Itô Stochastic Differentials

We give an infinitesimal meaning to the symbol dXt for a continuous semimartingale X at an instant in time t. We define a vector space structure on the space of differentials at time t and deduce key properties consistent with the classical Itô integration theory. In particular, we link our notion of a differential with Itô integration via a stochastic version of the Fundamental Theorem of Calculus. Our differentials obey a version of the chain rule, which is a local version of Itô’s lemma. We apply our results to financial mathematics to give a theory of portfolios at an instant in time

Gamma Hedging and Rough Paths

We apply rough path theory to study the discrete-time gamma-hedging strategy. We show that if a trader knows that the market price of a set of European options will be given by a diffusive pricing model, then the discrete-time gamma-hedging strategy will enable them to replicate other European options so long as the underlying price path is sufficiently regular. This is a sure result and does not require that the underlying price path has a quadratic variation corresponding to the pricing model. We show how to generalise this result to exotic derivatives when the gamma is defined to be the Gubinelli derivative of the delta by deriving rough-path versions of the Clark--Ocone formula which hold surely

Increased levels of transition metals in breast cancer tissue.

Abstract OBJECTIVES: High levels of transition metals such as iron, nickel, chromium, copper, and lead are closely related to free radical generation, lipid peroxidation, formation of DNA strand breaks, and tumor growth in cellular systems. In order to determine the correlation to malignant growth in humans, we investigated the accumulation of heavy metals in 20 breast cancer biopsies and compared the findings to the levels found in 8 healthy biopsies. METHODS: The concentration of transition metals in breast cancer and control biopsies was assessed by a standardized Atomic Absorption Spectrofotometry technique with acidic hydrolysis for sample preparation. Additionally, heavy metal analysis in control biopsies was also performed with an Inductive Coupled Plasma -Mass Spectroscopy technique. For statistical analysis of the results, the Mann-Whitney U Test was applied. RESULTS: A highly significant accumulation of iron (p<0.0001), nickel (p<0.00005), chromium (p<0.00005), zinc (p<0.00001), cadmium (p<0.005), mercury (p<0.005), and lead (p< 0.05) was found in the cancer samples when compared to the control group. Copper and silver showed no significant differences to the control group, whereas tin, gold, and palladium were not detectable in any biopsies. CONCLUSIONS: The data suggest that pathological accumulation of transition metals in breast tissue may be closely related to the malignant growth process

Challenges in Representation Learning: A report on three machine learning contests

The ICML 2013 Workshop on Challenges in Representation Learning focused on three challenges: the black box learning challenge, the facial expression recognition challenge, and the multimodal learning challenge. We describe the datasets created for these challenges and summarize the results of the competitions. We provide suggestions for organizers of future challenges and some comments on what kind of knowledge can be gained from machine learning competitions.Comment: 8 pages, 2 figure

Validity, practical utility, and reliability of the activPAL in preschool children

<p>Purpose: With the increasing global prevalence of childhood obesity, it is important to have appropriate measurement tools for investigating factors (e.g. sedentary time) contributing to positive energy balance in early childhood. For pre-school children, single unit monitors such as the activPALTM are promising. However, validation is required as activity patterns differ from adults.</p> <p>Methods: Thirty pre-school children participated in a validation study. Children were videoed for one hour undertaking usual nursery activity while wearing an activPALTM. Video (criterion method) was analyzed on a second-by-second basis to categorise posture and activity. This was compared with the corresponding activPALTM output. In a subsequent sub-study investigating practical utility and reliability, 20 children wore an activPALTM for seven consecutive 24-hour periods.</p> <p>Results: A total of 97,750 seconds of direct observation from 30 children were categorized as sit/lie (46%), stand (35%), walk (16%); with 3% of time in nonsit/lie/upright postures (e.g. crawl/crouch/kneel-up). Sensitivity for the overall total time matched seconds detected as activPALTM ‘sit/lie’ was 86.7%, specificity 97.1%, and positive predictive value (PPV) 96.3%. For individual children, the median (interquartile range) sensitivity for activPALTM sit/lie was 92.8% (76.1-97.4), specificity 97.3% (94.9-99.2), PPV 97.0% (91.5-99.1). The activPALTM underestimated total time spent sitting (mean difference -4.4%, p<0.01), and overestimated time standing (mean difference 7.1%, p<0.01). There was no difference in overall % time categorised as ‘walk’ (p=0.2). The monitors were well tolerated by children during a seven day period of free-living activity. In the reliability study, at least five days of monitoring were required to obtain an intraclass correlation coefficient of ≥0.8 for time spent sit/lie according to activPALTM output.</p> <p>Conclusion: The activPAL had acceptable validity, practical utility, and reliability for the measurement of posture and activity during freeliving activities in pre-school children.</p&gt

Sub-clinical left and right ventricular dysfunction in patients with COPD

SummaryBackgroundCardiovascular manifestations in COPD include increased arterial stiffness, ischaemic heart disease, chronic heart failure and cor pulmonale. We hypothesised that sub-clinical right (RV) and left ventricular (LV) dysfunction occurs in patients with COPD, related to the severity of airflow obstruction, arterial stiffness and systemic inflammation.MethodsThirty six patients and 14 controls, all free of overt cardiovascular disease underwent tissue Doppler echocardiography, spirometry, measurement of aortic pulse wave velocity (PWV) and venous sampling for inflammatory markers.ResultsMean LV myocardial strain and strain rate were less in patients than controls, p<0.05. LV isovolumic relaxation time (IVRT) was prolonged in patients (125±15.2ms) compared with controls (98.2±21.1ms), p<0.01, indicating LV diastolic dysfunction. The RV free wall strain and strain rate were less in patients than controls, both p<0.05, indicating RV systolic dysfunction. Patients had sub-clinical pulmonary arterial hypertension with a greater RV myocardial relaxation time and Tei index, both p<0.01. Patients with mild airways obstruction had LV and RV dysfunction and evidence of increased RV afterload compared with controls. In multivariate analyses aortic PWV predicted LV IVRT, p<0.01, while FEV1 predicted RV Tei index and myocardial relaxation time, both p<0.01.ConclusionsPatients with COPD have sub-clinical left ventricular dysfunction related to arterial stiffness, and right ventricular dysfunction related to airways obstruction. Both right and left ventricular dysfunction are present in patients with mild airways obstruction suggesting that cardiac co-morbidities commence early in the development of COPD

Uniqueness results for ill posed characteristic problems in curved space-times

We prove two uniqueness theorems for solutions of linear and nonlinear wave equations; the first theorem is in the Minkowski space while the second is in the domain of outer communication of a Kerr black hole. Both theorems concern ill posed Cauchy problems on smooth, bifurcate, characteristic hypersurfaces. In the case of the Kerr space-time this hypersurface is the event horizon of the black hole.Comment: Various correction

Existence, functional impairment, and lung repair potential of endothelial colony-forming cells in oxygen-induced arrested alveolar growth

BACKGROUND: Bronchopulmonary dysplasia and emphysema are life-threatening diseases resulting from impaired alveolar development or alveolar destruction. Both conditions lack effective therapies. Angiogenic growth factors promote alveolar growth and contribute to alveolar maintenance. Endothelial colony-forming cells (ECFCs) represent a subset of circulating and resident endothelial cells capable of self-renewal and de novo vessel formation. We hypothesized that resident ECFCs exist in the developing lung, that they are impaired during arrested alveolar growth in experimental bronchopulmonary dysplasia, and that exogenous ECFCs restore disrupted alveolar growth. METHODS AND RESULTS: Human fetal and neonatal rat lungs contain ECFCs with robust proliferative potential, secondary colony formation on replating, and de novo blood vessel formation in vivo when transplanted into immunodeficient mice. In contrast, human fetal lung ECFCs exposed to hyperoxia in vitro and neonatal rat ECFCs isolated from hyperoxic alveolar growth-arrested rat lungs mimicking bronchopulmonary dysplasia proliferated less, showed decreased clonogenic capacity, and formed fewer capillary-like networks. Intrajugular administration of human cord blood-derived ECFCs after established arrested alveolar growth restored lung function, alveolar and lung vascular growth, and attenuated pulmonary hypertension. Lung ECFC colony- and capillary-like network-forming capabilities were also restored. Low ECFC engraftment and the protective effect of cell-free ECFC-derived conditioned media suggest a paracrine effect. Long-term (10 months) assessment of ECFC therapy showed no adverse effects with persistent improvement in lung structure, exercise capacity, and pulmonary hypertension. CONCLUSIONS: Impaired ECFC function may contribute to arrested alveolar growth. Cord blood-derived ECFC therapy may offer new therapeutic options for lung diseases characterized by alveolar damage

A new scoring system to determine thromboembolic risk after heart valve replacement

Objective— To determine the most important inflammatory and hematologic predictors of thromboembolism (TE) in patients undergoing valve replacement (VR) to be used in conjunction with clinical risk factors for preoperative risk profiling. Methods and Results— Preoperative and immediately postoperative clinical, echocardiographic, hematologic, biochemical and microbiological parameters were examined prospectively in 370 patients undergoing VR (249 AVR, 93 MVR, 28 DVR). Mean follow-up was 4.4 years (max 6.6 years; total 1566 pt/yrs), and 96 TE events were documented (28 major and 68 minor). INR data were collected on all patients. Laboratory values were considered elevated if they exceeded the 80th percentile of those of 70 controls with the same distribution of age and gender. IgA antibody to Chlamydia pneumoniae (CP)≥1:64 was considered indicative of significant infection. Predictors of TE on multivariate analysis following AVR were (hazard ratios): CP infection (2.6), previous TE (2.5), raised eosinophils (2.4), cancer history (2.1), postoperative infection (2.0), hypertension (2.0), CABG × 3/4 (2.0), and diabetes (1.9). Predictors of TE following MVR/DVR were raised mean platelet volume (4.0), raised factor VII (3.1), CP infection (2.7), previous mitral valvotomy (2.5), raised fibrinogen (2.2), and raised reticulocytes (2.0). These risk factors were additive when present in the same patient, enabling a scoring system to be developed that accurately predicted risk of TE based on number of risk factors. Conclusions— Selected blood tests and clinical risk factors provide a scoring system that accurately predicts TE risk and may guide prosthesis choice and antithrombotic management

Postglacial adaptations enabled colonization and quasi-clonal dispersal of ammonia-oxidizing archaea in modern European large lakes

Ammonia-oxidizing archaea (AOA) play a key role in the aquatic nitrogen cycle. Their genetic diversity is viewed as the outcome of evolutionary processes that shaped ancestral transition from terrestrial to marine habitats. However, current genome-wide insights into AOA evolution rarely consider brackish and freshwater representatives or provide their divergence timeline in lacustrine systems. An unbiased global assessment of lacustrine AOA diversity is critical for understanding their origins, dispersal mechanisms, and ecosystem roles. Here, we leveraged continental-scale metagenomics to document that AOA species diversity in freshwater systems is remarkably low compared to marine environments. We show that the uncultured freshwater AOA, "Candidatus Nitrosopumilus limneticus," is ubiquitous and genotypically static in various large European lakes where it evolved 13 million years ago. We find that extensive proteome remodeling was a key innovation for freshwater colonization of AOA. These findings reveal the genetic diversity and adaptive mechanisms of a keystone species that has survived clonally in lakes for millennia