Constraints on Deflation from the Equation of State of Dark Energy

In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/\rho = -1 - \phi$ with $\phi > 0$. More accurate measurement of $\phi$ will constrain $N_{\rm cp}$. The critical density $\rho_c$ in the model has a lower bound $\rho_c \ge (10^9 {\rm GeV})^4$ or $\rho_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.Comment: 23 pages, 3 figures, typos fixe

Mersenne Primes, Polygonal Anomalies and String Theory Classification

It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

Higher order Josephson effects

Gaussian linking of superconducting loops containing Josephson junctions with enclosed magnetic fields give rise to interference shifts in the phase that modulates the current carried through the loop, proportional to the magnitude of the enclosed flux. We generalize these results to higher order linking of a superconducting loop with several magnetic solenoids, and show there may be interference shifts proportional to the product of two or more fluxes.Comment: 8 pages, 2 figure

Adapting Quality Assurance to Adaptive Systems: The Scenario Coevolution Paradigm

From formal and practical analysis, we identify new challenges that self-adaptive systems pose to the process of quality assurance. When tackling these, the effort spent on various tasks in the process of software engineering is naturally re-distributed. We claim that all steps related to testing need to become self-adaptive to match the capabilities of the self-adaptive system-under-test. Otherwise, the adaptive system's behavior might elude traditional variants of quality assurance. We thus propose the paradigm of scenario coevolution, which describes a pool of test cases and other constraints on system behavior that evolves in parallel to the (in part autonomous) development of behavior in the system-under-test. Scenario coevolution offers a simple structure for the organization of adaptive testing that allows for both human-controlled and autonomous intervention, supporting software engineering for adaptive systems on a procedural as well as technical level.Comment: 17 pages, published at ISOLA 201

Simulating non-Markovian stochastic processes

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general as it can be implemented very easily in cases, like for delays coupled to the evolution of the system, where other algorithms do not work or need adapted versions, less efficient in computational terms.Comment: Improvement of the algorithm, new results, and a major reorganization of the paper thanks to our coauthors L. Lafuerza and R. Tora

ASTROMAG: A Superconducting Particle Astrophysics Magnet Facility for the Space Station

This paper describes a superconducting magnet system which is the heart of a particle astrophysics facility to be mounted on a portion of the proposed NASA space station. This facility will complete the studies done by the electromagnetic observatories now under development and construction by NASA. The paper outlines the selection process of the type of magnet to be used to analyze the energy and momentum of charged particles from deep space. The ASTROMAG superconducting magnet must meet all the criteria for a shuttle launch and landing, and it must meet safety standards for use in or near a manned environment such as the space station. The magnet facility must have a particle gathering aperture of at least 1 square meter steradian and the facility should be capable of resolving heavy nuclei with a total energy of 10 Tev or more

Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",Comment: 19 pages, RevTe