The Concurrent Track Evolution Algorithm: Extension for Track Finding in the Inhomogeneous Magnetic Field of the HERA-B Spectrometer

The Concurrent Track Evolution method, which was introduced in a previous paper (DESY 97-054), has been further explored by applying it to the propagation of track candidates into an inhomogeneous magnetic field volume equipped with tracking detectors, as is typical for forward B spectrometers like HERA-B or LHCb. Compared to the field-free case, the method was extended to three-dimensional propagation, with special measures necessary to achieve fast transport in the presence of a fast-varying magnetic field. The performance of the method is tested on HERA-B Monte Carlo events with full detector simulation and a realistic spectrometer geometry.Comment: 26 pages (Latex), 11 figures (Postscript

Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar Potentials

In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.Comment: 10 pages, LaTeX, uses additional package

Maximal Generalized Rank in Graphical Matrix Spaces

In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.Comment: 10 page

Building the Bridge of Schr\"odinger: A Continuous Entropic Optimal Transport Benchmark

Over the last several years, there has been a significant progress in developing neural solvers for the Schr\"odinger Bridge (SB) problem and applying them to generative modeling. This new research field is justifiably fruitful as it is interconnected with the practically well-performing diffusion models and theoretically-grounded entropic optimal transport (EOT). Still the area lacks non-trivial tests allowing a researcher to understand how well do the methods solve SB or its equivalent continuous EOT problem. We fill this gap and propose a novel way to create pairs of probability distributions for which the ground truth OT solution in known by the construction. Our methodology is generic and works for a wide range of OT formulations, in particular, it covers the EOT which is equivalent to SB (the main interest of our study). This development allows us to create continuous benchmark distributions with the known EOT and SB solution on high-dimensional spaces such as spaces of images. As an illustration, we use these benchmark pairs to test how well do existing neural EOT/SB solvers actually compute the EOT solution. The benchmark is available via the link: https://github.com/ngushchin/EntropicOTBenchmark

Numerical and experimental estimation of void fraction of supersonic steam jet in sub-cooled water: a comparative study

Gas-liquid two-phase flows occur in a range of chemical, process, petroleum, metallurgical and power industries. Void fraction is a principal parameter. An effort has been made here to perform a comparative study in which the approximate void fraction of the supersonic steam jet into the sub-cooled water has been measured both numerically as well as experimentally. On a numerical basis, Direct Contact Condensation (DCC) model and on an experimental basis, Electrical Resistance Tomography (ERT) has been used for computing the void fraction. On an experimental basis, the overestimation is nearly 45% when the surrounding water temperature is 30°C with a steam inlet pressure of 1.5 bars and the over-estimation goes up to 83% at 60°C and 3.0 bars. The void fraction computed by the use of the DCC model at 1.5 bars and 300C is 17.66% whereas the computed void fraction at 3.0 bars of inlet pressure and 600C of water temperature is 31.1%

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO