Measurement of Parity Violation in the Early Universe using Gravitational-wave Detectors

A stochastic gravitational-wave background (SGWB) is expected to arise from the superposition of many independent and unresolved gravitational-wave signals, of either cosmological or astrophysical origin. Some cosmological models (characterized, for instance, by a pseudo-scalar inflaton, or by some modification of gravity) break parity, leading to a polarized SGWB. We present a new technique to measure this parity violation, which we then apply to the recent results from LIGO to produce the first upper limit on parity violation in the SGWB, assuming a generic power-law SGWB spectrum across the LIGO sensitive frequency region. We also estimate sensitivity to parity violation of the future generations of gravitational-wave detectors, both for a power-law spectrum and for a model of axion inflation. This technique offers a new way of differentiating between the cosmological and astrophysical sources of the isotropic SGWB, as astrophysical sources are not expected to produce a polarized SGWB.Comment: 5 pages, 2 figures, 1 tabl

Do Small Group Health Insurance Regulations Influence Small Business Size?

The cost of health insurance has been the primary concern of small business owners for several decades. State small group health insurance reforms, implemented in the 1990s, aimed to control the variability of health insurance premiums and to improve access to health insurance. Small group reforms only affected firms within a specific size range, and the definition of the upper size threshold for small firms varied by state and over time. As a result, small group reforms may have affected the size of small firms around the legislative threshold and may also have affected the propensity of small firms to offer health insurance. Previous research has examined the second issue, finding little to no effect of health insurance reforms on the propensity of small firms to offer health insurance. In this paper, we examine the relationship between small group reform and firm size. We use data from a nationally representative repeated cross-section survey of employers and data on state small group health insurance reform. Contrary to the intent of the reform, we find evidence that small firms just below the regulatory threshold that were offering health insurance grew in order to bypass reforms.Health insurance, small business

Health Savings Accounts for Small Businesses and Entrepreneurs: Shopping, Take-Up and Implementation Challenges

A combination of high deductible health plans (HDHPs) and health savings accounts (HSAs) holds promise for expanding health insurance for small firms. We provide information on HSA take-up and shopping behavior from a 2008 survey of female small business owners, revealing that the HSA marketplace can be confusing for small firms. HSAs may have expanded access to health insurance for the smallest firms (under three employees), but not for small firms more generally. A sizable number of firms offering HSA-eligible insurance did not offer attached HSAs. Firms offering HSAs were satisfied with their experiences, but faced challenges in implementing them.Health Savings Accounts, Health Insurance Costs, Small Business

Health Savings Accounts for Small Businesses and Entrepreneurs: Shopping, Take-Up and Implementation Challenges

A combination of high deductible health plans (HDHPs) and health savings accounts (HSAs) holds promise for expanding health insurance for small firms. We provide information on HSA take-up and shopping behavior from a 2008 survey of female small business owners, revealing that the HSA marketplace can be confusing for small firms. HSAs may have expanded access to health insurance for the smallest firms (under three employees), but not for small firms more generally. A sizable number of firms offering HSA-eligible insurance did not offer attached HSAs. Firms offering HSAs were satisfied with their experiences, but faced challenges in implementing them.Health Savings Accounts, Health Insurance Costs, Small Business

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

Simulation of underground gravity gradients from stochastic seismic fields

We present results obtained from a finite-element simulation of seismic displacement fields and of gravity gradients generated by those fields. The displacement field is constructed by a plane wave model with a 3D isotropic stochastic field and a 2D fundamental Rayleigh field. The plane wave model provides an accurate representation of stationary fields from distant sources. Underground gravity gradients are calculated as acceleration of a free test mass inside a cavity. The results are discussed in the context of gravity-gradient noise subtraction in third generation gravitational-wave detectors. Error analysis with respect to the density of the simulated grid leads to a derivation of an improved seismometer placement inside a 3D array which would be used in practice to monitor the seismic field.Comment: 24 pages, 12 figure

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