The jamming transition as probed by quasistatic shear flow

We study the rheology of amorphous packings of soft, frictionless particles close to jamming. Implementing a quasistatic simulation method we generate a well defined ensemble of states that directly samples the system at its yield-stress. A continuous jamming transition from a freely-flowing state to a yield stress situation takes place at a well defined packing fraction, where the scaling laws characteristic of isostatic solids are observed. We propose that long-range correlations observed below the transition are dominated by this isostatic point, while those that are observed above the transition are characteristic of dense, disordered elastic media.Comment: 4 pages, 6 figures, revised versio

Superdiffusive, heterogeneous, and collective particle motion near the jamming transition in athermal disordered materials

We use computer simulations to study the microscopic dynamics of an athermal assembly of soft particles near the fluid-to-solid, jamming transition. Borrowing tools developed to study dynamic heterogeneity near glass transitions, we discover a number of original signatures of the jamming transition at the particle scale. We observe superdiffusive, spatially heterogeneous, and collective particle motion over a characteristic scale which displays a surprising non-monotonic behavior across the transition. In the solid phase, the dynamics is an intermittent succession of elastic deformations and plastic relaxations, which are both characterized by scale-free spatial correlations and system size dependent dynamic susceptibilities. Our results show that dynamic heterogeneities in dense athermal systems and glass-formers are very different, and shed light on recent experimental reports of `anomalous' dynamical behavior near the jamming transition of granular and colloidal assemblies

Approximating Subdense Instances of Covering Problems

We study approximability of subdense instances of various covering problems on graphs, defined as instances in which the minimum or average degree is Omega(n/psi(n)) for some function psi(n)=omega(1) of the instance size. We design new approximation algorithms as well as new polynomial time approximation schemes (PTASs) for those problems and establish first approximation hardness results for them. Interestingly, in some cases we were able to prove optimality of the underlying approximation ratios, under usual complexity-theoretic assumptions. Our results for the Vertex Cover problem depend on an improved recursive sampling method which could be of independent interest

A Rare Encounter with Very Massive Stars in NGC 3125-A1

Super star cluster A1 in the nearby starburst galaxy NGC 3125 is characterized by broad He\ii \lam1640 emission (full width at half maximum, $FWHM\sim1200$ km s$^{-1}$) of unprecedented strength (equivalent width, $EW=7.1\pm0.4$ \AA). Previous attempts to characterize the massive star content in NGC 3125-A1 were hampered by the low resolution of the UV spectrum and the lack of co-spatial panchromatic data. We obtained far-UV to near-IR spectroscopy of the two principal emitting regions in the galaxy with the Space Telescope Imaging Spectrograph (STIS) and the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (\hst). We use these data to study three clusters in the galaxy, A1, B1, and B2. We derive cluster ages of 3-4 Myr, intrinsic reddenings of $E(B-V)=0.13$, 0.15, and 0.13, and cluster masses of $1.7\times10^5$, $1.4\times10^5$, and $1.1\times10^5$ M$_\odot$, respectively. A1 and B2 show O\vb \lam1371 absorption from massive stars, which is rarely seen in star-forming galaxies, and have Wolf-Rayet (WR) to O star ratios of $N(WN5-6)/N(O)=0.23$ and 0.10, respectively. The high $N(WN5-6)/N(O)$ ratio of A1 cannot be reproduced by models that use a normal IMF and generic WR star line luminosities. We rule out that the extraordinary He\ii \lam1640 emission and O\vb \lam1371 absorption of A1 are due to an extremely flat upper IMF exponent, and suggest that they originate in the winds of very massive ($>120\,M_\odot$) stars. In order to reproduce the properties of peculiar clusters such as A1, the present grid of stellar evolution tracks implemented in Starburst99 needs to be extended to masses $>120\,M_\odot$.Comment: Accepted for publication in ApJ. 34 pages, 12 figure

Predicting Lotto Numbers

We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”.gambler’s fallacy; hot hand fallacy; representativeness; law of small numbers

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material