Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion

We extend to a Engel type structure a cortically inspired model of perceptual completion initially proposed in the Lie group of positions and orientations with a sub-Riemannian metric. According to this model, a given image is lifted in the group and completed by a minimal surface. The main obstacle in extending the model to a higher dimensional group, which can code also curvatures, is the lack of a good definition of codimension 2 minimal surface. We present here this notion, and describe an application to image completion

Prognostic Value of Indeterminable Anaerobic Threshold in Heart Failure.

Background In patients with heart failure (HF), during maximal cardiopulmonary exercise test, anaerobic threshold (AT) is not always identified. We evaluated whether this finding has a prognostic meaning. Methods and Results We recruited and prospectively followed up, in 14 dedicated HF units, 3058 patients with systolic (left ventricular ejection fraction <40%) HF in stable clinical conditions, New York Heart Association class I to III, who underwent clinical, laboratory, echocardiographic, and cardiopulmonary exercise test investigations at study enrollment. We excluded 921 patients who did not perform a maximal exercise, based on lack of achievement of anaerobic metabolism (peak respiratory quotient 1.05). Primary study end point was a composite of cardiovascular death and urgent cardiac transplant, and secondary end point was all-cause death. Median follow-up was 3.01 (1.39-4.98) years. AT was identified in 1935 out of 2137 patients (90.54%). At multivariable logistic analysis, failure in detecting AT resulted significantly in reduced peak oxygen uptake and higher metabolic exercise and cardiac and kidney index score value, a powerful prognostic composite HF index (P<0.001). At multivariable analysis, the following variables were significantly associated with primary study end point: peak oxygen uptake (% pred; P<0.001; hazard ratio [HR]=0.977; confidence interval [CI]=0.97-0.98), ventilatory efficiency slope (P=0.01; HR=1.02; CI=1.01-1.03), hemoglobin (P<0.05; HR=0.931; CI=0.87-1.00), left ventricular ejection fraction (P<0.001; HR=0.948; CI=0.94-0.96), renal function (modification of diet in renal disease; P<0.001; HR=0.990; CI=0.98-0.99), sodium (P<0.05; HR=0.967; CI=0.94-0.99), and AT nonidentification (P<0.05; HR=1.41; CI=1.06-1.89). Nonidentification of AT remained associated to prognosis also when compared with metabolic exercise and cardiac and kidney index score (P<0.01; HR=1.459; CI=1.09-1.10). Similar results were obtained for the secondary study end point. Conclusions The inability to identify AT most often occurs in patients with severe HF, and it has an independent prognostic role in HF

Imaging the boundaries—innovative tools for microscopy of living cells and real-time imaging

Recently, light microscopy moved back into the spotlight, which is mainly due to the development of revolutionary technologies for imaging real-time events in living cells. It is truly fascinating to see enzymes “at work” and optically acquired images certainly help us to understand biological processes better than any abstract measurements. This review aims to point out elegant examples of recent cell-biological imaging applications that have been developed with a chemical approach. The discussed technologies include nanoscale fluorescence microscopy, imaging of model membranes, automated high-throughput microscopy control and analysis, and fluorescent probes with a special focus on visualizing enzyme activity, free radicals, and protein–protein interaction designed for use in living cells

VARIATIONAL FORMULAS FOR CURVES OF FIXED DEGREE

We consider a length functional for C1 curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be computed only if the curve can be deformed in a suitable sense, and this condition is expressed via a differential equation along the curve. In the classical differential geometry setting, the analogous condition was considered by Bryant and Hsu in [7, 21], who proved that it is equivalent to the surjectivity of a holonomy map. The purpose of this paper is to extend this deformation theory to curves of fixed degree providing several examples and applications. In particular, we give a useful sufficient condition to guarantee the possibility of deforming a curve

An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems

We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A careful adaptation of well known variational methods is required to deal with the possible existence of negative eigenvalues