Fixed point theorems for the sum of three classes of mixed monotone operators and applications

In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators, namely A(x,x)+B(x,x)+C(x,x)=x on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any t∈(0,1), there exists φ(t)∈(t,1] such that for all x,y∈P, A(tx,t−1y)≥φ(t)A(x,y); B is hypo-homogeneous, i.e. B satisfies that for any t∈(0,1), x,y∈P, B(tx,t−1y)≥tB(x,y); C is concave-convex, i.e. C satisfies that for fixed y, C(⋅,y):P→P is concave; for fixed x, C(x,⋅): P→P is convex. Also we study the solution of the nonlinear eigenvalue equation A(x,x)+B(x,x)+C(x,x)=λx and discuss its dependency to the parameter. Our work extends many existing results in the field of study. As an application, we utilize the results obtained in this paper for the operator equation to study the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions

Partial Volume Segmentation of Brain MRI Scans of any Resolution and Contrast

Partial voluming (PV) is arguably the last crucial unsolved problem in Bayesian segmentation of brain MRI with probabilistic atlases. PV occurs when voxels contain multiple tissue classes, giving rise to image intensities that may not be representative of any one of the underlying classes. PV is particularly problematic for segmentation when there is a large resolution gap between the atlas and the test scan, e.g., when segmenting clinical scans with thick slices, or when using a high-resolution atlas. In this work, we present PV-SynthSeg, a convolutional neural network (CNN) that tackles this problem by directly learning a mapping between (possibly multi-modal) low resolution (LR) scans and underlying high resolution (HR) segmentations. PV-SynthSeg simulates LR images from HR label maps with a generative model of PV, and can be trained to segment scans of any desired target contrast and resolution, even for previously unseen modalities where neither images nor segmentations are available at training. PV-SynthSeg does not require any preprocessing, and runs in seconds. We demonstrate the accuracy and flexibility of the method with extensive experiments on three datasets and 2,680 scans. The code is available at https://github.com/BBillot/SynthSeg.Comment: accepted for MICCAI 202

On single and double soft behaviors in NLSM

In this paper, we study the single and double soft behaviors of tree level off-shell currents and on-shell amplitudes in nonlinear sigma model(NLSM). We first propose and prove the leading soft behavior of the tree level currents with a single soft particle. In the on-shell limit, this single soft emission becomes the Adler's zero. Then we establish the leading and sub-leading soft behaviors of tree level currents with two adjacent soft particles. With a careful analysis of the on-shell limit, we obtain the double soft behaviors of on-shell amplitudes where the two soft particles are adjacent to each other. By applying Kleiss-Kuijf (KK) relation, we further obtain the leading and sub-leading behaviors of amplitudes with two nonadjacent soft particles.Comment: 41 pages, 6 tables, 9 figures, minor revised, more content about nonadjacent double soft limit, update the reference

PEDRo: A database for storing, searching and disseminating experimental proteomics data

Abstract Background Proteomics is rapidly evolving into a high-throughput technology, in which substantial and systematic studies are conducted on samples from a wide range of physiological, developmental, or pathological conditions. Reference maps from 2D gels are widely circulated. However, there is, as yet, no formally accepted standard representation to support the sharing of proteomics data, and little systematic dissemination of comprehensive proteomic data sets. Results This paper describes the design, implementation and use of a Proteome Experimental Data Repository (PEDRo), which makes comprehensive proteomics data sets available for browsing, searching and downloading. It is also serves to extend the debate on the level of detail at which proteomics data should be captured, the sorts of facilities that should be provided by proteome data management systems, and the techniques by which such facilities can be made available. Conclusions The PEDRo database provides access to a collection of comprehensive descriptions of experimental data sets in proteomics. Not only are these data sets interesting in and of themselves, they also provide a useful early validation of the PEDRo data model, which has served as a starting point for the ongoing standardisation activity through the Proteome Standards Initiative of the Human Proteome Organisation

Performance of the Quasar Spectral Templates for the Dark Energy Spectroscopic Instrument

Millions of quasar spectra will be collected by the Dark Energy Spectroscopic Instrument (DESI), leading to a fourfold increase in the number of known quasars. High-accuracy quasar classification is essential to tighten constraints on cosmological parameters measured at the highest redshifts DESI observes (z > 2.0). We present spectral templates for identification and redshift estimation of quasars in the DESI Year 1 data release. The quasar templates are comprised of two quasar eigenspectra sets, trained on spectra from the Sloan Digital Sky Survey. The sets are specialized to reconstruct quasar spectral variation observed over separate yet overlapping redshift ranges and, together, are capable of identifying DESI quasars from 0.05 < z < 7.0. The new quasar templates show significant improvement over the previous DESI quasar templates regarding catastrophic failure rates, redshift precision and accuracy, quasar completeness, and the contamination fraction in the final quasar sample