Making maps of cosmic microwave background polarization for B-mode studies: The POLARBEAR example

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable. \ua9 ESO, 2017

Precise Astronomical Polarization Angle Calibration and its Impact on Studying Lorentz and Parity Violation in the Cosmic Microwave Background

Precise measurements of the polarization of the Cosmic Microwave Background (CMB) provide a wealth of knowledge regarding fundamental physics and the origins of our universe. We are currently in an era where the CMB polarization B-mode power spectrum is being measured at both small and large angular scales, providing increasingly tighter constraints on both the effects of gravitational lensing and the amount of primordial gravitational waves generated during the epoch of inflation. As we look toward the next generation of ground-based CMB experiments such as the Simons Observatory and CMB-S4, we must further our understanding of the systematic uncertainties that currently limit constraining power on both the tensor-to-scalar ratio and searches for exotic new physics.Lorentz and parity violating physics such as cosmic birefringence have the effect of rotating the polarization of CMB photons as they traverse cosmological distances, generating B-mode polarization signal and non-zero correlations between the CMB temperature and B-mode power spectra as well as the CMB E-mode and B-mode power spectra, both of which are disallowed by the current standard model of cosmology. This cosmic polarization rotation (CPR) is degenerate with an overall detector misalignment of similar angle magnitude. The precision with which current state-of-the-art polarization calibrators are characterized is presently inadequate to allow for meaningful detections of non-zero CPR from physics that diverge from the standard model to be claimed.This dissertation provides an overview of the current CMB polarization calibration standards and methodology in the context of the POLARBEAR-1 and Simons Array experiments, as well as the design and characterization of a novel ground-based absolute polarization calibrator that will enable new searches for Lorentz and parity violating physics. The calibrator's repeatability between calibrations scans was proven to better than 0.1 degrees, and results from calibration performed on the POLARBEAR-1 telescope and the POLARBEAR-2b receiver are presented in this work

Generative Probabilistic Models for Analysis of Communication Event Data with Applications to Email Behavior

Our daily lives increasingly involve interactions with others via different communication channels, such as email, text messaging, and social media. In this context, the ability to analyze and understand our communication patterns is becoming increasingly important. This dissertation focuses on generative probabilistic models for describing different characteristics of communication behavior, focusing primarily on email communication.First, we present a two-parameter kernel density estimator for estimating the probability density over recipients of an email (or, more generally, items which appear in an itemset). A stochastic gradient method is proposed for efficiently inferring the kernel parameters given a continuous stream of data. Next, we apply the kernel model and the Bernoulli mixture model to two important prediction tasks: given a partially completed email recipient list, 1) predict which others will be included in the email, and 2) rank potential recipients based on their likelihood to be added to the email. Such predictions are useful in suggesting future actions to the user (i.e. which person to add to an email) based on their previous actions. We then investigate a piecewise-constant Poisson process model for describing the time-varying communication rate between an individual and several groups of their contacts, where changes in the Poisson rate are modeled as latent state changes within a hidden Markov model.We next focus on the time it takes for an individual to respond to an event, such as receiving an email. We show that this response time depends heavily on the individual's typical daily and weekly patterns - patterns not adequately captured in standard models of response time (e.g. the Gamma distribution or Hawkes processes). A time-warping mechanism is introduced where the absolute response time is modeled as a transformation of effective response time, relative to the daily and weekly patterns of the individual. The usefulness of applying the time-warping mechanism to standard models of response time, both in terms of log-likelihood and accuracy in predicting which events will be quickly responded to, is illustrated over several individual email histories

Precise Astronomical Polarization Angle Calibration and its Impact on Studying Lorentz and Parity Violation in the Cosmic Microwave Background

Precise measurements of the polarization of the Cosmic Microwave Background (CMB) provide a wealth of knowledge regarding fundamental physics and the origins of our universe. We are currently in an era where the CMB polarization B-mode power spectrum is being measured at both small and large angular scales, providing increasingly tighter constraints on both the effects of gravitational lensing and the amount of primordial gravitational waves generated during the epoch of inflation. As we look toward the next generation of ground-based CMB experiments such as the Simons Observatory and CMB-S4, we must further our understanding of the systematic uncertainties that currently limit constraining power on both the tensor-to-scalar ratio and searches for exotic new physics.Lorentz and parity violating physics such as cosmic birefringence have the effect of rotating the polarization of CMB photons as they traverse cosmological distances, generating B-mode polarization signal and non-zero correlations between the CMB temperature and B-mode power spectra as well as the CMB E-mode and B-mode power spectra, both of which are disallowed by the current standard model of cosmology. This cosmic polarization rotation (CPR) is degenerate with an overall detector misalignment of similar angle magnitude. The precision with which current state-of-the-art polarization calibrators are characterized is presently inadequate to allow for meaningful detections of non-zero CPR from physics that diverge from the standard model to be claimed.This dissertation provides an overview of the current CMB polarization calibration standards and methodology in the context of the POLARBEAR-1 and Simons Array experiments, as well as the design and characterization of a novel ground-based absolute polarization calibrator that will enable new searches for Lorentz and parity violating physics. The calibrator's repeatability between calibrations scans was proven to better than 0.1 degrees, and results from calibration performed on the POLARBEAR-1 telescope and the POLARBEAR-2b receiver are presented in this work

Generative Probabilistic Models for Analysis of Communication Event Data with Applications to Email Behavior

Our daily lives increasingly involve interactions with others via different communication channels, such as email, text messaging, and social media. In this context, the ability to analyze and understand our communication patterns is becoming increasingly important. This dissertation focuses on generative probabilistic models for describing different characteristics of communication behavior, focusing primarily on email communication. First, we present a two-parameter kernel density estimator for estimating the probability density over recipients of an email (or, more generally, items which appear in an itemset). A stochastic gradient method is proposed for efficiently inferring the kernel parameters given a continuous stream of data. Next, we apply the kernel model and the Bernoulli mixture model to two important prediction tasks: given a partially completed email recipient list, 1) predict which others will be included in the email, and 2) rank potential recipients based on their likelihood to be added to the email. Such predictions are useful in suggesting future actions to the user (i.e. which person to add to an email) based on their previous actions. We then investigate a piecewise-constant Poisson process model for describing the time-varying communication rate between an individual and several groups of their contacts, where changes in the Poisson rate are modeled as latent state changes within a hidden Markov model. We next focus on the time it takes for an individual to respond to an event, such as receiving an email. We show that this response time depends heavily on the individual's typical daily and weekly patterns - patterns not adequately captured in standard models of response time (e.g. the Gamma distribution or Hawkes processes). A time-warping mechanism is introduced where the absolute response time is modeled as a transformation of effective response time, relative to the daily and weekly patterns of the individual. The usefulness of applying the time-warping mechanism to standard models of response time, both in terms of log-likelihood and accuracy in predicting which events will be quickly responded to, is illustrated over several individual email histories

Dissociation of halted T7 RNA polymerase elongation complexes proceeds via a forward-translocation mechanism

A recent model for the mechanism of intrinsic transcription termination involves dissociation of the RNA from forward-translocated (hypertranslocated) states of the complex [Yarnell WS, Roberts JW (1999) Science, 284:611-615]. The current study demonstrates that halted elongation complexes of T7 RNA polymerase in the absence of termination signals can also dissociate via a forward-translocation mechanism. Shortening of the downstream DNA or the introduction of a stretch of mismatched DNA immediately downstream of the halt site reduces a barrier to forward translocation and correspondingly reduces the lifetime of halted complexes. Conversely, introduction of a cross-link downstream of the halt site increases the same barrier and leads to an increase in complex lifetime. Introduction of a mismatch within the bubble reduces a driving force for forward translocation and correspondingly increases the lifetime of the complex, but only for mismatches at the upstream edge of the bubble, as predicted by the model. Mismatching only the two most upstream of the eight bases in the bubble provides a maximal increase in complex stability, suggesting that dissociation occurs primarily from early forward-translocated states. Finally, addition in trans of an oligonucleotide complementary to the nascent RNA just beyond the hybrid complements the loss of driving force derived from placement of a mismatch within the bubble, confirming the expected additivity of effects. Thus, forward translocation is likely a general mechanism for dissociation of elongation complexes, both in the presence and absence of intrinsic termination signals