Discover the most talked about and latest scientific content & concepts.

Concept: Continuous function


Global changes in climate, atmospheric composition, and pollutants are altering ecosystems and the goods and services they provide. Among approaches for predicting ecosystem responses, long-term observations and manipulative experiments can be powerful approaches for resolving single-factor and interactive effects of global changes on key metrics such as net primary production (NPP). Here we combine both approaches, developing multidimensional response surfaces for NPP based on the longest-running, best-replicated, most-multifactor global-change experiment at the ecosystem scale-a 17-y study of California grassland exposed to full-factorial warming, added precipitation, elevated CO2, and nitrogen deposition. Single-factor and interactive effects were not time-dependent, enabling us to analyze each year as a separate realization of the experiment and extract NPP as a continuous function of global-change factors. We found a ridge-shaped response surface in which NPP is humped (unimodal) in response to temperature and precipitation when CO2 and nitrogen are ambient, with peak NPP rising under elevated CO2 or nitrogen but also shifting to lower temperatures. Our results suggest that future climate change will push this ecosystem away from conditions that maximize NPP, but with large year-to-year variability.

Concepts: Photosynthesis, Function, Stanford prison experiment, Earth, Climate, Ecosystem, Continuous function, Global warming


Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy is significantly improved when the localization is performed using a more realistic model. Here, we show how this can be achieved by considering three-dimensional (3-D) point spread function models for the wide field microscope. We introduce a least-squares point spread function fitting framework that utilizes the Gibson and Lanni model and propose a computationally efficient way for evaluating its derivative functions. We demonstrate the usefulness of the proposed approach with algorithms for particle localization and defocus estimation, both implemented as plugins for ImageJ.

Concepts: Mathematics, Biology, Function, Microscope, Derivative, Microscopy, Continuous function, Point spread function


In this paper we consider the problem of single image super-resolution and propose a novel algorithm that outperforms state-of-the-art methods without the need of learning patches pairs from external datasets. We achieve this by modeling images and, more precisely, lines of images as piecewise smooth functions and propose a resolution enhancement method for this type of functions. The method makes use of the theory of sampling signals with finite rate of innovation (FRI) and combines it with traditional linear reconstruction methods. We combine the two reconstructions by leveraging from the multiresolution analysis in wavelet theory and show how an FRI reconstruction and a linear reconstruction can be fused using filter-banks. We then apply this method along vertical, horizontal and diagonal directions in an image to obtain a single-image super-resolution algorithm. We also propose a further improvement of the method based on learning from the errors of our super-resolution result at lower resolution levels. Simulation results show that our method outperforms state-of-the-art algorithms under different blurring kernels.

Concepts: Algorithm, Computer graphics, Derivative, Continuous function, Piecewise linear function


The velocity associated with maximum aerobic power (vVO2max) is an important physiological parameter, which is utilized to determine relative workloads on the field. The testing modality adopted to evaluate it, though, may cause differences in v V O2 max assessment and, in turn, in training intensity. The aim of the study was to compare two different testing modalities (continuous incremental ramp and discontinuous square wave (SW) protocols) for vVO2max assessment on the treadmill.

Concepts: Fundamental physics concepts, Assessment, Psychometrics, Derivative, Continuous function, Exercise physiology, Test, Norm-referenced test


Three-dimensional fluorescence microscopy followed by image processing is routinely used to study biological objects at various scales such as cells and tissue. However, maximum intensity projection, the most broadly used rendering tool, extracts a discontinuous layer of voxels, obliviously creating important artifacts and possibly misleading interpretation. Here we propose smooth manifold extraction, an algorithm that produces a continuous focused 2D extraction from a 3D volume, hence preserving local spatial relationships. We demonstrate the usefulness of our approach by applying it to various biological applications using confocal and wide-field microscopy 3D image stacks. We provide a parameter-free ImageJ/Fiji plugin that allows 2D visualization and interpretation of 3D image stacks with maximum accuracy.

Concepts: Biology, Dimension, Mathematical analysis, Computer graphics, Manifold, Microscopy, Continuous function, 3D computer graphics


Tendons transmit muscle-generated force through an extracellular matrix of aligned collagen fibrils. The force applied by the muscle at one end of a microscopic fibril has to be transmitted through the macroscopic length of the tendon by mechanisms that are poorly understood. A key element in this structure-function relationship is the collagen fibril length. During embryogenesis short fibrils are produced but they grow rapidly with maturation. There is some controversy regarding fibril length in adult tendon, with mechanical data generally supporting discontinuity while structural investigations favor continuity. This study initially set out to trace the full length of individual fibrils in adult human tendons, using serial block face-scanning electron microscopy. But even with this advanced technique the required length could not be covered. Instead a statistical approach was used on a large volume of fibrils in shorter image stacks. Only a single end was observed after tracking 67.5 mm of combined fibril lengths, in support of fibril continuity. To shed more light on this observation, the full length of a short tendon (mouse stapedius, 125 μm) was investigated and continuity of individual fibrils was confirmed. In light of these results, possible mechanisms that could reconcile the opposing findings on fibril continuity are discussed.

Concepts: Collagen, Extracellular matrix, Microscope, Muscle, Cartilage, Continuous function, Tendon, Length


Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint by gradually removing variables based on a criterion and a schedule. The attractive fact that the problem size keeps dropping throughout the iterations makes it particularly suitable for big data learning. Our approach applies generically to the optimization of any differentiable loss function, and finds applications in regression, classification and ranking. The resultant algorithms build variable screening into estimation and are extremely simple to implement. We provide theoretical guarantees of convergence and selection consistency. In addition, one dimensional piecewise linear response functions are used to account for nonlinearity and a second order prior is imposed on these functions to avoid overfitting. Experiments on real and synthetic data show that the proposed method compares very well with other state of the art methods in regression, classification and ranking while being computationally very efficient and scalable.

Concepts: Algorithm, Function, Calculus, Machine learning, Real number, Derivative, Continuous function, Optimization


Shift change handoffs are known to be a point of vulnerability in the quality, safety and outcomes of healthcare. Despite numerous efforts to improve handoff reliability, few interventions have produced lasting change. Although the opportunity to ask questions during patient handoff has been required by some regulatory bodies, the function of questions during handoff has been less well explored and understood.

Concepts: Scientific method, Derivative, Continuous function, Point, Homomorphism, Morphism


Cortical processing reflects the interplay of synaptic excitation and synaptic inhibition. Rapidly accumulating evidence is highlighting the crucial role of inhibition in shaping spontaneous and sensory-evoked cortical activity and thus underscores how a better knowledge of inhibitory circuits is necessary for our understanding of cortical function. We discuss current views of how inhibition regulates the function of cortical neurons and point to a number of important open questions.

Concepts: Mathematics, Function, Action potential, Cerebral cortex, Knowledge, Continuous function, Open problem


In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter [Formula: see text]. We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness. Finally, we combine the Bojanic-Cheng decomposition method with some analysis techniques to derive an asymptotic estimate on the rate of convergence for some absolutely continuous functions.

Concepts: Mathematics, Function, Calculus, Derivative, Continuous function, Smooth function, Limit of a function, Absolute continuity