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  1. Discovered by Knöth in 1964, the 10-vertex closo -carborane anion [HCB 9 H 9 1− ] is a classical bicapped square antiprism that contains an unusual pentacoordinate carbon center. Compared to its larger icosahedral cousin [HCB 11 H 11 1− ], few investigations have been made into its use as a weakly coordinating anion or as a ligand substituent. Here we show that it is possible to prepare both a dianionic N-heterocyclic carbene (NHC) Li + adduct as well as a trianionic C-2, C-5 dilithio species featuring two 10-vertex carborane anion substituents. All compounds were characterized via multinuclear NMR spectroscopy, single crystal X-ray diffraction, and HRMS when possible. 
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  2. null (Ed.)
  3. Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping algorithms, cache-oblivious divide-and-conquer trapezoidal algorithms, and Krylov subspace methods. In this paper, we present two efficient parallel algorithms for performing linear stencil computations. Current direct solvers in this domain are computationally inefficient, and Krylov methods require manual labor and mathematical training. We solve these problems for linear stencils by using DFT preconditioning on a Krylov method to achieve a direct solver which is both fast and general. Indeed, while all currently available algorithms for solving general linear stencils perform Θ(NT) work, where N is the size of the spatial grid and T is the number of timesteps, our algorithms perform o(NT) work. To the best of our knowledge, we give the first algorithms that use fast Fourier transforms to compute final grid data by evolving the initial data for many timesteps at once. Our algorithms handle both periodic and aperiodic boundary conditions, and achieve polynomially better performance bounds (i.e., computational complexity and parallel runtime) than all other existing solutions. Initial experimental results show that implementations of our algorithms that evolve grids of roughly 10^7 cells for around 10^5 timesteps run orders of magnitude faster than state-of-the-art implementations for periodic stencil problems, and 1.3× to 8.5× faster for aperiodic stencil problems. 
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  4. The binary-forking model is a parallel computation model, formally defined by Blelloch et al., in which a thread can fork a concurrent child thread, recursively and asynchronously. The model incurs a cost of Theta(log n) to spawn or synchronize n tasks or threads. The binary-forking model realistically captures the performance of parallel algorithms implemented using modern multithreaded programming languages on multicore shared-memory machines. In contrast, the widely studied theoretical PRAM model does not consider the cost of spawning and synchronizing threads, and as a result, algorithms achieving optimal performance bounds in the PRAM model may not be optimal in the binary-forking model. Often, algorithms need to be redesigned to achieve optimal performance bounds in the binary-forking model and the non-constant synchronization cost makes the task challenging. In this paper, we show that in the binary-forking model we can achieve optimal or near-optimal span with negligible or no asymptotic blowup in work for comparison-based sorting, Strassen's matrix multiplication (MM), and the Fast Fourier Transform (FFT). Our major results are as follows: (1) A randomized comparison-based sorting algorithm with optimal O(log n) span and O(nlog n) work, both w.h.p. in n. (2) An optimal O(log n) span algorithm for Strassen's matrix multiplication (MM) with only a loglog n - factor blow-up in work as well as a near-optimal O(log n loglog log n) span algorithm with no asymptotic blow-up in work. (3) A near-optimal O(log n logloglog n) span Fast Fourier Transform (FFT) algorithm with less than a log n-factor blow-up in work for all practical values of n (i.e., n le 10 ^10,000) 
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  5. null (Ed.)
    The binary-forking model is a parallel computation model, formally defined by Blelloch et al., in which a thread can fork a concurrent child thread, recursively and asynchronously. The model incurs a cost of Theta(log n) to spawn or synchronize n tasks or threads. The binary-forking model realistically captures the performance of parallel algorithms implemented using modern multithreaded programming languages on multicore shared-memory machines. In contrast, the widely studied theoretical PRAM model does not consider the cost of spawning and synchronizing threads, and as a result, algorithms achieving optimal performance bounds in the PRAM model may not be optimal in the binary-forking model. Often, algorithms need to be redesigned to achieve optimal performance bounds in the binary-forking model and the non-constant synchronization cost makes the task challenging. In this paper, we show that in the binary-forking model we can achieve optimal or near-optimal span with negligible or no asymptotic blowup in work for comparison-based sorting, Strassen's matrix multiplication (MM), and the Fast Fourier Transform (FFT). Our major results are as follows: (1) A randomized comparison-based sorting algorithm with optimal O(log n) span and O(nlog n) work, both w.h.p. in n. (2) An optimal O(log n) span algorithm for Strassen's matrix multiplication (MM) with only a loglog n - factor blow-up in work as well as a near-optimal O(log n loglog log n) span algorithm with no asymptotic blow-up in work. (3) A near-optimal O(log n logloglog n) span Fast Fourier Transform (FFT) algorithm with less than a log n-factor blow-up in work for all practical values of n (i.e., n le 10 ^10,000 ). 
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