Let (M, g) be a time-oriented Lorentzian manifold and d the Lorentzian distance on M . The function τ(q) := supp<q d(p, q) is the cosmological time function of M , where as usual p < q means that p is in the causal past of q. This function is called regular iff τ(q) <∞ for all q and also τ → 0 along every past inextendible causal curve. If the cosmological time function τ of a spacetime (M, g) ...

We investigate the damage spreading effect in Fortuin-Kasteleyn random cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D function has a global maximum at p=q/(1+q) all q>0 also local maxima p=1/2 q≲0.75. 3D we observe q≲0.46 q≲4.5. The chaotic phase of model's (p,q)-parameter space is where coupling time exponential order locate points on its lower bound this may be eq...

Given two simple polygons P and Q we de ne the weight of a bridge p q with p P and q Q where de nes the boundary of the polygon between the two polygons as gd p P d p q gd q Q where d p q is the Euclidean distance between the points p and q and gd a A is the geodesic distance between a and its geodesic farthest neighbor on A An optimal bridge of minimum weight can be found in O n log n time as ...

Abstract Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length δx is performed after each time interval δt. In correlated discrete time random walks (CDTRWs), the probability q for two successive steps having the same sign is unequal 1/2. The resulting probability distribution P (∆x,∆t) that a displacement ∆x is observed after a ...