A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

Application of adaptive design and decision making to a phase II trial of a phosphodiesterase inhibitor for the treatment of intermittent claudication

Background: Claudication secondary to peripheral artery disease (PAD) is associated with substantial functional impairment. Phosphodiesterase (PDE) inhibitors have been shown to increase walking performance in these patients. K-134 is a selective PDE 3 inhibitor being developed as a potential treatment for claudication. The use of K-134, as with other PDE 3 inhibitors, in patients with PAD raises important safety and tolerability concerns, including the induction of cardiac ischemia, tachycardia, and hypotension. We describe the design, oversight, and implementation of an adaptive, phase II, dose-finding trial evaluating K-134 for the treatment of stable, intermittent claudication. Methods: The study design was a double-blind, multi-dose (25 mg, 50 mg, and 100 mg of K-134), randomized trial with both placebo and active comparator arms conducted in the United States and Russia. The primary objective of the study was to compare the highest tolerable dose of K-134 versus placebo using peak walking time after 26 weeks of therapy as the primary outcome. Study visits with intensive safety assessments were included early in the study period to provide data for adaptive decision making. The trial used an adaptive, dose-finding strategy to efficiently identify the highest dose(s) most likely to be safe and well tolerated, based on the side effect profiles observed within the trial, so that less promising doses could be abandoned. Protocol specified criteria for safety and tolerability endpoints were used and modeled prior to the adaptive decision making. The maximum target sample size was 85 subjects in each of the retained treatment arms. Results: When 199 subjects had been randomized and 28-day data were available from 143, the Data Monitoring Committee (DMC) recommended termination of the lowest dose (25 mg) treatment arm. Safety evaluations performed during 14- and 28-day visits which included in-clinic dosing and assessments at peak drug concentrations provided core data for the DMC review. At the time of review, no subject in any of the five treatment arms (placebo, three K-134-containing arms, and cilostazol) had met pre-specified definitions for resting tachycardia or ischemic changes on exercise ECG. If, instead of dropping the 25-mg K-134 treatment arm, all arms had been continued to full enrollment, then approximately 43 additional research subjects would have been required to complete the trial. Conclusions: In this phase II, dose-finding trial of K-134 in the treatment of stable intermittent claudication, no concerning safety signals were seen at interim analysis, allowing the discontinuation of the lowest-dose-containing arm and the retention of the two highest-dose-containing arms. The adaptive design facilitated safe and efficient evaluation of K-134 in this high-risk cardiovascular population

Early death during chemotherapy in patients with small-cell lung cancer: derivation of a prognostic index for toxic death and progression

Based on an increased frequency of early death (death within the first treatment cycle) in our two latest randomized trials of combination chemotherapy in small-cell lung cancer (SCLC), we wanted to identify patients at risk of early non-toxic death (ENTD) and early toxic death (ETD). Data were stored in a database and logistic regression analyses were performed to identify predictive factors for early death. During the first cycle, 118 out of 937 patients (12.6%) died. In 38 patients (4%), the cause of death was sepsis. Significant risk factors were age, performance status (PS), lactate dehydrogenase (LDH) and treatment with epipodophyllotoxins and platinum in the first cycle (EP). Risk factors for ENTD were age, PS and LDH. Extensive stage had a hazard ratio of 1.9 (P = 0.07). Risk factors for ETD were EP, PS and LDH, whereas age and stage were not. For EP, the hazard ratio was as high as 6.7 (P = 0.0001). We introduced a simple prognostic algorithm including performance status, LDH and age. Using a prognostic algorithm to exclude poor-risk patients from trials, we could minimize early death, improve long-term survival and increase the survival differences between different regimens. We suggest that other groups evaluate our algorithm and exclude poor prognosis patients from trials of dose intensification. © 1999 Cancer Research Campaig

Reductionist and system approaches to study the role of infection in preterm labor and delivery

A substantial number of patients with preterm labor and delivery do not show clinical signs of infection, however, it is the subclinical form which is the main causative factor and often results in premature delivery. The hitherto commonly applied methods of inflammation detection are based either on potentially hazardous amniocentesis or still insufficient inflammation-related protein measurement in the serum or other biological fluids

A Protective Role for Complement C3 Protein during Pandemic 2009 H1N1 and H5N1 Influenza A Virus Infection

Highly pathogenic H5N1 influenza infections are associated with enhanced inflammatory and cytokine responses, severe lung damage, and an overall dysregulation of innate immunity. C3, a member of the complement system of serum proteins, is a major component of the innate immune and inflammatory responses. However, the role of this protein in the pathogenesis of H5N1 infection is unknown. Here we demonstrate that H5N1 influenza virus infected mice had increased levels of C5a and C3 activation byproducts as compared to mice infected with either seasonal or pandemic 2009 H1N1 influenza viruses. We hypothesized that the increased complement was associated with the enhanced disease associated with the H5N1 infection. However, studies in knockout mice demonstrated that C3 was required for protection from influenza infection, proper viral clearance, and associated with changes in cellular infiltration. These studies suggest that although the levels of complement activation may differ depending on the influenza virus subtype, complement is an important host defense mechanism

Beyond the standard seesaw: neutrino masses from Kahler operators and broken supersymmetry

We investigate supersymmetric scenarios in which neutrino masses are generated by effective d=6 operators in the Kahler potential, rather than by the standard d=5 superpotential operator. First, we discuss some general features of such effective operators, also including SUSY-breaking insertions, and compute the relevant renormalization group equations. Contributions to neutrino masses arise at low energy both at the tree level and through finite threshold corrections. In the second part we present simple explicit realizations in which those Kahler operators arise by integrating out heavy SU(2)_W triplets, as in the type II seesaw. Distinct scenarios emerge, depending on the mechanism and the scale of SUSY-breaking mediation. In particular, we propose an appealing and economical picture in which the heavy seesaw mediators are also messengers of SUSY breaking. In this case, strong correlations exist among neutrino parameters, sparticle and Higgs masses, as well as lepton flavour violating processes. Hence, this scenario can be tested at high-energy colliders, such as the LHC, and at lower energy experiments that measure neutrino parameters or search for rare lepton decays.Comment: LaTeX, 34 pages; some corrections in Section

MRI of the lung (3/3)-current applications and future perspectives

BACKGROUND: MRI of the lung is recommended in a number of clinical indications. Having a non-radiation alternative is particularly attractive in children and young subjects, or pregnant women. METHODS: Provided there is sufficient expertise, magnetic resonance imaging (MRI) may be considered as the preferential modality in specific clinical conditions such as cystic fibrosis and acute pulmonary embolism, since additional functional information on respiratory mechanics and regional lung perfusion is provided. In other cases, such as tumours and pneumonia in children, lung MRI may be considered an alternative or adjunct to other modalities with at least similar diagnostic value. RESULTS: In interstitial lung disease, the clinical utility of MRI remains to be proven, but it could provide additional information that will be beneficial in research, or at some stage in clinical practice. Customised protocols for chest imaging combine fast breath-hold acquisitions from a "buffet" of sequences. Having introduced details of imaging protocols in previous articles, the aim of this manuscript is to discuss the advantages and limitations of lung MRI in current clinical practice. CONCLUSION: New developments and future perspectives such as motion-compensated imaging with self-navigated sequences or fast Fourier decomposition MRI for non-contrast enhanced ventilation- and perfusion-weighted imaging of the lung are discussed. Main Messages • MRI evolves as a third lung imaging modality, combining morphological and functional information. • It may be considered first choice in cystic fibrosis and pulmonary embolism of young and pregnant patients. • In other cases (tumours, pneumonia in children), it is an alternative or adjunct to X-ray and CT. • In interstitial lung disease, it serves for research, but the clinical value remains to be proven. • New users are advised to make themselves familiar with the particular advantages and limitations

Mannose Binding Lectin Is Required for Alphavirus-Induced Arthritis/Myositis

Mosquito-borne alphaviruses such as chikungunya virus and Ross River virus (RRV) are emerging pathogens capable of causing large-scale epidemics of virus-induced arthritis and myositis. The pathology of RRV-induced disease in both humans and mice is associated with induction of the host inflammatory response within the muscle and joints, and prior studies have demonstrated that the host complement system contributes to development of disease. In this study, we have used a mouse model of RRV-induced disease to identify and characterize which complement activation pathways mediate disease progression after infection, and we have identified the mannose binding lectin (MBL) pathway, but not the classical or alternative complement activation pathways, as essential for development of RRV-induced disease. MBL deposition was enhanced in RRV infected muscle tissue from wild type mice and RRV infected MBL deficient mice exhibited reduced disease, tissue damage, and complement deposition compared to wild-type mice. In contrast, mice deficient for key components of the classical or alternative complement activation pathways still developed severe RRV-induced disease. Further characterization of MBL deficient mice demonstrated that similar to C3−/− mice, viral replication and inflammatory cell recruitment were equivalent to wild type animals, suggesting that RRV-mediated induction of complement dependent immune pathology is largely MBL dependent. Consistent with these findings, human patients diagnosed with RRV disease had elevated serum MBL levels compared to healthy controls, and MBL levels in the serum and synovial fluid correlated with severity of disease. These findings demonstrate a role for MBL in promoting RRV-induced disease in both mice and humans and suggest that the MBL pathway of complement activation may be an effective target for therapeutic intervention for humans suffering from RRV-induced arthritis and myositis

MetaPath: identifying differentially abundant metabolic pathways in metagenomic datasets

Enabled by rapid advances in sequencing technology, metagenomic studies aim to characterize entire communities of microbes bypassing the need for culturing individual bacterial members. One major goal of metagenomic studies is to identify specific functional adaptations of microbial communities to their habitats. The functional profile and the abundances for a sample can be estimated by mapping metagenomic sequences to the global metabolic network consisting of thousands of molecular reactions. Here we describe a powerful analytical method (MetaPath) that can identify differentially abundant pathways in metagenomic datasets, relying on a combination of metagenomic sequence data and prior metabolic pathway knowledge. First, we introduce a scoring function for an arbitrary subnetwork and find the max-weight subnetwork in the global network by a greedy search algorithm. Then we compute two p values (p abund and p struct ) using nonparametric approaches to answer two different statistical questions: (1) is this subnetwork differentically abundant? (2) What is the probability of finding such good subnetworks by chance given the data and network structure? Finally, significant metabolic subnetworks are discovered based on these two p values. In order to validate our methods, we have designed a simulated metabolic pathways dataset and show that MetaPath outperforms other commonly used approaches. We also demonstrate the power of our methods in analyzing two publicly available metagenomic datasets, and show that the subnetworks identified by MetaPath provide valuable insights into the biological activities of the microbiome. We have introduced a statistical method for finding significant metabolic subnetworks from metagenomic datasets. Compared with previous methods, results from MetaPath are more robust against noise in the data, and have significantly higher sensitivity and specificity (when tested on simulated datasets). When applied to two publicly available metagenomic datasets, the output of MetaPath is consistent with previous observations and also provides several new insights into the metabolic activity of the gut microbiome. The software is freely available at http://metapath.cbcb.umd.edu .https://doi.org/10.1186/1753-6561-5-S2-S

Clinical decision modeling system

<p>Abstract</p> <p>Background</p> <p>Decision analysis techniques can be applied in complex situations involving uncertainty and the consideration of multiple objectives. Classical decision modeling techniques require elicitation of too many parameter estimates and their conditional (joint) probabilities, and have not therefore been applied to the problem of identifying high-performance, cost-effective combinations of clinical options for diagnosis or treatments where many of the objectives are unknown or even unspecified.</p> <p>Methods</p> <p>We designed a Java-based software resource, the Clinical Decision Modeling System (CDMS), to implement Naïve Decision Modeling, and provide a use case based on published performance evaluation measures of various strategies for breast and lung cancer detection. Because cost estimates for many of the newer methods are not yet available, we assume equal cost. Our use case reveals numerous potentially high-performance combinations of clinical options for the detection of breast and lung cancer.</p> <p>Results</p> <p>Naïve Decision Modeling is a highly practical applied strategy which guides investigators through the process of establishing evidence-based integrative translational clinical research priorities. CDMS is not designed for clinical decision support. Inputs include performance evaluation measures and costs of various clinical options. The software finds trees with expected emergent performance characteristics and average cost per patient that meet stated filtering criteria. Key to the utility of the software is sophisticated graphical elements, including a tree browser, a receiver-operator characteristic surface plot, and a histogram of expected average cost per patient. The analysis pinpoints the potentially most relevant pairs of clinical options ('critical pairs') for which empirical estimates of conditional dependence may be critical. The assumption of independence can be tested with retrospective studies prior to the initiation of clinical trials designed to estimate clinical impact. High-performance combinations of clinical options may exist for breast and lung cancer detection.</p> <p>Conclusion</p> <p>The software could be found useful in simplifying the objective-driven planning of complex integrative clinical studies without requiring a multi-attribute utility function, and it could lead to efficient integrative translational clinical study designs that move beyond simple pair wise competitive studies. Collaborators, who traditionally might compete to prioritize their own individual clinical options, can use the software as a common framework and guide to work together to produce increased understanding on the benefits of using alternative clinical combinations to affect strategic and cost-effective clinical workflows.</p