Speeding up Glauber Dynamics for Random Generation of Independent Sets

The maximum independent set (MIS) problem is a well-studied combinatorial optimization problem that naturally arises in many applications, such as wireless communication, information theory and statistical mechanics. MIS problem is NP-hard, thus many results in the literature focus on fast generation of maximal independent sets of high cardinality. One possibility is to combine Gibbs sampling with coupling from the past arguments to detect convergence to the stationary regime. This results in a sampling procedure with time complexity that depends on the mixing time of the Glauber dynamics Markov chain. We propose an adaptive method for random event generation in the Glauber dynamics that considers only the events that are effective in the coupling from the past scheme, accelerating the convergence time of the Gibbs sampling algorithm

The room temperature phosphine-free synthesis of near-infrared emitting HgSe quantum dots

Luminescent mercury selenide (HgSe) quantum dots have been synthesised by a phosphine-free method using oleic acid as a capping agent. The modification of experimental conditions such as temperature resulted in particles of various sizes (15–100 nm) and morphologies not previously seen in HgSe, with emission tuneable between 1000 nm and 1350 nm

Some examples and counterexamples for (min,+) filtering operations

This paper collects a serie of examples and counterexamples encountered in the study of the algorithmics of Network Calculus operations. Network Calculus is a deterministic queuing theory which aims at providing bounds on the performances of communication networks thanks to a nice formalization in (min,+) algebra. Often presented as a (min,+) filtering theory by analogy with the (+,x) filtering of traditional system theory, it makes use a well-defined set of operations. Their algorithmic aspects have not been much addressed. For this reason, we describe and analyze in a previous report a set of algorithms implementing these Network Calculus operations for a well-chosen class of functions. During this work, we had to construct some examples and counterexamples in order to draw the limits of our results or to illustrate them. Many of them have been omitted in that report and are now presented in this companion-paper

An Algorithmic Toolbox for Network Calculus

Network Calculus offers powerful tools to analyze the performances in communication networks, in particular to obtain deterministic bounds. This theory is based on a strong mathematical ground, notably by the use of (min,+) algebra. However the algorithmic aspects of this theory have not been much addressed yet. This paper is an attempt to provide some efficient algorithms implementing Network Calculus operations for some classical functions. Some functions which are often used are the piecewise affine functions which ultimately have a constant growth. As a first step towards algorithmic design, we present a class containing these functions and closed under the Network Calculus operations: the piecewise affine functions which are ultimately pseudo-periodic. They can be finitely described which enables us to propose some algorithms for each of the Network Calculus operations. We finally analyze their computational complexity

Shaping plasmon beams via the controlled illumination of finite-size plasmonic crystals

Plasmonic crystals provide many passive and active optical functionalities, including enhanced sensing, optical nonlinearities, light extraction from LEDs and coupling to and from subwavelength waveguides. Here we study, both experimentally and numerically, the coherent control of SPP beam excitation in finite size plasmonic crystals under focussed illumination. The correct combination of the illuminating spot size, its position relative to the plasmonic crystal, wavelength and polarisation enables the efficient shaping and directionality of SPP beam launching. We show that under strongly focussed illumination, the illuminated part of the crystal acts as an antenna, launching surface plasmon waves which are subsequently filtered by the surrounding periodic lattice. Changing the illumination conditions provides rich opportunities to engineer the SPP emission pattern. This offers an alternative technique to actively modulate and control plasmonic signals, either via micro- and nano-electromechanical switches or with electro- and all-optical beam steering which have direct implications for the development of new integrated nanophotonic devices, such as plasmonic couplers and switches and on-chip signal demultiplexing. This approach can be generalised to all kinds of surface waves, either for the coupling and discrimination of light in planar dielectric waveguides or the generation and control of non-diffractive SPP beams

Exact Worst-case Delay in FIFO-multiplexing Feed-forward Networks

In this paper, we compute the actual worst-case end-to-end delay for a flow in a feed-forward network of first-in–first-out (FIFO)-multiplexing service curve nodes, where flows are shaped by piecewise-affine concave arrival curves, and service curves are piecewise affine and convex. We show that the worst-case delay problem can be formulated as a mixed integer linear programming problem, whose size grows exponentially with the number of nodes involved. Furthermore, we present approximate solution schemes to find upper and lower delay bounds on the worst-case delay. Both only require to solve just one linear programming problem and yield bounds that are generally more accurate than those found in the previous work, which are computed under more restrictive assumptions