A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Drug ranking using machine learning systematically predicts the efficacy of anti-cancer drugs

Artificial intelligence and machine learning (ML) promise to transform cancer therapies by accurately predicting the most appropriate therapies to treat individual patients. Here, we present an approach, named Drug Ranking Using ML (DRUML), which uses omics data to produce ordered lists of >400 drugs based on their anti-proliferative efficacy in cancer cells. To reduce noise and increase predictive robustness, instead of individual features, DRUML uses internally normalized distance metrics of drug response as features for ML model generation. DRUML is trained using in-house proteomics and phosphoproteomics data derived from 48 cell lines, and it is verified with data comprised of 53 cellular models from 12 independent laboratories. We show that DRUML predicts drug responses in independent verification datasets with low error (mean squared error < 0.1 and mean Spearman’s rank 0.7). In addition, we demonstrate that DRUML predictions of cytarabine sensitivity in clinical leukemia samples are prognostic of patient survival (Log rank p < 0.005). Our results indicate that DRUML accurately ranks anti-cancer drugs by their efficacy across a wide range of pathologies

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

K\"ahlerian Twistor Spinors

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.

Spectral Bounds for Dirac Operators on Open Manifolds

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure

Understanding childhood asthma in focus groups: perspectives from mothers of different ethnic backgrounds

BACKGROUND: Diagnosing childhood asthma is dependent upon parental symptom reporting but there are problems in the use of words and terms. The purpose of this study was to describe and compare understandings of childhood 'asthma' by mothers from three different ethnic backgrounds who have no personal experience of diagnosing asthma. A better understanding of parents' perceptions of an illness by clinicians should improve communication and management of the illness. METHOD: Sixty-six mothers living in east London describing their ethnic backgrounds as Bangladeshi, white English and black Caribbean were recruited to 9 focus groups. Discussion was semi-structured. Three sessions were conducted with each ethnic group. Mothers were shown a video clip of a boy with audible wheeze and cough and then addressed 6 questions. Sessions were recorded and transcribed verbatim. Responses were compared within and between ethnic groups. RESULTS: Each session, and ethnic group overall, developed a particular orientation to the discussion. Some mothers described the problem using single signs, while others imitated the sound or made comparisons to other illnesses. Hereditary factors were recognised by some, although all groups were concerned with environmental triggers. Responses about what to do included 'normal illness' strategies, use of health services and calls for complementary treatment. All groups were concerned about using medication every day. Expectations about the quality of life were varied, with recognition that restrictions may be based on parental beliefs about asthma, rather than asthma itself. CONCLUSION: Information from these focus groups suggests mothers know a great deal about childhood asthma even though they have no personal experience of it. Knowledge of how mothers from these ethnic backgrounds perceive asthma may facilitate doctor – patient communication with parents of children experiencing breathing difficulties

Home exposure to Arabian incense (bakhour) and asthma symptoms in children: a community survey in two regions in Oman

<p>Abstract</p> <p>Background</p> <p>Incense burning has been reported to adversely affect respiratory health. The aim of this study was to explore whether exposure to bakhour contributes to the prevalence of asthma and/or triggers its symptoms in Omani children by comparing two Omani regions with different prevalence of asthma.</p> <p>Methods</p> <p>A randomly selected sample of 10 years old schoolchildren were surveyed using an Arabic version of ISAAC Phase II questionnaires with the addition of questions concerning the use and effect of Arabian incense on asthma symptoms. Current asthma was defined as positive response to wheeze in the past 12 months or positive response to "ever had asthma" together with a positive response to exercise wheeze or night cough in the past 12 months. Simple and multivariable logistic regression analyses were performed to estimate the effect of bakhour exposure and other variables on current asthma diagnosis and parents' response to the question: "Does exposure to bakhour affect your child breathing?"</p> <p>Results</p> <p>Of the 2441 surveyed children, 15.4% had current asthma. Bakhour use more than twice a week was three times more likely to affect child breathing compared to no bakhour use (adjusted OR 3.01; 95% CI 2.23–4.08) and this effect was 2.55 times higher in asthmatics (adjusted OR 2.55; 95% CI 1.97–3.31) compared to non-asthmatics. In addition, bakhour caused worsening of wheeze in 38% of the asthmatics, making it the fourth most common trigger factor after dust (49.2%), weather (47.6%) and respiratory tract infections (42.2%). However, there was no significant association between bakhour use and the prevalence of current asthma (adjusted OR 0.87; 95% CI 0.63–1.20).</p> <p>Conclusion</p> <p>Arabian incense burning is a common trigger of wheezing among asthmatic children in Oman. However, it is not associated with the prevalence asthma.</p

An Estimator for statistical anisotropy from the CMB bispectrum

Various data analyses of the Cosmic Microwave Background (CMB) provide observational hints of statistical isotropy breaking. Some of these features can be studied within the framework of primordial vector fields in inflationary theories which generally display some level of statistical anisotropy both in the power spectrum and in higher-order correlation functions. Motivated by these observations and the recent theoretical developments in the study of primordial vector fields, we develop the formalism necessary to extract statistical anisotropy information from the three-point function of the CMB temperature anisotropy. We employ a simplified vector field model and parametrize the bispectrum of curvature fluctuations in such a way that all the information about statistical anisotropy is encoded in some parameters lambda_{LM} (which measure the anisotropic to the isotropic bispectrum amplitudes). For such a template bispectrum, we compute an optimal estimator for lambda_{LM} and the expected signal-to-noise ratio. We estimate that, for f_{NL} ~ 30, an experiment like Planck can be sensitive to a ratio of the anisotropic to the isotropic amplitudes of the bispectrum as small as 10%. Our results are complementary to the information coming from a power spectrum analysis and particularly relevant for those models where statistical anisotropy turns out to be suppressed in the power spectrum but not negligible in the bispectrum.Comment: 25 pages, LaTeX file. Matches version accepted for publication in JCAP; some references added; Appendix C added to explain the order of the Edgeworth expansion employe

Probiotic Microbes Sustain Youthful Serum Testosterone Levels and Testicular Size in Aging Mice

The decline of circulating testosterone levels in aging men is associated with adverse health effects. During studies of probiotic bacteria and obesity, we discovered that male mice routinely consuming purified lactic acid bacteria originally isolated from human milk had larger testicles and increased serum testosterone levels compared to their age-matched controls. Further investigation using microscopy-assisted histomorphometry of testicular tissue showed that mice consuming Lactobacillus reuteri in their drinking water had significantly increased seminiferous tubule cross-sectional profiles and increased spermatogenesis and Leydig cell numbers per testis when compared with matched diet counterparts This showed that criteria of gonadal aging were reduced after routinely consuming a purified microbe such as L. reuteri. We tested whether these features typical of sustained reproductive fitness may be due to anti-inflammatory properties of L. reuteri, and found that testicular mass and other indicators typical of old age were similarly restored to youthful levels using systemic administration of antibodies blocking pro-inflammatory cytokine interleukin-17A. This indicated that uncontrolled host inflammatory responses contributed to the testicular atrophy phenotype in aged mice. Reduced circulating testosterone levels have been implicated in many adverse effects; dietary L. reuteri or other probiotic supplementation may provide a viable natural approach to prevention of male hypogonadism, absent the controversy and side-effects of traditional therapies, and yield practical options for management of disorders typically associated with normal aging. These novel findings suggest a potential high impact for microbe therapy in public health by imparting hormonal and gonad features of reproductive fitness typical of much younger healthy individuals.National Institutes of Health (U.S.) (Grant P30-ES002109)National Institutes of Health (U.S.) (Grant U01 CA164337)National Institutes of Health (U.S.) (Grant RO1CA108854