A numerical approach to harmonic non-commutative spectral field theory

The object of this work is the numerical investigation of a non-commutative field theory defined via the spectral action principle. The Starting point is a spectral triple (A,H,D) referred to as harmonic. The construction of these data relies on an 8-dimensional Clifford algebra. The spectral action is computed for the product of the triple (A,H,D) with a matrix-valued spectral triple. Renormalization theory associates to the spectral action a probability measure. Its associated correlation functions define then a field theory. In the perturbative approach this measure is constructed as a formal power series. This requires explicit knowledge of the solutions of the Euler-Lagrange equations. For the model under consideration, it turns out impossible to obtain these solutions. An alternative approach consists in a discretization of all variables and a numerical investigation of the behavior of the correlation functions when the discretization becomes finer. Despite the complexity of the approximated spectral action, some reliable numerical results are obtained, showing that a numerical treatment of this kind of models in the Moyal matrix basis is possible.Comment: author's PhD Thesi

A numerical approach to harmonic non-commutative spectral field theory

We present a first numerical investigation of a non-commutative gauge theory defined via the spectral action for Moyal space with harmonic propagation. This action is approximated by finite matrices. Using Monte Carlo simulation we study various quantities such as the energy density, the specific heat density and some order parameters, varying the matrix size and the independent parameters of the model. We find a peak structure in the specific heat which might indicate possible phase transitions. However, there are mathematical arguments which show that the limit of infinite matrices is very different from the original spectral model

Event reconstruction for KM3NeT/ORCA using convolutional neural networks

The KM3NeT research infrastructure is currently under construction at two locations in the Mediterranean Sea. The KM3NeT/ORCA water-Cherenkov neutrino detector off the French coast will instrument several megatons of seawater with photosensors. Its main objective is the determination of the neutrino mass ordering. This work aims at demonstrating the general applicability of deep convolutional neural networks to neutrino telescopes, using simulated datasets for the KM3NeT/ORCA detector as an example. To this end, the networks are employed to achieve reconstruction and classification tasks that constitute an alternative to the analysis pipeline presented for KM3NeT/ORCA in the KM3NeT Letter of Intent. They are used to infer event reconstruction estimates for the energy, the direction, and the interaction point of incident neutrinos. The spatial distribution of Cherenkov light generated by charged particles induced in neutrino interactions is classified as shower- or track-like, and the main background processes associated with the detection of atmospheric neutrinos are recognized. Performance comparisons to machine-learning classification and maximum-likelihood reconstruction algorithms previously developed for KM3NeT/ORCA are provided. It is shown that this application of deep convolutional neural networks to simulated datasets for a large-volume neutrino telescope yields competitive reconstruction results and performance improvements with respect to classical approaches

Event reconstruction for KM3NeT/ORCA using convolutional neural networks

The KM3NeT research infrastructure is currently under construction at two locations in the Mediterranean Sea. The KM3NeT/ORCA water-Cherenkov neutrino de tector off the French coast will instrument several megatons of seawater with photosensors. Its main objective is the determination of the neutrino mass ordering. This work aims at demonstrating the general applicability of deep convolutional neural networks to neutrino telescopes, using simulated datasets for the KM3NeT/ORCA detector as an example. To this end, the networks are employed to achieve reconstruction and classification tasks that constitute an alternative to the analysis pipeline presented for KM3NeT/ORCA in the KM3NeT Letter of Intent. They are used to infer event reconstruction estimates for the energy, the direction, and the interaction point of incident neutrinos. The spatial distribution of Cherenkov light generated by charged particles induced in neutrino interactions is classified as shower-or track-like, and the main background processes associated with the detection of atmospheric neutrinos are recognized. Performance comparisons to machine-learning classification and maximum-likelihood reconstruction algorithms previously developed for KM3NeT/ORCA are provided. It is shown that this application of deep convolutional neural networks to simulated datasets for a large-volume neutrino telescope yields competitive reconstruction results and performance improvements with respect to classical approaches

A numerical approach to harmonic non-commutative spectral field theory

Gegenstand der Arbeit ist die numerische Untersuchung einer über das Spektralwirkungsprinzip definierten nichtkommutativen Feldtheorie. Ausgangspunkt dieser Konstruktion ist ein spektrales Tripel. Dabei ist A die 4-dimensionale nichtkommutative Moyal-Algebra und D ein selbstadjungierter (Dirac-)Operator auf dem Hilbert-Raum H. Für das Produkt aus dem Tripel (A,H,D) mit einem matrixwertigen spektralen Tripel wird analog zum Standardverfahren der nichtkommutativen Geometrie die Spektralwirkung berechnet. Die Renormierungstheorie assoziiert zur Spektralwirkung ein Wahrscheinlichkeitsmaß, Voraussetzung dafür ist die Kenntnis der Lösungen der Euler-Lagrange-Gleichungen. Für das betrachtete Modell erweist es sich als unmöglich, diese Lösungen zu gewinnen. Ein alternatives Verfahren besteht in der Diskretisierung aller Variablen und der numerischen Untersuchung des Verhaltens der Korrelationsfunktionen bei Verfeinerung der Diskretisierung. Durch Monte-Carlo-Simulationen werden wichtige Korrelationsfunktionen wie die Energiedichte, die spezifische Wärme sowie einige Ordnungsparameter untersucht. Dabei werden trotz der Komplexität der approximierten Spektralwirkung verläßliche numerische Resultate erzielt. The object of this work is the numerical investigation of a non-commutative field theory defined via the spectral action principle. The Starting point is a spectral triple (A,H,D) referred to as harmonic. The construction of these data relies on an 8-dimensional Clifford algebra. The spectral action is computed for the product of the triple (A,H,D) with a matrix-valued spectral triple. Renormalization theory associates to the spectral action a probability measure. Its associated correlation functions define then a field theory. In the perturbative approach this measure is constructed as a formal power series. This requires explicit knowledge of the solutions of the Euler-Lagrange equations. For the model under consideration, it turns out impossible to obtain these solutions. An alternative approach consists in a discretization of all variables and a numerical investigation of the behavior of the correlation functions when the discretization becomes finer. Despite the complexity of the approximated spectral action, some reliable numerical results are obtained, showing that a numerical treatment of this kind of models in the Moyal matrix basis is possible

NONCOMMUTATIVE FIELD THEORY: NUMERICAL ANALYSIS WITH THE FUZZY DISK

The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for three different limits for the rank of the matrix going to infinity. The numerical simulations reveal three different phases: uniform and disordered phases already the present in the commutative scalar field theory and a nonuniform ordered phase as a noncommutative effects. We have computed the transition curves between phases and their scaling. This is in agreement with studies on the fuzzy sphere, although the speed of convergence for the disc seems to be better. We have performed also three the limits for the theory in the cases of the theory going to the commutative plane or commutative disc. In this case the theory behaves differently, showing the intimate relationship between the nonuniform phase and noncommutative geometry.Comment: Typos corrected. Some references adde

ROAst (ROot extension for Astronomy)

The ROOT framework is one of the most used software tool-sets for particle physics analysis.The goal of ROAst (ROot extension for Astronomy) is to extend the ROOT capabilities adding packages and tools for astrophysical research bridging the gap between particle physics and astronomy. The focus is on the integration of astronomical catalogues and on the support for astronomical coordinate transformations, manipulations as well as the graphical representation of astronomical regions

An http data-federation ecosystem with caching functionality using DPM and Dynafed

The implementation of cache systems in the computing model of HEP experiments enables to accelerate access to hot data sets by scientists, opening new scenarios of data distribution and enable to exploit the paradigm of storage-less sites. In this work, we present a study for the creation of an http data-federation ecosystem with caching functionality. We created plug-in integrated in the logic of a DPM Storage, able to reproduce a cache behaviour, taking advantage from the new feature introduced in the last version of Disk Pool Manager, called volatile-pool. Then we used Dynafed as lightweight federation system to aggregate a set of standard Grid Storage together with the caching system. With the designed setup, clients asking for a file present on the Data-Grid are automatically redirected to the cache, if the cache is the closest storage, thanks to the action of the geo-plugin run by Dynafed. As proof of the concept, we tested the whole system in a controlled environment within the Belle II computing infrastructure using a set of files located in production Storage Elements. Preliminary results demonstrate the proper functionality of the logic and encourage continuing the work

An http data-federation ecosystem with caching functionality using DPM and Dynafed

The implementation of cache systems in the computing model of HEP experiments enables to accelerate access to hot data sets by scientists, opening new scenarios of data distribution and enable to exploit the paradigm of storage-less sites. In this work, we present a study for the creation of an http data-federation ecosystem with caching functionality. We created plug-in integrated in the logic of a DPM Storage, able to reproduce a cache behaviour, taking advantage from the new feature introduced in the last version of Disk Pool Manager, called volatile-pool. Then we used Dynafed as lightweight federation system to aggregate a set of standard Grid Storage together with the caching system. With the designed setup, clients asking for a file present on the Data-Grid are automatically redirected to the cache, if the cache is the closest storage, thanks to the action of the geo-plugin run by Dynafed. As proof of the concept, we tested the whole system in a controlled environment within the Belle II computing infrastructure using a set of files located in production Storage Elements. Preliminary results demonstrate the proper functionality of the logic and encourage continuing the work.</jats:p