Multiscale Adaptive Representation of Signals: I. The Basic Framework

We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative

Advanced study of video signal processing in low signal to noise environments - Multi-filter phase-locked loop demodulation Quarterly progress report, Feb. - May 1970

Multi-filter phase locked loop demodulatio

The Dependent Coverage Provision Is Good for Mothers, Good for Children, and Good for Taxpayers

Importance The effect of the Affordable Care Act (ACA) dependent coverage provision on pregnancy-related health care and health outcomes is unknown. Objective To determine whether the dependent coverage provision was associated with changes in payment for birth, prenatal care, and birth outcomes. Design, Setting, and Participants Retrospective cohort study, using a differences-in-differences analysis of individual-level birth certificate data comparing live births among US women aged 24 to 25 years (exposure group) and women aged 27 to 28 years (control group) before (2009) and after (2011-2013) enactment of the dependent coverage provision. Results were stratified by marital status. Main Exposures The dependent coverage provision of the ACA, which allowed young adults to stay on their parent’s health insurance until age 26 years. Main Outcomes and Measures Primary outcomes were payment source for birth, early prenatal care (first visit in first trimester), and adequate prenatal care (a first trimester visit and 80% of expected visits). Secondary outcomes were cesarean delivery, premature birth, low birth weight, and infant neonatal intensive care unit (NICU) admission. Results The study population included 1 379 005 births among women aged 24 to 25 years (exposure group; 299 024 in 2009; 1 079 981 in 2011-2013), and 1 551 192 births among women aged 27 to 28 years (control group; 325 564 in 2009; 1 225 628 in 2011-2013). From 2011-2013, compared with 2009, private insurance payment for births increased in the exposure group (36.9% to 35.9% [difference, −1.0%]) compared with the control group (52.4% to 51.1% [difference, −1.3%]), adjusted difference-in-differences, 1.9 percentage points (95% CI, 1.6 to 2.1). Medicaid payment decreased in the exposure group (51.6% to 53.6% [difference, 2.0%]) compared with the control group (37.4% to 39.4% [difference, 1.9%]), adjusted difference-in-differences, −1.4 percentage points (95% CI, −1.7 to −1.2). Self-payment for births decreased in the exposure group (5.2% to 4.3% [difference, −0.9%]) compared with the control group (4.9% to 4.3% [difference, −0.5%]), adjusted difference-in-differences, −0.3 percentage points (95% CI, −0.4 to −0.1). Early prenatal care increased from 70% to 71.6% (difference, 1.6%) in the exposure group and from 75.7% to 76.8% (difference, 0.6%) in the control group (adjusted difference-in-differences, 0.6 percentage points [95% CI, 0.3 to 0.8]). Adequate prenatal care increased from 73.5% to 74.8% (difference, 1.3%) in the exposure group and from 77.5% to 78.8% (difference, 1.3%) in the control group (adjusted difference-in-differences, 0.4 percentage points [95% CI, 0.2 to 0.6]). Preterm birth decreased from 9.4% to 9.1% in the exposure group (difference, −0.3%) and from 9.1% to 8.9% in the control group (difference, −0.2%) (adjusted difference-in-differences, −0.2 percentage points (95% CI, −0.3 to −0.03). Overall, there were no significant changes in low birth weight, NICU admission, or cesarean delivery. In stratified analyses, changes in payment for birth, prenatal care, and preterm birth were concentrated among unmarried women. Conclusions and Relevance In this study of nearly 3 million births among women aged 24 to 25 years vs those aged 27 to 28 years, the Affordable Care Act dependent coverage provision was associated with increased private insurance payment for birth, increased use of prenatal care, and modest reduction in preterm births, but was not associated with changes in cesarean delivery rates, low birth weight, or NICU admission

Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in \F_{p^m}[x] of degree $d$ over the finite field \F_{p^m}, one can view it as a map from \F_{p^m} to \F_{p^m}, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}