Quantum geometry and quantum algorithms

Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the q-deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirard

Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality

We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the twistorial N-points function, describing Dirichlet correlations over the moduli space of open N-bordered genus g surfaces, is naturally mapped into the Witten-Kontsevich intersection theory over the moduli space of N-pointed closed Riemann surfaces of the same genus. We also discuss various aspects of the geometrical setting which connects this model to PSL(2,C) Chern-Simons theory.Comment: 35 pages, references added, slightly revised introductio

Induction of Blood Brain Barrier Tight Junction Protein Alterations by CD8 T Cells

Disruption of the blood brain barrier (BBB) is a hallmark feature of immune-mediated neurological disorders as diverse as viral hemorrhagic fevers, cerebral malaria and acute hemorrhagic leukoencephalitis. Although current models hypothesize that immune cells promote vascular permeability in human disease, the role CD8 T cells play in BBB breakdown remains poorly defined. Our laboratory has developed a novel murine model of CD8 T cell mediated central nervous system (CNS) vascular permeability using a variation of the Theiler's virus model of multiple sclerosis. In previous studies, we observed that MHC class II−/− (CD4 T cell deficient), IFN-γR−/−, TNF-α−/−, TNFR1−/−, TNFR2−/−, and TNFR1/TNFR2 double knockout mice as well as those with inhibition of IL-1 and LTβ activity were susceptible to CNS vascular permeability. Therefore, the objective of this study was to determine the extent immune effector proteins utilized by CD8 T cells, perforin and FasL, contributed to CNS vascular permeability. Using techniques such as fluorescent activated cell sorting (FACS), T1 gadolinium-enhanced magnetic resonance imaging (MRI), FITC-albumin leakage assays, microvessel isolation, western blotting and immunofluorescent microscopy, we show that in vivo stimulation of CNS infiltrating antigen-specific CD8 T cells initiates astrocyte activation, alteration of BBB tight junction proteins and increased CNS vascular permeability in a non-apoptotic manner. Using the aforementioned techniques, we found that despite having similar expansion of CD8 T cells in the brain as wildtype and Fas Ligand deficient animals, perforin deficient mice were resistant to tight junction alterations and CNS vascular permeability. To our knowledge, this study is the first to demonstrate that CNS infiltrating antigen-specific CD8 T cells have the capacity to initiate BBB tight junction disruption through a non-apoptotic perforin dependent mechanism and our model is one of few that are useful for studies in this field. These novel findings are highly relevant to the development of therapies designed to control immune mediated CNS vascular permeability

Targeting Microvasculature for Neuroprotection after SCI

Spinal cord injury (SCI) is characterized by secondary degeneration, which leads to tissue loss at the epicenter and subsequent functional deficits. This review provides insight into the pathophysiology of microvascular dysfunction and endothelial cell loss, which are among the earliest responses during the first postinjury day. The enigmatic role of the angiogenic response in the penumbra around the lost tissue, which occurs during the first 2 weeks, is also discussed. The importance of stabilizing and rescuing the injured vasculature is now well-recognized, and several pharmacological and genetic treatments have emerged in the past few years. We conclude with suggestions for future experimental research, including development of vascular-selective treatments and exploitation of genetic models. In summary, vascular dysfunction following SCI is an important contributor to neurological deficits, as proposed long ago. However, there now appears to be new and potentially powerful opportunities for treating acute SCI by targeting the vascular responses