Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams

While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called {\em densest subgraph problem}. We develop an algorithm that achieves time- and space-efficiency for this problem simultaneously. It is one of the first of its kind for graph problems to the best of our knowledge. In a graph $G = (V, E)$, the "density" of a subgraph induced by a subset of nodes $S \subseteq V$ is defined as $|E(S)|/|S|$, where $E(S)$ is the set of edges in $E$ with both endpoints in $S$. In the densest subgraph problem, the goal is to find a subset of nodes that maximizes the density of the corresponding induced subgraph. For any $\epsilon>0$, we present a dynamic algorithm that, with high probability, maintains a $(4+\epsilon)$-approximation to the densest subgraph problem under a sequence of edge insertions and deletions in a graph with $n$ nodes. It uses $\tilde O(n)$ space, and has an amortized update time of $\tilde O(1)$ and a query time of $\tilde O(1)$. Here, $\tilde O$ hides a O(\poly\log_{1+\epsilon} n) term. The approximation ratio can be improved to $(2+\epsilon)$ at the cost of increasing the query time to $\tilde O(n)$. It can be extended to a $(2+\epsilon)$-approximation sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm is the first streaming algorithm that can maintain the densest subgraph in {\em one pass}. The previously best algorithm in this setting required $O(\log n)$ passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our algorithm is tight up to a polylogarithmic factor.Comment: A preliminary version of this paper appeared in STOC 201

'Unfit for human consumption': a study of the contamination of formula milk fed to young children in East Java, Indonesia.

To examine levels of bacterial contamination in formula feeding bottles in Sidoarjo, East Java, and to assess the preparation practices that may have been responsible. Cross-sectional study. We randomly selected 92 households with children under the age of two who were bottle-fed formula. In each household we carried out video observation of mothers/caregivers preparing bottles, and examined samples of formula for coliform bacteria and Escherichia coli (E. coli). In-depth interviews were conducted with a sub-sample of 20 mothers. 88% of the formula feeds were contaminated with total coliforms at a level >10 MPN/ml, and 45% contained E. coli. These feeds were defined as 'unfit for human consumption'. In the video observations, none of the mothers complied with all five WHO-recommended measures of hygienic formula feed preparation. Only two mothers washed their hands with soap prior to formula preparation. Most mothers also failed to clean or sterilise the bottle and clean the preparation area. In-depth interviews confirmed that such suboptimal hygiene practices were common. The high levels of contamination found highlight that bottles are an important faecal-oral exposure pathway resulting from poor hygiene practices during bottle preparation. This article is protected by copyright. All rights reserved

Gravitational hydrodynamics of large scale structure formation

The gravitational hydrodynamics of the primordial plasma with neutrino hot dark matter is considered as a challenge to the bottom-up cold dark matter paradigm. Viscosity and turbulence induce a top-down fragmentation scenario before and at decoupling. The first step is the creation of voids in the plasma, which expand to 37 Mpc on the average now. The remaining matter clumps turn into galaxy clusters. Turbulence produced at expanding void boundaries causes a linear morphology of 3 kpc fragmenting protogalaxies along vortex lines. At decoupling galaxies and proto-globular star clusters arise; the latter constitute the galactic dark matter halos and consist themselves of earth-mass H-He planets. Frozen planets are observed in microlensing and white-dwarf-heated ones in planetary nebulae. The approach also explains the Tully-Fisher and Faber-Jackson relations, and cosmic microwave temperature fluctuations of micro-Kelvins.Comment: 6 pages, no figure

Mirror matter admixtures and isospin breaking in the \Delta I=1/2 rule in \Omega^- two body non-leptonic decays

We discuss a description of \Omega^- two body non-leptonic decays based on possible, albeit tiny, admixtures of mirror matter in ordinary hadrons. The \Delta I=1/2 rule enhancement is obtained as a result of isospin symmetry and, more importantly, the rather large observed deviations from this rule result from small isospin breaking. This analysis lends support to the possibility that the enhancement phenomenon observed in low energy weak interactions may be systematically described by mirror matter admixtures in ordinary hadrons.Comment: Changed conten

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Spectroscopy of a Cooper-Pair box in the Autler-Townes configuration

A theoretical spectroscopic analysis of a microwave driven superconducting charge qubit (Cooper-pair box coupled) to an RLC oscillator model is performed. By treating the oscillator as a probe through the backreaction effect of the qubit on the oscillator circuit, we extract frequency splitting features analogous to the Autler-Townes effect from quantum optics, thereby extending the analogies between superconducting and quantum optical phenomenology. These features are found in a frequency band that avoids the need for high frequency measurement systems and therefore may be of use in qubit characterization and coupling schemes. In addition we find this frequency band can be adjusted to suit an experimental frequency regime by changing the oscillator frequency.Comment: 13 pages, 7 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

A predictive processing theory of sensorimotor contingencies: explaining the puzzle of perceptual presence and its absence in synesthesia

Normal perception involves experiencing objects within perceptual scenes as real, as existing in the world. This property of “perceptual presence” has motivated “sensorimotor theories” which understand perception to involve the mastery of sensorimotor contingencies. However, the mechanistic basis of sensorimotor contingencies and their mastery has remained unclear. Sensorimotor theory also struggles to explain instances of perception, such as synesthesia, that appear to lack perceptual presence and for which relevant sensorimotor contingencies are difficult to identify. On alternative “predictive processing” theories, perceptual content emerges from probabilistic inference on the external causes of sensory signals, however, this view has addressed neither the problem of perceptual presence nor synesthesia. Here, I describe a theory of predictive perception of sensorimotor contingencies which (1) accounts for perceptual presence in normal perception, as well as its absence in synesthesia, and (2) operationalizes the notion of sensorimotor contingencies and their mastery. The core idea is that generative models underlying perception incorporate explicitly counterfactual elements related to how sensory inputs would change on the basis of a broad repertoire of possible actions, even if those actions are not performed. These “counterfactually-rich” generative models encode sensorimotor contingencies related to repertoires of sensorimotor dependencies, with counterfactual richness determining the degree of perceptual presence associated with a stimulus. While the generative models underlying normal perception are typically counterfactually rich (reflecting a large repertoire of possible sensorimotor dependencies), those underlying synesthetic concurrents are hypothesized to be counterfactually poor. In addition to accounting for the phenomenology of synesthesia, the theory naturally accommodates phenomenological differences between a range of experiential states including dreaming, hallucination, and the like. It may also lead to a new view of the (in)determinacy of normal perception

Polar Cremona Transformations and Monodromy of Polynomials

Consider the gradient map associated to any non-constant homogeneous polynomial f\in \C[x_0,...,x_n] of degree $d$, defined by \phi_f=grad(f): D(f)\to \CP^n, (x_0:...:x_n)\to (f_0(x):...:f_n(x)) where D(f)=\{x\in \CP^n; f(x)\neq 0\} is the principal open set associated to $f$ and $f_i=\frac{\partial f}{\partial x_i}$. This map corresponds to polar Cremona transformations. In Proposition \ref{p1} we give a new lower bound for the degree $d(f)$ of $\phi_f$ under the assumption that the projective hypersurface $V:f=0$ has only isolated singularities. When $d(f)=1$, Theorem \ref{t4} yields very strong conditions on the singularities of $V$.Comment: 8 page

Spin photocurrents and circular photon drag effect in (110)-grown quantum well structures

We report on the study of spin photocurrents in (110)-grown quantum well structures. Investigated effects comprise the circular photogalvanic effect and so far not observed circular photon drag effect. The experimental data can be described by an analytical expression derived from a phenomenological theory. A microscopic model of the circular photon drag effect is developed demonstrating that the generated current has spin dependent origin.Comment: 6 pages, 3 figure

Gapped Surface States in a Strong-Topological-Semimetal

A three-dimensional strong-topological-insulator or -semimetal hosts topological surface states which are often said to be gapless so long as time-reversal symmetry is preserved. This narrative can be mistaken when surface state degeneracies occur away from time-reversal-invariant momenta. The mirror-invariance of the system then becomes essential in protecting the existence of a surface Fermi surface. Here we show that such a case exists in the strong-topological-semimetal Bi$_4$Se$_3$. Angle-resolved photoemission spectroscopy and \textit{ab initio} calculations reveal partial gapping of surface bands on the Bi$_2$Se$_3$-termination of Bi$_4$Se$_3$(111), where an 85 meV gap along $\bar{\Gamma}\bar{K}$ closes to zero toward the mirror-invariant $\bar{\Gamma}\bar{M}$ azimuth. The gap opening is attributed to an interband spin-orbit interaction that mixes states of opposite spin-helicity.Comment: 5 pages, 3 figure