The Gysin map is compatible with mixed Hodge structures

We prove that the Gysin map is compatible with mixed Hodge Structures.Comment: Published in CRM Proceedings and Lecture Series, vol. 38, 200

A New Theory of Consciousness: The Missing Link - Organization

What is consciousness and what is the missing link between the sensory input and the cortical centre in the brain for consciousness? In the literature there are more than a million pages written about consciousness. The perspectives range from the field of metaphysics to those of quantum mechanics. However, no one today has produced a theory which is universally accepted. Consciousness is “something” which the majority of humans know that they posses, they use it when they want to understand their environment. However, no individual human knows whether other humans also posses consciousness. unless some tests such as she is looking at me, he is talking etc., are performed. We are caught in an intellectual sort of recursive carousel – we need consciousness to understand consciousness. To understand consciousness we have to understand the mechanism of its function, which is to effectively organize sensory inputs from our environment. Consciousness is the outcome of the process of organizing these sensory inputs. This implies that organization is an act which precedes consciousness. Since every activity in nature is to organize/disorganize, what is the element which compels this action? I am proposing that just like energy is the physical element that causes action, there is another physical element I have called it NASCIUM which has the capacity to cause organization. This is the missing link. Understanding the nature of organization, i.e. nascium, will enhance our capability to understand consciousness

Time Evolution of Non-Lethal Infectious Diseases: A Semi-Continuous Approach

A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment in the number of infectious individuals and depends upon a limited number of parameters. Predictions are in good qualitative agreement with data on influenza.Comment: 21 page

Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.

The projectors of the decomposition theorem are motivic

We prove that the projectors arising from the decomposition theorem applied to a projective map of quasi projective varieties are absolute Hodge, Andr\'e motivated, Tate and Ogus classes. As a by-product, we introduce, in characteristic zero, the notions of algebraic de Rham intersection cohomology groups of a quasi projective variety and of intersection cohomology motive of a projective variety