arXiv subjects

Tianyi Yang

Publications and source records attributed to Tianyi Yang.

61 records · Page 4Linked to original sources

arXiv2021

Schrödinger PCA: On the Duality between Principal Component Analysis and Schrödinger Equation

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to discover meaningful modes. In particular, PCA will fail the spatial Gaussian Process (GP) model in the undersampling regime, i.e. the averaged distance of neighboring anchor points (spatial features) is greater than the correlation length of GP. Counterintuitively, by drawing the connection between PCA and Schrödinger equation, we can not only attack the undersampling challenge but also compute in an efficient and decoupled way with the proposed algorithm called Schrödinger PCA. Our algorithm only requires variances of features and estimated correlation length as input, constructs the corresponding Schrödinger equation, and solves it to obtain the energy eigenstates, which coincide with principal components. We will also establish the connection of our algorithm to the model reduction techniques in the partial differential equation (PDE) community, where the steady-state Schrödinger operator is identified as a second-order approximation to the covariance function. Numerical experiments are implemented to testify the validity and efficiency of the proposed algorithm, showing its potential for unsupervised learning tasks on general graphs and manifolds.

physics.comp-ph↗

arXiv2021

Longitudinally polarized ZZ scattering at the Muon Collider

Measuring longitudinally polarized vector boson scattering in, e.g., the ZZ channel is a promising way to investigate the unitarization scheme from the Higgs and possible new physics beyond the Standard Model. However, at the LHC, it demands the end of the HL-LHC lifetime luminosity, 3000/fb, and advanced data analysis technique to reach the discovery threshold due to its small production rates. Instead, there could be great potential for future colliders. In this paper, we perform a Monte Carlo study and examine the projected sensitivity of longitudinally polarized ZZ scattering at a TeV scale muon collider. We conduct studies at 14 TeV and 6 TeV muon colliders respectively and find that a 5 standard deviation discovery can be achieved at a 14 TeV muon collider, with 3000/fb of data collected. While a 6 TeV muon collider can already surpass HL-LHC, reaching 2 standard deviations with around 4000/fb of data. The effect from lepton isolation and detector granularity is also discussed, which may be more obvious at higher energy muon colliders, as the leptons from longitudinally polarized Z decays tend to be closer.

hep-ph↗

arXiv2021

A Survey on Automated Log Analysis for Reliability Engineering

Logs are semi-structured text generated by logging statements in software source code. In recent decades, software logs have become imperative in the reliability assurance mechanism of many software systems because they are often the only data available that record software runtime information. As modern software is evolving into a large scale, the volume of logs has increased rapidly. To enable effective and efficient usage of modern software logs in reliability engineering, a number of studies have been conducted on automated log analysis. This survey presents a detailed overview of automated log analysis research, including how to automate and assist the writing of logging statements, how to compress logs, how to parse logs into structured event templates, and how to employ logs to detect anomalies, predict failures, and facilitate diagnosis. Additionally, we survey work that releases open-source toolkits and datasets. Based on the discussion of the recent advances, we present several promising future directions toward real-world and next-generation automated log analysis.

cs.SE↗

arXiv2020

The physics case for an electron-muon collider

An electron-muon collider with an asymmetric collision profile targeting multi-ab$^{-1}$ integrated luminosity is proposed. This novel collider, operating at collisions energies of e.g. 20-200 GeV, 50-1000 GeV and 100-3000 GeV, would be able to probe charged lepton flavor violation and measure Higgs boson properties precisely. The collision of an electron and muon beam leads to less physics background compared with either an electron-electron or a muon-muon collider, since electron-muon interactions proceed mostly through higher order vector boson fusion and vector boson scattering processes. The asymmetric collision profile results in collision products that are boosted towards the electron beam side, which can be exploited to reduce beam-induced background from the muon beam to a large extent. With this in mind, one can imagine a lepton collider complex, starting from colliding order 10 GeV electron and muon beams for the first time in history and to probe charged lepton flavor violation, then to be upgraded to a collider with 50-100 GeV electron and 1-3 TeV muon beams to measure Higgs properties and search for new physics, and finally to be transformed to a TeV scale muon muon collider. The cost should vary from order 100 millions to a few billion dollars, corresponding to different stages, which make the funding situation more practical.

hep-ph↗

arXiv2020

Barter Exchange via Friends' Friends

Barter exchange studies the setting where each agent owns a good, and they can exchange with each other if that gives them more preferred goods. This exchange will give better outcomes if there are more participants. The challenge here is how to get more participants and our goal is to incentivize the existing participants to invite new participants. However, new participants might be competitors for the existing participants. Therefore, we design an exchange mechanism based on the classical Top Trading Cycle (TTC) algorithm to solve their conflicts. Our mechanism is truthful in terms of revealing their preferences and also guarantees that inviting all their neighbors is a dominant strategy for all participants. The mechanism can be applied in settings where more participants are preferred but no extra budget to reach new participants.

cs.GT↗

arXiv2020

How dark are filaments in the cosmic web?

The cold dark matter model predicts that dark matter haloes are connected by filaments. Direct measurements of the masses and structure of these filaments are difficult, but recently several studies have detected these dark-matter-dominated filaments using weak lensing. Here we study the efficiency of galaxy formation within the filaments by measuring their total mass-to-light ratios and stellar mass fractions. Specifically, we stack pairs of Luminous Red Galaxies (LRGs) with a typical separation on the sky of $8 h^{-1}$ Mpc. We stack background galaxy shapes around pairs to obtain mass maps through weak lensing, and we stack galaxies from the Sloan Digital Sky Survey (SDSS) to obtain maps of light and stellar mass. To isolate the signal from the filament, we construct two matched catalogues of physical and non-physical (projected) LRG pairs, with the same distributions of redshift and separation. We then subtract the two stacked maps. Using LRG pair samples from the BOSS survey at two different redshifts, we find that the evolution of the mass in filament is consistent with the predictions from perturbation theory. The filaments are not entirely dark: their mass-to-light ratios ($M/L = 351\pm137$ in solar units in the $r$-band) and stellar mass fractions ($M_{\rm stellar}/M = 0.0073\pm0.0030$) are consistent with the cosmic values (and with their redshift evolutions)

astro-ph.CO↗

arXiv2017

An observer's guide to the (Local Group) dwarf galaxies: predictions for their own dwarf satellite populations

A recent surge in the discovery of new ultrafaint dwarf satellites of the Milky Way has inspired the idea of searching for faint satellites, $10^3\, \mathrm{M_{\odot}} < M_* < 10^6\, \mathrm{M_{\odot}}$, around less massive field galaxies in the Local Group. Such satellites would be subject to weaker environmental influences than Milky Way satellites, and could lead to new insights on low mass galaxy formation. In this paper, we predict the number of luminous satellites expected around field dwarf galaxies by applying several abundance matching models and a reionization model to the dark-matter only \textit{Caterpillar} simulation suite. For three of the four abundance matching models used, we find a $>99\%$ chance that at least one satellite with stellar mass $M_*> 10^5\, \mathrm{M_{\odot}}$ exists around the combined five Local Group field dwarf galaxies with the largest stellar mass. When considering satellites with $M_*> 10^4\, \mathrm{M_{\odot}}$, we predict a combined $5-25$ satellites for the five largest field dwarfs, and $10-50$ for the whole Local Group field dwarf population. Because of the relatively small number of predicted dwarfs, and their extended spatial distribution, a large fraction each Local Group dwarf's virial volume will need to be surveyed to guarantee discoveries. We compute the predicted number of satellites in a given field of view of specific Local Group galaxies, as a function of minimum satellite luminosity, and explicitly obtain such values for the Solitary Local dwarfs survey. Uncertainties in abundance matching and reionization models are large, implying that comprehensive searches could lead to refinements of both models.

astro-ph.GA↗