Naked Singularities as Particle Accelerators II

We generalize here our earlier results on particle acceleration by naked singularities. We showed recently[1] that the naked singularities that form due to gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center of mass energies. However, we focussed there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that when the particles interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore the nature of naked singularities, both at classical and quantum level could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of Cauchy horizon that participate in extreme high energy collisions.Comment: 13 pages, 5 figures, Accepted for publication in Phys. Rev. D, Reference and Acknowledgments adde

Increased nitric oxide activity compensates for increased oxidative stress to maintain endothelial function in rat aorta in early type 1 diabetes

Hyperglycaemia and oxidative stress are known to acutely cause endothelial dysfunction in vitro, but in the initial stages of diabetes, endothelium-dependent relaxation is preserved. The aim of this study was to investigate how endothelium-dependent relaxation is maintained in the early stages of type 1 diabetes. Diabetes was induced in Sprague-Dawley rats with a single injection of streptozotocin (48 mg/kg, i.v.), and after 6 weeks, endothelium-dependent and endothelium-independent relaxations were examined in the thoracic aorta in vitro. Lucigenin-enhanced chemiluminescence was used to measure superoxide generation from the aorta. Diabetes increased superoxide generation by the aorta (2,180 +/- 363 vs 986 +/- 163 AU/mg dry tissue weight)

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures