Exact formulae for the Lovasz Theta Function of sparse Circulant Graphs

The Lovasz theta function has attracted a lot of attention for its connection with diverse issues, such as communicating without errors and computing large cliques in graphs. Indeed this function enjoys the remarkable property of being computable in polynomial time, despite being sandwitched between clique and chromatic number, two well known hard to compute quantities. In this paper I provide a closed formula for the Lovasz function of a specific class of sparse circulant graphs thus generalizing Lovasz results on cycle graphs (circulant graphs of degree 2)

The Theory of Trackability with Applications to Sensor Networks

In this paper, we formalize the concept of tracking in a sensor network and develop a rigorous theory of {\em trackability} that investigates the rate of growth of the number of consistent tracks given a sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a nondeterministic finite automaton and the sensor network is modelled by an observer capable of detecting events related, typically ambiguously, to the states of the underlying automaton. More formally, an input string, $Z^t$, of $t+1$ symbols (the sensor network observations) that is presented to a nondeterministic finite automaton, $M$, (the model) determines a set, ${\cal H}_M(Z^t)$, of state sequences (the tracks or hypotheses) that are capable of generating the input string $Z^t$. We study the growth of the size of this set, $|{\cal H}_M(Z^t)|$, as a function of the length of the input string, $t+1$. Our main result is that for a given automaton and sensor coverage, the worst-case rate of growth is either polynomial or exponential in $t$, indicating a kind of phase transition in tracking accuracy. The techniques we use include the Joint Spectral Radius, $\rho(\Sigma)$, of a finite set, $\Sigma$, of $(0,1)$-matrices derived from $M$. Specifically, we construct a set of matrices, $\Sigma$, corresponding to $M$ with the property that $\rho(\Sigma) \leq 1$ if and only if $|{\cal H}_M(Z^t)|$ grows polynomially in $t$. We also prove that for $(0,1)$-matrices, the decision problem $\rho(\Sigma)\leq 1$ is Turing decidable and, therefore, so is the problem of deciding whether worst case state sequence growth for a given automaton is polynomial or exponential. These results have applications in sensor networks, computer network security and autonomic computing as well as various tracking problems of recent interest involving detecting phenomena using noisy observations of hidden states

Corporate governance and MNE strategies in emerging economies

We explore factors of convergence and divergence in corporate governance of emerging and developed market economies, focussing on the role of firm internationalisation. In particular, foreign investments by emerging economy firms led to upgrade of their governance capabilities. These firms also became advocates for home-country policy reforms that mandated the development of similar capabilities for local firms. We present a broad overview of the literature and propose an approach that considers the evolution of corporate governance, both at the national level and the firm level, with MNEs from both emerging market economies and developed economies as active actors in this process