MM Algorithms for Minimizing Nonsmoothly Penalized Objective Functions

In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the majorization-minimization (MM) algorithm as its core optimization engine. The resulting algorithms rely on iterated soft-thresholding, implemented componentwise, allowing for fast, stable updating that avoids the need for any high-dimensional matrix inversion. We establish a local convergence theory for this class of algorithms under weaker assumptions than previously considered in the statistical literature. We also demonstrate the exceptional effectiveness of new acceleration methods, originally proposed for the EM algorithm, in this class of problems. Simulation results and a microarray data example are provided to demonstrate the algorithm's capabilities and versatility.Comment: A revised version of this paper has been published in the Electronic Journal of Statistic

A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity

It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation gradient has discrete values, i.e. if the deformation is piecewise affine linear and satisfies the Hadamard jump condition. In this note, we expand upon these results and show that they do not hold for arbitrary deformations by explicitly giving an example of a strictly rank-one convex energy and a non-homogeneous deformation such that the induced Cauchy stress tensor is constant. In the planar case, our example is related to another previous result concerning criteria for generalized convexity properties of conformally invariant energy functions, which we extend to the case of strict rank-one convexity

Bat Transmitted Rabies

Up to a few years ago, all the information one needed for a full understanding of rabies as a disease seemed to be readily available in most text-books. The rapidity with which changes in our concepts of this disease are now taking place, and the multiplicity of publications dealing with this disease both make frequent reviews desirable. Actually, bat-transmitted rabies created problems long before it was even recognized. A paralytic disease of epizoonotic proportions in horses, mules, and cattle in Brazil in 1908 was not even identified as rabies until three years after the outbreak started

Model of Transcriptional Activation by MarA in Escherichia coli

We have developed a mathematical model of transcriptional activation by MarA in Escherichia coli, and used the model to analyze measurements of MarA-dependent activity of the marRAB, sodA, and micF promoters in mar-rob- cells. The model rationalizes an unexpected poor correlation between the mid-point of in vivo promoter activity profiles and in vitro equilibrium constants for MarA binding to promoter sequences. Analysis of the promoter activity data using the model yielded the following predictions regarding activation mechanisms: (1) MarA activation of the marRAB, sodA, and micF promoters involves a net acceleration of the kinetics of transitions after RNA polymerase binding, up to and including promoter escape and message elongation; (2) RNA polymerase binds to these promoters with nearly unit occupancy in the absence of MarA, making recruitment of polymerase an insignificant factor in activation of these promoters; and (3) instead of recruitment, activation of the micF promoter might involve a repulsion of polymerase combined with a large acceleration of the kinetics of polymerase activity. These predictions are consistent with published chromatin immunoprecipitation assays of interactions between polymerase and the E. coli chromosome. A lack of recruitment in transcriptional activation represents an exception to the textbook description of activation of bacterial sigma-70 promoters. However, use of accelerated polymerase kinetics instead of recruitment might confer a competitive advantage to E. coli by decreasing latency in gene regulation.Comment: 30 pages, 2 figure

Nuclear star formation on 100 parsec scales: 10" resolution radio continuum, HI and CO observations

A program of radio line and continuum studies of star formation in nearby spiral galaxies is reported. The objective is a search for hot gas and peculiar dynamics in spiral nuclei with 10" to 30" angular resolution. Vigorous star formation is found to be a common phenomenon in the inner kpc of spirals. Arcsecond resolution observations of radio continuum emission at 6 and 2 cm were used to separate the thermal and nonthermal radio components. It was found that thermal and nonthermal emission are well mixed even on sizescales of 10 pc. To understand the reason for the increased level of star formation activity in spiral nuclei, HI and CO emission in these galaxies is studied. The CO transition was detected in M51, M82, NGC 253, NGC 6946 and IC 342 with T sub a approx. 0.5 to 2.0 K, at 20" angular resolution. The dynamics and spatial distribution of nuclear gas are being studied using VLA HI maps with 30" synthesized beams. Evidence for noncircular motions in HI was found in the nucleus of IC 342

Progress in Renewables

This is a status report on progress made in the conduct of eleven Federally-supported renewable energy programs. Considerable progress has been made in the establishment and development of an infrastructure to support sustained growth. Unique technical problems led to the research and development of materials and designs which have achieved energy conversion efficiencies of up to 25% for electricity and 92% for heat in solar thermal systems. Overall, enough real progress has been made to provide a sound technology base upon which renewable energy systems industries can reasonably continue development

Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1

Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4+ T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that approximately 2,000-fold reductions are required to permit a majority of patients to interrupt ART for one year without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the lab to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.Comment: 8 pages main text (4 figures). In PNAS Early Edition http://www.pnas.org/content/early/2014/08/05/1406663111. Ancillary files: SI, 24 pages SI (7 figures). File .htm opens a browser-based application to calculate rebound times (see SI). Or, the .cdf file can be run with Mathematica. The most up-to-date version of the code is available at http://www.danielrosenbloom.com/reboundtimes

High Temporal Resolution XMM Monitoring of PKS 2155-304

The bright, strongly variable BL Lac object PKS 2155-304 was observed by XMM for two essentially uninterrupted periods of ~11 and 16 hr on 30-31 May 2000. The strongest variations occurred in the highest energy bands. After scaling for this effect, the three softest bands (0.1-1.7 keV) showed strong correlation with no measurable lag to reliable limits of \tau \ls 0.3 hr. However, the hardest band (~3 keV) was less well-correlated with the other three, especially on short time scales, showing deviations of ~10-20% in ~1 hr although, again, no significant interband lag was detected. This result and examination of previous ASCA and BeppoSAX cross-correlation functions suggest that previous claims of soft lags on time scales of 0.3-4 hr could well be an artifact of periodic interruptions due to Earth-occultation every 1.6 hr. Previous determinations of the magnetic field/bulk Lorentz factor were therefore premature, as these data provide only a lower limit of B \gamma^{1/3} \gs 2.5 G. The hardest band encompasses the spectral region above the high-energy break; its enhanced variability could be indicating that the break energy of the synchrotron spectrum, and therefore of the underlying electron energy distribution, changes independently of the lower energies.Comment: 13 pages, 3 figures, accepted by Ap

Replicability and Recurrence in the Experimental Evolution of a Group I Ribozyme

In order to explore the variety of possible responses available to a ribozyme population evolving a novel phenotype, five Tetrahymena thermophila group I intron ribozyme pools were evolved in parallel for cleavage of a DNA oligonucleotide. These ribozyme populations were propagated under identical conditions and characterized when they reached apparent phenotypic plateaus; the populations that reached the highest plateau showed a near 100-fold improvement in DNA cleavage activity. A detailed characterization of the evolved response in these populations reveals at least two distinct phenotypic trajectories emerging as a result of the imposed selection. Not only do these distinct solutions exhibit differential DNA cleavage activity, but they also exhibit a very different correlation with a related, but unselected, phenotype: RNA cleavage activity. In turn, each of these trajectories is underwritten by differing genotypic profiles. This study underscores the complex network of possible trajectories through sequence space available to an evolving population and uncovers the diversity of solutions that result when the process of experimental evolution is repeated multiple times in a simple, engineered system