Parallel algorithms and concentration bounds for the Lovasz Local Lemma via witness DAGs

The Lov\'{a}sz Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser & Tardos (2010) provides an efficient randomized algorithm to implement it. This can be parallelized to give an algorithm that uses polynomially many processors and runs in $O(\log^3 n)$ time on an EREW PRAM, stemming from $O(\log n)$ adaptive computations of a maximal independent set (MIS). Chung et al. (2014) developed faster local and parallel algorithms, potentially running in time $O(\log^2 n)$, but these algorithms require more stringent conditions than the LLL. We give a new parallel algorithm that works under essentially the same conditions as the original algorithm of Moser & Tardos but uses only a single MIS computation, thus running in $O(\log^2 n)$ time on an EREW PRAM. This can be derandomized to give an NC algorithm running in time $O(\log^2 n)$ as well, speeding up a previous NC LLL algorithm of Chandrasekaran et al. (2013). We also provide improved and tighter bounds on the run-times of the sequential and parallel resampling-based algorithms originally developed by Moser & Tardos. These apply to any problem instance in which the tighter Shearer LLL criterion is satisfied

Charge-localization and isospin-blockade in vertical double quantum dots

Charge localization seems unlikely to occur in two vertically coupled symmetric quantum dots even if a small bias voltage breaks the exact isospin-symmetry of the system. However for a three-electron double quantum dot we find a strong localization of charges at certain vertically applied magnetic fields. The charge localization is directly connected to new ground state transitions between eigenstates differing only in parity. The transitions are driven by magnetic field dependent Coulomb correlations between the electrons and give rise to strong isospin blockade signatures in transport through the double dot system.Comment: 10 pages, 4 figure

A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth-Uhlenbeck approach

We consider a cluster expansion for strongly correlated quark matter where the clusters are baryons with spectral properties that are described within the generalized Beth-Uhlenbeck approach by a medium dependent phase shift. We employ a simple ansatz for the phase shift which fulfils the Levinson theorem by describing an on-shell bound state with an effective mass and models the continuum by an anti-bound state located at the mass of the three-quark threshold. The quark and baryon interactions are accounted for by the coupling to scalar and vector meson mean fields modelled by density functionals. At increasing density and temperature, due to the different medium-dependence of quark and baryon masses, the Mott dissociation of baryons occurs and the nuclear cluster contributions to the thermodynamics vanish. It is demonstrated on this simple example that this unified approach to quark-nuclear matter is capable of describing crossover as well as first order phase transition behaviour in the phase diagram with a critical endpoint. Changing the meson mean field, the case of a "crossover all over" in the phase diagram is also obtained.Comment: 7 pages, 5 figure

Uncovering the Temporal Dynamics of Diffusion Networks

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission rates between nodes and transmission sources are unknown. Inferring the underlying dynamics is of outstanding interest since it enables forecasting, influencing and retarding infections, broadly construed. To this end, we model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Given cascade data -- observed infection times of nodes -- we infer the edges of the global diffusion network and estimate the transmission rates of each edge that best explain the observed data. The optimization problem is convex. The model naturally (without heuristics) imposes sparse solutions and requires no parameter tuning. The problem decouples into a collection of independent smaller problems, thus scaling easily to networks on the order of hundreds of thousands of nodes. Experiments on real and synthetic data show that our algorithm both recovers the edges of diffusion networks and accurately estimates their transmission rates from cascade data.Comment: To appear in the 28th International Conference on Machine Learning (ICML), 2011. Website: http://www.stanford.edu/~manuelgr/netrate

Increased variability of microbial communities in restored salt marshes nearly 30 years after tidal flow restoration

We analyzed microbial diversity and community composition from four salt marsh sites that were impounded for 40–50 years and subsequently restored and four unimpounded sites in southeastern Connecticut over one growing season. Community composition and diversity were assessed by terminal restriction fragment length polymorphism (TRFLP) and sequence analysis of 16S ribosomal RNA (rRNA) genes. Our results indicated diverse communities, with sequences representing 14 different bacterial divisions. Proteobacteria, Bacteroidetes, and Planctomycetes dominated clone libraries from both restored and unimpounded sites. Multivariate analysis of the TRFLP data suggest significant site, sample date, and restoration status effects, but the exact causes of these effects are not clear. Composition of clone libraries and abundance of bacterial 16S rRNA genes were not significantly different between restored sites and unimpounded sites, but restored sites showed greater temporal and spatial variability of bacterial communities based on TRFLP profiles compared with unimpounded sites, and variability was greatest at sites more recently restored. In summary, our study suggests there may be long-lasting effects on stability of bacterial communities in restored salt marshes and raises questions about the resilience and ultimate recovery of the communities after chronic disturbance

Emotion meets action : towards an integration of research and theory

Action Contro

Quantifying causal influences

Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other $n-1$ variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution. Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1145 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org