In situ analysis for intelligent control

We report a pilot study on in situ analysis of backscatter data for intelligent control of a scientific instrument on an Autonomous Underwater Vehicle (AUV) carried out at the Monterey Bay Aquarium Research Institute (MBARI). The objective of the study is to investigate techniques which use machine intelligence to enable event-response scenarios. Specifically we analyse a set of techniques for automated sample acquisition in the water-column using an electro-mechanical "Gulper", designed at MBARI. This is a syringe-like sampling device, carried onboard an AUV. The techniques we use in this study are clustering algorithms, intended to identify the important distinguishing characteristics of bodies of points within a data sample. We demonstrate that the complementary features of two clustering approaches can offer robust identification of interesting features in the water-column, which, in turn, can support automatic event-response control in the use of the Gulper

Quasi-morphisms and L^p-metrics on groups of volume-preserving diffeomorphisms

Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. We show that every homogeneous quasi-morphism on the identity component $Diff_0(M,vol)$ of the group of volume preserving diffeomorphisms of M, which is induced by a quasi-morphism on the fundamental group, is Lipschitz with respect to the L^p-metric on the group $Diff_0(M,vol)$. As a consequence, assuming certain conditions on the fundamental group, we construct bi-Lipschitz embeddings of finite dimensional vector spaces into $Diff_0(M,vol)$.Comment: This is a published versio

Capillary origami: spontaneous wrapping of a droplet with an elastic sheet

The interaction between elasticity and capillarity is used to produce three dimensional structures, through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tayloring the initial geometry of the flat membrane. A 2D model shows the evolution of open sheets to closed structures and predicts a critical length scale below which encapsulation cannot occur, which is verified experimentally. This {\it elastocapillary length} is found to depend on the thickness as $h^{3/2}$, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nano-scale objects.Comment: 5 pages, 5 figure

Do logarithmic proximity measures outperform plain ones in graph clustering?

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.Comment: 11 pages, 5 tables, 9 figures. Accepted for publication in the Proceedings of 6th International Conference on Network Analysis, May 26-28, 2016, Nizhny Novgorod, Russi

Anxiety: An Evolutionary Approach

Anxiety disorders are among the most common mental illnesses, with huge attendant suffering. Current treatments are not universally effective, suggesting that a deeper understanding of the causes of anxiety is needed. To understand anxiety disorders better, it is first necessary to understand the normal anxiety response. This entails considering its evolutionary function as well as the mechanisms underlying it. We argue that the function of the human anxiety response, and homologues in other species, is to prepare the individual to detect and deal with threats. We use a signal detection framework to show that the threshold for expressing the anxiety response ought to vary with the probability of threats occurring, and the individual's vulnerability to them if they do occur. These predictions are consistent with major patterns in the epidemiology of anxiety. Implications for research and treatment are discussed

Statistical properties of eigenstate amplitudes in complex quantum systems

We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wavefunction amplitudes in a real-space basis. For single-particle 'quantum billiards', these real-space amplitudes are known to have Gaussian distribution for chaotic systems. In this work, we formulate and address the corresponding question for many-body lattice quantum systems. For integrable many-body systems, we examine the deviation from Gaussianity and provide evidence that the distribution generically tends toward power-law behavior in the limit of large sizes. We relate the deviation from Gaussianity to the entanglement content of many-body eigenstates. For integrable billiards, we find several cases where the distribution has power-law tails.Comment: revised version, with appendices; 15 pages, 10 figure