Network Community Detection on Metric Space

Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings

Doctoral Education and Academic Research (in India)

[Excerpt] The state of doctoral education and academic research in India is poor and the country has scant representation among the world’s great universities. The decline has happened in spite of early achievements. Reasons behind this are complex and defy easy explanations. Several probable causes in terms of resources / facilities / opportunities granted to Ph.D. students, faculty quality, financial resources, academic leadership and other issues are explored and some suggestions for improvement are provided

Vertical diversity and equilbrium growth

This paper examines the effect of an increase in vertical diversity in workers' skill on the long run growth rate of an economy. It uses a two-secror model where the techonology of the consumption-good sector is supermodular and that of the R&D sector is submodular. By adopting Grossman and Maggi's(2000) model to a framework of growth based on R&D, it shows first that diversity is condutive to growth. As the main innovation, communication gap is introduced among workers. It is then shown that growth may not be increasing with diversity. There may be an inverse-U shaped relationship.Diversity, talent distribution, supermodular technology, submodular technology, growth, skill, R&D, innovations

Deterrence, preemption and panic: A Common-enemy problem of terrorism

We develop a game-theoretic analysis of terrorism that examines the interaction between a terrorist organization and multiple target countries, and considers both pre-emption and deterrence as counterterrorist policies. The damage from terror includes not only the material cost of fatality, injury and loss of property, but also the resultant fear. The fear-effect leads to different kinds of equilibria and implications for counter-terrorism policies. In particular, the model identifies conditions under which greater pre-emption may be the rational response to an increase in terrorism, i.e., it analyzes the merit of the dictum: "offense is the best defense." Further, it examines the characteristics of cooperative behavior among target countries in dealing with the threat of terrorism.Terrorism; Preemption; Panic; Deterrence; Cooperation; Target Countries

Extremal Paths on a Random Cayley Tree

We investigate the statistics of extremal path(s) (both the shortest and the longest) from the root to the bottom of a Cayley tree. The lengths of the edges are assumed to be independent identically distributed random variables drawn from a distribution \rho(l). Besides, the number of branches from any node is also random. Exact results are derived for arbitrary distribution \rho(l). In particular, for the binary {0,1} distribution \rho(l)=p\delta_{l,1}+(1-p)\delta_{l,0}, we show that as p increases, the minimal length undergoes an unbinding transition from a `localized' phase to a `moving' phase at the critical value, p=p_c=1-b^{-1}, where b is the average branch number of the tree. As the height n of the tree increases, the minimal length saturates to a finite constant in the localized phase (p<p_c), but increases linearly as v_{min}(p)n in the moving phase (p>p_c) where the velocity v_{min}(p) is determined via a front selection mechanism. At p=p_c, the minimal length grows with n in an extremely slow double logarithmic fashion. The length of the maximal path, on the other hand, increases linearly as v_{max}(p)n for all p. The maximal and minimal velocities satisfy a general duality relation, v_{min}(p)+v_{max}(1-p)=1, which is also valid for directed paths on finite-dimensional lattices.Comment: 7 pages Revtex, 3 eps figure

Endogeneous Distribution and the Political Economy of Trade Policy

This paper examines the political economy of trade policy in the context of a small open economy, when factor ownerships are variable. The median voter hypothesis is used. In the long run, both trade protection and distribution of wealth and income are endogenous, and the paper investigates how these are affected by basic parameters like terms of trade and technology

Endogenous distribution, politics and the growth-equity tradeoff

In comparison to the standard literature on inequality and growth which assumes the former to be exogenous, we formulate a model in which inequality and growth are both endogenous. Furthermore, long-run distribution, at least locally, is shown to be independent of the initial distribution of factor ownership. It is shown that exogenous policy changes that are primarily targeted towards growth and foster less inequality do enhance growth. But those that are primarily redistributive and imply more equal distribution reduce growth. This is consistent with recent empirical work which shows that inequality and growth may be positively related.Median Voter, Endogenous Growth, Wealth Distribution, Distributive Conflict, Redistributive Policy

Maximum of N Independent Brownian Walkers till the First Exit From the Half Space

We consider the one-dimensional target search process that involves an immobile target located at the origin and $N$ searchers performing independent Brownian motions starting at the initial positions $\vec x = (x_1,x_2,..., x_N)$ all on the positive half space. The process stops when the target is first found by one of the searchers. We compute the probability distribution of the maximum distance $m$ visited by the searchers till the stopping time and show that it has a power law tail: $P_N(m|\vec x)\sim B_N (x_1x_2... x_N)/m^{N+1}$ for large $m$. Thus all moments of $m$ up to the order $(N-1)$ are finite, while the higher moments diverge. The prefactor $B_N$ increases with $N$ faster than exponentially. Our solution gives the exit probability of a set of $N$ particles from a box $[0,L]$ through the left boundary. Incidentally, it also provides an exact solution of the Laplace's equation in an $N$-dimensional hypercube with some prescribed boundary conditions. The analytical results are in excellent agreement with Monte Carlo simulations.Comment: 18 pages, 9 figure

Endogenous trading bloc formation in a North-South global economy

Majority of the trading blocs to date are between similar countries, rather than between developed and developing countries. This paper provides a rationale for why trading blocs among similar countries may arise as an equilibrium phenomenon. It develops a model of an asymmetric world economy, in which there are at least four countries. The countries are differentiated with respect to their market size and market structure.