Design,synthesis and use of binary encoded synthetic chemical libraries

Summary With the advent of combinatorial chemistry a new paradigm is evolving in the field of drug discovery. The approach is based on an integration of chemistry, high-throughput screening and automation engineering. The chemistry arm is usually based on solid-phase synthesis technology as the preferred approach to library construction. One of the most powerful of the solid-phase methods is encoded split synthesis, in which the reaction history experience by each polymeric bead is unambiguously recorded. This split-and-pool approach, employing chemically robust tags, was used to construct a 85 000-membered dihydrobenzopyran library.     

Vehicle routing with split deliveries

This paper considers a relaxation of the classical vehicle routing problem (VRP), in which split deliveries are allowed. As the classical VRP, this problem is NP-hard, but nonetheless it seems more difficult to solve exactly. It is first formulated as an integer linear program. Several new classes of valid constraints are derived, and a hierarchy between these is established. A constraint relaxation branch and bound algorithm for the problem is then described. Computational results indicate that by using an appropriate combination of constraints, the gap between the lower and upper bounds at the root of the search tree can be reduced considerably. These results also confirm the quality of a previously published heuristic for this problem.     

Ba6Ge25: low-temperature Ge-Ge bond breaking during temperature-induced structure transformation

In order to find the optimal conditions for sample preparation of the binary germanide Ba₆Ge₂₅, the germanium-rich part of the Ba-Ge phase diagram was redetermined by means of metallography, X-ray powder diffraction and differential thermal analysis. The temperature behavior of cubic Ba₆Ge₂₅ was investigated both on polycrystalline samples and single crystals. The temperature dependence of the lattice parameter exhibits two anomalies at about 180 and 230 K, respectively, which are caused by a structure transformation in two steps with hysteresis. Powder (T=10-295 K) and single-crystal (T=95-295 K) X-ray diffraction studies confirm that the symmetry of Ba₆Ge₂₅ (space group P4₁32) remains unchanged within the entire temperature range. A reconstructive behavior of the structural transformation is observed, involving Ge-Ge bond breaking and barium cation displacements. Some Ge4 type atoms (∼28%) are so significantly displaced during cooling that Ge4-Ge6 bonds break and new three-bonded (3b)Ge⁻ species (electron acceptors) are formed. Consequently, the number of charge carriers is reduced, affecting the physical properties. The reversible bond breaking involved in this process is a typical characteristic of a solid-state chemical reaction.     

Geometric characterizations of finite Chevalley groups of type B

Finite Moufang generalized quadrangles were classified in 1974 as a corollary to the classification of finite groups with a split BN-pair of rank , by P. Fong and G. M. Seitz (1973), (1974). Later on, work of S. E. Payne and J. A. Thas culminated in an almost complete, elementary proof of that classification; see Finite Generalized Quadrangles, 1984. Using slightly more group theory, first W. M. Kantor (1991), then the first author (2001), and finally, essentially without group theory, J. A. Thas (preprint), completed this geometric approach. Recently, J. Tits and R. Weiss classified all (finite and infinite) Moufang polygons (2002), and this provides a third independent proof for the classification of finite Moufang quadrangles.

In the present paper, we start with a much weaker condition on a BN-pair of Type and show that it must correspond to a Moufang quadrangle, proving that the BN-pair arises from a finite Chevalley group of (relative) Type . Our methods consist of a mixture of combinatorial, geometric and group theoretic arguments, but we do not use the classification of finite simple groups. The condition on the BN-pair translates to the generalized quadrangle as follows: for each point , the stabilizer of all lines through that point acts transitively on the points opposite .

     

New second order Mumford–Shah model based on Γ-convergence approximation for image processing

In this paper, a second order variational model named the Mumford–Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford–Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H¹ regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss–Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.     

Unidirectional total variation destriping using difference curvature in MODIS emissive bands

This paper presents a method of unidirectional total variation destriping using difference curvature in MODIS (Moderate Resolution Imaging Spectrometer) emissive bands. First, difference curvature is utilized to extract spatial information at each pixel; and the spatially weighted parameters that constructed by extracted spatial information are incorporated into the unidirectional total variation model to adaptively adjust the destriping strength for achieving a better destriping result and preserving the detail information meantime. Second, the split Bregman iteration method is employed to optimize the proposed model. Finally, experimental results from MODIS emissive bands and comparisons with other methods demonstrate the potential of the presented method for MODIS image destriping.     

Adaptive subgradient method for the split quasi-convex feasibility problems

In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.     

A stable numerical method for space fractional Landau–Lifshitz equations

In this paper, we proposed a simple and unconditional stable time-split Gauss–Seidel projection (GSP) method for the space fractional Landau–Lifshitz (FLL) equations. Numerical results are presented to demonstrate the effectiveness and stability of this method.     

On the radius and the attachment number of tetravalent half-arc-transitive graphs

In this paper, we study the relationship between the radius $r$ and the attachment number $a$ of a tetravalent graph admitting a half-arc-transitive group of automorphisms. These two parameters were first introduced in Maru?i? (1998), where among other things it was proved that $a$ always divides $2r$. Intrigued by the empirical data from the census (Poto?nik et al., 2015) of all such graphs of order up to 1000 we pose the question of whether all examples for which $a$ does not divide $r$ are arc-transitive. We prove that the answer to this question is positive in the case when $a$ is twice an odd number. In addition, we completely characterise the tetravalent graphs admitting a half-arc-transitive group with $r=3$ and $a=2$, and prove that they arise as non-sectional split $2$-fold covers of line graphs of $2$-arc-transitive cubic graphs.     

Large-Scale Structured Sparsity via Parallel Fused Lasso on Multiple GPUs

We present a massively parallel algorithm for the fused lasso, powered by a multiple number of graphics processing units (GPUs). Our method is suitable for a class of large-scale sparse regression problems on which a two-dimensional lattice structure among the coefficients is imposed. This structure is important in many statistical applications, including image-based regression in which a set of images are used to locate image regions predictive of a response variable such as human behavior. Such large datasets are increasingly common. In our study, we employ the split Bregman method and the fast Fourier transform, which jointly have a high data-level parallelism that is distinct in a two-dimensional setting. Our multi-GPU parallelization achieves remarkably improved speed. Specifically, we obtained as much as 433 times improved speed over that of the reference CPU implementation. We demonstrate the speed and scalability of the algorithm using several datasets, including 8100 samples of 512 × 512 images. Compared to the single GPU counterpart, our method also showed improved computing speed as well as high scalability. We describe the various elements of our study as well as our experience with the subtleties in selecting an existing algorithm for parallelization. It is critical that memory bandwidth be carefully considered for multi-GPU algorithms. Supplementary material for this article is available online.