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.     

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.     

CD(4) has bounded width

We prove that the constraint languages invariant under a short sequence of Jónsson terms (containing at most three non-trivial ternary terms) are tractable by showing that they have bounded width. This improves a previous result by Kiss and Valeriote and presents some evidence that the Larose–Zádori conjecture holds in the congruence-distributive case. The first author was supported by EPSRC grant EP/C54384X/1. The second author was supported by the MEC under grant TIN 2006-15387-C03-03, the EU PASCAL Network of Excellence IST-2002-506778, and the MODNET Marie Curie Research Training Network MRTN-CT-2004-512234. The third author was supported by grant no. 144011G of the Ministry of Science and Environment of Serbia. The fourth author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809 and K 60148.     

Fluorescent Orthopalladated Complexes of 4-Aryliden-5(4H)-oxazolones from the Kaede Protein: Synthesis and Characterization

The goal of the work reported here was to amplify the fluorescent properties of 4-aryliden-5(4H)-oxazolones by suppression of the hula-twist non-radiative deactivation pathway. This aim was achieved by simultaneous bonding of a Pd center to the N atom of the heterocycle and the ortho carbon of the arylidene ring. Two different 4-((Z)-arylidene)-2-((E)-styryl)-5(4H)-oxazolones, the structures of which are closely related to the chromophore of the Kaede protein and substituted at the 2- and 4-positions of the arylidene ring (1a OMe; 1b F), were used as starting materials. Oxazolones 1a and 1b were reacted with Pd(OAc)₂ to give the corresponding dinuclear orthometalated palladium derivates 2a and 2b by regioselective C–H activation of the ortho-position of the arylidene ring. Reaction of 2a (2b) with LiCl promoted the metathesis of the bridging carboxylate by chloride ligands to afford dinuclear 3a (3b). Mononuclear complexes containing the orthopalladated oxazolone and a variety of ancillary ligands (acetylacetonate (4a, 4b), hydroxyquinolinate (5a), aminoquinoline (6a), bipyridine (7a), phenanthroline (8a)) were prepared from 3a or 3b through metathesis of anionic ligands or substitution of neutral weakly bonded ligands. All species were fully characterized and the X-ray determination of the molecular structure of 7a was carried out. This structure has strongly distorted ligands due to intramolecular interactions. Fluorescence measurements showed an increase in the quantum yield (QY) by up to one order of magnitude on comparing the free oxazolone (QY < 1%) with the palladated oxazolone (QY = 12% for 6a). This fact shows that the coordination of the oxazolone to the palladium efficiently suppresses the hula-twist deactivation pathway.     

Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization

Numerical Algorithms - This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled...