A cochain level proof of Adem relations in the mod 2 Steenrod algebra

In 1947, N.E. Steenrod defined the Steenrod Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup-i products of cocycles. He later recast the construction in more general homological terms, using group homology and acyclic model methods, rather than explicit cochain formulae, to define mod p operations for all primes p. Steenrod's student J. Adem applied the homological point of view to prove fundamental relations, known as the Adem relations, in the algebra of cohomology operations generated by the Steenrod operations. In this paper we give a proof of the mod 2 Adem relations at the cochain level. Specifically, given a mod 2 cocycle, we produce explicit cochain formulae whose coboundaries are the Adem relations among compositions of Steenrod Squares applied to the cocycle, using Steenrod's original cochain definition of the Square operations

Bloggers Behavior and Emergent Communities in Blog Space

Interactions between users in cyberspace may lead to phenomena different from those observed in common social networks. Here we analyse large data sets about users and Blogs which they write and comment, mapped onto a bipartite graph. In such enlarged Blog space we trace user activity over time, which results in robust temporal patterns of user--Blog behavior and the emergence of communities. With the spectral methods applied to the projection on weighted user network we detect clusters of users related to their common interests and habits. Our results suggest that different mechanisms may play the role in the case of very popular Blogs. Our analysis makes a suitable basis for theoretical modeling of the evolution of cyber communities and for practical study of the data, in particular for an efficient search of interesting Blog clusters and further retrieval of their contents by text analysis

Chaotic scalar fields as models for dark energy

We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena is the self interaction strength is strong. The stochastically quantized dynamics can degenerate to a chaotic dynamics conjugated to a Bernoulli shift in fictitious time, and the right amount of vacuum energy density can be generated without fine tuning. It is numerically observed that the scalar field dynamics distinguishes fundamental parameters such as the electroweak and strong coupling constants as corresponding to local minima in the dark energy landscape. Chaotic fields can offer possible solutions to the cosmological coincidence problem, as well as to the problem of uniqueness of vacua.Comment: 30 pages, 3 figures. Replaced by final version accepted by Phys. Rev.

Rotation and Spin in Physics

We delineate the role of rotation and spin in physics, discussing in order Newtonian classical physics, special relativity, quantum mechanics, quantum electrodynamics and general relativity. In the latter case, we discuss the generalization of the Kepler formula to post-Newtonian order $(c^{-2}$) including spin effects and two-body effects. Experiments which verify the theoretical results for general relativistic spin-orbit effects are discussed as well as efforts being made to verify the spin-spin effects

University of California Research Seminar Network: A Prospectus

By webcasting the hundreds of seminars presented in the University of California system each week, UC educators hope to enhance the exchange of scientific information for their campuses and create the foundation for an international research seminar network

Freeze-Dried Somatic Cells Direct Embryonic Development after Nuclear Transfer

The natural capacity of simple organisms to survive in a dehydrated state has long been exploited by man, with lyophylization the method of choice for the long term storage of bacterial and yeast cells. More recently, attempts have been made to apply this procedure to the long term storage of blood cells. However, despite significant progress, practical application in a clinical setting is still some way off. Conversely, to date there are no reports of attempts to lyophilize nucleated somatic cells for possible downstream applications. Here we demonstrate that lyophilised somatic cells stored for 3 years at room temperature are able to direct embryonic development following injection into enucleated oocytes. These remarkable results demonstrate that alternative systems for the long-term storage of cell lines are now possible, and open unprecedented opportunities in the fields of biomedicine and for conservation strategies