Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.     

Solvent effects on charge spatial extent in DNA and implications for transfer

To clarify the role played by water in facilitating long-range DNA charge transport, carefully designed, state-of-the-art, self-interaction corrected density-functional quantum mechanical and molecular mechanical (SIC-QM/MM) simulations are performed for the first time on two ionized adenine:thymine bridge models in explicit water solvent at finite temperature. For random solvent configurations, the charge is partially delocalized. However, a charge localization on different, well-separated adenines can be induced and is correlated with a restructuring of their first solvation shells. Thus, the importance of water in the mechanism of long-range charge transport is explicitly demonstrated, and the microscopic conditions for a charge localization are revealed.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

Molecular Pom Poms from Self‐Assembling α,γ‐Cyclic Peptides

The hierarchical self‐assembly properties of a dimer‐forming cyclic peptide that bears a nicotinic acid moiety to form molecular pom‐pom‐like structures are described. This dimeric assembly self organizes into spherical structures that can encapsulate small organic molecules owing to its porosity and it can also facilitate metal deposition on its surface directed by the pyridine moiety.     

Symmetry-Breaking Charge-Transfer Chromophore Interactions Supported by Carbon Nanodots

Carbon dots (CDs) and their derivatives are useful platforms for studying electron-donor/acceptor interactions and dynamics therein. Herein, we couple amorphous CDs with phthalocyanines (Pcs) that act as electron donors with a large extended π-surface and intense absorption across the visible range of the solar spectrum. Investigations of the intercomponent interactions by means of steady-state and pump-probe transient absorption spectroscopy reveal symmetry-breaking charge transfer/separation and recombination dynamics within pairs of phthalocyanines. The CDs facilitate the electronic interactions between the phthalocyanines. Thus, our findings suggest that CDs could be used to support electronic couplings in multichromophoric systems and further increase their applicability in organic electronics, photonics, and artificial photosynthesis.     

Permutation Entropy-Based Interpretability of Convolutional Neural Network Models for Interictal EEG Discrimination of Subjects with Epileptic Seizures vs. Psychogenic Non-Epileptic Seizures

The differential diagnosis of epileptic seizures (ES) and psychogenic non-epileptic seizures (PNES) may be difficult, due to the lack of distinctive clinical features. The interictal electroencephalographic (EEG) signal may also be normal in patients with ES. Innovative diagnostic tools that exploit non-linear EEG analysis and deep learning (DL) could provide important support to physicians for clinical diagnosis. In this work, 18 patients with new-onset ES (12 males, 6 females) and 18 patients with video-recorded PNES (2 males, 16 females) with normal interictal EEG at visual inspection were enrolled. None of them was taking psychotropic drugs. A convolutional neural network (CNN) scheme using DL classification was designed to classify the two categories of subjects (ES vs. PNES). The proposed architecture performs an EEG time-frequency transformation and a classification step with a CNN. The CNN was able to classify the EEG recordings of subjects with ES vs. subjects with PNES with 94.4% accuracy. CNN provided high performance in the assigned binary classification when compared to standard learning algorithms (multi-layer perceptron, support vector machine, linear discriminant analysis and quadratic discriminant analysis). In order to interpret how the CNN achieved this performance, information theoretical analysis was carried out. Specifically, the permutation entropy (PE) of the feature maps was evaluated and compared in the two classes. The achieved results, although preliminary, encourage the use of these innovative techniques to support neurologists in early diagnoses.     

Thermolytic behavior of polydienyllithium and polystyryllithium

UV absorption spectra of thermolyzed polybutadienyl- and polyisoprenyl-lithium reveal a chromophore group previously not recognized for such systems; its absorption band at 271 nm has been assigned to a structure with three conjugated double bonds. A two-step mechanism for the formation of this trienic structure is proposed: an intermolecular metallation of associated living ends is followed by lithium hydride (LiH) elimination. Along thermolysis the presence of a dienic structure was also recognized, the latter arising from intramolecular elimination of LiH. The trienyllithium structure is also considered to be an effective species for the observed molecular weight distribution (MWD) variations. The observed different extent of high molecular weight (HMW) for polyisoprenyl- and polybutadienyl-lithium is explained on the basis of a different stability of the intermediates present along the proposed reaction mechanism. The thermolytic behavior of polystyryllithium does not provide any significant change in MWD: the disappearance of the living chain ends, UV detected, is due to an intramolecular LiH elimination which obeys first-order kinetics. The influence of temperature and of the tetrahydrofuran (THF) level on kinetic rate constants was investigated. © 1996 John Wiley & Sons, Inc.     

Human mobility and COVID-19 initial dynamics

Nonlinear Dynamics - Countries in Europe took different mobility containment measures to curb the spread of COVID-19. The European Commission asked mobile network operators to share on a...     

Computational maturation of a single-domain antibody against Aβ42 aggregation

The expansion of structural databases and the increase in computing power are enabling approaches for antibody discovery based on computational design. It has already been shown that it is possible to use this approach to generate antibodies for specific epitopes on challenging targets. Here we describe an application of this procedure for antibody maturation through the computational design of mutational variants of increased potency. We illustrate this procedure in the case of a single-domain antibody targeting an epitope in the N-terminal region of Aβ42, a peptide whose aggregation is closely associated with Alzheimer''s disease. We show that this approach enables the generation of an antibody variant with over 200-fold increased potency against the primary nucleation process in Aβ42 aggregation. Our results thus demonstrate that potentiated antibody variants can be obtained by computational maturation.

A computational maturation method enables the generation of an antibody variant with over 200-fold increased potency against the primary nucleation process in Aβ42 aggregation.