Using computational results required in the proof, we show the non-existence of symplectic resolutions for symplectic quotient singularities corresponding to three exceptional symplectic reflection groups, thus reducing further the number of cases for which the existence question remains open.

Group Theory Algebraic Geometry Representation Theory

Following previous works about integro-differential equations of parabolic type modelling the Darwinian evolution of a population, we study a two-population system in the cooperative case.

Analysis of PDEs

In addition, when mvd(G) is large and all blocks of G are minimally 2-connected triangle-free graphs, we characterize G. On these bases, we show that any graph whose blocks are all minimally 2-connected graphs of small order, can be computed mvd(G) and given an mvd-coloring in polynomial time.

Combinatorics 05C15, 05C40, 05C85

To show the asymptotic optimality of the proposed procedure, the asymptotically optimal sampling ratios which optimize large deviations rate of the probability of false selection for selecting top-$m$ alternatives has been rigorously defined.

Optimization and Control Statistics Theory Statistics Theory

We will generalize the combinatorial algorithms for computing $\pi(x)$ to compute sums ${F(x) = \sum_{p \leq x} p^k}$ for $k \in \mathbb{Z}_{\geq 0}$.

Number Theory 11N05 (Primary) 11Y16, 11Y55, 11Y70 (Secondary)

Multi-forecast model predictive control (MF-MPC) is a control policy that creates a plan of actions over a horizon for each of a given set of forecasted scenarios or contingencies, with the constraint that the first action in all plans be the same.

Optimization and Control

We survey the theory of locally homogeneous almost-Hermitian spaces.

Differential Geometry Complex Variables

The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget.

Optimization and Control

To guarantee the finite step convergence, the existing active set methods all need strict conditions or some additional strategies, which greatly affect the efficiency of the algorithm.

Optimization and Control 90C20, 90C25, 65K05

Path homology is a topological invariant for directed graphs, which is sensitive to their asymmetry and can discern between digraphs which are indistinguishable to the directed flag complex.

Algebraic Topology Combinatorics Probability 05C20, 05C80, 55U15, 60C05, 62F03