Information flow in a kinetic ising model peaks in the disordered phase

There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition

Convex Rank Tests and Semigraphoids

Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the linear extensions of a partially ordered set specified by data. Our methods refine existing rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for exploratory analysis of ordinal data. We establish a bijection between convex rank tests and probabilistic conditional independence structures known as semigraphoids. The subclass of submodular rank tests is derived from faces of the cone of submodular functions, or from Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Of particular interest are graphical tests, which correspond to both graphical models and to graph associahedra

Marginals of DAG-Isomorphic Independence Models

Probabilistic and graphical independence models both satisfy the semi-graphoid axioms, but their respective modelling powers are not equal. For every graphical independence model that is represented by d-separation in a directed acyclic graph, there exists an isomorphic probabilistic independence model, i.e. it has exactly the same independence statements. The reverse does not hold, as there exist probability distributions for which there are no perfect maps. We investigate if a given probabilistic independence model can be augmented with latent variables to a new independence model that is isomorphic with a graphical independence model of a directed acyclic graph. The original independence model can then be viewed as the marginal of the model with latent variables. We show that for some independence models we need infinitely many latent variables to accomplish this

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease in entropy for the joint distribution of $N$ variables relative to the maximum entropy allowed by all the observed $N-1$ variable distributions. We calculate the ``connected information'' terms for several examples, and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.Comment: 4 pages, 3 figure

Detecting unknown attacks in wireless sensor networks that contain mobile nodes

As wireless sensor networks are usually deployed in unattended areas, security policies cannot be updated in a timely fashion upon identification of new attacks. This gives enough time for attackers to cause significant damage. Thus, it is of great importance to provide protection from unknown attacks. However, existing solutions are mostly concentrated on known attacks. On the other hand, mobility can make the sensor network more resilient to failures, reactive to events, and able to support disparate missions with a common set of sensors, yet the problem of security becomes more complicated. In order to address the issue of security in networks with mobile nodes, we propose a machine learning solution for anomaly detection along with the feature extraction process that tries to detect temporal and spatial inconsistencies in the sequences of sensed values and the routing paths used to forward these values to the base station. We also propose a special way to treat mobile nodes, which is the main novelty of this work. The data produced in the presence of an attacker are treated as outliers, and detected using clustering techniques. These techniques are further coupled with a reputation system, in this way isolating compromised nodes in timely fashion. The proposal exhibits good performances at detecting and confining previously unseen attacks, including the cases when mobile nodes are compromised

Assessing the Influence of Different ROI Selection Strategies on Functional Connectivity Analyses of fMRI Data Acquired During Steady-State Conditions

In blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI), assessing functional connectivity between and within brain networks from datasets acquired during steady-state conditions has become increasingly common. However, in contrast to connectivity analyses based on task-evoked signal changes, selecting the optimal spatial location of the regions of interest (ROIs) whose timecourses will be extracted and used in subsequent analyses is not straightforward. Moreover, it is also unknown how different choices of the precise anatomical locations within given brain regions influence the estimates of functional connectivity under steady-state conditions. The objective of the present study was to assess the variability in estimates of functional connectivity induced by different anatomical choices of ROI locations for a given brain network. We here targeted the default mode network (DMN) sampled during both resting-state and a continuous verbal 2-back working memory task to compare four different methods to extract ROIs in terms of ROI features (spatial overlap, spatial functional heterogeneity), signal features (signal distribution, mean, variance, correlation) as well as strength of functional connectivity as a function of condition. We show that, while different ROI selection methods produced quantitatively different results, all tested ROI selection methods agreed on the final conclusion that functional connectivity within the DMN decreased during the continuous working memory task compared to rest