Abstract:

A major activity in forest management is planning silviculture activities. Mixed integer programming (MIP) has been used to obtain optimal plans considering management objectives and constraints (e.g. carbon stock, biodiversity, and soil erosion). Our contribution is addressing fire not as an attribute/parameter of the MIP model, but by simulating its spread. Initially, the MIP model is solved. Subsequently, a worst-case fire spread simulation is conducted to identify fire paths with an excessively high rate of spread. Each identified unacceptable path results in an additional constraint in the MIP. This process is repeated until no unacceptable paths are identified, ensuring that no fire paths will have a rate of spread higher than a specified threshold.

Title: Subgaussian Kahane-Salem-Zygmund inequalities in Banach spaces.

Speaker: Mieczysław Mastyło (Adam Mickiewicz University, Poznań, Poland).

Time: Wednesday, 8 May 2024, from 14:15 to 15:15.

Place: Room1.6, building VII.

Abstract: We will discuss approaches to the famous Kahane-Salem-Zygmund inequalities. In particular we will present estimates of the exponential Orlicz norms for $\sup_{1\leq j\leq N}\big|\sum_{i=1}^Ka_i(j) \gamma_i\big|$, where $(a_i(j))_{j=1}^N \in \ell_\infty^N, \,1 \leq i \leq K$ and $(\gamma_i)$ is a sequence of subgaussian random variables. Using tools from probability theory, Banach spaces and interpolation, we obtain new Kahane-Salem-Zygmund type random inequalities for the space of subgaussian polynomials on finite-dimensional Banach spaces, as well as for subgaussian Dirichlet polynomials. The talk is based on joint work with Andreas Defant.