We prove that under certain spectral assumptions on the monodromy group, solutions of the Fuchsian system of linear equations on the Riemann sphere admit explicit global bounds on the number of their isolated zeros.

The recent proliferation of digital databases of cultural and linguistic data, together with new statistical techniques becoming available has lead to a rise in so-called nomothetic studies [1]-[8]. These seek relationships between demographic variables and cultural traits from large, cross-cultural datasets. The insights from these studies are important for understanding how cultural traits ev...

We propose a new family of mapped WENO schemes by using several adaptive control functions and smoothing approximation the signum function. The proposed introduce adaptivity admit an extensive permitted range parameters in mapping functions. Consequently, they have capacity to achieve optimal convergence rates, even near critical points. Particularly, one these with fine-tuned illustrates signi...

We define a notion of viscous shock solution the stochastic Burgers equation that connects "top" and "bottom" spatially stationary solutions same equation. Such shocks generally travel in space, but we show they admit time-invariant measures when viewed their own reference frames. Under such measure, is deterministic function bottom top location. However, measure must be tilted to account for c...

Crossover operator plays a crucial role in the efficiency of genetic algorithm (GA). Several crossover operators have been proposed for solving the travelling salesman problem (TSP) in the literature. These operators have paid less attention to the characteristics of the traveling salesman problem, and majority of these operators can only generate feasible solutions. In this paper, a crossover ...

We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....

We study shock statistics in the scalar conservation law ∂tu+∂xf(u) = 0, x ∈ R, t > 0, with a convex flux f and random initial data. We show that a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps) is preserved by the entropy solution to the conservation law and we derive kinetic equations that describe the evolution ...

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables...

We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....