Hamiltonian Loop Group Actions and T-Duality for group manifolds

We carry out a Hamiltonian analysis of Poisson-Lie T-duality based on the loop geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of equivariant momentum maps on the phase spaces such that the reduced phase space of the WZW model and a pure central extension coadjoint orbit work as a bridge linking both the sigma models. These momentum maps are associated to Hamiltonian actions of the loop group of the Drinfeld double on both spaces and the duality transformations are explicitly constructed in terms of these actions. Compatible dynamics arise in a general collective form and the resulting Hamiltonian description encodes all known aspects of this duality and its generalizations.Comment: 34 page

WZW orientifolds and finite group cohomology

The simplest orientifolds of the WZW models are obtained by gauging a Z_2 symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion g \mapsto (\zeta g)^{-1}, where \zeta is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in hep-th/0512283. More generally, one may gauge orientifold symmetry groups \Gamma = Z_2 \ltimes Z that combine the Z_2-action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-\Gamma cohomology that we solve for all simple simply-connected compact Lie groups G and all orientifold groups \Gamma = Z_2 \ltimes Z.Comment: 48+1 pages, 11 figure

A theoretical study of factors influencing calcium-secretion coupling in a presynaptic active zone model

A theoretical analysis of some of the relevant factors influencing the calcium time course and the strength and timing of release probabilities of vesicles evoked by an action potential in a calyx-type active zone is presented in this paper. In particular, our study focus on the comparison of cooperative vs non-cooperative calcium binding by the release site and the effect of the number of Ca2+ binding sites on the calcium sensitivity for release. Regarding the comparison of cooperative and non-cooperative kinetic schemes, our simulations show that quite different results are obtained when considering one or another: a reduction in the release probability of more than a 50% is obtained when considering the cooperative kinetic scheme. Also, a delay in the average time for release appears when using this model for the calcium sensor. Our study also shows that a non-cooperative kinetic binding scheme gives rise to a well defined average calcium level for release assuming that the same kinetic constants are considered for all the sites. Our results also suggest that the central value of the calcium sensitivity for release depends on the number of binding sites N and the dissociation constant KD with a scaling law depending on NKD

Entanglement and the three-dimensionality of the Bloch ball

We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this we impose two very natural assumptions: the continuity and reversibility of dynamics, and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories interacting dynamics is impossible. This result reveals that "existence of entanglement" is the requirement with minimal logical content which singles out quantum theory from our family of theories

Three-Dimensional, Tomographic Super-Resolution Fluorescence Imaging of Serially Sectioned Thick Samples

Three-dimensional fluorescence imaging of thick tissue samples with near-molecular resolution remains a fundamental challenge in the life sciences. To tackle this, we developed tomoSTORM, an approach combining single-molecule localization-based super-resolution microscopy with array tomography of structurally intact brain tissue. Consecutive sections organized in a ribbon were serially imaged with a lateral resolution of 28 nm and an axial resolution of 40 nm in tissue volumes of up to 50 µm×50 µm×2.5 µm. Using targeted expression of membrane bound (m)GFP and immunohistochemistry at the calyx of Held, a model synapse for central glutamatergic neurotransmission, we delineated the course of the membrane and fine-structure of mitochondria. This method allows multiplexed super-resolution imaging in large tissue volumes with a resolution three orders of magnitude better than confocal microscopy

Modelling Vesicular Release at Hippocampal Synapses

We study local calcium dynamics leading to a vesicle fusion in a stochastic, and spatially explicit, biophysical model of the CA3-CA1 presynaptic bouton. The kinetic model for vesicle release has two calcium sensors, a sensor for fast synchronous release that lasts a few tens of milliseconds and a separate sensor for slow asynchronous release that lasts a few hundred milliseconds. A wide range of data can be accounted for consistently only when a refractory period lasting a few milliseconds between releases is included. The inclusion of a second sensor for asynchronous release with a slow unbinding site, and thereby a long memory, affects short-term plasticity by facilitating release. Our simulations also reveal a third time scale of vesicle release that is correlated with the stimulus and is distinct from the fast and the slow releases. In these detailed Monte Carlo simulations all three time scales of vesicle release are insensitive to the spatial details of the synaptic ultrastructure. Furthermore, our simulations allow us to identify features of synaptic transmission that are universal and those that are modulated by structure