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REWIRE: An optimization-based framework for unstructured data center network design
TLDR
A data center network design framework, that is called REWIRE, to design networks using an optimization algorithm, which significantly outperforms previous solutions and has up to 100-500% more bisection bandwidth and less end-to-end network latency than equivalent-cost DCNs built with best practices.
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A reliable triangular mesh intersection algorithm and its application in geological modelling
TLDR
The mesh intersection algorithm is used within a general framework for modelling and meshing of geological formations, which are essential for reliable mathematical modelling of oil reservoirs.
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A generative geometric kernel
TLDR
This work designs and implements a generative geometric kernel that achieves genericity through a layered design deriving concepts from affine geometry, linear algebra and abstract algebra, and achieves parametrization and type-safety by using OCaml's module system, including higher order modules.
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A consistent octree hanging node elimination algorithm for hexahedral mesh generation
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Fast computation of Smith forms of sparse matrices over local rings
TLDR
An algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small is given, and a method for dimension reduction while preserving the invariant Factors is described.
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Relating $p$-Adic eigenvalues and the local Smith normal form
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Schrödinger Operators on Graphs and Branched Manifolds
We consider the Schrodinger operators on graphs with a finite or countable number of edges and Schr?dinger operators on branched manifolds of variable dimension. In particular, a description of…
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Ranks of Quotients, Remainders and $p$-Adic Digits of Matrices
TLDR
Upper bounds are proven for the $\mathbb{Z}/p p A/A/p Z-rank of A for all $i \ge 0$ when $p = 2$, and a conjecture is presented for odd primes.
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A GENERATIVE APPROACH TO MESHING GEOMETRY
TLDR
The design and implementation of a generative geometric kernel suitable for supporting a family of mesh generation programs is presented, designed as a program generator which is generic, parametric, type-safe, and maintainable.
Smith Normal Form over Local Rings and Related Problems
TLDR
The ultimate goal is to extend the applications of numerical algorithms for computing eigenvalues to computing the invariant factors of symbolic matrices as well as to design an algorithm for computing uniform samples from the nullspace.
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