Markov chains provided us with a way to model 1D objects such as contours probabilistically, in a way that led to nice, tractable computations. We now consider 2D Markov models. These are more powerful, but not as easy to compute with. In addition we will consider two additional issues. First, we will consider adding observations to our models. These observations are conditioned on the value of...

We discuss some problems of arithmetic distribution, including conjectures of Cohen-Lenstra, Malle, and Bhargava; we explain how such conjectures can be heuristically understood for function fields over finite fields, and discuss a general approach to their proof in the function field context based on the topology of Hurwitz spaces. This approach also suggests that the Schur multiplier plays a ...

800x600 as a tendency to use new technologies, gadgets such as laptop computers are becoming more popular among students, teachers, businessmen and office workers. today laptops are a great tool for education and learning, work and personal multimedia. millions of men, especially those in the reproductive age, are frequently using their laptop computers on the lap (thigh). over the past several...

background : substantial evidence indicates that exposure to electromagnetic fields (emf) above certain levels can affect human health through triggering some biological responses. according to who, short-term exposure to emf at the levels present in the home/environment do not cause any apparent detrimental effects in healthy individuals. however, now, there is a debate on whether long-term ex...