Loredana Ricciardi

Photo-sensitive liquid crystals for optically controlled diffraction gratings

We report on the fabrication and characterization of diffraction gratings based on a polymeric microstructure including a light responsive material, which enables an all-optical control of the diffraction of light. The enhanced performances of a mesogenic azo dye are combined with the outstanding properties of reconfigurability and fluidity of nematic liquid crystals; the mesogenic affinity between the two substances enables realization of a photosensitive liquid crystal whose optical properties can be controlled by means of low power light. Long range order and high mechanical stability of the photosensitive liquid crystal composition are obtained by using the universal organizing capability of a channeled polymeric template, without the need for any kind of surface treatment. The structure exhibits strong contrast ratio and a high diffraction efficiency, both optically controlled.

Rheological and photophysical investigations of chromonic-like supramolecular mesophases formed by luminescent iridium(III) ionic complexes in water

ABSTRACT Luminescent complexes with general formula [(C^N)2Ir(N^N)]OCOCH3, where C^N = 2-phenylpyridine (ppy) and N^N = 2,2ʹ-bipyridine (bpy), self-assemble into ordered ‘soft’ viscous mesophases of chromonic type. By changing the ancillary ligand with 1,10-phenanthroline (phen), a new mesomorphic complex was obtained. The self-assembly into ordered liquid crystalline phases of chromonic type in water was investigated by comprehensive rheological and photophysical studies. By changing the ancillary ligand bpy with phen, assembly into smaller, more symetric aggregates is favoured, resulting in lower viscosity and more dynamic mesophase. Graphical Abstract

Neural Networks: Reverberations, Constants of Motion, General Behavior

Suppose the brain is a machine made of variously structured and interconnected biological decision elements (the neurons), and attempt to approximate its behavior with some highly schematized model composed of artificial (hardware or purely mathematical) binary decisors (which are still called “neurons” for simplicity): this is, reduced to bare essentials, a “neural network”, of which the theory is approached here from a novel angle, different from standard boolean algebra or probabilistic descriptions. Our tool is ordinary matrix algebra; our aim, the formulation and solution of some central theoretical problems (those mentioned in the title), the nature of which seems to discourage different approaches. We shall insist neither on details nor on generality, referring for lengthier discussions to the works cited in the references; we only note that most of our results hold also if the number of neurons is infinite, and in some cases even continuous: this should suffice to show the difference between standard automata theory and our methods.

Note on Relating Pfaffians and Hafnians with Determinants and Permanents

In connection with renormalization problems in quantum field theory, Pfaffians and Hafnians are considered. A noteworthy expansion of determinants and permanents is given, in terms of Pfaffian‐like and Hafnian‐like objects, that immediately leads to the known reduction of a determinant to a single Pfaffian. Finally, some auxiliary results are presented.

Decomposition of a matrix as the sum of direct products. Applications to neural networks

The rank of a matrix can be expressed as the least number of sums of direct products into which the matrix can be decomposed.Some applications to nets of linear threshold elements are given.