We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose influence games (IGs) as a game-theoretic (GT) model of the behavior of a large but finite networked population. IGs allow both positive and negative influence factors, permitting reversals in behavioral choices. We embrace pure-strategy Nash equilibrium (PSNE), an important solution concept in non-cooperative game theory, to formally define the stable outcomes of an IG and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the most influential individuals, and approach it algorithmically using PSNE computation. Computationally, we provide (a) complexity characterizations of various problems on IGs; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. Experimentally, we evaluate our approach using both synthetic IGs and real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. Mathematically, we connect IGs to important GT models: potential and polymatrix games.

We explore the art gallery problem for the special case that the domain (gallery) P is an mpolyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P . In particular, we show that ⌊ m+1 3 ⌋ point guards are always sufficient and sometimes necessary to cover an m-polyomino, possibly with holes. When m ≤ 3n 4 − 4, the sufficiency condition yields a strictly lower guard number than ⌊ n 4 ⌋, given by the art gallery theorem for orthogonal polygons.

Drip paintings by the American Abstract Expressionist Jackson Pollock have been analyzed through computer image methods, generally in support of authentication studies. The earliest and most thoroughly explored methods are based on an estimate of a "fractal dimension" by means of box-counting algorithms, in which the painting's image is divided into ever finer grids of boxes and the proportion of boxes containing some paint is counted. The plot of this proportion (on a log-log scale) reveals scaling or fractal properties of the work. These methods have been extended in a number of ways, including multifractal analysis, where an information measure replaces simple box paint occupancy. Recent studies suggest that it is unlikely that any single measure, including those based on such box counting, will yield highly accurate authentication; for example, a broad class of highly artificial angular sketches created in software reveal the same "fractal" properties as genuine Pollock paintings. Others have argued that this result precludes the value of such fractal-based features for such authentication. We show theoretically that even if a visual feature (taken alone) is "uninformative," such a feature can enhance discrimination when it is combined in a classifier with other features-even if these other features are themselves also individually uninformative. We describe simple classifiers for distinguishing genuine Pollocks from fakes based on multiple features such as fractal dimension, topological genus, "energy" in oriented spatial filters, and so forth. We trained linear-discriminant and nearest-neighbor classifiers using these features and found that our classifiers gave slightly improved recognition accuracy on human generated drip paintings. Most importantly, we found that although fractal features, taken alone might have low discriminative power, such features improved accuracy in multi-feature classifiers. We conclude that it is premature to reject the use of visual features based on box-counting statistics for the authentication of Pollock's dripped works, particularly if such measures are used in conjunction with multiple features, machine learning and art material studies and connoisseurship.

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