Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.     

Impact of Molecular Size and Shape on the Supramolecular Co-Assembly of Chiral Tricarboxamides: A Comparative Study

A comparative investigation of the chiral amplification features of a series of three families of C₃-symmetric tricarboxamides, 1,3,5-triphenylbenzenetricarboxamides (TPBAs), benzenetricarboxamides (BTAs) and oligo(phenylene ethynylene) tricarboxamides (OPE-TAs), is here reported. As previously observed for BTAs and OPE-TAs, a similar dichroic response is obtained for TPBAs decorated with one, two or three chiral side chains bearing stereogenic centers, thus confirming the efficient transfer of point chirality to the supramolecular helical aggregates. Unlike BTAs and OPE-TAs, the chiral amplification ability of TPBAs in majority rules experiments shows a negligible dependence on the number of chiral centers per monomeric unit, and stands the largest among the series of tricarboxamides. Detailed experimental and theoretical studies demonstrate that the rotation angle between the TPBA units in the helical stack is intermediate to that observed for BTAs and OPE-TAs. This feature strongly conditions the steric interactions between vicinal molecules in the stack and the final chiral amplification outcome. Furthermore, theoretical calculations show that achiral side chains favor the interdigitation of the helical aggregates and thereby the formation of bundle superstructures.     

Spectrally accurate space-time solution of Hamiltonian PDEs

Numerical Algorithms - Recently, the numerical solution of multi-frequency, highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral...     

Co-Training for Visual Object Recognition Based on Self-Supervised Models Using a Cross-Entropy Regularization

Automatic recognition of visual objects using a deep learning approach has been successfully applied to multiple areas. However, deep learning techniques require a large amount of labeled data, which is usually expensive to obtain. An alternative is to use semi-supervised models, such as co-training, where multiple complementary views are combined using a small amount of labeled data. A simple way to associate views to visual objects is through the application of a degree of rotation or a type of filter. In this work, we propose a co-training model for visual object recognition using deep neural networks by adding layers of self-supervised neural networks as intermediate inputs to the views, where the views are diversified through the cross-entropy regularization of their outputs. Since the model merges the concepts of co-training and self-supervised learning by considering the differentiation of outputs, we called it Differential Self-Supervised Co-Training (DSSCo-Training). This paper presents some experiments using the DSSCo-Training model to well-known image datasets such as MNIST, CIFAR-100, and SVHN. The results indicate that the proposed model is competitive with the state-of-art models and shows an average relative improvement of 5% in accuracy for several datasets, despite its greater simplicity with respect to more recent approaches.     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.