Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Gravitational-Wave Stochastic Background from Kinks and Cusps on Cosmic Strings

We compute the contribution of kinks on cosmic string loops to stochastic background of gravitational waves (SBGW).We find that kinks contribute at the same order as cusps to the SBGW.We discuss the accessibility of the total background due to kinks as well as cusps to current and planned gravitational wave detectors, as well as to the big bang nucleosynthesis (BBN), the cosmic microwave background (CMB), and pulsar timing constraints. As in the case of cusps, we find that current data from interferometric gravitational wave detectors, such as LIGO, are sensitive to areas of parameter space of cosmic string models complementary to those accessible to pulsar, BBN, and CMB bounds.Comment: 24 pages, 3 figure

Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population

The millisecond pulsars, old-recycled objects spinning with high frequency $\mathcal{O}$(kHz) sustaining the deformation from their spherical shape, may emit gravitational-waves (GW). These are one of the potential candidates contributing to the anisotropic stochastic gravitational-wave background (SGWB) observable in the ground-based GW detectors. Here, we present the results from a likelihood-based targeted search for the SGWB due to millisecond pulsars in the Milky Way, by analyzing the data from the first three observing runs of Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB power spectra and the sky distribution is known a priori from the population synthesis model. The information of the ensemble source properties, i.e., the in-band number of pulsars, $N_{obs}$ and the averaged ellipticity, $\mu_\epsilon$ is encoded in the maximum likelihood statistic. We do not find significant evidence for the SGWB signal from the considered source population. The best Bayesian upper limit with $95\%$ confidence for the parameters are $N_{obs}\leq8.8\times10^{4}$ and $\mu_\epsilon\leq1.1\times10^{-7}$, which is comparable to the bounds on mean ellipticity with the GW observations of the individual pulsars. Finally, we show that for the plausible case of $N_{obs}=40,000$, with the one year of observations, the one-sigma sensitivity on $\mu_\epsilon$ might reach $10^{-8}$ and $2.7\times10^{-9}$ for the second-generation detector network having A+ sensitivity and third-generation detector network respectively

Radiation hardness of CMS pixel barrel modules

Pixel detectors are used in the innermost part of the multi purpose experiments at LHC and are therefore exposed to the highest fluences of ionising radiation, which in this part of the detectors consists mainly of charged pions. The radiation hardness of all detector components has thoroughly been tested up to the fluences expected at the LHC. In case of an LHC upgrade, the fluence will be much higher and it is not yet clear how long the present pixel modules will stay operative in such a harsh environment. The aim of this study was to establish such a limit as a benchmark for other possible detector concepts considered for the upgrade. As the sensors and the readout chip are the parts most sensitive to radiation damage, samples consisting of a small pixel sensor bump-bonded to a CMS-readout chip (PSI46V2.1) have been irradiated with positive 200 MeV pions at PSI up to 6E14 Neq and with 21 GeV protons at CERN up to 5E15 Neq. After irradiation the response of the system to beta particles from a Sr-90 source was measured to characterise the charge collection efficiency of the sensor. Radiation induced changes in the readout chip were also measured. The results show that the present pixel modules can be expected to be still operational after a fluence of 2.8E15 Neq. Samples irradiated up to 5E15 Neq still see the beta particles. However, further tests are needed to confirm whether a stable operation with high particle detection efficiency is possible after such a high fluence.Comment: Contribution to the 11th European Symposium on Semiconductor Detectors June 7-11, 2009 Wildbad Kreuth, German

Some model-independent phenomenological consequences of flexible brane worlds

In this work we will review the main properties of brane-world models with low tension. Starting from very general principles, it is possible to obtain an effective action for the relevant degrees of freedom at low energies (branons). Using the cross sections for high-energy processes involving branons, we set bounds on the different parameters appearing in these models. We also show that branons provide a WIMP candidate for dark matter in a natural way. We consider cosmological constraints on its thermal and non-thermal relic abundances. We derive direct detection limits and compare those limits with the preferred parameter region in the case in which the EGRET excess in the diffuse galactic gamma rays is due to dark matter annihilation. Finally we will discuss the constraints coming from the precision tests of the Standard Model and the muon anomalous magnetic moment.Comment: 10 pages, 6 figures. Contribution to the Proceedings of the Second International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, IRGAC 2006, Barcelona, 11-15 July, 200

Radiation Hardness of Thin Low Gain Avalanche Detectors

Low Gain Avalanche Detectors (LGAD) are based on a n++-p+-p-p++ structure where an appropriate doping of the multiplication layer (p+) leads to high enough electric fields for impact ionization. Gain factors of few tens in charge significantly improve the resolution of timing measurements, particularly for thin detectors, where the timing performance was shown to be limited by Landau fluctuations. The main obstacle for their operation is the decrease of gain with irradiation, attributed to effective acceptor removal in the gain layer. Sets of thin sensors were produced by two different producers on different substrates, with different gain layer doping profiles and thicknesses (45, 50 and 80 um). Their performance in terms of gain/collected charge and leakage current was compared before and after irradiation with neutrons and pions up to the equivalent fluences of 5e15 cm-2. Transient Current Technique and charge collection measurements with LHC speed electronics were employed to characterize the detectors. The thin LGAD sensors were shown to perform much better than sensors of standard thickness (~300 um) and offer larger charge collection with respect to detectors without gain layer for fluences <2e15 cm-2. Larger initial gain prolongs the beneficial performance of LGADs. Pions were found to be more damaging than neutrons at the same equivalent fluence, while no significant difference was found between different producers. At very high fluences and bias voltages the gain appears due to deep acceptors in the bulk, hence also in thin standard detectors

Using impression data to improve models of online social influence

Influence, the ability to change the beliefs and behaviors of others, is the main currency on social media. Extant studies of influence on social media, however, are limited by publicly available data that record expressions (active engagement of users with content, such as likes and comments), but neglect impressions (exposure to content, such as views) and lack “ground truth” measures of influence. To overcome these limitations, we implemented a social media simulation using an original, web-based micro-blogging platform. We propose three influence models, leveraging expressions and impressions to create a more complete picture of social influence. We demonstrate that impressions are much more important drivers of influence than expressions, and our models accurately identify the most influential accounts in our simulation. Impressions data also allow us to better understand important social media dynamics, including the emergence of small numbers of influential accounts and the formation of opinion echo chambers