Dimers and cluster integrable systems

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph. The sum of Hamiltonians is essentially the partition function of the dimer model. Any graph on a torus gives rise to a bipartite graph on the torus. We show that the phase space of the latter has a Lagrangian subvariety. We identify it with the space parametrizing resistor networks on the original graph.We construct several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci. EN

Semiclassical analysis of Wigner 3j3j-symbol

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.Comment: 7 figure file

Source Coding Optimization for Distributed Average Consensus

Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the nodes of the network using only near-neighbor communications. In real-world scenarios, these communications must undergo quantization, which introduces distortion to the internode messages. In this thesis, a model for the evolution of the network state statistics at each iteration is developed under the assumptions of Gaussian data and additive quantization error. It is shown that minimization of the communication load in terms of aggregate source coding rate can be posed as a generalized geometric program, for which an equivalent convex optimization can efficiently solve for the global minimum. Optimization procedures are developed for rate-distortion-optimal vector quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform quantization. Numerical results demonstrate the performance of these approaches. For small numbers of iterations, the fixed-rate optimizations are verified using exhaustive search. Comparison to the prior art suggests competitive performance under certain circumstances but strongly motivates the incorporation of more sophisticated coding strategies, such as differential, predictive, or Wyner-Ziv coding.Comment: Master's Thesis, Electrical Engineering, North Carolina State Universit

Journal Maps, Interactive Overlays, and the Measurement of Interdisciplinarity on the Basis of Scopus Data (1996-2012)

Using Scopus data, we construct a global map of science based on aggregated journal-journal citations from 1996-2012 (N of journals = 20,554). This base map enables users to overlay downloads from Scopus interactively. Using a single year (e.g., 2012), results can be compared with mappings based on the Journal Citation Reports at the Web-of-Science (N = 10,936). The Scopus maps are more detailed at both the local and global levels because of their greater coverage, including, for example, the arts and humanities. The base maps can be interactively overlaid with journal distributions in sets downloaded from Scopus, for example, for the purpose of portfolio analysis. Rao-Stirling diversity can be used as a measure of interdisciplinarity in the sets under study. Maps at the global and the local level, however, can be very different because of the different levels of aggregation involved. Two journals, for example, can both belong to the humanities in the global map, but participate in different specialty structures locally. The base map and interactive tools are available online (with instructions) at http://www.leydesdorff.net/scopus_ovl.Comment: accepted for publication in the Journal of the Association for Information Science and Technology (JASIST

Cooperative high-performance computing with FPGAs - matrix multiply case-study

In high-performance computing, there is great opportunity for systems that use FPGAs to handle communication while also performing computation on data in transit in an ``altruistic'' manner--that is, using resources for computation that might otherwise be used for communication, and in a way that improves overall system performance and efficiency. We provide a specific definition of \textbf{Computing in the Network} that captures this opportunity. We then outline some overall requirements and guidelines for cooperative computing that include this ability, and make suggestions for specific computing capabilities to be added to the networking hardware in a system. We then explore some algorithms running on a network so equipped for a few specific computing tasks: dense matrix multiplication, sparse matrix transposition and sparse matrix multiplication. In the first instance we give limits of problem size and estimates of performance that should be attainable with present-day FPGA hardware