Boundedness of anti-canonical volumes of singular log Fano threefolds

We prove Weak Borisov--Alexeev--Borisov Conjecture in dimension three which states that the anti-canonical volume of an $\epsilon$-klt log Fano pair of dimension three is bounded from above.Comment: 20 pages. Comments are welcome; v2: slightly modified; v3: 19 pages, proof slightly modifie

A divide and conquer method for symbolic regression

Symbolic regression aims to find a function that best explains the relationship between independent variables and the objective value based on a given set of sample data. Genetic programming (GP) is usually considered as an appropriate method for the problem since it can optimize functional structure and coefficients simultaneously. However, the convergence speed of GP might be too slow for large scale problems that involve a large number of variables. Fortunately, in many applications, the target function is separable or partially separable. This feature motivated us to develop a new method, divide and conquer (D&C), for symbolic regression, in which the target function is divided into a number of sub-functions and the sub-functions are then determined by any of a GP algorithm. The separability is probed by a new proposed technique, Bi-Correlation test (BiCT). D&C powered GP has been tested on some real-world applications, and the study shows that D&C can help GP to get the target function much more rapidly