Polarization Swings Reveal Magnetic Energy Dissipation in Blazars

The polarization signatures of the blazar emissions are known to be highly variable. In addition to small fluctuations of the polarization angle around a mean value, sometimes large (> 180^o) polarization angle swings are observed. We suggest that such p henomena can be interpreted as arising from light-travel-time effects within an underlying axisymmetric emission region. We present the first simultaneous fitting of the multi-wavelength spectrum, variability and time-dependent polarization features of a correlated optical and gamma-ray flaring event of the prominent blazar 3C279, which was accompanied by a drastic change of its polarization signatures. This unprecedented combination of spectral, variability, and polarization information in a coherent physical model allows us to place stringent constraints on the particle acceleration and magnetic-field topology in the relativistic jet of a blazar, strongly favoring a scenario in which magnetic energy dissipation is the primary driver of the flare event.Comment: Accepted for Publication in The Astrophysical Journa

Efficient Production of High-energy Nonthermal Particles during Magnetic Reconnection in a Magnetically-dominated Ion-Electron Plasma

Magnetic reconnection is a leading mechanism for dissipating magnetic energy and accelerating nonthermal particles in Poynting-flux dominated flows. In this letter, we investigate nonthermal particle acceleration during magnetic reconnection in a magnetically-dominated ion-electron plasma using fully kinetic simulations. For an ion-electron plasma with the total magnetization $\sigma_0=B^2/(4\pi n(m_i+m_e)c^2)$, the magnetization for each species is $\sigma_i \sim \sigma_0$ and $\sigma_e \sim (m_i/m_e) \sigma_0$, respectively. We have studied the magnetically dominated regime by varying $\sigma_{e} = 10^3 - 10^5$ with initial ion and electron temperatures $T_i = T_e = 5 - 20 m_ec^2$ and mass ratio $m_i/m_e = 1 - 1836$. The results demonstrate that reconnection quickly establishes power-law energy distributions for both electrons and ions within several ($2-3$) light-crossing times. For the cases with periodic boundary conditions, the power-law index is $1<s<2$ for both electrons and ions. The hard spectra limit the power-law energies for electrons and ions to be $\gamma_{be} \sim \sigma_e$ and $\gamma_{bi} \sim \sigma_i$, respectively. The main acceleration mechanism is a Fermi-like acceleration through the drift motions of charged particles. When comparing the spectra for electrons and ions in momentum space, the spectral indices $s_p$ are identical as predicted in Fermi acceleration. We also find that the bulk flow can carry a significant amount of energy during the simulations. We discuss the implication of this study in the context of Poynting-flux dominated jets and pulsar winds especially the applications for explaining the nonthermal high-energy emissions.Comment: 7 pages, 5 figures. ApJL in pres

Longitudinal Data Analysis with Composite Likelihood Methods

Longitudinal data arise commonly in many fields including public health studies and survey sampling. Valid inference methods for longitudinal data are of great importance in scientific researches. In longitudinal studies, data collection are often designed to follow all the interested information on individuals at scheduled times. The analysis in longitudinal studies usually focuses on how the data change over time and how they are associated with certain risk factors or covariates. Various statistical models and methods have been developed over the past few decades. However, these methods could become invalid when data possess additional features. First of all, incompleteness of data presents considerable complications to standard modeling and inference methods. Although we hope each individual completes all of the scheduled measurements without any absence, missing observations occur commonly in longitudinal studies. It has been documented that biased results could arise if such a feature is not properly accounted for in the analysis. There has been a large body of methods in the literature on handling missingness arising either from response components or covariate variables, but relatively little attention has been directed to addressing missingness in both response and covariate variables simultaneously. Important reasons for the sparsity of the research on this topic may be attributed to substantially increased complexity of modeling and computational difficulties. In Chapter 2 and Chapter 3 of the thesis, I develop methods to handle incomplete longitudinal data using the pairwise likelihood formulation. The proposed methods can handle longitudinal data with missing observations in both response and covariate variables. A unified framework is invoked to accommodate various types of missing data patterns. The performance of the proposed methods is carefully assessed under a variety of circumstances. In particular, issues on efficiency and robustness are investigated. Longitudinal survey data from the National Population Health Study are analyzed with the proposed methods. The other difficulty in longitudinal data is model selection. Incorporating a large number of irrelevant covariates to the model may result in computation, interpretation and prediction difficulties, thus selecting parsimonious models are typically desirable. In particular, the penalized likelihood method is commonly employed for this purpose. However, when we apply the penalized likelihood approach in longitudinal studies, it may involve high dimensional integrals which are computationally expensive. We propose an alternative method using the composite likelihood formulation. Formulation of composite likelihood requires only a partial structure of the correlated data such as marginal or pairwise distributions. This strategy shows modeling tractability and computational cheapness in model selection. Therefore, in Chapter 4 of this thesis, I propose a composite likelihood approach with penalized function to handle the model selection issue. In practice, we often face the model selection problem not only from choosing proper covariates for regression predictor, but also from the component of random effects. Furthermore, the specification of random effects distribution could be crucial to maintain the validity of statistical inference. Thus, the discussion on selecting both covariates and random effects as well as misspecification of random effects are also included in Chapter 4. Chapter 5 of this thesis mainly addresses the joint features of missingness and model selection. I propose a specific composite likelihood method to handle this issue. A typical advantage of the approach is that the inference procedure does not involve explicit missing process assumptions and nuisance parameters estimation

Training Transformers with 4-bit Integers

Quantizing the activation, weight, and gradient to 4-bit is promising to accelerate neural network training. However, existing 4-bit training methods require custom numerical formats which are not supported by contemporary hardware. In this work, we propose a training method for transformers with all matrix multiplications implemented with the INT4 arithmetic. Training with an ultra-low INT4 precision is challenging. To achieve this, we carefully analyze the specific structures of activation and gradients in transformers to propose dedicated quantizers for them. For forward propagation, we identify the challenge of outliers and propose a Hadamard quantizer to suppress the outliers. For backpropagation, we leverage the structural sparsity of gradients by proposing bit splitting and leverage score sampling techniques to quantize gradients accurately. Our algorithm achieves competitive accuracy on a wide range of tasks including natural language understanding, machine translation, and image classification. Unlike previous 4-bit training methods, our algorithm can be implemented on the current generation of GPUs. Our prototypical linear operator implementation is up to 2.2 times faster than the FP16 counterparts and speeds up the training by up to 35.1%.Comment: 9 pages, 8 figure