An accelerated minimal gradient method with momentum for strictly convex quadratic optimization

BIT Numerical Mathematics - In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well-known...     

Retractions onto series-parallel posets

The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable, and, for such a poset P, we describe posets admitting a retraction onto P.     

Catalytic Enantioselective Synthesis of N,Cα,Cα‐Trisubstituted α‐Amino Acid Derivatives Using 1H‐Imidazol‐4(5H)‐ones as Key Templates

1H‐Imidazol‐4(5H)‐ones are introduced as novel nucleophilic α‐amino acid equivalents in asymmetric synthesis. These compounds not only allow highly efficient construction of tetrasubstituted stereogenic centers, but unlike hitherto known templates, provide direct access to N‐substituted (alkyl, allyl, aryl) α‐amino acid derivatives.     

Highly Efficient Transition Metal Nanoparticle Catalysts in Aqueous Solutions

A ligand design is proposed for transition metal nanoparticle (TMNP) catalysts in aqueous solution. Thus, a tris(triazolyl)‐polyethylene glycol (tris‐trz‐PEG) amphiphilic ligand, 2 , is used for the synthesis of very small TMNPs with Fe, Co, Ni, Cu, Ru, Pd, Ag, Pt, and Au. These TMNP‐ 2 catalysts were evaluated and compared for the model 4‐nitrophenol reduction, and proved to be extremely efficient. High catalytic efficiencies involving the use of only a few ppm metal of PdNPs, RuNPs, and CuNPs were also exemplified in Suzuki–Miyaura, transfer hydrogenation, and click reactions, respectively.     

Time-dependent density-functional theory in massively parallel computer architectures: the OCTOPUS project

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.     

Responsive Polyelectrolyte Multilayers Assembled at High Ionic Strength with an Unusual Collapse at Low Ionic Strength

Responsive polyelectrolyte multilayers (PEMs) of poly(diallyl dimethyl ammonium chloride) (PDADMAC) and poly(styrene sodium sulfonate) (PSS) with thicknesses between 350 and 400 nm for 11 deposited polyelectrolyte layers were fabricated assembling the polyelectrolytes at 3 M NaCl. When the 3 M NaCl bulk solution is replaced by water, the PEMs release water, approximately a 46% of the total mass, and experience a thickness reduction of more than 200 nm. Changes in thickness and water content are fully reversible. The film recovers its original thickness and water content when it is exposed again to a 3 M NaCl solution. A responsive polymer film is achieved with the capability of swelling at high ionic strength and collapsing in water with variations in thickness of hundred of nanometers.     

Recent advances in the use of the quartz crystal microbalance with dissipation for the study of the collapse of polyelectrolyte brushes

The combination of Quartz Crystal Microbalance and ellipsometry to quantify polyelectrolyte brush hydration and how this impacts on the study of brush collapse is discussed here. Recent articles study collapse after quantifying hydration of poly (2-methacryloyloxy ethyl trimethyl ammonium chloride) (PMETAC) and poly(potassium sulfo propyl methacrylate). Water lost increases with ionic strength but only a 50% of their water content is lost at 1 M NaCl. For PMETAC brushes the exchange of Cl⁻ by ClO₄⁻ is more effective, causing 50% lost at 0.05 M. The hydration and water lost for PMETAC brushes synthesized from thiol monolayers with variable density of initiators from 1 to 100% show that the freely entrapped water of the brushes is around a 10%. Irrespectively of initiator percentage the brush does not lose at 1 M NaCl more than 50% of the original water content. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1068–1072     

The distribution of the quasispecies for the Wright–Fisher model on the sharp peak landscape

We consider the classical Wright–Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in Cerf (2014), a quasispecies is formed. We find explicitly the distribution of this quasispecies, which turns out to be the same distribution as for the Moran model.     

TWO NOVEL GRADIENT METHODS WITH OPTIMAL STEP SIZES

In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems.The proposed step sizes employ second-order information in order to obtain faster gradient-type methods.Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of the objective function.A convergence analysis of the proposed algorithm is provided.Some numerical experiments are performed in order to compare the efficiency and effectiveness of the proposed methods with similar methods in the literature.Experimentally,it is observed that our proposals accelerate the gradient method at nearly no extra computational cost,which makes our proposal a good alternative to solve large-scale problems.     

Crystallization of Fe75Zr25 metallic glass: a two‐step process involving metastable bcc‐Fe and polymorphic transformation

The crystallization process of mechanically alloyed Fe₇₅Zr₂₅ metallic glasses is investigated by means of both thermo‐magnetization and in situ neutron powder thermo‐diffraction experiments in the temperature range 300–1073 K. It was found that the crystallization takes place in a two‐step process, involving firstly the appearance of metastable Fe and Fe₂Zr crystalline phases between 880 K and 980 K, and a subsequent polymorphic transformation into Fe₃Zr above 980 K. These findings explain the anomalous magnetization vs. temperature behaviour on heating–cooling cycles.