Abstract Given a smooth projective variety, Chow–Künneth decomposition is called multiplicative if it compatible with the intersection product. Following works of Beauville and Voisin, Shen Vial conjectured that hyper-Kähler varieties admit decomposition. In this paper, based on mysterious link between Fano cohomology K3 type varieties, we ask whether also decomposition, provide evidence by est...

Abstract Using probabilistic tools, we prove that any weak* continuous semigroup $(T_t)_{t \geqslant 0}$ of self-adjoint unital completely positive measurable Schur multipliers acting on the space $\mathrm {B}({\mathrm {L}}^2(X))$ bounded operators Hilbert ${\mathrm {L}}^2(X)$ , where X is a suitable measure space, can be dilated by group Markov $*$ -automorphisms bigger von Neumann algebra. We...

We introduce a stochastic approximation method for the solution of a KullbackLeibler optimization problem, which is a generalization of Z-learning introduced by [Todorov, 2007]. A KL-optimization problem is Markov decision process with a finite state space and continuous control space. Because the control cost has a special form involving the Kullback-Leibler divergence, it can be shown that th...

The exchange graph of a quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph. Building on work of Iyama, Reiten, Thomas, and Todorov, we show that this directed graph is a semidistributive lattice by using the isomorphism to the lattice of functorially finite torsion cla...

Social experiences may moderate genetic influences on alcohol dependence (AD) symptoms. Consistent with this hypothesis, Park, Sher, Todorov, and Heath (2011) previously reported interactions between the dopamine D4 receptor gene (DRD4) and developmentally specific environments in the etiology of AD symptoms during emerging and young adulthood. Using a longitudinal cohort of n = 367 White parti...

The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...