Some Tetranychoid Mites of Michigan

Excerpt: Tetranychoid mites are plant feeders, and many of them are of considerable economic importance. Prior to the present study, only seven species of these mites were known from Michigan; Oligonychus ilicis (McGregor) (McGregor, 1931); Tertranychus mcdanieli McGregor (McGregor, 1931; Pritchard and Baker, 1955); Euryteranychus buxi (Garman) (Ries, 1935; McGregor 1950); Tettranychus atlanticus McGregor (Tuttle and Baker, 1964); Bryobia praetiosa Koch, Panoychus ulmi (Koch), and Tetranychus telarius (L.) (Ghate and Howitt, 1965)

Landau theory of restart transitions

We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate. Like in the original theory of Landau, the optimal restart rate can undergo a first or second order transition depending on the details of the system. Nonetheless, there exists no unified framework which can capture the onset of such novel phenomena. We unravel this in a comprehensive manner and show how the transition can be understood by analyzing the first passage time moments. Power of our approach is demonstrated in two canonical paradigm setup namely the Michaelis Menten chemical reaction and diffusion under restart

A class of index coding problems with rate 1/3

An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\frac{1}{3}$ is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate $\frac{1}{3}$ is achievable. In the process, we also obtain a stricter necessary condition for rate $\frac{1}{3}$ feasibility than what is known in literature.Comment: Shorter version submitted to ISIT 201

A Long-Run Risks Model of Asset Pricing with Fat Tails

WWe explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. We estimate the structural parameters of the proposed model by maximum likelihood. We find that the homoskedastic model with fat tails leads to significant increase in implied risk premia and volatility of price-dividend ratio over the benchmark Gaussian model, but similar volatility of market return, expected risk free rate and its volatility.asset pricing, long run risks, equity risk premium, fat tails, Dampened Power Law, Levy process

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio