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We develop algorithms to control the scope of an infection spread on a network by allocating a fixed immunization budget to edges of the graph. We assume that the infection propagates according to an independent cascade model and interventions operate by reducing the propensities of edges to transmit the infection. We formulate this problem as a constrained min-max optimization problem with respect to the placements of interventions and the location of the worst-case seed nodes. However, the result is a challenging bilevel mixed integer optimization problem. Furthermore, gradients of the objective function with respect to the continuous variables are unavailable in closed form. We employ tools from derivative-free optimization and stochastic optimization to optimize the objective by iterating between the outer minimization and inner maximization problems. In the inner loop, we use a weighted degree discount (WDD) method to select the seed set of the influence maximization problem. In the outer loop, we utilize two methods: a sample-based simultaneous perturbation Nelder-Mead (SBSP-NM) algorithm and a simultaneous perturbation stochastic approximation (SPSA) algorithm. We perform simulations on synthetic graphs and three larger-scale real-world datasets and illustrate the computational feasibility of our algorithms and their efficacy at controlling epidemic spreads.

Despite the established effectiveness of the brain-computer interface (BCI) therapy during stroke rehabilitation (Song et al., 2014a, 2015; Young et al., 2014a,b,c, 2015; Remsik et al., 2016), little is understood about the connections between motor network reorganization and functional motor improvements. The aim of this study was to investigate changes in the network reorganization of the motor cortex during BCI therapy. Graph theoretical approaches are used on resting-state functional magnetic resonance imaging (fMRI) data acquired from stroke patients to evaluate these changes. Correlations between changes in graph measurements and behavioral measurements were also examined. Right hemisphere chronic stroke patients (average time from stroke onset = 38.23 months, standard deviation (SD) = 46.27 months, n = 13, 6 males, 10 right-handed) with upper-extremity motor deficits received interventional rehabilitation therapy using a closed-loop neurofeedback BCI device. Eyes-closed resting-state fMRI (rs-fMRI) scans, along with T-1 weighted anatomical scans on 3.0T MRI scanners were collected from these patients at four test points. Immediate therapeutic effects were investigated by comparing pre and post-therapy results. Results displayed that th average clustering coefficient of the motor network increased significantly from pre to post-therapy. Furthermore, increased regional centrality of ipsilesional primary motor area (p = 0.02) and decreases in regional centrality of contralesional thalamus (p = 0.05), basal ganglia (p = 0.05 in betweenness centrality analysis and p = 0.03 for degree centrality), and dentate nucleus (p = 0.03) were observed (uncorrected). These findings suggest an overall trend toward significance in terms of involvement of these regions. Increased centrality of primary motor area may indicate increased efficiency within its interactive network as an effect of BCI therapy. Notably, changes in centrality of the bilateral cerebellum regions have strong correlations with both clinical variables [the Action Research Arm Test (ARAT), and the Nine-Hole Peg Test (9-HPT)]

In recent years, tools from information theory have played an increasingly prevalent role in statistical machine learning. In addition to developing efficient, computationally feasible algorithms for analyzing complex datasets, it is of theoretical importance to determine whether such algorithms are “optimal” in the sense that no other algorithm can lead to smaller statistical error. This paper provides a survey of various techniques used to derive information-theoretic lower bounds for estimation and learning. We focus on the settings of parameter and function estimation, community recovery, and online learning for multi-armed bandits. A common theme is that lower bounds are established by relating the statistical learning problem to a channel decoding problem, for which lower bounds may be derived involving information-theoretic quantities such as the mutual information, total variation distance, and Kullback–Leibler divergence. We close by discussing the use of information-theoretic quantities to measure independence in machine learning applications ranging from causality to medical imaging, and mention techniques for estimating these quantities efficiently in a data-driven manner.