Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems

Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities

The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.Comment: 18 pages, 5 figures, pdfLatex, RevTe

Seeing with sound? Exploring different characteristics of a visual-to-auditory sensory substitution device

Sensory substitution devices convert live visual images into auditory signals, for example with a web camera (to record the images), a computer (to perform the conversion) and headphones (to listen to the sounds). In a series of three experiments, the performance of one such device (‘The vOICe’) was assessed under various conditions on blindfolded sighted participants. The main task that we used involved identifying and locating objects placed on a table by holding a webcam (like a flashlight) or wearing it on the head (like a miner’s light). Identifying objects on a table was easier with a hand-held device, but locating the objects was easier with a head-mounted device. Brightness converted into loudness was less effective than the reverse contrast (dark being loud), suggesting that performance under these conditions (natural indoor lighting, novice users) is related more to the properties of the auditory signal (ie the amount of noise in it) than the cross-modal association between loudness and brightness. Individual differences in musical memory (detecting pitch changes in two sequences of notes) was related to the time taken to identify or recognise objects, but individual differences in self-reported vividness of visual imagery did not reliably predict performance across the experiments. In general, the results suggest that the auditory characteristics of the device may be more important for initial learning than visual associations

Persistent detwinning of iron pnictides by small magnetic fields

Our comprehensive study on EuFe$_2$As$_2$ reveals a dramatic reduction of magnetic detwinning fields compared to other AFe$_2$As$_2$ (A = Ba, Sr, Ca) iron pnictides by indirect magneto-elastic coupling of the Eu$^{2+}$ ions. We find that only 0.1T are sufficient for persistent detwinning below the local Eu$^{2+}$ ordering; above $T_\text{Eu}$ = 19K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetrybreaking external force.Comment: accepted by Physical Review Letter

Influence of changing carbonate chemistry on morphology and weight of coccoliths formed by Emiliania huxleyi

The coccolithophore Emiliania huxleyi is a marine phytoplankton species capable of forming small calcium carbonate scales (coccoliths) which cover the organic part of the cell. Calcification rates of E. huxleyi are known to be sensitive to changes in seawater carbonate chemistry. It has, however, not yet been clearly determined how these changes are reflected in size and weight of individual coccoliths and which specific parameter(s) of the carbonate system drive morphological modifications. Here, we compare data on coccolith size, weight, and malformation from a set of five experiments with a large diversity of carbonate chemistry conditions. This diversity allows distinguishing the influence of individual carbonate chemistry parameters such as carbon dioxide (CO2), bicarbonate (HCO3−), carbonate ion (CO32−), and protons (H+) on the measured parameters. Measurements of fine-scale morphological structures reveal an increase of coccolith malformation with decreasing pH suggesting that H+ is the major factor causing malformations. Coccolith distal shield area varies from about 5 to 11 μm2. Changes in size seem to be mainly induced by varying [HCO3−] and [H+] although influence of [CO32−] cannot be entirely ruled out. Changes in coccolith weight were proportional to changes in size. Increasing CaCO3 production rates are reflected in an increase in coccolith weight and an increase of the number of coccoliths formed per unit time. The combined investigation of morphological features and coccolith production rates presented in this study may help to interpret data derived from sediment cores, where coccolith morphology is used to reconstruct calcification rates in the water column

Second order perturbation theory for embedded eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure

The Tabby cat locus maps to feline chromosome B1.

The Tabby markings of the domestic cat are unique coat patterns for which no causative candidate gene has been inferred from other mammals. In this study, a genome scan was performed on a large pedigree of cats that segregated for Tabby coat markings, specifically for the Abyssinian (Ta-) and blotched (tbtb) phenotypes. There was linkage between the Tabby locus and eight markers on cat chromosome B1. The most significant linkage was between marker FCA700 and Tabby (Z = 7.56, theta = 0.03). Two additional markers in the region supported linkage, although not with significant LOD scores. Pairwise analysis of the markers supported the published genetic map of the cat, although additional meioses are required to refine the region. The linked markers cover a 17-cM region and flank an evolutionary breakpoint, suggesting that the Tabby gene has a homologue on either human chromosome 4 or 8. Alternatively, Tabby could be a unique locus in cats