is cascaded down in its application. Cascading use implies a system in which biomass progresses through a series of uses before finally being burned to recover energy. The aim is to preserve the material quality and prioritize the use based on the maximum added value that can potentially be generated from it. For instance, sawn wood should preferably be used for building, furniture and other products with a long life span, while bioenergy should be derived from the use of wood residues. However, identifying the best valorisation routes requires appropriate measurement and monitoring tools to quantify the degree of cascading, which is still lacking.

Statistical entropy analysis (SEA) has been put forward as a method to quantify resource quality. This could be a powerful tool to assess cascading use. SEA measures the concentration of material along its life cycle and determines the efficiency of a system based on its ability to concentrate or dilute a substance. The concentration of material has been proposed as a proxy for quality; the higher the concentration of a material, the higher is its availability, and hence the higher would be its recoverability and recyclability. However, in the case of biological material, in particular wood, along with concentration product-size dictates the quality. Product-size is not considered in the traditional SEA methodologies, which limits its applicability to the biological material. The goal of this study is to adapt the SEA methodology to incorporate physical dimensionality. The adapted method, demonstrated by comparing different wood cascading scenarios in Flanders (Belgium), reveals valuable information about key drivers of quality loss in the value chain and identifies hotspots for improvement.

Developing a brain mapping for emotional changes over the brain regions remains a crucial goal for improving the process of emotional recognition. The EEGs of forty volunteer individuals were gotten while the individuals were shown seven, short video clips (i.e. anger, anxiety, disgust, happiness, sadness, surprise and neutral). The motivation of this work is twofold. First, it aims to propose the brain electrical activity mapping using the effectiveness of the multiscale fuzzy entropy () feature. Second, it aims to detect the optimal EEG channels for anger, anxiety, disgust, happiness, sadness, surprise and neutral emotional states over the brain regions (i.e. frontal, temporal, parietal and occipital) using the differential evolution-based channel selection algorithm (DEFS_Ch). The results revealed that the frontal region was statistically significant from temporal, parietal and occipital. Moreover, anger emotional state was significantly different from the other emotional states. Furthermore, the anger, sadness and anxiety were significantly different from disgust, happiness, surprise and neutral at the occipital region. For more inspection, DEFS_Ch algorithm has been used to select the most effective emotional channels over the brain regions, anger and anxiety were shared the channels in the frontal, temporal and occipital regions. Disgust was identified by the frontal, temporal, parietal and occipital channels. Sadness and disgust were identified by the channels from the frontal and temporal regions. Surprise and happiness were identified by the left frontal, parietal and occipital channels. Finally, the neutral emotional states were identified by the channels from the lateral regions of the brain particularly in right and left frontal and temporal regions. The main novelty of this study was in building up an EEG brain mapping over the brain regions for different emotional changes to help the clinician for improving the procedure of emotional recognition from the EEG signals.

Hydrothermal processes modify the chemical and mineralogical composition of a rock. These modifications can be regarded as a form of information imposed on the rock and may potentially be quantifiable. However, there are no existing single measures to quantify these effects, nor do we have a good notion of what parameters should be measured. In this presentation, concepts from information theory are used to provide new insights into the effect of hydrothermal processes on rock, which enable measurement and quantification.

We used the Shannon entropy to quantify the differences in chemical compositions, and the shortwave infrared spectral response between altered and unaltered rocks. The results showed that the Shannon entropy can capture these differences in compositions, where hydrothermally altered rocks have lower entropies compared to their precursors. A relationship was found between the heat of a magma source and Shannon entropy, where the heat of a cooling sub-volcanic intrusion drove fluid circulation in the hydrothermal system causing intense alteration of rock and a decrease in Shannon entropy. We show that the Shannon entropy has the potential to be used as a proxy for parts of the thermodynamic entropy of hydrothermally altered environments. The insights from this study enable new directions of research on the relationships between hydrothermal processes, entropies, information and the effects on mineralized and early life environments.

Complexity measures in the context of the Integrated Information Theory of consciousness, developed mainly by Tononi [7], try to asses the strength of the causal connections between different neurons. This is done by minimizing the Kullback-Leibler-Divergence between a full system and one without causal connections. Various measures have been proposed in this setting and compared in, for example, [3],[5]. Oizumi et al. develop in [6] a unified framework for these measures and postulate properties that they should fulfill. Furthermore, they introduce an important candidate of these measures, denoted by Φ, based on conditional independence statements. Unfortunately it cannot be computed analytically in general and the KL-Divergence has to be optimized numerically.

We propose an alternative approach using a latent variable which models a common exterior influence. This leads to a measure, causal information integration, that satisfies all of the required conditions provided the state space of the latent variable is large enough and it can serve as an upper bound for Φ. Our measure can be calculated using an iterative information geometric algorithm, the em-algorithm. Therefore we are able to compare its behavior to existing integrated information measures.

[1] S. Amari, N.Tsuchiya, and M. Oizumi. “Geometry of Information Integration”. In: Information Geometry and Its Applications.

[2] N. Ay. “Information Geometry on Complexity and Stochastic Interaction”. Entropy(2015).

[3] M. Kanwal, J. Grochow, and N. Ay. “Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines”. Entropy(2017).

[4] C. Langer. “Theoretical Approaches to Integrated Information and Complexity”. master thesis, 2019.

[5] P. Mediano, A. Seth, and A. Barrett. “Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation”. Entropy(2019).

[6] M. Oizumi, N. Tsuchiya, and S. Amari. “Unified framework for information integration based on information geometry”. PNAS. 2016.

[7] G. Tononi. “An information integration theory of consciousness”. BMC Neuroscience(2004).

In recent years, the theory of OT has become a fundamental tool in statistical research, e.g. the Wasserstein distance being a prominent method for inferential purposes. The large computational complexity, however, has hindered OT in becoming a routine methodology for the analysis of large scale data sets. This has encouraged the formulation of regularized OT which often turns out to be computationally more accessible. The most prominent proposal is given by entropic regularization (c.f. [1] ) that serves to define an entropic OT distance (EOTD) and Sinkhorn divergence.

In the present study, we derive limit distributions for empirical EOTD (i.e. when data are sampled randomly) between probability measures supported on countable discrete spaces. In particular, we consider a general class of cost functions and state conditions on the probability measures to ensure general weak convergence for empirical EOTD. Furthermore, for bounded cost functions we show that the empirical entropic transport plan itself converges weakly in $\ell^1$-sense to a Gaussian process. The theory generalizes results derived by [2] for finite discrete spaces. Moreover, they complement recent findings by [3] for the empirical EOTD between more general probability measures on $\mathbb{R}^m$ with quadratic cost.

Our approach is based on a sensitivity analysis of necessary and sufficient optimality conditions for the entropic transport plan. We demonstrate possible application for colocalization analysis of protein networks in biology.

This is joint work with Marcel Klatt and Axel Munk.

References:
[1] - Marco Cuturi. Sinkhorn Distances: Lightspeed Computation of Optimal Transport. In Advances in Neural Information Processing Systems 26, pages 2292-2300, 2013
[2] - Marcel Klatt, Carla Tameling, and Axel Munk. Empirical Regularized Optimal Transport: Statistical Theory and Applications. arXiv, 2018
[3] - Gonzalo Mena, and Jonathan Weed. Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem. arXiv, 2019