Analysis of Optimization Algorithms via Sum-of-Squares

Journal of Optimization Theory and Applications - We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms for...     

Phenethyl Ester of Gallic Acid Ameliorates Experimental Autoimmune Encephalomyelitis

Gallic acid is a phenolic acid present in various plants, nuts, and fruits. It is well known for its anti-oxidative and anti-inflammatory properties. The phenethyl ester of gallic acid (PEGA) was synthesized with the aim of increasing the bioavailability of gallic acid, and thus its pharmacological potential. Here, the effects of PEGA on encephalitogenic cells were examined, and PEGA was found to modulate the inflammatory activities of T cells and macrophages/microglia. Specifically, PEGA reduced the release of interleukin (IL)-17 and interferon (IFN)-γ from T cells, as well as NO, and IL-6 from macrophages/microglia. Importantly, PEGA ameliorated experimental autoimmune encephalomyelitis, an animal model of chronic inflammatory disease of the central nervous system (CNS)—multiple sclerosis. Thus, PEGA is a potent anti-inflammatory compound with a perspective to be further explored in the context of CNS autoimmunity and other chronic inflammatory disorders.     

Nematic and columnar ordering of a PEG-peptide conjugate in aqueous solution

The self-assembly in aqueous solution of a PEG-peptide conjugate is studied by spectroscopy, electron microscopy, rheology and small-angle X-ray and neutron scattering (SAXS and SANS). The peptide fragment, FFKLVFF is based on fragment KLVFF of the amyloid beta-peptide, Abeta(16-20), extended by two hydrophobic phenylalanine units. This is conjugated to PEG which confers water solubility and leads to distinct self-assembled structures. Small-angle scattering reveals the formation of cylindrical fibrils comprising a peptide core and PEG corona. This constrained structure leads to a model parallel beta-sheet self-assembled structure with a radial arrangement of beta sheets. On increasing concentration, successively nematic and hexagonal columnar phases are formed. The flow-induced alignment of both structures was studied in situ by SANS using a Couette cell. Shear-induced alignment is responsible for the shear thinning behaviour observed by dynamic shear rheometry. Incomplete recovery of moduli after cessation of shear is consistent with the observation from SANS of retained orientation in the sample.     

Optimal disturbances above and upstream of a flat plate with an elliptic-type leading edge

Adjoint-based iterative methods are employed to compute linear optimal disturbances in a spatially growing boundary layer around an elliptic leading edge. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. The optimisation problem is solved using power iterations combined with a matrix-free formulation, where the state is marched forward in time with a standard direct numerical simulation solver and backward with the adjoint solver until a chosen convergence criterion is fulfilled. We consider the global and, more relevant to receptivity studies, the upstream localised optimal initial condition leading to the largest possible energy amplification at time T. We find that the two-dimensional initial condition with the largest potential for growth is a Tollmien–Schlichting-like wave packet that includes the Orr mechanism and is located inside the boundary layer downstream of the leading edge. Three-dimensional optimal disturbances induce streaks by the lift-up mechanism. Requiring the optimal initial condition to be localised upstream of the plate enables us to better study the effects of the leading edge on the boundary layer receptivity mechanisms. Two-dimensional upstream disturbances are inefficient at triggering unstable eigenmodes, whereas three-dimensional disturbances induce streamwise streaks with significant growth.     

A non-Karplus effect: evidence from phosphorus heterocycles and DFT calculations of the dependence of vicinal phosphorus-hydrogen NMR coupling constants on lone-pair conformation

In contrast to literature reports of a Karplus-type curve that correlates (3)J(PH) with phosphorus-hydrogen dihedral angle, a recently reported glycine-derived 1,3,2-oxazaphospholidine (7c) has two hydrogen atoms on the ring with identical PNCH dihedral angles but measured coupling constants of ～6 and 1.5 Hz. DFT calculations were in accord with these values and suggested that the smaller coupling constant is negative. Experimental evidence of the opposite signs of these coupling constants was obtained by analysis of the ABX NMR spectrum of the new glycine-derived N-p-toluenesulfonyl phosphorus heterocycle 6c. DFT calculations on 6c and on Me(2)NPCl(2) and t-BuPCl(2) were also in accord with NMR data and allowed confirmation of unusual features including a lone pair effect on (3)J(PH), the negative coupling constant, temperature-dependent chemical shifts due to rotation about the sulfonamide S-N bond, and vicinal phosphorus-hydrogen coupling constants over 40 Hz. Calculation of phosphorus-hydrogen coupling constants both as a function of PYCH dihedral angle θ (Y = O, N, C) and lone pair-PYC dihedral angle ω shows similar θ,ω surfaces for (3)J(PH) with a range of (3)J(PH) from -4.4 to +51 Hz and demonstrates the large non-Karplus effect of lone-pair conformation on vicinal phosphorus-hydrogen coupling constants.     

Optimal strategies for water quality control

In this paper, the use of optimal control theory to obtain optimal strategies for the control of aquatic models is illustrated. Several types of control variables are used including the rate of nutrient application and the rates of change of nutrient concentration in both the phytoplankton and zooplankton populations. Techniques are given to show how optimal control theory can be applied to several models with different states and control variables constraints. Explicit expressions and optimality conditions are given for singular controls whenever they exist. Some numerical techniques are suggested to couple the optimal control parts in the proper sequence.     

Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matrices

In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number of generators of a finitely generated abelian semigroup or group of matrices with a dense or a somewhere dense orbit by computing the minimal number of generators of a dense subsemigroup (or subgroup) of the connected component of the identity of its Zariski closure.     

Controlled modulation of mesoporosities in metal (M = Al, Fe) phosphate solids

Mesoporous solids which possess average pore diameters between 7 and 20 nm, depending on the composition, have been prepared. The solids have the general formula Al₁₀₀P_χM₂₀ where M = Al or Fe, and χ = 0, 4.5, 9, 18, 36, 72 or 144. The initial addition of phosphorus as phosphate transforms the originally crystalline oxide/oxides into amorphous solids. These amorphous materials possess a narrow pore size distribution: 80–90% of the pores lie within 1–2 nm of the average pore diameter. Subsequent incremental amounts of phosphorus transform the material into a crystalline solid whilst the pore size distribution becomes much wider and the maximum moves towards larger pore diameters. Substitution of 20% of the aluminium by iron results, at a low phosphorus content, in pores with smaller pore volumes and smaller surface areas.

The data in the dV_p/dD_p = > D_p) graphs, where V_p is the incremental pore volume and D_p is the average pore diameter, can be approximated using an admixture of Gaussian and Lorentzian curves. For low phosphorus contents the dV_p/dD_p = (D_p) curves have a mainly Gaussian profile but the gradual addition of phosphorus transforms them to Lorentzian-type curves. An attempt to approximate the histograms dV_p =(D_p) with the minimum number of distribution curves made up of the corresponding Gaussian and Lorentzian components indicates that each successive addition of phosphorus creates a dominant new pore component at a larger pore diameter. At the same time, the components at smaller pore diameters are diminished and eventually disappear as more phosphorus is added.     

On a covering problem related to the centered Hardy-Littlewood maximal inequality

We find the exact value of the best possible constant associated with a covering problem on the real line.