Spherical trigonometry, Yule's PARCOR identity and FLRS algorithms

Yule's PARCOR Identity, in statistics, and the fundamental law of cosines, in spherical trigonometry, are indeed the same formula . This observation establishes a link between Fast Recursive Least Squares FRLS adaptive filtering and spherical trigonometry, sinc e the fully—normalized FRLS lattice algorithm of Lee et al . consists of three particular applications of Yule's PARCOR Identity . In that framework, the six PARCORs propagated by the fully—normalized FRLS lattice filter are the cosines of the six elements of a spherica l triangle, and this lattice algorithm is one solution to an important spherical triangle problem that arises naturally in navigation an d astronomy. The practical interest of this new geometric interpretation is that one can take advantage of the well—trodden path o f spherical trigonometry to derive unnoticed recursions among PARCORs, and thus among FRLS quantities (a particular case) . These new formulas enable us to design alternatives to the original solution of Lee et al. We thus propose two new minimal (in the system theory sense) FRLS algorithms . One of these algorithms happens to be a normalized version of the QR—decomposition-based leas t squares lattice algorithm .Yule's PARCOR Identity, in statistics, and the fundamental law of cosines, in spherical trigonometry, are indeed the same formula . This observation establishes a link between Fast Recursive Least Squares FRLS adaptive filtering and spherical trigonometry, sinc e the fully—normalized FRLS lattice algorithm of Lee et al . consists of three particular applications of Yule's PARCOR Identity . In that framework, the six PARCORs propagated by the fully—normalized FRLS lattice filter are the cosines of the six elements of a spherica l triangle, and this lattice algorithm is one solution to an important spherical triangle problem that arises naturally in navigation an d astronomy. The practical interest of this new geometric interpretation is that one can take advantage of the well—trodden path o f spherical trigonometry to derive unnoticed recursions among PARCORs, and thus among FRLS quantities (a particular case) . These new formulas enable us to design alternatives to the original solution of Lee et al. We thus propose two new minimal (in the system theory sense) FRLS algorithms . One of these algorithms happens to be a normalized version of the QR—decomposition-based leas t squares lattice algorithm .L'identité de Yule, en statistique, et la loi des cosinus, en trigonométrie sphérique, sont une seule et même formule. Cette constatation met en lumière l'existence de liens entre filtrage adaptatif des Moindres Carrés Récursifs Rapides (MCRR) et trigonométrie sphérique, puisque les équations du treillis normalisé en angle de Lee et al. sont trois applications particulières de l'identité de Yule. De ce nouveau point de vue, les six coefficients de corrélation partielle (PARCORs) propagés par l'algorithme de Lee et al. sont les cosinus des six éléments d'un triangle sphérique, et les récurrences de ce treillis sont une solution particulière à un problème de triangle sphérique important qui admet des applications naturelles en navigation et en astronomie. L'intérêt pratique de cette nouvelle interprétation géométrique est que l'on peut exploiter l'outil trigonométrie sphérique pour établir des récurrences nowelles entre PARCORs et donc, comme cas particulier, entre quantités intervenant dans les algorithmes MCRR. Ces relations nouvelles nous permettent de construire des alternatives à la solution originelle de Lee et al. Nous proposons ainsi deux algorithmes MCRR nouveaux, minimaux au sens de la théorie des systèmes, dont l'un se trouve être une version normalisée de l'algorithme en treillis à base de rotations de Givens

The CMS experiment at the CERN LHC

The Compact Muon Solenoid (CMS) detector is described. The detector operates at the Large Hadron Collider (LHC) at CERN. It was conceived to study proton-proton (and leadlead) collisions at a centre-of-mass energy of 14 TeV (5.5 TeV nucleon-nucleon) and at luminosities up to 1034 cm-2s-1 (1027 cm-2s-1). At the core of the CMS detector sits a high-magnetic field and large-bore superconducting solenoid surrounding an all-silicon pixel and strip tracker, a lead-tungstate scintillating-crystals electromagnetic calorimeter, and a brass-scintillator sampling hadron calorimeter. The iron yoke of the flux-return is instrumented with four stations of muon detectors covering most of the 4π solid angle. Forward sampling calorimeters extend the pseudorapidity coverage to high values (|η| ≤ 5) assuring very good hermeticity. The overall dimensions of the CMS detector are a length of 21.6 m, a diameter of 14.6 m and a total weight of 12500 t

The Evolution of Galaxies and Their Environment

The Third Teton Summer School on Astrophysics discussed the formation of galaxies, star formation in galaxies, galaxies and quasars at high red shift, and the intergalactic and intercluster medium and cooling flows. Observation and theoretical research on these topics was presented at the meeting and summaries of the contributed papers are included in this volume

The CMS experiment at the CERN LHC

The Compact Muon Solenoid (CMS) detector is described. The detector operates at the Large Hadron Collider (LHC) at CERN. It was conceived to study proton-proton (and lead-lead) collisions at a centre-of-mass energy of 14 TeV (5.5 TeV nucleon-nucleon) and at luminosities up to 10^(34) cm^(−2) s^(−1) (10^(27) cm^(−2) s^(−1)). At the core of the CMS detector sits a high-magnetic-field and large-bore superconducting solenoid surrounding an all-silicon pixel and strip tracker, a lead-tungstate scintillating-crystals electromagnetic calorimeter, and a brass-scintillator sampling hadron calorimeter. The iron yoke of the flux-return is instrumented with four stations of muon detectors covering most of the 4π solid angle. Forward sampling calorimeters extend the pseudorapidity coverage to high values (|η| ≤ 5) assuring very good hermeticity. The overall dimensions of the CMS detector are a length of 21.6 m, a diameter of 14.6 m and a total weight of 12500 t

The CMS experiment at the CERN LHC

The Compact Muon Solenoid (CMS) detector is described. The detector operates at the Large Hadron Collider (LHC) at CERN. It was conceived to study proton-proton (and lead-lead) collisions at a centre-of-mass energy of 14 TeV (5.5 TeV nucleon-nucleon) and at luminosities up to 10^(34) cm^(−2) s^(−1) (10^(27) cm^(−2) s^(−1)). At the core of the CMS detector sits a high-magnetic-field and large-bore superconducting solenoid surrounding an all-silicon pixel and strip tracker, a lead-tungstate scintillating-crystals electromagnetic calorimeter, and a brass-scintillator sampling hadron calorimeter. The iron yoke of the flux-return is instrumented with four stations of muon detectors covering most of the 4π solid angle. Forward sampling calorimeters extend the pseudorapidity coverage to high values (|η| ≤ 5) assuring very good hermeticity. The overall dimensions of the CMS detector are a length of 21.6 m, a diameter of 14.6 m and a total weight of 12500 t

The TOTEM Experiment at the CERN Large Hadron Collider

The TOTEM Experiment will measure the total pp cross-section with the luminosity independent method and study elastic and diffractive scattering at the LHC. To achieve optimum forward coverage for charged particles emitted by the pp collisions in the interaction point IP5, two tracking telescopes, T1 and T2, will be installed on each side in the pseudorapidity region 3,1 <h< 6,5, and Roman Pot stations will be placed at distances of 147m and 220m from IP5. Being an independent experiment but technically integrated into CMS, TOTEM will first operate in standalone mode to pursue its own physics programme and at a later stage together with CMS for a common physics programme. This article gives a description of the TOTEM apparatus and its performance

A variational autoencoder application for real-time anomaly detection at CMS

Despite providing invaluable data in the field of High Energy Physics, towards higher luminosity runs the Large Hadron Collider (LHC) will face challenges in discovering interesting results through conventional methods used in previous run periods. Among the proposed approaches, the one we focus on in this thesis work – in collaboration with CERN teams, involves the use of a joint variational autoencoder (JointVAE) machine learning model, trained on known physics processes to identify anomalous events that correspond to previously unidentified physics signatures. By doing so, this method does not rely on any specific new physics signatures and can detect anomalous events in an unsupervised manner, complementing the traditional LHC search tactics that rely on model-dependent hypothesis testing. The algorithm produces a list of anomalous events, which experimental collaborations will examine and eventually confirm as new physics phenomena. Furthermore, repetitive event topologies in the dataset can inspire new physics model building and experimental searches. Implementing this algorithm in the trigger system of LHC experiments can detect previously unnoticed anomalous events, thus broadening the discovery potential of the LHC. This thesis presents a method for implementing the JointVAE model, for real-time anomaly detection in the Compact Muon Solenoid (CMS) experiment. Among the challenges of implementing machine learning models in fast applications, such as the trigger system of the LHC experiments, low latency and reduced resource consumption are essential. Therefore, the JointVAE model has been studied for its implementation feasibility in Field-Programmable Gate Arrays (FPGAs), utilizing a tool based on High-Level Synthesis (HLS) named HLS4ML. The tool, combined with the quantization of neural networks, will reduce the model size, latency, and energy consumption