In the energy sudden (ES) approximation for nonreactive molecular collisions,there exist factorization relations by which an arbitrary T‐matrix element can be predicted as a spectroscopic linear combination of those out of some other, input state. These were first discovered for ground state input but this restriction was later removed. This general form of the spectroscopicfactorization relati...

Matrix factorization in the presence of missing data is at the core of many computer vision problems such as structure from motion (SfM), non-rigid SfM and photometric stereo. We formulate the problem of matrix factorization with missing data as a low-rank semidefinite program (LRSDP) with the advantage that: 1) an efficient quasi-Newton implementation of the LRSDP enables us to solve large-sca...

αand β-divergence based nonnegative tensor factorization (NTF) is combined with nonlinear band expansion (NBE) for blind decomposition of the magnetic resonance image (MRI) of the brain. Concentrations and 3D tensor of spatial distributions of brain substances are identified from the Tucker3 model of the 3D MRI tensor. NBE enables to account for the presence of more brain substances than number...

This talk reports on recent work where we studied the connection between the description of semi-inclusive DIS at high transverse momentum (based on collinear factorization) and low transverse momentum (based on transversemomentum-dependent factorization). We used power counting to determine the leading behavior of the structure functions at intermediate transverse momentum in the two descripti...

Over recent years, the Lie and Hopf algebra structures of Feynman graphs have been firmly established in collaboration with Alain Connes and David Broadhurst [1–11]. Hopefully, they find their way now into the algorithmic toolkit of the practitioner of QFT. They directly address the computational practice of momentum space Feynman integrals, but can be equivalently formulated in coordinate spac...

By relating the projective camera model to the perspective one, using homogenous coordinates representation, the interior orientation parameters constitute what is called the calibration matrix. This paper presents two new algorithms to retrieve the calibration matrix from the projective camera model. In both algorithms, a collective approach was adopted, using matrix factorization. The calibra...

Factorization, in the sense defined for inclusive hard scattering, is discussed for diffractive hard scattering. A factorization theorem similar to its inclusive counterpart is presented for diffractive DIS. For hadron-hadron diffractive hard scattering, in contrast to its inclusive counterpart, the expected breakdown of factorization is discussed. Cross section estimates are given from a simpl...

This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm consists of a symbolic phase and a factorization phase. In the symbolic phase, a ILU(k) nonzero pattern is established from the point-wise structure extracted fro...

Since the x dependence of the axial-anomaly effect in inclusive polarized deep inelastic scattering is fixed, the transformation from the MS scheme to different factorization schemes are not arbitrary. If the quark spin distribution is demanded to be anomaly-free so that it does not evolve with Q and hard gluons contribute to the first moment of g1(x), then all the moments of coefficient and sp...

Consider the Cholesky factorization of a sparse symmetric positive de nite matrix, A = LL . The rst two steps use symbolic, graph-theoretic techniques to order A to reduce ll in L, and to determine the exact sparsity structure of L. The factor L is computed in a third \numeric factorization" step. The two leading schemes for numeric factorization are a blocked column-oriented scheme, and a mult...