A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Detecting stealthy attacks: Efficient monitoring of suspicious activities on computer networks

Stealthy attackers move patiently through computer networks - taking days, weeks or months to accomplish their objectives in order to avoid detection. As networks scale up in size and speed, monitoring for such attack attempts is increasingly a challenge. This paper presents an efficient monitoring technique for stealthy attacks. It investigates the feasibility of proposed method under number of different test cases and examines how design of the network affects the detection. A methodological way for tracing anonymous stealthy activities to their approximate sources is also presented. The Bayesian fusion along with traffic sampling is employed as a data reduction method. The proposed method has the ability to monitor stealthy activities using 10-20% size sampling rates without degrading the quality of detection.