Reachability and Shortest Paths in the Broadcast CONGEST Model

In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter D of the underlying network is constant. We show that for the case where D = 1 there is, quite surprisingly, a very simple algorithm that solves the reachability problem in 1(!) round. In contrast, for networks with D = 2, we show that any distributed algorithm (possibly randomized) for this problem requires Omega(sqrt{n/ log{n}}) rounds. Our results therefore completely resolve (up to a small polylog factor) the complexity of the single-source reachability problem for a wide range of diameters. Furthermore, we show that when D = 1, it is even possible to get an almost 3 - approximation for the all-pairs shortest path problem (for directed unweighted graphs) in just 2 rounds. We also prove a stronger lower bound of Omega(sqrt{n}) for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is 2. As far as we know this is the first lower bound that achieves Omega(sqrt{n}) for this problem

Networks of silicon nanowires: a large-scale atomistic electronic structure analysis

Networks of silicon nanowires possess intriguing electronic properties surpassing the predictions based on quantum confinement of individual nanowires. Employing large-scale atomistic pseudopotential computations, as yet unexplored branched nanostructures are investigated in the subsystem level, as well as in full assembly. The end product is a simple but versatile expression for the bandgap and band edge alignments of multiply-crossing Si nanowires for various diameters, number of crossings, and wire orientations. Further progress along this line can potentially topple the bottom-up approach for Si nanowire networks to a top-down design by starting with functionality and leading to an enabling structure.Comment: Published version, 5+2 pages (including supplementary material

Electrospinning predictions using artificial neural networks

Electrospinning is a relatively simple method of producing nanofibres. Currently there is no method to predict the characteristics of electrospun fibres produced from a wide range of polymer/solvent combinations and concentrations without first measuring a number of solution properties. This paper shows how artificial neural networks can be trained to make electrospinning predictions using only commonly available prior knowledge of the polymer and solvent. Firstly, a probabilistic neural network was trained to predict the classification of three possibilities: no fibres (electrospraying); beaded fibres; and smooth fibres with > 80% correct predictions. Secondly, a generalised neural network was trained to predict fibre diameter with an average absolute percentage error of 22.3% for the validation data. These predictive tools can be used to reduce the parameter space before scoping exercises

Compound droplet manipulations on fiber arrays

Recent works demonstrated that fiber arrays may constitue the basis of an open digital microfluidics. Various processes, such as droplet motion, fragmentation, trapping, release, mixing and encapsulation, may be achieved on fiber arrays. However, handling a large number of tiny droplets resulting from the mixing of several liquid components is still a challenge for developing microreactors, smart sensors or microemulsifying drugs. Here, we show that the manipulation of tiny droplets onto fiber networks allows for creating compound droplets with a high complexity level. Moreover, this cost-effective and flexible method may also be implemented with optical fibers in order to develop fluorescence-based biosensor