A Review of the Mass Measurement Techniques proposed for the Large Hadron Collider

We review the methods which have been proposed for measuring masses of new particles at the Large Hadron Collider paying particular attention to the kinematical techniques suitable for extracting mass information when invisible particles are expected.Comment: 72 pages - in form to be published in JPhys

A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external cost $\mathcal{C}:SE(2) \to [\delta,1]$, $\delta>0$, computed from image data. The method consists of a first step where a SR-distance map is computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system derived via Pontryagin's Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. For $\mathcal{C}=1$ we show that our method produces the global minimizers. Comparison with exact solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics. We present numerical computations of Maxwell points and cusp points, which we again verify for the uniform cost case $\mathcal{C}=1$. Regarding image analysis applications, tracking of elongated structures in retinal and synthetic images show that our line tracking generically deals with crossings. We show the benefits of including the sub-Riemannian geometry.Comment: Extended version of SSVM 2015 conference article "Data-driven Sub-Riemannian Geodesics in SE(2)

Automated Design of Tissue Engineering Scaffolds by Advanced CAD

The design of scaffolds with an intricate and controlled internal structure represents a challenge for Tissue Engineering. Several scaffold manufacturing techniques allow the creation of complex and random architectures, but have little or no control over geometrical parameters such as pore size, shape and interconnectivity- things that are essential for tissue regeneration. The combined use of CAD software and layer manufacturing techniques allow a high degree of control over those parameters, resulting in reproducible geometrical architectures. However, the design of the complex and intricate network of channels that are required in conventional CAD, is extremely time consuming: manually setting thousands of different geometrical parameters may require several days in which to design the individual scaffold structures. This research proposes an automated design methodology in order to overcome those limitations. The combined use of Object Oriented Programming and advanced CAD software, allows the rapid generation of thousands of different geometrical elements. Each has a different set of parameters that can be changed by the software, either randomly or according to a given mathematical formula, so that they match the different distribution of geometrical elements such as pore size and pore interconnectivity. This work describes a methodology that has been used to design five cubic scaffolds with pore size ranging from about 200 to 800 µm, each with an increased complexity of the internal geometry.Mechanical Engineerin

Polynomials, Riemann surfaces, and reconstructing missing-energy events

We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.Comment: 28 pages, 6 figures; version accepted for publication, with discussion of Higgs to tau tau deca

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available