Spectral Properties of Elementwise-Transformed Spiked Matrices

This work concerns elementwise-transformations of spiked matrices: $Y_n = n^{-1/2} f( \sqrt{n} X_n + Z_n)$. Here, $f$ is a function applied elementwise, $X_n$ is a low-rank signal matrix, and $Z_n$ is white noise. We find that principal component analysis is powerful for recovering signal under highly nonlinear or discontinuous transformations. Specifically, in the high-dimensional setting where $Y_n$ is of size $n \times p$ with $n,p \rightarrow \infty$ and $p/n \rightarrow \gamma > 0$, we uncover a phase transition: for signal-to-noise ratios above a sharp threshold -- depending on $f$, the distribution of elements of $Z_n$, and the limiting aspect ratio $\gamma$ -- the principal components of $Y_n$ (partially) recover those of $X_n$. Below this threshold, the principal components of $Y_n$ are asymptotically orthogonal to the signal. In contrast, in the standard setting where $X_n + n^{-1/2}Z_n$ is observed directly, the analogous phase transition depends only on $\gamma$. A similar phenomenon occurs with $X_n$ square and symmetric and $Z_n$ a generalized Wigner matrix

A Slight Excess of Large Scale Power from Moments of the Peculiar Velocity Field

The peculiar motions of galaxies can be used to infer the distribution of matter in the Universe. It has recently been shown that measurements of the peculiar velocity field indicates an anomalously high bulk flow of galaxies in our local volume. In this paper we find the implications of the high bulk flow for the power spectrum of density fluctuations. We find that analyzing only the dipole moment of the velocity field yields an average power spectrum amplitude which is indeed much higher than the LCDM value. However, by also including shear and octupole moments of the velocity field, and marginalizing over possible values for the growth rate, an average power spectrum amplitude which is consistent with LCDM is recovered. We attempt to infer the shape of the matter power spectrum from moments of the velocity field, and find a slight excess of power on scales ~ h-1 Gpc.Comment: 6 pages,6 figures, updated to match accepted versio

Optimal Eigenvalue Shrinkage in the Semicircle Limit

Recent studies of high-dimensional covariance estimation often assume the proportional growth asymptotic, where the sample size $n$ and dimension $p$ are comparable, with $n, p \rightarrow \infty$ and $\gamma_n \equiv p/n \rightarrow \gamma > 0$. Yet, many datasets have very different numbers of rows and columns. Consider instead disproportional growth, where $n, p \rightarrow \infty$ and $\gamma_n \rightarrow 0$ or $\gamma_n \rightarrow \infty$. With far fewer dimensions than observations, the disproportional limit $\gamma_n \rightarrow 0$ may seem similar to classical fixed-$p$ asymptotics. In fact, either disproportional limit induces novel phenomena distinct from the proportional and fixed-$p$ limits. We study the spiked covariance model, finding for each of 15 different loss functions optimal shrinkage and thresholding rules. Readers who initially view the disproportionate limit $\gamma_n \rightarrow 0$ as similar to classical fixed-$p$ asymptotics may expect, given the dominance in that setting of the sample covariance estimator, that there is no alternative here. On the contrary, our optimal procedures demand extensive eigenvalue shrinkage and offer substantial performance benefits. The sample covariance is similarly improvable in the disproportionate limit $\gamma_n \rightarrow \infty$. Practitioners may worry how to choose between proportional and disproportional growth frameworks in practice. Conveniently, under the spiked covariance model there is no conflict between the two and no choice is needed; one unified set of closed forms (used with the aspect ratio $\gamma_n$ of the practitioner's data) offers full asymptotic optimality in both regimes. At the heart of these phenomena is the spiked Wigner model. Via a connection to the spiked covariance model as $\gamma_n \rightarrow 0$, we derive optimal shrinkers for the Wigner setting

Hubble Space Telescope Observations of Comet 9P/Tempel 1 during the Deep Impact Encounter

We report on the Hubble Space Telescope program to observe periodic comet 9P/Tempel 1 in conjunction with NASA's Deep Impact mission. Our objectives were to study the generation and evolution of the coma resulting from the impact and to obtain wide-band images of the visual outburst generated by the impact. Two observing campaigns utilizing a total of 17 HST orbits were carried out: the first occurred on 2005 June 13-14 and fortuitously recorded the appearance of a new, short-lived fan in the sunward direction on June 14. The principal campaign began two days before impact and was followed by contiguous orbits through impact plus several hours and then snapshots one, seven, and twelve days later. All of the observations were made using the Advanced Camera for Surveys (ACS). For imaging, the ACS High Resolution Channel (HRC) provides a spatial resolution of 36 km (16 km/pixel) at the comet at the time of impact. Baseline images of the comet, made prior to impact, photometrically resolved the comet's nucleus. The derived diameter, 6.1 km, is in excellent agreement with the 6.0 +/- 0.2 km diameter derived from the spacecraft imagers. Following the impact, the HRC images illustrate the temporal and spatial evolution of the ejecta cloud and allow for a determination of its expansion velocity distribution. One day after impact the ejecta cloud had passed out of the field-of-view of the HRC.Comment: 15 pages, 14 postscript figures. Accepted for publication in Icarus special issue on Deep Impac

Susceptibility to intestinal infection and diarrhoea in Zambian adults in relation to HIV status and CD4 count.

BACKGROUND: The HIV epidemic in sub-Saharan Africa has had a major impact on infectious disease, and there is currently great interest in the impact of HIV on intestinal barrier function. A three year longitudinal cohort study in a shanty compound in Lusaka, Zambia, carried out before anti-retroviral therapy was widely available, was used to assess the impact of HIV on susceptibility to intestinal infectious disease. We measured the incidence and seasonality of intestinal infection and diarrhoea, aggregation of disease in susceptible individuals, clustering by co-habitation and genetic relatedness, and the disease-to-infection ratio. METHODS: Adults living in a small section of Misisi, Lusaka, were interviewed every two weeks to ascertain the incidence of diarrhoea. Monthly stool samples were analysed for selected pathogens. HIV status and CD4 count were determined annually. RESULTS: HIV seroprevalence was 31% and the prevalence of immunosuppression (CD4 count 200 cells/microL or less) was 10%. Diarrhoea incidence was 1.1 episodes per year and the Incidence Rate Ratio for HIV infection was 2.4 (95%CI 1.7-3.3; p < 0.001). The disease-to-infection ratio was increased at all stages of HIV infection. Aggregation of diarrhoea in susceptible individuals was observed irrespective of immunosuppression, but there was little evidence of clustering by co-habitation or genetic relatedness. There was no evidence of aggregation of asymptomatic infections. CONCLUSION: HIV has an impact on intestinal infection at all stages, with an increased disease-to-infection ratio. The aggregation of disease in susceptible individuals irrespective of CD4 count suggests that this phenomenon is not a function of cell mediated immunity

Genomic Education – Bench to Bedside: A Novel Approach to Teaching Genetic Diagnosis

Problem: Teaching genetic diagnosis is required in all medical schools and physician assistant programs. However, with thousands of relevant findings and thousands more rare diseases, lectures and narrative resources are inadequate for the task. Whatever information that is taught is easily forgotten and does not carry over into the clinic. Many rare disease patients suffer through “diagnostic odysseys” (3 to 30 years to correct diagnosis). Approach: We used a commercially available diagnostic decision support system (DDSS) that encompasses all Mendelian disorders with known genes, together with other conditions in their differential diagnosis, and a case-based educational approach to teach diagnostic skills in a way that could then be replicated in the clinic. After a lecture, which included a demonstration using the DDSS with a sample case, 74 students were assigned to replicate the sample case at home and then complete 7 other anonymized cases, all with known rare diagnoses. After each case, students saved the “patient summary” that included the findings entered and differential diagnosis list and submitted it as homework. Students also completed a questionnaire about their experience, including satisfaction. Outcomes: Students were effective at diagnosing rare diseases in 483 of the 514 testing instances, a 94% success rate, with success defined as the correct diagnosis being listed in the differential diagnosis. Eighty-five percent of students rated this interactive learning session “highly,” encouraged us to repeat the assignment next year, and 89% reported that they wanted to use the DDSS during their clinical rotations in the coming year. Next Steps: We plan to refine the cases, add more material on findings, and ensure that all the synonyms students might use are in the software tool. We plan to repeat the program next year and recommend its use more widely in medical education

Improved Probability Method for Estimating Signal in the Presence of Background

A suggestion is made for improving the Feldman Cousins method of estimating signal counts in the presence of background. The method concentrates on finding essential information about the signal and ignoring extraneous information about background. An appropriate method is found which uses the condition that the number of background events obtained does not exceed the total number of events obtained. Several alternative approaches are explored.Comment: Modified 12/21 for singlespace to save trees, 9 pages, 1 figure. Modified 8/11/99 to add small modifications made for the Phys. Rev. articl

Macrophage-released ADAMTS1 promotes muscle stem cell activation.

Coordinated activation of muscle stem cells (known as satellite cells) is critical for postnatal muscle growth and regeneration. The muscle stem cell niche is central for regulating the activation state of satellite cells, but the specific extracellular signals that coordinate this regulation are poorly understood. Here we show that macrophages at sites of muscle injury induce activation of satellite cells via expression of Adamts1. Overexpression of Adamts1 in macrophages in vivo is sufficient to increase satellite cell activation and improve muscle regeneration in young mice. We demonstrate that NOTCH1 is a target of ADAMTS1 metalloproteinase activity, which reduces Notch signaling, leading to increased satellite cell activation. These results identify Adamts1 as a potent extracellular regulator of satellite cell activation and have significant implications for understanding the regulation of satellite cell activity and regeneration after muscle injury.Satellite cells are crucial for growth and regeneration of skeletal muscle. Here the authors show that in response to muscle injury, macrophages secrete Adamts1, which induces satellite cell activation by modulating Notch1 signaling

Micro-Valences: Perceiving Affective Valence in Everyday Objects

Perceiving the affective valence of objects influences how we think about and react to the world around us. Conversely, the speed and quality with which we visually recognize objects in a visual scene can vary dramatically depending on that scene’s affective content. Although typical visual scenes contain mostly “everyday” objects, the affect perception in visual objects has been studied using somewhat atypical stimuli with strong affective valences (e.g., guns or roses). Here we explore whether affective valence must be strong or overt to exert an effect on our visual perception. We conclude that everyday objects carry subtle affective valences – “micro-valences” – which are intrinsic to their perceptual representation