A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the detection of a subset of entities whose connectivity is anomalous with respect to the rest of the data. While the detection of such anomalous subgraphs has received a substantial amount of attention, no application-agnostic framework exists for analysis of signal detectability in graph-based data. In this paper, we describe a framework that enables such analysis using the principal eigenspace of a graph's residuals matrix, commonly called the modularity matrix in community detection. Leveraging this analytical tool, we show that the framework has a natural power metric in the spectral norm of the anomalous subgraph's adjacency matrix (signal power) and of the background graph's residuals matrix (noise power). We propose several algorithms based on spectral properties of the residuals matrix, with more computationally expensive techniques providing greater detection power. Detection and identification performance are presented for a number of signal and noise models, including clusters and bipartite foregrounds embedded into simple random backgrounds as well as graphs with community structure and realistic degree distributions. The trends observed verify intuition gleaned from other signal processing areas, such as greater detection power when the signal is embedded within a less active portion of the background. We demonstrate the utility of the proposed techniques in detecting small, highly anomalous subgraphs in real graphs derived from Internet traffic and product co-purchases.Comment: In submission to the IEEE, 16 pages, 8 figure

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1. Overarm throws made with the nondominant arm are usually less accurate than those made with the dominant arm. The objective was to determine the errors in the joint rotations associated with this inaccuracy, and thereby to gain insight into the neural mechanisms that contribute to skill in overarm throwing. 2. Overarm throws from both left and right arms were recorded on different occasions as six right-handed subjects sat with a fixed trunk and threw 150 tennis balls at about the same speed at a 6-cm square on a target grid 3 m away. Joint rotations at the shoulder, elbow, wrist, and finger, and arm translations, were computed from recordings of arm segment orientations made with the magnetic-field search-coil technique. 3. All subjects threw less accurately in this task with the left (nondominant) arm. For throws made with the left arm, the height of ball impact on the target grid was related to hand trajectory length and to hand orientation in space at ball release, but not to hand trajectory height. 4. Two hypotheses were proposed to explain the decreased ball accuracy in the high-low direction during throwing with the nondominant arm: that it was caused by increased variability in the velocity or timing of onset of rotations at proximal joints (which determine the path of the hand through space) or increased variability in the velocity or timing of onset of finger extension (which determine the moment of ball release). 5. A prediction of the first hypothesis was that proximal joint rotations should be more variable in throws with the left arm. This was the case for the majority of proximal joint rotations in the six subjects when variability was examined in joint space. However, some proximal joint rotations were more variable in the right arm. 6. The first hypothesis was directly tested by determining whether hand angular position in space (which represents the sum of all proximal joint rotations) was related to ball impact height on the target grid at a fixed translational position in the throw. No relation was found between these variables for throws with the left arm in four subjects, whereas a weak relation was found for two subjects. It was concluded that, considering all subjects, the first hypothesis could not explain the results. 7. In contrast, in agreement with the second hypothesis, a strong relation (P < 0.001) was found in all subjects between ball impact height on the target grid and time of ball release for throws with the left arm, and with time of onset of finger extension. 8. Across all six subjects the timing precision (windows) for 95% of the throws was (for ball release) right arm, 9.3 ms; left arm, 22.5 ms; (for onset of finger extension) right arm, 13.7 ms; left arm, 26.7 ms. 9. Timing of onset of finger extension was no less accurate than timing of onset of other joint rotations for both left and right arms. However, simulations of throws showed that, for the same error in timing, finger extension had twice as large an effect on ball direction as any other joint rotation. Timing e...

How precisely does the CNS control the timing of finger muscle contractions in skilled movements? For overarm throwing, it has been calculated that a ball release window of less than 1 ms is needed for accuracy in long throws. The objective was to investigate the timing precision of ball release and finge opening for 100 overarm throws made using only the arm. Subjects sat with a fixed trunk and threw balls fast and accurately at a 6-cm-square target when it was 1.5, 3.0 and 4.5 m away. Three-dimensional angular positions in space of the clavicle, upper arm, forearm, hand and distal phalanx of the middle finger were simultaneously recorded at 1000 Hz using the magnetic-field search-coil technique. Ball release was determined by pressure-sensitive microswitches on the proximal and distal phalanges of the middle finger (proximal and distal triggers). Variability of ball release, defined in terms of the standard deviation (SD) of the means of release times, was different when synchronized to different hand kinematic parameters. It was highest to the start of movement (when the hand started rotating vertically forward and up around a space-fixed horizontal axis) and was lowest when synchronized to the moment near ball release when the hand was vertical. These values did not depend on target distance. When throws were synchronized to vertical hand position, and SDs were averaged across the 10 subjects, the average interval for 95% of the throws (4xSD) was 9.6 ms for ball release and 10.0 ms for onset of finger opening. Thus, two independent measures of timing precision gave similar results. It is concluded that for 100 fast and accurate throws made by male recreational ball players, timing of finger opening and ball release was controlled precisely but not to fractions of a millisecond.

Nature’s light manipulation strategies—in particular those at the origin of bright iridescent colors—have fascinated humans for centuries. In recent decades, insights into the fundamental concepts and physics underlying biological light-matter interactions have enabled a cascade of attempts to copy nature’s optical strategies in synthetic structurally colored materials. However, despite rapid advances in bioinspired materials that emulate and exceed nature’s light manipulation abilities, we tend to create these materials via methods that have little in common with the processes used by biology. In this review, we compare the processes that enable the formation of biological photonic structures with the procedures employed by scientists and engineers to fabricate biologically inspired photonic materials. This comparison allows us to reflect upon the broader strategies employed in synthetic processes and to identify biological strategies which, if incorporated into the human palette of fabrication approaches, could significantly advance our abilities to control material structure in three dimensions across all relevant length scales.

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Graphs are canonical examples of high-dimensional non-Euclidean data sets, and are emerging as a common data structure in many fields. While there are many algorithms to analyze such data, a signal processing theory for evaluating these techniques akin to detection and estimation in the classical Euclidean setting remains to be developed. In this paper we show the conceptual advantages gained by formulating graph analysis problems in a signal processing framework by way of a practical example: detection of a subgraph embedded in a background graph. We describe an approach based on detection theory and provide empirical results indicating that the test statistic proposed has reasonable power to detect dense subgraphs in large random graphs.

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