Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art

Dynamical compactification from de Sitter space

We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of which are completely non-singular. The dynamical compactification mechanism populates lower-dimensional vacua very differently from false vacuum eternal inflation, which occurs entirely within the context of four-dimensions. We outline the phenomenology of the nucleation rates, finding that the dimensionality of the vacuum plays a key role and that among vacua of the same dimensionality, the rate is highest for smaller values of the cosmological constant. We consider the cosmological constant problem and propose a novel model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and added reference

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm

A unified account of tilt illusions, association fields, and contour detection based on Elastica

As expressed in the Gestalt law of good continuation, human perception tends to associate stimuli that form smooth continuations. Contextual modulation in primary visual cortex, in the form of association fields, is believed to play an important role in this process. Yet a unified and principled account of the good continuation law on the neural level is lacking. In this study we introduce a population model of primary visual cortex. Its contextual interactions depend on the elastica curvature energy of the smoothest contour connecting oriented bars. As expected, this model leads to association fields consistent with data. However, in addition the model displays tilt-illusions for stimulus configurations with grating and single bars that closely match psychophysics. Furthermore, the model explains not only pop-out of contours amid a variety of backgrounds, but also pop-out of single targets amid a uniform background. We thus propose that elastica is a unifying principle of the visual cortical network

Measurement of the near-threshold e+e−→DDˉe^+e^- \to D \bar D cross section using initial-state radiation

We report measurements of the exclusive cross section for $e^+e^- \to D \bar D$, where $D=D^0$ or $D^+$, in the center-of-mass energy range from the $D \bar D$ threshold to $5\mathrm{GeV}/c^2$ with initial-state radiation. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of 673 $\mathrm{fb}^{-1}$.Comment: Presented at EPS07 and LP07 conferences, published in PRD(RC

Improved measurement of CP-violating parameters in rho+rho- decays

We present a measurement of the CP-violating asymmetry in rho+rho- decays using 535 million BBbar pairs collected with the Belle detector at the KEKB e+e- collider. We measure CP-violating coefficients A = 0.16 +- 0.21(stat) +- 0.07 (syst) and S = 0.19 +- 0.30(stat) +- 0.07 (syst}. These values are used to determine the unitarity triangle angle phi_2 using an isospin analysis; the solution consistent with Standard Model lies in the range 53 < phi_2 < 114 deg. at 90 C.L.Comment: 6 pages, 4 figures, presented at JPS/DPF 2006 (Added KEK, BELLE preprint numbers, submitted to PRD(RC)

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Measurement of CP asymmetry in Cabibbo suppressed D0 decays

We measure the CP-violating asymmetries in decays to the D0 -> K+K- and D0 -> pi+pi- CP eigenstates using 540 fb^{-1} of data collected with the Belle detector at or near the Upsilon(4S) resonance. Cabibbo-favored D0 -> K-pi+ decays are used to correct for systematic detector effects. The results, A_{CP}^{KK} = (-0.43 +- 0.30 +- 0.11)% and A_{CP}^{pipi} = (+0.43 +- 0.52 +- 0.12)%, are consistent with no CP violation.Comment: Submitted to Phys. Lett.