Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Experimentally realizable characterizations of continuous- variable Gaussian states

Measures of entanglement, fidelity, and purity are basic yardsticks in quantum-information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous-variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge that is relevant to current experiments.

Nonclassicality of a photon-subtracted Gaussian field

We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.

Entanglement of a two-mode squeezed state in a phase-sensitive Gaussian environment

Some non-classical properties such as squeezing, sub-Poissonian photon statistics or oscillations in photon-number distributions may survive longer in a phase-sensitive environment than in a phase-insensitive environment. We examine if entanglement, which is an inter-mode non-classical feature, can also survive longer in a phase-sensitive environment. Differently from the single-mode case, we find that making the environment phase-sensitive does not aid in prolonging the inter-mode non-classical nature, i.e. entanglement.

Role of conformational constraints of position 7 of the disulphide bridge of h-alpha-CGRP derivatives in their agonist versus antagonist properties

Previous structure-activity studies have shown that the disulphide bridge of calcitonin gene-related peptide (CGRP) is important for the highly potent, CGRP receptor-mediated effects of this peptide. In this study penicillamine (Pen) was substituted for one or both of the cysteinyl residues to determine conformational and topographical properties of the disulphide bridge favourable for binding to CGRP receptors and/or receptor activation. Pen constrains the conformational flexibility of disulphide bridges in other peptides. Binding affinities were measured using a radioligand binding assay with membranes prepared from pig coronary arteries and I-125-h-alpha-CGRP. Functional effects were characterized using a previously reported pig coronary artery relaxation bioassay. The binding affinity of [Pen(2)]h-alpha-CGRP was not significantly different from that of h-alpha-CGRP. All other analogues showed reduced affinity for CGRP receptors. [Pen(2)]h-alpha-CGRP also caused relaxation of coronary arteries. The remaining analogues either caused relaxation with significantly reduced potency or failed to relax the arteries at concentrations up to 1 x 10(-5) M. All analogues that did not relax coronary arteries contained a D-Pen in position 7 and inhibited CGRP-induced relaxation. [D-Pen(2,7)]h-alpha- CGRP was the most potent antagonist with a K-B value of 630 nM. This affinity is similar to that of the classical CGRP receptor antagonist, h-alpha-CGRP(8-37), on these arteries (K-B, 212 nM). These studies show that modifying the topography of the disulphide bridge can cause large and variable effects on ligand binding and activation of CGRP receptors. The contribution of position 7 to the conformation and topography of the disulphide bridge of h-alpha-CGRP is crucial to the future design of agonists of CGRP receptors. Furthermore, position 7 is important for the development of new CGRP receptor antagonists with structures based on the whole sequence of h-alpha-CGRP.