Improving accuracy by subpixel smoothing in the finite-difference time domain

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.     

Parallel Versus Antiparallel β-Sheet Structure in Cyclic Peptide Hybrids Containing γ- or δ-Cyclic Amino Acids

Cyclic peptides with disc-shaped structures have emerged as potent building blocks for the preparation of new biomaterials in fields ranging from biological to material science. In this work, we analyze in depth the self-assembling properties of a new type of cyclic peptides based on the alternation of α-residues and cyclic δ-amino acids (α,δ-CPs). To examine the preferred stacking properties adopted by cyclic peptides bearing this type of amino acids, we carried out a synergistic in vitro/in silico approximation by using simple dimeric models and then extended to nanotubes. Although these new cyclic peptides (α,δ-CPs) can interact either in a parallel or antiparallel fashion, our results confirm that although the parallel β-sheet is more stable, it can be switched to the antiparallel stacking by choosing residues that can establish favorable cross-strand interactions. Moreover, the subsequent comparison by using the same methodology but applied to α,γ-CPs models, up to the moment assumed as antiparallel-like d,l -α-CPs, led to unforeseen conclusions that put into question preliminary conjectures about these systems. Surprisingly, they tend to adopt a parallel β-sheet directed by the skeleton interactions. These results imply a change of paradigm with respect to cyclic peptide designs that should be considered for dimers and nanotubes.     

Transition-Metal-Free Multiple Functionalization of Piperidines to 4-Substituted and 3,4-Disubstituted 2-Piperidinones

Remote and multiple functionalization of piperidines without the use of transition-metal catalysts and elaborate directing groups is one of the major challenges in organic synthesis. Herein is reported an unprecedented two-step protocol that enables the multiple functionalization of piperidines to either 4-substituted or trans-3,4-disubstituted 2-piperidones. First, by exploiting the duality of TEMPO reactivity, which under oxidative and thermal conditions fluctuates between cationic and persistent-radical form, a novel multiple C(sp³)-H oxidation of piperidines to α,β-unsaturated 2-piperidones was developed. Second, the intrinsic low reactivity of the unsaturated piperidones toward conjugated Grignard additions was overcome by using trimethylsilyl chloride (TMSCl) as Lewis acid. Subsequently, conjugated Grignard addition/electrophilic trapping protocol provided substituted 2-piperidone intermediates, some of which were then transformed into pharmaceutical alkaloids.     

The Spectral Density Function for the Laplacian on High Tensor Powers of a Line Bundle

For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin–Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density function. We give an explicit computation of the spectral density function, by constructing certain quasimodes on the associated principle bundle.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters

The elastic and radiative ⁺ p scattering are studied in the framework of an effective Lagrangian model for the ⁺⁺ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole ( ⁺⁺) and background contributions ( ⁰, , , and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the ⁺⁺ obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative ⁺ p scattering is nuclear magnetons.     

On Multi-threaded Metrical Task Systems

Traditionally, on-line problems have been studied under the assumption that there is a unique sequence of requests that must be served. This approach is common to most general models of on-line computation, such as Metrical Task Systems. However, there exist on-line problems in which the requests are organized in more than one independent thread. In this more general framework, at every moment the first unserved request of each thread is available. Therefore, apart from deciding how to serve a request, at each stage it is necessary to decide which request to serve among several possibilities.In this paper we introduce Multi-threaded Metrical Task Systems, that is, the generalization of Metrical Task Systems to the case in which there are many threads of tasks. We study the problem from a competitive analysis point of view, proving lower and upper bounds on the competitiveness of on-line algorithms. We consider finite and infinite sequences of tasks, as well as deterministic and randomized algorithms. In this work we present the first steps towards a more general framework for on-line problems which is not restricted to a sequential flow of information.