This paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions, M-convex functions and L-convex functions. Simple tie-breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain. Combination of the present results with a standard scaling approach leads to an efficient algor...

Let X be an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective. Then we have: (i) X contains an exceptional divisor of several types, which we classify explicitly, (ii) X has a morphism to a projective nonsingular surface whose fibers are conics, (iii) X has a morphism to a projective nonsingular curve whose general fibers are Del Pezzo surfaces, or (iv)...

We show, for an arbitrary adjunction F U : B → A with B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type, meaning that the free T-algebra functor F : A → AT is comonadic. This result is applied to several situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed ...

We present in this paper a systematic study on how to morph a well-trained neural network to a new one so that its network function can be completely preserved. We define this as network morphism in this research. After morphing a parent network, the child network is expected to inherit the knowledge from its parent network and also has the potential to continue growing into a more powerful one...