Can we make a Finsler metric complete by a trivial projective change?

A trivial projective change of a Finsler metric $F$ is the Finsler metric $F + df$. I explain when it is possible to make a given Finsler metric both forward and backward complete by a trivial projective change. The problem actually came from lorentz geometry and mathematical relativity: it was observed that it is possible to understand the light-line geodesics of a (normalized, standard) stationary 4-dimensional space-time as geodesics of a certain Finsler Randers metric on a 3-dimensional manifold. The trivial projective change of the Finsler metric corresponds to the choice of another 3-dimensional slice, and the existence of a trivial projective change that is forward and backward complete is equivalent to the global hyperbolicity of the space-time.Comment: 11 pages, one figure, submitted to the proceedings of VI International Meeting on Lorentzian Geometry (Granada

Finsler geodesics in the presence of a convex function and their applications

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.Comment: 16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version. This preprint and arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG

A note on the existence of standard splittings for conformally stationary spacetimes

Let $(M,g)$ be a spacetime which admits a complete timelike conformal Killing vector field $K$. We prove that $(M,g)$ splits globally as a standard conformastationary spacetime with respect to $K$ if and only if $(M,g)$ is distinguishing (and, thus causally continuous). Causal but non-distinguishing spacetimes with complete stationary vector fields are also exhibited. For the proof, the recently solved "folk problems" on smoothability of time functions (moreover, the existence of a {\em temporal} function) are used.Comment: Metadata updated, 6 page

Legumes as basic ingredients in the production of dairy-free cheese alternatives: a review

Research into dairy-free alternative products, whether plant-based or cell-based, is growing fast and the food industry is facing a new challenge of creating innovative, nutritious, accessible, and natural dairy-free cheese alternatives. The market demand for these products is continuing to increase owing to more people choosing to reduce or eliminate meat and dairy products from their diet for health, environmental sustainability, and/or ethical reasons. This review investigates the current status of dairy product alternatives. Legume proteins have good technological properties and are cheap, which gives them a strong commercial potential to be used in plant-based cheese-like products. However, few legume proteins have been explored in the formulation, development, and manufacture of a fully dairy-free cheese because of their undesirable properties: heat stable anti-nutritional factors and a beany flavor. These can be alleviated by novel or traditional and economical techniques. The improvement and diversification of the formulation of legume-based cheese alternatives is strongly suggested as a low-cost step towards more sustainable food chains. © 2021 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry

LHCb VELO Upgrade: Technical Design Report

The upgraded LHCb VELO silicon vertex detector is a lightweight hybrid pixel detector capable of 40 MHz readout at a luminosity of 2×10^33 cm^−2 s^−1. The track reconstruction speed and precision is enhanced relative to the current VELO detector even at the high occupancy conditions of the upgrade, due to the pixel geometry and a closest distance of approach to the LHC beams of just 5.1 mm for the first sensitive pixel. Cooling is provided by evaporative CO2 circulating in microchannel cooling substrates. The detector contains 41 million 55μ×55μ pixels, read out by the custom developed VeloPix front end ASIC. The detector will start operation together with the rest of the upgraded LHCb experiment after the LHC LS2 shutdown, currently scheduled to end in 2019. This Technical Design Report describes the upgraded VELO system, planned construction and installation, and gives an overview of the expected detector performanc

A MOS-based Dynamic Memetic Differential Evolution Algorithm for Continuous Optimization: A Scalability Test

Continuous optimization is one of the areas with more activity in the field of heuristic optimization. Many algorithms have been proposed and compared on several benchmarks of functions, with different performance depending on the problems. For this reason, the combination of different search strategies seems desirable to obtain the best performance of each of these approaches. This contribution explores the use of a hybrid memetic algorithm based on the multiple offspring framework. The proposed algorithm combines the explorative/exploitative strength of two heuristic search methods that separately obtain very competitive results. This algorithm has been tested with the benchmark problems and conditions defined for the special issue of the Soft Computing Journal on Scalability of Evolutionary Algorithms and other Metaheuristics for Large Scale Continuous Optimization Problems. The proposed algorithm obtained the best results compared with both its composing algorithms and a set of reference algorithms that were proposed for the special issue

The artificial retina for track reconstruction at the LHC crossing rate

We present the results of an R&D study for a specialized processor capable of precisely reconstructing events with hundreds of charged-particle tracks in pixel and silicon strip detectors at $40\,\rm MHz$, thus suitable for processing LHC events at the full crossing frequency. For this purpose we design and test a massively parallel pattern-recognition algorithm, inspired to the current understanding of the mechanisms adopted by the primary visual cortex of mammals in the early stages of visual-information processing. The detailed geometry and charged-particle's activity of a large tracking detector are simulated and used to assess the performance of the artificial retina algorithm. We find that high-quality tracking in large detectors is possible with sub-microsecond latencies when the algorithm is implemented in modern, high-speed, high-bandwidth FPGA devices.Comment: 3 pages, 3 figures, ICHEP14. arXiv admin note: text overlap with arXiv:1409.089

Simulation and performance of an artificial retina for 40 MHz track reconstruction

We present the results of a detailed simulation of the artificial retina pattern-recognition algorithm, designed to reconstruct events with hundreds of charged-particle tracks in pixel and silicon detectors at LHCb with LHC crossing frequency of $40\,\rm MHz$. Performances of the artificial retina algorithm are assessed using the official Monte Carlo samples of the LHCb experiment. We found performances for the retina pattern-recognition algorithm comparable with the full LHCb reconstruction algorithm.Comment: Final draft of WIT proceedings modified according to JINST referee's comment

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

A Specialized Processor for Track Reconstruction at the LHC Crossing Rate

We present the results of an R&D study of a specialized processor capable of precisely reconstructing events with hundreds of charged-particle tracks in pixel detectors at 40 MHz, thus suitable for processing LHC events at the full crossing frequency. For this purpose we design and test a massively parallel pattern-recognition algorithm, inspired by studies of the processing of visual images by the brain as it happens in nature. We find that high-quality tracking in large detectors is possible with sub-$\mu$s latencies when this algorithm is implemented in modern, high-speed, high-bandwidth FPGA devices. This opens a possibility of making track reconstruction happen transparently as part of the detector readout.Comment: Presented by G.Punzi at the conference on "Instrumentation for Colliding Beam Physics" (INSTR14), 24 Feb to 1 Mar 2014, Novosibirsk, Russia. Submitted to JINST proceeding