Convergence of Discrete Green Functions with Neumann Boundary Conditions

In this article we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Our methods rely on local central limit theorems for convergence of random walks on discretizations of smooth domains to Reflected Brownian motion.     

Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.     

Sharp superconductor-insulator transition in short wires

Recent experiments on short MoGe nanowires show a sharp superconducting-insulating transition at the universal resistance R(Q)=h/(4e(2)), contrary to the expectation of a smooth temperature dependence of the resistance for such Josephson-like systems. We present a self-consistent renormalization-group treatment of interacting quantum phase slips in short superconducting wires, which reproduces this sharp universal transition. Our method should also apply to other systems in the sine-Gordon universality class, in the previously inaccessible intermediate-coupling regime.     

Optical AND gate based on soliton interaction in a fiber Bragg grating

Using computer simulations, we demonstrate an optical cascadable AND gate based on soliton interaction in a fiber Bragg grating. A single soliton that is launched into the device is backreflected. When two solitons are launched, one of the solitons is transmitted while the other is backreflected. The time delay between the solitons may be few times longer than the duration of the solitons. We show that the interaction causes an increase in the frequency of one of the solitons that enables its transmission through the grating bandgap.     

Hereditary and maximal crossed product orders

We first deal with classical crossed products , where is a finite group acting on a Dedekind domain and (the -invariant elements in ) a DVR, admitting a separable residue fields extension. Here is a 2-cocycle. We prove that is hereditary if and only if is semi-simple. In particular, the heredity property may hold even when is not tamely ramified (contradicting standard textbook references). For an arbitrary Krull domain , we use the above to prove that under the same separability assumption, is a maximal order if and only if its height one prime ideals are extended from . We generalize these results by dropping the residual separability assumptions. An application to non-commutative unique factorization rings is also presented.

     

New Coins from Old, Smoothly

Given a (known) function f:[0,1]→(0,1), we consider the problem of simulating a coin with probability of heads f(p) by tossing a coin with unknown heads probability p, as well as a fair coin, N times each, where N may be random. The work of Keane and O’Brien (ACM Trans. Model. Comput. Simul. 4(2):213–219, 1994) implies that such a simulation scheme with the probability ℙ _p (N<∞) equal to 1 exists if and only if f is continuous. Nacu and Peres (Ann. Appl. Probab. 15(1A):93–115, 2005) proved that f is real analytic in an open set S⊂(0,1) if and only if such a simulation scheme exists with the probability ℙ _p (N>n) decaying exponentially in n for every p∈S. We prove that for α>0 noninteger, f is in the space C ^α [0,1] if and only if a simulation scheme as above exists with ℙ _p (N>n)≤C(Δ _n (p)) ^α , where \varDelta _n(x):=max{?{x(1-x)/n},1/n}\varDelta _{n}(x):=\max\{\sqrt{x(1-x)/n},1/n\}. The key to the proof is a new result in approximation theory: Let B⁺_n\mathcal{B}^{+}_{n} be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree n. We show that a function f:[0,1]→(0,1) is in C ^α [0,1] if and only if f has a series representation ?_n=1^￥F_n\sum_{n=1}^{\infty}F_{n} with F_n ? B⁺_nF_{n}\in \mathcal{B}^{+}_{n} and ∑ _k>n F _k (x)≤C(Δ _n (x)) ^α for all x∈[0,1] and n≥1. We also provide a counterexample to a theorem stated without proof by Lorentz (Math. Ann. 151:239–251, 1963), who claimed that if some j_n ? B⁺_n\varphi_{n}\in\mathcal{B}^{+}_{n} satisfy |f(x)−φ _n (x)|≤C(Δ _n (x)) ^α for all x∈[0,1] and n≥1, then f∈C ^α [0,1].     

Time-resolved emission of flavin adenine dinucleotide in water and water-methanol mixtures

Time-resolved fluorescence decay of flavin adenine dinucleotide (FAD) was studied at room temperature in water and water-methanol mixtures by a fluorescence upconversion technique. The observations were focused on the most initial decay phase (200 ps), before the residual fluorescence assumes a single exponential decay, typical for an extended conformation of the fluorophore. Within the first few picoseconds, where most of the electron transfer coupled quenching takes place, the emission decay curves could be fitted by a stretched exponent, compatible with the inhomogeneous distance dependent electron transfer model. This implies that the population of the excited FAD molecules exhibits a large number of non-identical states, each with its own separation between the donor (adenine) and acceptor (isoalloxazine) moieties, having its own rate of electron transfer. To evaluate the distribution of the separation between the donor-acceptor pair, we carried out molecular dynamics simulations of closed conformation of the FAD in water and water-methanol mixtures, sampling the structure at 10 fs intervals. The analysis of the dynamics reveals that within the 4 ps time frame, where most of the nonexponential fluorescence relaxation takes place, the relative motion of the donor-acceptor pair is consistent with a one-dimensional Brownian motion, where the diffusion coefficient and the shape of the confining potential well are solvent dependent. The presence of methanol enhances the diffusion constant and widens the width of the potential well. On the basis of these parameters, the relaxation dynamics was accurately reconstructed as an electron transfer reaction in an inhomogeneous system where the reactants are diffusing within the time frame of the observation.     

Modeling the nonradiative decay rate of electronically excited thioflavin T

A computational model of nonradiative decay is developed and applied to explain the time-dependent emission spectrum of thioflavin T (ThT). The computational model is based on a previous model developed by Glasbeek and co-workers (van der Meer, M. J.; Zhang, H.; Glasbeek, M. J. Chem. Phys. 2000, 112, 2878) for auramine O, a molecule that, like ThT, exhibits a high nonradiative rate. The nonradiative rates of both auramine O and ThT are inversely proportional to the solvent viscosity. The Glasbeek model assumes that the excited state consists of an adiabatic potential surface constructed by adiabatic coupling of emissive and dark states. For ThT, the twist angle between the benzothiazole and the aniline is responsible for the extensive mixing of the two excited states. At a twist angle of 90°, the S(1) state assumes a charge-transfer-state character with very small oscillator strength, which causes the emission intensity to be very small as well. In the ground state, the twist angle of ThT is rather small. The photoexcitation leads first to a strongly emissive state (small twist angle). As time progresses, the twist angle increases and the oscillator strength decreases. The fit of the experimental results by the model calculations is good for times longer than 3 ps. When a two-coordinate model is invoked or a solvation spectral-shift component is added, the fit to the experimental results is good at all times.