Bark beetles cause widespread damages in the coniferous-dominated forests of central Europe and North America. In the future, areas affected by bark beetles may further increase due to climate change. However, the early detection of the bark beetle green attack can guide management decisions to prevent larger damages. For this reason, a field-based bark beetle monitoring program is currently im...

The principle of maximum entropy, along with empirical considerations, can provide consistent basis for constructing a consistent probability distribution model for highly varying geophysical processes. Here we examine the potential of using this principle with the Boltzmann-Gibbs-Shannon entropy definition in the probabilistic modelling of rainfall in different areas worldwide. We define and t...

As our colleague so aptly demonstrated ( http://www.win-vector.com/blog/2011/09/the-simplerderivation-of-logistic-regression/ (link) ) there is one derivation of Logistic Regression that is particularly beautiful. It is not as general as that found in Agresti[Agresti, 1990] (which deals with generalized linear models in their full generality), but gets to the important balance equations very qu...

We present two versions of the maximum principle for nonsmooth hybrid optimal control problems, the first one of which requires differentiability along the reference trajectory and yields an adjoint equation of the usual kind, while the second one only requires approximability to first order by Lipschitz maps, and yields an adjoint differential inclusion involving a generalized gradient of the ...

8. Introduction Critical points of distance functions Toponogov's theorem; first application:a Background on finiteness theorems Homotopy Finiteness Appendix. Some volume estimates Betti numbers and rank Appendix: The generalized Mayer-Vietoris estimate Rank, curvature and diameter Ricci curvature, volume and the Laplacian Appendix. The maximum principle Ricci curvature, diameter growth and fin...

We study a class of optimization problems of Mayer form, for the strictly hyperbolic nonlinear controlled system of conservation laws ut + [ F (u) ] x = h(t, x, u, z), where z = z(t, x) is the control variable. Introducing a family of “generalized cotangent vectors”, we derive necessary conditions for a solution û to be optimal, stated in the form of a Maximum Principle.

By introducing a quantum entropy functional of the reduced density matrix, we construct a rigorous scheme to develop quantum hydrodynamic models. The principle of quantum maximum entropy permits to solve the closure problem for a quantum hydrodynamic set of balance equations corresponding to an arbitrary number of moments in the framework of extended thermodynamics. Quantum contributions are ex...

Existence of stationary states is established by means of the method of upper and lower solutions. The structure of the solution set is discussed and a uniqueness property for certain classes is proved by a generalized maximum principle. It is then shown that all solutions of the parabolic equation converge to a stationary state.

Shepard developed a scheme for interpolation to arbitrarily spaced discrete bivariate data. This scheme provides an explicit global representation for an interpolant which satisfies a maximum principle and which reproduces constant functions. The interpolation method is basically an inverse distance formula which is generalized to any Euclidean metric. These techniques extend to include interpo...

Using the generalized maximum entropy principle based on the nonextensive q entropy, a family of random matrix ensembles is generated. This family unifies previous extensions of random matrix theory (RMT) and gives rise to an orthogonal invariant stable Lévy ensemble with new statistical properties. Some of them are analytically derived.