Lower and upper estimates on the excitation threshold for breathers in DNLS lattices

We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized and time periodic solutions) in DNLS lattices with power nonlinearity. The estimation depending explicitly on the lattice parameters, is derived by a combination of a comparison argument on appropriate lower bounds depending on the frequency of each solution with a simple and justified heuristic argument. The numerical studies verify that the analytical estimates can be of particular usefulness, as a simple analytical detection of the activation energy for breathers in DNLS lattices.Comment: 10 pages, 3 figure

Design of a fault tolerant airborne digital computer. Volume 2: Computational requirements and technology

This final report summarizes the work on the design of a fault tolerant digital computer for aircraft. Volume 2 is composed of two parts. Part 1 is concerned with the computational requirements associated with an advanced commercial aircraft. Part 2 reviews the technology that will be available for the implementation of the computer in the 1975-1985 period. With regard to the computation task 26 computations have been categorized according to computational load, memory requirements, criticality, permitted down-time, and the need to save data in order to effect a roll-back. The technology part stresses the impact of large scale integration (LSI) on the realization of logic and memory. Also considered was module interconnection possibilities so as to minimize fault propagation

Advances in genome-wide RNAi cellular screens: a case study using the Drosophila JAK/STAT pathway

BACKGROUND: Genome-scale RNA-interference (RNAi) screens are becoming ever more common gene discovery tools. However, whilst every screen identifies interacting genes, less attention has been given to how factors such as library design and post-screening bioinformatics may be effecting the data generated. RESULTS: Here we present a new genome-wide RNAi screen of the Drosophila JAK/STAT signalling pathway undertaken in the Sheffield RNAi Screening Facility (SRSF). This screen was carried out using a second-generation, computationally optimised dsRNA library and analysed using current methods and bioinformatic tools. To examine advances in RNAi screening technology, we compare this screen to a biologically very similar screen undertaken in 2005 with a first-generation library. Both screens used the same cell line, reporters and experimental design, with the SRSF screen identifying 42 putative regulators of JAK/STAT signalling, 22 of which verified in a secondary screen and 16 verified with an independent probe design. Following reanalysis of the original screen data, comparisons of the two gene lists allows us to make estimates of false discovery rates in the SRSF data and to conduct an assessment of off-target effects (OTEs) associated with both libraries. We discuss the differences and similarities between the resulting data sets and examine the relative improvements in gene discovery protocols. CONCLUSIONS: Our work represents one of the first direct comparisons between first- and second-generation libraries and shows that modern library designs together with methodological advances have had a significant influence on genome-scale RNAi screens

A Complexity Measure for Continuous Time Quantum Algorithms

We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over the chromatic index of the interaction graph. This defines a complexity measure of continuous and discrete quantum algorithms which are in exact one-to-one correspondence. Furthermore we prove a lower bound on the growth of large-scale entanglement depending on the chromatic index.Comment: 6 pages, Revte

Existence of Multistring Solutions of the Self-Gravitating Massive W−W-Boson

We consider a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in \cite{yan}Comment: 12 page

Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure

Lagrange Multipliers in Infinite-Dimensional Systems, Methods of

International audienceThis entry will describe Lagrange multipliers method using a formulation which is valid for infinite-dimensional dynamical systems. The method of Lagrange multipliers is employed to deal with systems subject to constraints. The theoretical foundations of this method are presented, and a proof of the main theorem is illustrated for the relevant case of constraints defined on a Banach vector space