Markovian description of unbiased polymer translocation

We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general Markovian framework for unbiased three-dimensional polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literature by the present authors.     

Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces

In this paper we introduce a notion of asymptotic almost-equivalence of two evolution systems and provide simple tests that guarantee that two evolution systems have the same qualitative asymptotic properties. In this way we are able to unify and extend many previously known results and also to understand what is behind equally behaved systems. In particular, we establish convergence, ergodic convergence and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits.     

Decoupled field integral equations for electromagnetic scattering from homogeneous penetrable obstacles

We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one for the electric field and one for the magnetic field. This permits the derivation of resonance-free Fredholm equations of the second kind that are stable at all frequencies, insensitive to the genus of the scatterers, and invertible for all passive materials including those with negative permittivities or permeabilities. We refer to these as decoupled field integral equations.     

Testing with Exponentially Tilted Empirical Likelihood

Imposing restrictions without assuming underlying distributions to modelize complex realities is a valuable methodological tool. However, if a subset of restrictions were not correctly specified, the usual test-statistics for correctly specified models tend to reject erronously a simple null hypothesis. In this setting, we may say that the model suffers from misspecification. We study the behavior of empirical phi-divergence test-statistics, introduced in Balakrishnan et al. Statistics 49:951–977 (2015), by using the exponential tilted empirical likelihood estimators of Schennach Ann Stat 35:634–672 (2007), as a good compromise between the efficiency of the significance level for small sample sizes and the robustness under misspecification.     

Computing the Homology of Real Projective Sets

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on its size and is singly exponential in the number of variables (the dimension of the ambient space) and polynomial in the condition and the degrees of the defining polynomials. In addition, we show that outside of an exceptional set of measure exponentially small in the size of the data, the algorithm takes exponential time.     

Machines Over the Reals and Non-Uniformity

We survey the research performed in the last few years on a specific topic: the power of real machines over binary inputs. This research attempts to characterize the classes of decision problems over a finite alphabet - say {0,1} - which can be decided by real machines working under several resource restrictions. Non-uniformity appears here in a natural way. However, since this is a technical concept which is not widely known, we summarize in Section 2 some of the intuitive notions, as well as a few basic theorems related to it. In Section 3 we do this for the subject of real machines and then, in Section 4 we present the state of the art of the surveyed topic. We devote Section 1 to introduce the main concepts of complexity theory. Proofs in this article are quite sketchy and are included more to convey intuitive ideas than to completely prove the claimed statements. Bibliographical references to the original literature are supplied for the latter purpose.     

Oxazolidines From Sugars. III. A New Method for N-Alkyl and N,N-Dialkyl-D-Glucosamine Derivatives

Abstract

Title compounds can be synthesised by an easy two-step method from the readily available benzyl 2-acylamino-4,6-O-benzylidene-2-deoxy-D-glucopyranosides (1–5), by nucleophilic cleavage of the oxazolidine ring previously formed between the positions 2 and 3 of the aminosugars.