Electrochemical Properties of Li3N Dissolved in Molten LiCl at 900 K

Thermodynamic properties of Li3N dissolved in the molten LiCl salt at 900 K were explored using electrochemical methods. It was difficult to determine precisely the decomposition voltage of Li3N dissolved in the molten salt by cyclic voltammetry. The oxidation wave of N3– ion could not be located with high accuracy. However, the lithium activity of the Pb-Li alloy in equilibrium with the molten salt containing dissolved Li3N under nitrogen atmosphere could be measured electrochemically with high accuracy using the Li/Li + reference electrode. Under the conditions used in this study, the potential of the Li-Pb electrode is equal to the decomposition voltage of Li3N. The activity of Li3N in molten LiCl was determined for anionic fractions of N3– ranging from xN3– = 10–4 to 0.028. The nitride ion concentration in the salt was determined by chemical titration. The activity coefficient of the Li3N at high dilution was found to be very low, around 10–4. The activity coefficient increases sharply with composition and has a value of 0.25 at xN3– = 0.028. ©2001 The Electrochemical Society. All rights reserved.

K(2)O(2): The most stable oxide of K

We have analyzed the stability of various oxides of K and find that K(2)O(2) is the most stable one. The additional stability is traced to the presence of oxygen dimers in K(2)O(2) which interact to form molecular orbitals. Other oxides such as KO(2) and KO(3) which also have dimers/trimers of oxygens are found to be less stable. This is traced to the shorter O-O bonds that one finds in them which gives rise to a significant coulomb repulsion between the electrons on the oxygen atoms making up the dimer/trimer, making them less stable.

On synthesis of easily testable (k, K) circuits

A (k-, K) circuit is one which can be decomposed into nonintersecting blocks of gates where each block has no more than K external inputs, such that the graph formed by letting each block be a node and inserting edges between blocks if they share a signal line, is a partial k-tree. (k, K) circuits are special in that they have been shown to be testable in time polynomial in the number of gates in the circuit, and are useful if the constants k and K are small. We demonstrate a procedure to synthesise (k, K) circuits from a special class of Boolean expressions.

Rainbow Connection Number and Radius

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) <= r(r+2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that, for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (K_{1,n} for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) <= rk. Hitherto, the only reported upper bound on the rainbow connection number of bridgeless graphs is 4n/5 - 1, where n is order of the graph [Caro et al., 2008]

Network Rhythms Influence the Relationship between Spike-Triggered Local Field Potential and Functional Connectivity

Characterizing the functional connectivity between neurons is key for understanding brain function. We recorded spikes and local field potentials (LFPs) from multielectrode arrays implanted in monkey visual cortex to test the hypotheses that spikes generated outward-traveling LFP waves and the strength of functional connectivity depended on stimulus contrast, as described recently. These hypotheses were proposed based on the observation that the latency of the peak negativity of the spike-triggered LFP average (STA) increased with distance between the spike and LFP electrodes, and the magnitude of the STA negativity and the distance over which it was observed decreased with increasing stimulus contrast. Detailed analysis of the shape of the STA, however, revealed contributions from two distinct sources-a transient negativity in the LFP locked to the spike (similar to 0 ms) that attenuated rapidly with distance, and a low-frequency rhythm with peak negativity similar to 25 ms after the spike that attenuated slowly with distance. The overall negative peak of the LFP, which combined both these components, shifted from similar to 0 to similar to 25 ms going from electrodes near the spike to electrodes far from the spike, giving an impression of a traveling wave, although the shift was fully explained by changing contributions from the two fixed components. The low-frequency rhythm was attenuated during stimulus presentations, decreasing the overall magnitude of the STA. These results highlight the importance of accounting for the network activity while using STAs to determine functional connectivity.

Determining Top K Nodes in Social Networks using the Shapley Value

In this paper, we consider the problem of selecting, for any given positive integer k, the top-k nodes in a social network, based on a certain measure appropriate for the social network. This problem is relevant in many settings such as analysis of co-authorship networks, diffusion of information, viral marketing, etc. However, in most situations, this problem turns out to be NP-hard. The existing approaches for solving this problem are based on approximation algorithms and assume that the objective function is sub-modular. In this paper, we propose a novel and intuitive algorithm based on the Shapley value, for efficiently computing an approximate solution to this problem. Our proposed algorithm does not use the sub-modularity of the underlying objective function and hence it is a general approach. We demonstrate the efficacy of the algorithm using a co-authorship data set from e-print arXiv (www.arxiv.org), having 8361 authors.

Connectivity-aware Routing in Sensor Networks

Sensor network applications such as environmental monitoring demand that the data collection process be carried out for the longest possible time. Our paper addresses this problem by presenting a routing scheme that ensures that the monitoring network remains connected and hence the live sensor nodes deliver data for a longer duration. We analyze the role of relay nodes (neighbours of the base-station) in maintaining network connectivity and present a routing strategy that, for a particular class of networks, approaches the optimal as the set of relay nodes becomes larger. We then use these findings to develop an appropriate distributed routing protocol using potential-based routing. The basic idea of potential-based routing is to define a (scalar) potential value at each node in the network and forward data to the neighbor with the highest potential. We propose a potential function and evaluate its performance through simulations. The results show that our approach performs better than the well known lifetime maximization policy proposed by Chang and Tassiulas (2004), as well as AODV [Adhoc on demand distance vector routing] proposed by Perkins (1997).

Efficient Algorithms for Computing All Low s-t Edge Connectivities and Related Problems

Given an undirected unweighted graph G = (V, E) and an integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk3) for this problem, where |V| = n and |E| = m. Our output is a weighted tree T whose nodes are the sets V1, V2,..., V l of a partition of V, with the property that the edge connectivity in G between any two vertices s ε Vi and t ε Vj, for i ≠ j, is equal to the weight of the lightest edge on the path between Vi and Vj in T. Also, two vertices s and t belong to the same Vi for any i if and only if they have an edge connectivity greater than k. Currently, the best algorithm for this problem needs to compute all-pairs min-cuts in an O(nk) edge graph; this takes Õ(m + n5/2kmin{k1/2, n1/6}) time. Our algorithm is much faster for small values of k; in fact, it is faster whenever k is o(n5/6). Our algorithm yields the useful corollary that in Õ(m + nc3) time, where c is the size of the global min-cut, we can compute the edge connectivities of all those pairs of vertices whose edge connectivity is at most αc for some constant α. We also present an Õ(m + n) Monte Carlo algorithm for the approximate version of this problem. This algorithm is applicable to weighted graphs as well. Our algorithm, with some modifications, also solves another problem called the minimum T-cut problem. Given T ⊆ V of even cardinality, we present an Õ(m + nk3) algorithm to compute a minimum cut that splits T into two odd cardinality components, where k is the size of this cut.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.