A Combinatorial, Strongly Polynomial-Time Algorithm for Minimizing Submodular Functions

This paper presents the first combinatorial polynomial-time algorithm for minimizing submodular set functions, answering an open question posed in 1981 by Grotschel, Lovasz, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the function value. The paper also presents a strongly polynomial-time version that runs in time bounded by a polynomial in the size of the underlying set independent of the function value.Comment: 17 page

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators

We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with constant coefficients for the $M$-indexed orthogonal polynomials, it is expected that the systems satisfy the generalized closure relations. In fact we can verify this statement for small $M$ examples. The generalized closure relation gives the exact Heisenberg operator solution of a certain operator, from which the creation and annihilation operators of the system are obtained.Comment: 33 page

CALICE ScECAL Beam Test at Fermilab

The scintillator-strip electromagnetic calorimeter (ScECAL) is one of the calorimeter technologies which can achieve fine granularity required for the particle flow algorithm. Second prototype of the ScECAL has been built and tested with analog hadron calorimeter (AHCAL) and tail catcher (TCMT) in September 2008 at Fermilab meson test beam facility. Data are taken with 1 to 32 GeV of electron, pion and muon beams to evaluate all the necessary performances of the ScECAL, AHCAL and TCMT system. This manuscript describes overview of the beam test and very preliminary results focusing on the ScECAL part.Comment: proceedings on ILCWS0