New bounds on the average distance from the Fermat–Weber center of a planar convex body

The Fermat–Weber center of a planar body Q is a point in the plane from which the average distance to the points in Q is minimal. We first show that for any convex body Q in the plane, the average distance from the Fermat–Weber center of Q to the points in Q is larger than , where Δ(Q) is the diameter of Q. This proves a conjecture of Carmi, Har-Peled and Katz. From the other direction, we prove that the same average distance is at most . The new bound substantially improves the previous bound of due to Abu-Affash and Katz, and brings us closer to the conjectured value of . We also confirm the upper bound conjecture for centrally symmetric planar convex bodies.     

Corrector-predictor methods for sufficient linear complementarity problems

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity, the same as Miao’s method, but our error estimates are sightly better. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also present a family of infeasible higher order corrector-predictor methods that are superlinearly convergent even in the absence of strict complementarity. The algorithms of this class are globally convergent for general positive starting points. They have \(O((1+\kappa)\sqrt{n}L)\)-iteration complexity for feasible, or “almost feasible”, starting points and O((1+κ)² nL)-iteration complexity for “sufficiently large” infeasible starting points.     

Numerical calculation of the neutral fermion gap at the ν=5/2 fractional quantum Hall state

We present the first numerical computation of the neutral fermion gap, Δ(F), in the ν=5/2 quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find Δ(F)≈0.027e(2)/ε?(0), comparable to the charge gap. We also deduce an effective Fermi velocity v(F) for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length ξ(F)=v(F)/Δ(F)≈1.3?(0). We comment on implications for experiments, topological quantum information processing, and electronic mechanisms of superconductivity.     

Neutron powder diffraction and magnetic studies of mesoporous Co3O4

Samples of mesoporous Co₃O₄, created by using mesoporous silicas KIT-6 and SBA-16 as hard templates to control the growth of Co₃O₄ have been investigated with SQUID magnetometry and neutron powder diffraction, to reveal the effects of high surface area on the magnetic and electronic properties. DC magnetic susceptibility measurements show lower Néel ordering temperatures and lower magnetic moments than in a “bulk” reference. A lower second transition temperature is also observed in the mesoporous samples, associated with the freezing of the surface (shell) magnetic moments. Measurements taken with increasing applied field at constant temperature show the materials to be antiferromagnetic as expected. Complementary parametric neutron powder diffraction studies show similar trends between the two mesoporous samples when looking at their Néel temperatures, and verify long range order within the samples.     

Pathways of Electrochemical Oxidation of Indolic Compounds

The electrochemical behaviour of indole and a group of indole‐containing compounds with a substituent at the C3 position, indol‐3‐acetamide (IAM), tryptamine, gramine, indole acetic acid (IAA), indole propionic acid (IPA), indole butyric acid (IBA) and tryptophan, was investigated at a glassy carbon electrode, in order to determine their oxidation pathways. Indole undergoes one irreversible pH dependent oxidation, whereas the oxidation process of indole derivatives was more complex, a two step, the oxidation at C2 position on the pyrrole ring followed by the hydroxylation at the C7 position of the benzene moiety of indoles, irreversible pH dependent oxidation.     

The rational development of molecularly imprinted polymer-based sensors for protein detection

The detection of specific proteins as biomarkers of disease, health status, environmental monitoring, food quality, control of fermenters and civil defence purposes means that biosensors for these targets will become increasingly more important. Among the technologies used for building specific recognition properties, molecularly imprinted polymers (MIPs) are attracting much attention. In this critical review we describe many methods used for imprinting recognition for protein targets in polymers and their incorporation with a number of transducer platforms with the aim of identifying the most promising approaches for the preparation of MIP-based protein sensors (277 references).     

Real time evolution of liquid crystalline nanostructure during the digestion of formulation lipids using synchrotron small-angle X-ray scattering

The role of the digestion of lipids in facilitating absorption of poorly water-soluble compounds, such as vitamins, is not only an important nutritional issue but is increasingly being recognized as an important determinant in the effectiveness of lipid-based drug formulations. It has been known for some time that lipids often form complex liquid crystalline structures during digestion and that this may impact drug solubilization and absorption. However, until recently we have been unable to detect and characterize those structures in real time and have been limited in establishing the interplay between composition, digestion, and nanostructure. Here, we establish the use of an in vitro lipid digestion model used in conjunction with synchrotron small-angle X-ray scattering by first confirming its validity using known, nondigestible liquid crystalline systems, and then extend the model to study the real time evolution of nanostructure during the digestion of common formulation lipids. The formation of liquid crystalline structures from unstructured liquid formulations is discovered, and the kinetics of formation and dependence on composition is investigated.     

Catching the first oligomerization event in the catalytic formation of polyaminoboranes: H3B·NMeHBH2·NMeH2 bound to iridium

We report the first insertion step at a metal center for the catalytic dehydropolymerization of H(3)B·NMeH(2) to form the simplest oligomeric species, H(3)B·NMeHBH(2)·NMeH(2), by the addition of 1 equiv of H(3)B·NMeH(2) to [Ir(PCy(3))(2)(H)(2)(η(2)-H(3)B·NMeH(2))][BAr(F)(4)] to give [Ir(PCy(3))(2)(H)(2)(η(2)-H(3)B·NMeHBH(2)·NMeH(2))][BAr(F)(4)]. This reaction is also catalytic for the formation of the free linear diborazane, but this is best obtained by an alternative stoichiometric synthesis.     

Nonsmooth optimization via quasi-Newton methods

We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f, not necessarily convex. We introduce an inexact line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the Armijo and Wolfe conditions if f is absolutely continuous along the line. Furthermore, the line search is guaranteed to terminate if f is semi-algebraic. It seems quite difficult to establish a convergence theorem for quasi-Newton methods applied to such general classes of functions, so we give a careful analysis of a special but illuminating case, the Euclidean norm, in one variable using the inexact line search and in two variables assuming that the line search is exact. In practice, we find that when f is locally Lipschitz and semi-algebraic with bounded sublevel sets, the BFGS (Broyden–Fletcher–Goldfarb–Shanno) method with the inexact line search almost always generates sequences whose cluster points are Clarke stationary and with function values converging R-linearly to a Clarke stationary value. We give references documenting the successful use of BFGS in a variety of nonsmooth applications, particularly the design of low-order controllers for linear dynamical systems. We conclude with a challenging open question.