Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps

On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This version has updated reference

In Vivo Raman Spectroscopy for Biochemical Monitoring of the Human Cervix Throughout Pregnancy

Background The cervix must undergo significant biochemical remodeling to allow for successful parturition. This process is not fully understood, especially in instances of spontaneous preterm birth. In vivo Raman spectroscopy is an optical technique that can be used to investigate the biochemical composition of tissue longitudinally and noninvasively in human beings, and has been utilized to measure physiology and disease states in a variety of medical applications. Objective The purpose of this study is to measure in vivo Raman spectra of the cervix throughout pregnancy in women, and to identify biochemical markers that change with the preparation for delivery and postpartum repair. Study Design In all, 68 healthy pregnant women were recruited. Raman spectra were measured from the cervix of each patient monthly in the first and second trimesters, weekly in the third trimester, and at the 6-week postpartum visit. Raman spectra were measured using an in vivo Raman system with an optical fiber probe to excite the tissue with 785 nm light. A spectral model was developed to highlight spectral regions that undergo the most changes throughout pregnancy, which were subsequently used for identifying Raman peaks for further analysis. These peaks were analyzed longitudinally to determine if they underwent significant changes over the course of pregnancy (P \u3c .05). Finally, 6 individual components that comprise key biochemical constituents of the human cervix were measured to extract their contributions in spectral changes throughout pregnancy using a linear combination method. Patient factors including body mass index and parity were included as variables in these analyses. Results Raman peaks indicative of extracellular matrix proteins (1248 and 1254 cm−1) significantly decreased (P \u3c .05), while peaks corresponding to blood (1233 and 1563 cm–1) significantly increased (P \u3c .0005) in a linear manner throughout pregnancy. In the postpartum cervix, significant increases in peaks corresponding to actin (1003, 1339, and 1657 cm–1) and cholesterol (1447 cm–1) were observed when compared to late gestation, while signatures from blood significantly decreased. Postpartum actin signals were significantly higher than early pregnancy, whereas extracellular matrix proteins and water signals were significantly lower than early weeks of gestation. Parity had a significant effect on blood and extracellular matrix protein signals, with nulliparous patients having significant increases in blood signals throughout pregnancy, and higher extracellular matrix protein signals in early pregnancy compared to patients with prior pregnancies. Body mass index significantly affected actin signal contribution, with low body mass index patients showing decreasing actin contribution throughout pregnancy and high body mass index patients demonstrating increasing actin signals. Conclusion Raman spectroscopy was successfully used to biochemically monitor cervical remodeling in pregnant women during prenatal visits. This foundational study has demonstrated sensitivity to known biochemical dynamics that occur during cervical remodeling, and identified patient variables that have significant effects on Raman spectra throughout pregnancy. Raman spectroscopy has the potential to improve our understanding of cervical maturation, and be used as a noninvasive preterm birth risk assessment tool to reduce the incidence, morbidity, and mortality caused by preterm birth

Degeneracy in infinite horizon optimization

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47919/1/10107_2005_Article_BF01582295.pd

Curcumin-induced HDAC inhibition and attenuation of medulloblastoma growth in vitro and in vivo

<p>Abstract</p> <p>Background</p> <p>Medulloblastoma is the most common brain tumor in children, and its prognosis is worse than for many other common pediatric cancers. Survivors undergoing treatment suffer from serious therapy-related side effects. Thus, it is imperative to identify safer, effective treatments for medulloblastoma. In this study we evaluated the anti-cancer potential of curcumin in medulloblastoma by testing its ability to induce apoptosis and inhibit tumor growth <it>in vitro </it>and <it>in vivo </it>using established medulloblastoma models.</p> <p>Methods</p> <p>Using cultured medulloblastoma cells, tumor xenografts, and the Smo/Smo transgenic medulloblastoma mouse model, the antitumor effects of curcumin were tested <it>in vitro </it>and <it>in vivo</it>.</p> <p>Results</p> <p>Curcumin induced apoptosis and cell cycle arrest at the G2/M phase in medulloblastoma cells. These effects were accompanied by reduced histone deacetylase (HDAC) 4 expression and activity and increased tubulin acetylation, ultimately leading to mitotic catastrophe. In <it>in vivo </it>medulloblastoma xenografts, curcumin reduced tumor growth and significantly increased survival in the Smo/Smo transgenic medulloblastoma mouse model.</p> <p>Conclusions</p> <p>The <it>in vitro </it>and <it>in vivo </it>data suggest that curcumin has the potential to be developed as a therapeutic agent for medulloblastoma.</p

Epigenetic targeting of Hedgehog pathway transcriptional output through BET bromodomain inhibition

Hedgehog signaling drives oncogenesis in several cancers and strategies targeting this pathway have been developed, most notably through inhibition of Smoothened. However, resistance to Smoothened inhibitors occurs via genetic changes of Smoothened or other downstream Hedgehog components. Here, we overcome these resistance mechanisms by modulating GLI transcription via inhibition of BET bromodomain proteins. We show the BET bromodomain protein, BRD4, regulates GLI transcription downstream of SMO and SUFU and chromatin immunoprecipitation studies reveal BRD4 directly occupies GLI1 and GLI2 promoters, with a substantial decrease in engagement of these sites upon treatment with JQ1, a small molecule inhibitor targeting BRD4. Globally, genes associated with medulloblastoma-specific GLI1 binding sites are downregulated in response to JQ1 treatment, supporting direct regulation of GLI activity by BRD4. Notably, patient- and GEMM-derived Hedgehog-driven tumors (basal cell carcinoma, medulloblastoma and atypical teratoid/rhabdoid tumor) respond to JQ1 even when harboring genetic lesions rendering them resistant to Smoothened antagonists

ctDNA-based detection of molecular residual disease in stage I-III non-small cell lung cancer patients treated with definitive radiotherapy

BackgroundSensitive and reliable biomarkers for early detection of recurrence are needed to improve post-definitive radiation risk stratification, disease management, and outcomes for patients with unresectable early-stage or locally advanced non-small cell lung cancer (NSCLC) who are treated with definitive radiation therapy (RT). This prospective, multistate single-center, cohort study investigated the association of circulating tumor DNA (ctDNA) status with recurrence in patients with unresectable stage I-III NSCLC who underwent definitive RT.MethodsA total of 70 serial plasma samples from 17 NSCLC patients were collected before, during, and after treatment. A personalized, tumor-informed ctDNA assay was used to track a set of up to 16 somatic, single nucleotide variants in the associated patient’s plasma samples.ResultsPre-treatment ctDNA detection rate was 82% (14/17) and varied based on histology and stage. ctDNA was detected in 35% (6/17) of patients at the first post-RT timepoint (median of 1.66 months following the completion of RT), all of whom subsequently developed clinical progression. At this first post-RT time point, patients with ctDNA-positivity had significantly worse progression-free survival (PFS) [hazard ratio (HR): 24.2, p=0.004], and ctDNA-positivity was the only significant prognostic factor associated with PFS (HR: 13.4, p=0.02) in a multivariate analysis. All patients who developed clinical recurrence had detectable ctDNA with an average lead time over radiographic progression of 5.4 months, and post-RT ctDNA positivity was significantly associated with poor PFS (p&lt;0.0001).ConclusionPersonalized, longitudinal ctDNA monitoring can detect recurrence early in patients with unresectable NSCLC patients undergoing curative radiation and potentially risk-stratify patients who might benefit most from treatment intensification

The epidemiology of adolescents living with perinatally acquired HIV: A cross-region global cohort analysis

Background Globally, the population of adolescents living with perinatally acquired HIV (APHs) continues to expand. In this study, we pooled data from observational pediatric HIV cohorts and cohort networks, allowing comparisons of adolescents with perinatally acquired HIV in “real-life” settings across multiple regions. We describe the geographic and temporal characteristics and mortality outcomes of APHs across multiple regions, including South America and the Caribbean, North America, Europe, sub-Saharan Africa, and South and Southeast Asia. Methods and findings Through the Collaborative Initiative for Paediatric HIV Education and Research (CIPHER), individual retrospective longitudinal data from 12 cohort networks were pooled. All children infected with HIV who entered care before age 10 years, were not known to have horizontally acquired HIV, and were followed up beyond age 10 years were included in this analysis conducted from May 2016 to January 2017. Our primary analysis describes patient and treatment characteristics of APHs at key time points, including first HIV-associated clinic visit, antiretroviral therapy (ART) start, age 10 years, and last visit, and compares these characteristics by geographic region, country income group (CIG), and birth period. Our secondary analysis describes mortality, transfer out, and lost to follow-up (LTFU) as outcomes at age 15 years, using competing risk analysis. Among the 38,187 APHs included, 51% were female, 79% were from sub-Saharan Africa and 65% lived in low-income countries. APHs from 51 countries were included (Europe: 14 countries and 3,054 APHs; North America: 1 country and 1,032 APHs; South America and the Caribbean: 4 countries and 903 APHs; South and Southeast Asia: 7 countries and 2,902 APHs; sub-Saharan Africa, 25 countries and 30,296 APHs). Observation started as early as 1982 in Europe and 1996 in sub-Saharan Africa, and continued until at least 2014 in all regions. The median (interquartile range [IQR]) duration of adolescent follow-up was 3.1 (1.5–5.2) years for the total cohort and 6.4 (3.6–8.0) years in Europe, 3.7 (2.0–5.4) years in North America, 2.5 (1.2–4.4) years in South and Southeast Asia, 5.0 (2.7–7.5) years in South America and the Caribbean, and 2.1 (0.9–3.8) years in sub-Saharan Africa. Median (IQR) age at first visit differed substantially by region, ranging from 0.7 (0.3–2.1) years in North America to 7.1 (5.3–8.6) years in sub-Saharan Africa. The median age at ART start varied from 0.9 (0.4–2.6) years in North America to 7.9 (6.0–9.3) years in sub-Saharan Africa. The cumulative incidence estimates (95% confidence interval [CI]) at age 15 years for mortality, transfers out, and LTFU for all APHs were 2.6% (2.4%–2.8%), 15.6% (15.1%–16.0%), and 11.3% (10.9%–11.8%), respectively. Mortality was lowest in Europe (0.8% [0.5%–1.1%]) and highest in South America and the Caribbean (4.4% [3.1%–6.1%]). However, LTFU was lowest in South America and the Caribbean (4.8% [3.4%–6.7%]) and highest in sub-Saharan Africa (13.2% [12.6%–13.7%]). Study limitations include the high LTFU rate in sub-Saharan Africa, which could have affected the comparison of mortality across regions; inclusion of data only for APHs receiving ART from some countries; and unavailability of data from high-burden countries such as Nigeria. Conclusion To our knowledge, our study represents the largest multiregional epidemiological analysis of APHs. Despite probable under-ascertained mortality, mortality in APHs remains substantially higher in sub-Saharan Africa, South and Southeast Asia, and South America and the Caribbean than in Europe. Collaborations such as CIPHER enable us to monitor current global temporal trends in outcomes over time to inform appropriate policy responses

Protein-altering germline mutations implicate novel genes related to lung cancer development

Few germline mutations are known to affect lung cancer risk. We performed analyses of rare variants from 39,146 individuals of European ancestry and investigated gene expression levels in 7,773 samples. We find a large-effect association with an ATM L2307F (rs56009889) mutation in adenocarcinoma for discovery (adjusted Odds Ratio = 8.82, P = 1.18 × 10−15) and replication (adjusted OR = 2.93, P = 2.22 × 10−3) that is more pronounced in females (adjusted OR = 6.81 and 3.19 and for discovery and replication). We observe an excess loss of heterozygosity in lung tumors among ATM L2307F allele carriers. L2307F is more frequent (4%) among Ashkenazi Jewish populations. We also observe an association in discovery (adjusted OR = 2.61, P = 7.98 × 10−22) and replication datasets (adjusted OR = 1.55, P = 0.06) with a loss-of-function mutation, Q4X (rs150665432) of an uncharacterized gene, KIAA0930. Our findings implicate germline genetic variants in ATM with lung cancer susceptibility and suggest KIAA0930 as a novel candidate gene for lung cancer risk