Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are compared with known exact results for $\beta=1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.Comment: 4 pages, 2 figure

Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering

Dynamical Inequality in Growth Models

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.Comment: 6 pages, 4 figure

Predicted signatures of p-wave superfluid phases and Majorana zero modes of fermionic atoms in RF absorption

We study the superfluid phases of quasi-2D atomic Fermi gases interacting via a p-wave Feshbach resonance. We calculate the absorption spectra of these phases under a hyperfine transition, for both non-rotating and rotating superfluids. We show that one can identify the different phases of the p-wave superfluid from the absorption spectrum. The absorption spectrum shows clear signatures of the existence of Majorana zero modes at the cores of vortices of the weakly-pairing $p_x+ip_y$ phase

Distributed CSMA with pairwise coding

We consider distributed strategies for joint routing, scheduling, and network coding to maximize throughput in wireless networks. Network coding allows for an increase in network throughput under certain routing conditions. We previously developed a centralized control policy to jointly optimize for routing and scheduling combined with a simple network coding strategy using max-weight scheduling (MWS) [9]. In this work we focus on pairwise network coding and develop a distributed carrier sense multiple access (CSMA) policy that supports all arrival rates allowed by the network subject to the pairwise coding constraint. We extend our scheme to optimize for packet overhearing to increase the number of beneficial coding opportunities. Simulation results show that the CSMA strategy yields the same throughput as the optimal centralized policy of [9], but at the cost of increased delay. Moreover, overhearing provides up to an additional 25% increase in throughput on random topologies.United States. Dept. of Defense. Assistant Secretary of Defense for Research & EngineeringUnited States. Air Force (Air Force Contract FA8721-05-C-0002

Modeling cancer metabolism on a genome scale

Cancer cells have fundamentally altered cellular metabolism that is associated with their tumorigenicity and malignancy. In addition to the widely studied Warburg effect, several new key metabolic alterations in cancer have been established over the last decade, leading to the recognition that altered tumor metabolism is one of the hallmarks of cancer. Deciphering the full scope and functional implications of the dysregulated metabolism in cancer requires both the advancement of a variety of omics measurements and the advancement of computational approaches for the analysis and contextualization of the accumulated data. Encouragingly, while the metabolic network is highly interconnected and complex, it is at the same time probably the best characterized cellular network. Following, this review discusses the challenges that genome‐scale modeling of cancer metabolism has been facing. We survey several recent studies demonstrating the first strides that have been done, testifying to the value of this approach in portraying a network‐level view of the cancer metabolism and in identifying novel drug targets and biomarkers. Finally, we outline a few new steps that may further advance this field

Optimal routing and scheduling for a simple network coding scheme

We consider jointly optimal routing, scheduling, and network coding strategies to maximize throughput in wireless networks. While routing and scheduling techniques for wireless networks have been studied for decades, network coding is a relatively new technique that allows for an increase in throughput under certain topological and routing conditions. In this work we introduce k-tuple coding, a generalization of pairwise coding with next-hop decodability, and fully characterize the region of arrival rates for which the network queues can be stabilized under this coding strategy. We propose a dynamic control policy for routing, scheduling, and k-tuple coding, and prove that our policy is throughput optimal subject to the k-tuple coding constraint. We provide analytical bounds on the coding gain of our policy, and present numerical results to support our analytical findings. We show that most of the gains are achieved with pairwise coding, and that the coding gain is greater under 2-hop than 1-hop interference. Simulations show that under 2-hop interference our policy yields median throughput gains of 31% beyond optimal scheduling and routing on random topologies with 16 nodes.National Science Foundation (U.S.) (grant CNS-0915988)United States. Office of Naval Research (grant N00014-12-1-0064)United States. Office of Naval Research. Multidisciplinary University Research Initiative (grant number W911NF-08-1-0238)United States. Air ForceUnited States. Dept. of Defense (Contract No. FA8721-05-C-0002

Anisotropy and periodicity in the density distribution of electrons in a quantum-well

We use low temperature near-field optical spectroscopy to image the electron density distribution in the plane of a high mobility GaAs quantum well. We find that the electrons are not randomly distributed in the plane, but rather form narrow stripes (width smaller than 150 nm) of higher electron density. The stripes are oriented along the [1-10 ] crystal direction, and are arranged in a quasi-periodic structure. We show that elongated structural mounds, which are intrinsic to molecular beam epitaxy, are responsible for the creation of this electron density texture.Comment: 10 pages, 3 figure

Throughput Optimization in Mobile Backbone Networks

This paper describes new algorithms for throughput optimization in a mobile backbone network. This hierarchical communication framework combines mobile backbone nodes, which have superior mobility and communication capability, with regular nodes, which are constrained in mobility and communication capability. An important quantity of interest in mobile backbone networks is the number of regular nodes that can be successfully assigned to mobile backbone nodes at a given throughput level. This paper develops a novel technique for maximizing this quantity in networks of fixed regular nodes using mixed-integer linear programming (MILP). The MILP-based algorithm provides a significant reduction in computation time compared to existing methods and is computationally tractable for problems of moderate size. An approximation algorithm is also developed that is appropriate for large-scale problems. This paper presents a theoretical performance guarantee for the approximation algorithm and also demonstrates its empirical performance. Finally, the mobile backbone network problem is extended to include mobile regular nodes, and exact and approximate solution algorithms are presented for this extension.United States. Air Force Office of Scientific Research (AFOSR grant FA9550- 04-1-0458)National Science Foundation (U.S.) (grant CCR-0325401)National Science Foundation (U.S.) (grant CNS-091598)National Science Foundation (U.S.) (Graduate Fellowship