Relative entropy in higher spin holography

We examine relative entropy in the context of the higher spin/CFT duality. We consider 3D bulk configurations in higher spin gravity which are dual to the vacuum and a high temperature state of a CFT with W-algebra symmetries in the presence of a chemical potential for a higher spin current. The relative entropy between these states is then evaluated using the Wilson line functional for holographic entanglement entropy. In the limit of small entangling intervals, the relative entropy should vanish for a generic quantum system. We confirm this behavior by showing that the difference in the expectation values of the modular Hamiltonian between the states matches with the difference in the entanglement entropy in the short-distance regime. Additionally, we compute the relative entropy of states corresponding to smooth solutions in the SL(2, Z) family with respect to the vacuum.

Compiler/Runtime Framework for Dynamic Dataflow Parallelization of Tiled Programs

Task-parallel languages are increasingly popular. Many of them provide expressive mechanisms for intertask synchronization. For example, OpenMP 4.0 will integrate data-driven execution semantics derived from the StarSs research language. Compared to the more restrictive data-parallel and fork-join concurrency models, the advanced features being introduced into task-parallelmodels in turn enable improved scalability through load balancing, memory latency hiding, mitigation of the pressure on memory bandwidth, and, as a side effect, reduced power consumption. In this article, we develop a systematic approach to compile loop nests into concurrent, dynamically constructed graphs of dependent tasks. We propose a simple and effective heuristic that selects the most profitable parallelization idiom for every dependence type and communication pattern. This heuristic enables the extraction of interband parallelism (cross-barrier parallelism) in a number of numerical computations that range from linear algebra to structured grids and image processing. The proposed static analysis and code generation alleviates the burden of a full-blown dependence resolver to track the readiness of tasks at runtime. We evaluate our approach and algorithms in the PPCG compiler, targeting OpenStream, a representative dataflow task-parallel language with explicit intertask dependences and a lightweight runtime. Experimental results demonstrate the effectiveness of the approach.

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

While the tradeoff between the amount of data stored and the repair bandwidth of an (n, k, d) regenerating code has been characterized under functional repair (FR), the case of exact repair (ER) remains unresolved. It is known that there do not exist ER codes which lie on the FR tradeoff at most of the points. The question as to whether one can asymptotically approach the FR tradeoff was settled recently by Tian who showed that in the (4, 3, 3) case, the ER region is bounded away from the FR region. The FR tradeoff serves as a trivial outer bound on the ER tradeoff. In this paper, we extend Tian's results by establishing an improved outer bound on the ER tradeoff which shows that the ER region is bounded away from the FR region, for any (n; k; d). Our approach is analytical and builds upon the framework introduced earlier by Shah et. al. Interestingly, a recently-constructed, layered regenerating code is shown to achieve a point on this outer bound for the (5, 4, 4) case. This represents the first-known instance of an optimal ER code that does not correspond to a point on the FR tradeoff.

A Modified Sum-Product Algorithm over Graphs with Isolated Short Cycles

We investigate into the limitations of the sum-product algorithm in the probability domain over graphs with isolated short cycles. By considering the statistical dependency of messages passed in a cycle of length 4, we modify the update equations for the beliefs at the variable and check nodes. We highlight an approximate log domain algebra for the modified variable node update to ensure numerical stability. At higher signal-to-noise ratios (SNR), the performance of decoding over graphs with isolated short cycles using the modified algorithm is improved compared to the original message passing algorithm (MPA).

3-D GPU Based Real Time Diffuse Optical Tomographic System

3-Dimensional Diffuse Optical Tomographic (3-D DOT) image reconstruction algorithm is computationally complex and requires excessive matrix computations and thus hampers reconstruction in real time. In this paper, we present near real time 3D DOT image reconstruction that is based on Broyden approach for updating Jacobian matrix. The Broyden method simplifies the algorithm by avoiding re-computation of the Jacobian matrix in each iteration. We have developed CPU and heterogeneous CPU/GPU code for 3D DOT image reconstruction in C and MatLab programming platform. We have used Compute Unified Device Architecture (CUDA) programming framework and CUDA linear algebra library (CULA) to utilize the massively parallel computational power of GPUs (NVIDIA Tesla K20c). The computation time achieved for C program based implementation for a CPU/GPU system for 3 planes measurement and FEM mesh size of 19172 tetrahedral elements is 806 milliseconds for an iteration.

Water Dispersible, Positively and Negatively Charged MoS2 Nanosheets: Surface Chemistry and the Role of Surfactant Binding

Stable aqueous dispersions of atomically thin layered MoS2 nanosheets have been obtained by sonication in the presence of ionic surfactants. The dispersions are stabilized by electrostatic repulsion between the sheets, and we show that the sign of the charge on the MoS2 nanosheets, either positive or negative, can be can be controlled by the choice of the surfactant. Using techniques from solution NMR, we show that the surfactant chains are weakly bound to the MoS2 sheets and undergo rapid exchange with free surfactant chains present in the dispersion. In situ nuclear Overhauser effect spectroscopic measurements provide direct evidence that the surfactant chains lie flat, arranged randomly on the basal plane of the MoS2 nanosheets with their charged headgroup exposed. These results provide a chemical perspective for understanding the stability of these inorganic nanosheets in aqueous dispersions and the origin of the charge on the sheets.

Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.