Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations

We present an approach to the bright soliton solution of the NLS equation from the standpoint of introducing a constant potential term in the equation. We discuss a `nongauge' bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sech^p solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2Comment: ~4 pages, 3 figures, 16 references, published versio

Convective solar nebula

Analyzing turbulent flows with rotation, Dubrulle and Valdettaro have concluded that some new effects come into play and may modify the standard picture we have concerning turbulence. In that respect the value of the Rossby number is of crucial importance since it will determine the transition between regimes where rotation is or is not important. With rotation there will be a tendency to constrain the motion to the plane perpendicular to the rotation axis and as a consequence the horizontal scale will increase as compared to the longitudinal one, which means that the turnover time in this direction will increase. The net effect is that the energy cascade down process is hindered by rotation. As a matter of fact, when rotation is present one observes two cascades: an enstrophy (vorticity) cascade from large scales to small scales; and an inverse energy cascade from small scales to large scales. Since the first process is not efficient on transporting energy to the dissipation range, what we see is energy storage in the large structures at the expense of the small structures. This kind of behavior has been confirmed experimentally. For a very large gamma we obtain, in the inertial range, a spectrum of k(exp -3) instead of the usual Kilmogorov's k(exp -5/3) spectrum. In reality, when rotation is dominant, energy gets stored in inertial waves that propagate it essentially in the longitudinal direction. In that case, we can no longer assign just one viscosity to the fluid and, what is most important, the concept of viscosity loses its meaning since we no longer have local transport of energy. Such results, however, were derived considering a hot disk, in which opacity is mainly given by electron scattering. In the present work we have applied the formulation developed in the previous work for the description of the viscous-stage solar nebula

Morphological Estimation of Cellularity on Neo-Adjuvant Treated Breast Cancer Histological Images

This paper describes a methodology that extracts key morphological features from histological breast cancer images in order to automatically assess Tumour Cellularity (TC) in Neo-Adjuvant treatment (NAT) patients. The response to NAT gives information on therapy efficacy and it is measured by the residual cancer burden index, which is composed of two metrics: TC and the assessment of lymph nodes. The data consist of whole slide images (WSIs) of breast tissue stained with Hematoxylin and Eosin (H&E) released in the 2019 SPIE Breast Challenge. The methodology proposed is based on traditional computer vision methods (K-means, watershed segmentation, Otsu’s binarisation, and morphological operations), implementing colour separation, segmentation, and feature extraction. Correlation between morphological features and the residual TC after a NAT treatment was examined. Linear regression and statistical methods were used and twenty-two key morphological parameters from the nuclei, epithelial region, and the full image were extracted. Subsequently, an automated TC assessment that was based on Machine Learning (ML) algorithms was implemented and trained with only selected key parameters. The methodology was validated with the score assigned by two pathologists through the intra-class correlation coefficient (ICC). The selection of key morphological parameters improved the results reported over other ML methodologies and it was very close to deep learning methodologies. These results are encouraging, as a traditionally-trained ML algorithm can be useful when limited training data are available preventing the use of deep learning approaches

Nongauge Bright Soliton of the Nonlinear Schrodinger (NLS) Equation and a Family of Generalized NLS Equations

We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sechpsechp solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg–de Vries (KdV) and Benjamin–Bona–Mahony (BBM) equations when p=2

Morphological estimation of Cellularity on Neo-adjuvant treated breast cancer histological images

This paper describes a methodology that extracts morphological features from histological breast cancer images stained for Hematoxilyn and Eosin (H&E). Cellularity was estimated and the correlation between features and the residual tumour size cellularity after a Neo-Adjuvant treatment (NAT) was examined. Images from whole slide imaging (WSI) were processed automatically with traditional computer vision methods to extract twenty two morphological parameters from the nuclei, epithelial region and the global image. The methodology was applied to a set of images from breast cancer under NAT. The data came from the BreastPathQ Cancer Cellularity Challenge 2019, and consisted of 2579 patches of 255×255 pixels of H&E histopatological samples from NAT treatment patients. The methodology automatically implements colour separation, segmentation and morphological analysis using traditional algorithms (K-means grouping, watershed segmentation, Otsu’s binarisation). Linear regression methods were applied to determine strongest correlation between the parameters and the cancer cellularity. The morphological parameters showed correlation with the residual tumour cancer cellularity. The strongest correlations corresponded to the stroma concentration value (r = −0.9786) and value from HSV image colour space (r = −0.9728), both from a global image parameters

Estimation of cellularity in tumours treated with Neoadjuvant therapy: A comparison of Machine Learning algorithms

This paper describes a method for residual tumour cellularity (TC) estimation in Neoadjuvant treatment (NAT) of advanced breast cancer. This is determined manually by visual inspection by a radiologist, then an automated computation will contribute to reduce time workload and increase precision and accuracy. TC is estimated as the ratio of tumour area by total image area estimated after the NAT. The method proposed computes TC by using machine learning techniques trained with information on morphological parameters of segmented nuclei in order to classify regions of the image as tumour or normal. The data is provided by the 2019 SPIE Breast challenge, which was proposed to develop automated TC computation algorithms. Three algorithms were implemented: Support Vector Machines, Nearest K-means and Adaptive Boosting (AdaBoost) decision trees. Performance based on accuracy is compared and evaluated and the best result was obtained with Support Vector Machines. Results obtained by the methods implemented were submitted during ongoing challenge with a maximum of 0.76 of prediction probability of success

The magnetorotational instability across the dead zone of protoplanetary disks

We examine the linear stability of a flow threaded by a weak, vertical magnetic field in a disk with a keplerian rotation profile and a vertical stratification of the ionization degree as that predicted for vast portions of protoplanetary disks. A quasi-global analysis is carried out, where the form of the perturbations in the vertical direction is determined. Considering the ohmic magnetic diffusivity of the gas, the conditions leading to the magnetorotational instability are analyzed as a function of the diffusivity at the disk surfaces, its vertical profile and the strength of the unperturbed magnetic field. For typical conditions believed to prevail in protoplanetary disks at radial distances between 0.1 and 10 AU, where the so-called dead zone is proposed to exist, we find that generally the instability is damped. This implies that, if the MRI is considered the only possible source of turbulence in protoplanetary disks, no viscous angular momentum transport occursat those radii.Comment: 33 pages, 8 figure

Multi-filter transit observations of WASP-39b and WASP-43b with three San Pedro M\'artir telescopes

Three optical telescopes located at the San Pedro M\'artir National Observatory were used for the first time to obtain multi-filter defocused photometry of the transiting extrasolar planets WASP-39b and WASP-43b. We observed WASP-39b with the 2.12m telescope in the U filter for the first time, and additional observations were carried out in the R and I filters using the 0.84m telescope. WASP-43b was observed in VRI with the same instrument, and in the i filter with the robotic 1.50m telescope. We reduced the data using different pipelines and performed aperture photometry with the help of custom routines, in order to obtain the light curves. The fit of the light curves (1.5--2.5mmag rms), and of the period analysis, allowed a revision of the orbital and physical parameters, revealing for WASP-39b a period ($4.0552947 \pm 9.65 \times 10^{-7}$ days) which is $3.084 \pm 0.774$ seconds larger than previously reported. Moreover, we find for WASP-43b a planet/star radius ($0.1738 \pm 0.0033$) which is $0.01637 \pm 0.00371$ larger in the i filter with respect to previous works, and that should be confirmed with additional observations. Finally, we confirm no evidence of constant period variations in WASP-43b.Comment: 13 pages, 7 figures, accepted in PASP, scheduled for the February 1, 2015 issu

Synchrotron radiation photoionization mass spectrometry of laser ablated species

The present paper describes an experimental apparatus suitable to create and study free clusters by combining laser ablation and synchrotron radiation. First tests on sulfur samples, S, showed the production, through laser ablation, of neutral Sn clusters (n = 1–8). These clusters were ionized using synchrotron radiation at photon energies from 160 eV to 175 eV, across the S 2p core edge. The feasibility of such combined ablation–synchrotron radiation experiments is demonstrated, opening new possibilities on the investigation of free clusters and radical