For a curve C over perfect field k of characteristic p > 0 we study the tame cohomology $$\mathcal{C}$$ = Spa(C, k) introduced in [Hüb21]. We prove that groups with p-torsion coefficients satisfy cohomological purity (which is not true full generality for étale cohomology). Using show Poincaré duality coefficients.

We show how to estimate (1) the number of functions that can be implemented by a particular network architecture, (2) how much analog precision is needed in the connections in the network, and (3) the number of training examples the network must see before it can be expected to form reliable generalizations. Generality versus Training Data Required Consider the following objectives: First, the ...

Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at ...

Hyper-heuristics are easy-to-implement emerging search and optimisation strategies which have been used instead of meta-heuristics for providing higher level generalized structures to solve mainly combinatorial optimisation problems. The motivation behind them is generally expressed as raising the level of generality. That is, they are the answers to the following question: How can we create or...