As a first step towards the complete calculation of deep-inelastic scattering at third order of massless pertur-bative QCD, we have computed the fermionic (n f) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic scattering. We briefly discuss the approach chosen for this calculation, the problems we encountered and the status of the project. We show the ...

Variational problems with topological constraints can exhibit many interesting mathematical properties. There are many open mathematical questions in this area. The diverse properties these problems possess give them the potential for different applications. We find variational problems with topological constraints in high energy physics, hydrodynamics, and material science, [9, 3, 48]. Usually...

For a real central arrangement A, Salvetti introduced a construction of a finite complex Sal(A) which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement Ak−1, the Salvetti complex Sal(Ak−1) serves as a good combinatorial model for the homotopy type of the configuration space F (C, k) of k points in C, which is homotopy equivalent to th...

Homotopy type theory is an extension of Martin-Löf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type becomes proof-relevant, and corresponds to paths in a space. This allows for a new class of datatypes, called higher inductive types, which are specified by constructors not only for points but also fo...

Progress in the development of a homotopy continuation method to globalize the spatiallydiscretized steady flow equations in computational fluid dynamics (CFD) is presented. The algorithm contains many new features developed specifically for application to the large sparse highly parallelized systems encountered in modern CFD. A second-difference dissipation operator common in finite-difference...

We compare two different root-finding methods, eigenvalue methods and homotopy methods, using three test problems: Mandelbrot polynomials, Fibonacci-Mandelbrot polynomials, and Narayana-Mandelbrot polynomials. For the eigenvalue methods, using both MATLAB and Maple, we computed the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix, inspired by Piers Lawr...

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong collapse and it is a particular kind of simplicial collapse. The advantage of using strong collapses is the existence and uniqueness of cores and their relati...

The evolutionary tree reconstruction algorithm called SEMPHY using structural expectation maximization (SEM) is an efficient approach but has local optimality problem. To improve SEMPHY, a new algorithm named HSEMPHY based on the homotopy continuation principle is proposed in the present study for reconstructing evolutionary trees. The HSEMPHY algorithm computes the condition probability of hid...