Poly(epichlorohydrin) modified with 3,4,5‐tris(dodecyloxy)benzoate: The structure and dynamics of the aliphatic side chains in the columnar mesophase

We investigated the dynamics and structure of the aliphatic side chains of a randomly grafted copolymer, obtained through the chemical modification of poly(epichlorohydrin) with potassium 3,4,5‐tris(dodecyloxy)benzoate, with solid‐state ¹³C NMR. Below 283 K, the aliphatic chains partially crystallized in an all‐anti conformation. The calorimetric data were compatible with an orthorhombic packing. Below 323 K, the polymer exhibited a columnar mesophase. Spin–lattice relaxation times were determined in this temperature range and at 333 K, that is, in the isotropic phase. In the liquid‐crystalline state, some carbons exhibited a double decay in the spin–lattice relaxation, and this was attributed to presence of the liquid‐crystalline phase. This hypothesis was supported by a conformational analysis performed by molecular modeling. The activation energies of the relaxation processes in the mesophase were also estimated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2099–2111, 2005     

A parametric approach to correspondence analysis

We compare correspondence analysis (CA) and the alternative approach using Hellinger distance (HD), for representing categorical data in a contingency table. As both methods may be appropriate, we introduce a parameter and define a generalized version of correspondence analysis (GCA) which contains CA and HD as particular cases. Comparison with alternative approaches are performed. We propose a coefficient which globally measures the similarity between CA and GCA, which can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions on the difference between both representations. Two criteria for choosing the best value of the parameter are proposed.     

Linear Key Predistribution Schemes

In a key predistribution scheme, some secret information is distributed among a set of users. For a given family of privileged groups, this secret information must enable every user in a privileged group to compute a common key associated with that group. Besides, this common key must remain unknown to some specified coalitions of users outside the privileged group. We present in this paper a new model, based on linear algebraic techniques, for the design of key predistribution schemes that unifies all previous proposals. This new model provides a common mathematical formulation and a better understanding of key predistribution schemes. Two new families of key predistribution schemes that are obtained by using this model are presented. Those families provide, for some specification structures, schemes that have better information rates than the ones given in previous proposals or fit in situations that have not been considered before.     

Lattice dynamics of the transition metal pentatellurides ZrTe5 and HfTe5

Fresh Raman data collected from the (001) face of a ZrTe₅ single crystal and from polycrystalline powders of ZrTe₅ and HfTe₅ are presented. A simple model assuming only central interactions between nearest neighbour atoms is used for lattice dynamical calculations at $\text{k}\text{=}\text{0}$. The model accounts for the observations and places emphasis on the virtually lacking dynamical coupling between the two basic structural units in these pentatellurides [trigonal-prismatic (MTe₃)_n rods and zig-zag (Te₂)₂ chains].     

Some homoclinic phenomena in the three-body problem

We prove the existence of transversal homoclinic points in the collinear three-body problem, restricted and general, and in the planar circular restricted three-body problem. As a consequence the shift of Bernoulli is proved to be included as a subsystem of a suitable section of the flow for the three cases studied. Then the existence of all the possible types of final evolution follows.     

Minimal Blow-Up Solutions to the Mass-Critical Inhomogeneous NLS Equation

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the critical point is a maximum, this solution has minimal mass among the blow-up solutions. As a corollary, we also obtain unstable blow-up solutions of the mass-critical Schrödinger equation on some surfaces. The proof is based on properties of the linearized operator around the ground state, and on a full use of the invariances of the equation with an homogeneous nonlinearity and no potential, via time-dependent modulations.     

Finite Time Extinction by Nonlinear Damping for the Schrödinger Equation

We consider the Schrödinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.     

Supervised Domain Adaptation for Automated Semantic Segmentation of the Atrial Cavity

Atrial fibrillation (AF) is the most common cardiac arrhythmia. At present, cardiac ablation is the main treatment procedure for AF. To guide and plan this procedure, it is essential for clinicians to obtain patient-specific 3D geometrical models of the atria. For this, there is an interest in automatic image segmentation algorithms, such as deep learning (DL) methods, as opposed to manual segmentation, an error-prone and time-consuming method. However, to optimize DL algorithms, many annotated examples are required, increasing acquisition costs. The aim of this work is to develop automatic and high-performance computational models for left and right atrium (LA and RA) segmentation from a few labelled MRI volumetric images with a 3D Dual U-Net algorithm. For this, a supervised domain adaptation (SDA) method is introduced to infer knowledge from late gadolinium enhanced (LGE) MRI volumetric training samples (80 LA annotated samples) to a network trained with balanced steady-state free precession (bSSFP) MR images of limited number of annotations (19 RA and LA annotated samples). The resulting knowledge-transferred model SDA outperformed the same network trained from scratch in both RA (Dice equals 0.9160) and LA (Dice equals 0.8813) segmentation tasks.     

Rank Two Integral Representations of the Infinite Dihedral Group

We give an effective classification of the representations of the infinite dihedral group in GL ₂(R) where R is either the valuation ring ?_(p) or the ring of p-adic integers.