Luis Salinas

ON BRANNAN'S COEFFICIENT CONJECTURE AND APPLICATIONS

D. Brannans conjecture says that for 0 x |=1, and n ∈ N one has | A 2 n −1 (α,β, x )|≤| A 2 n −1 (α,β,1)|, where We prove this for the case α=β, and also prove a differentiated version of the Brannan conjecture. This has applications to estimates for Gegenbauer polynomials and also to coefficient estimates for univalent functions in the unit disk that are ‘starlike with respect to a boundary point’. The latter application has previously been conjectured by H. Silverman and E. Silvia. The proofs make use of various properties of the Gauss hypergeometric function.

Subordination by cesàro means

We discuss the question of to which extent the Cesaro means of fixed order α≥0 and a given f univalent in the unit disk form an univalent subordination chain for n = 1.2,…. Our results vastly extend previous ones of Robertson, Bustoz, and others, and imply an affirmative partial solution of a recent conjecture stated in [10].

On the preservation of periodic monotonicity

AbstractA 2π-periodic continuous real functionf is said to beperiodically monotone if it has the following property: there exist numbert1≤t2≤t3≔t1+2π such thatf is nonincreasing fort1≤t2 and nondecreasing int2≤t≤t3. For any 2π-periodic, integrable real functiong with ∫02π|g(t|dt<∞) we define

Online Ridge Regression Method Using Sliding Windows

(f * g)(x): = \frac{1}{{2\pi }}\int_0^{2\pi } {f(t)} g(x - t)dt

Large Scale Simulations of a Neural Network Model for the Graph Bisection Problem on Geometrically Connected Graphs

g is said to beperiodic monotonicity preserving (g∈PMP) iff*g is periodically monotone wheneverf is periodically monotone. This class of functions was introduced by I. J. Schoenberg in 1959. In the present paper we give an explicit description of the members inPMP. It turns out that an old necessary condition due to Loewner is (essentially) also sufficient. Our result extends to noncontinuous periodically monotone functions, solves Schoenbergs problem about the preservation of convex curves, and even improves on the present knowledge concerning properties of cyclic variation diminishing transforms.

Segmentation of HER2 protein overexpression in immunohistochemically stained breast cancer images using Support Vector Machines

HIGHLIGHTSWe propose an automatic segmentation algorithm for histological images.The algorithm uses persistent homology in a computational topology framework.We evaluated 856 images and compared with automated output validated by experts.The approach successfully detected cell nuclei; overall per‐object accuracy: 84.6%.Fully automated detection provides tangible benefits for clinical decision‐making. ABSTRACT The segmentation of cell nuclei is an important step towards the automated analysis of histological images. The presence of a large number of nuclei in whole‐slide images necessitates methods that are computationally tractable in addition to being effective. In this work, a method is developed for the robust segmentation of cell nuclei in histological images based on the principles of persistent homology. More specifically, an abstract simplicial homology approach for image segmentation is established. Essentially, the approach deals with the persistence of disconnected sets in the image, thus identifying salient regions that express patterns of persistence. By introducing an image representation based on topological features, the task of segmentation is less dependent on variations of color or texture. This results in a novel approach that generalizes well and provides stable performance. The method conceptualizes regions of interest (cell nuclei) pertinent to their topological features in a successful manner. The time cost of the proposed approach is lower‐bounded by an almost linear behavior and upper‐bounded by Symbol in a worst‐case scenario. Time complexity matches a quasilinear behavior which is Symbol for &egr; < 1. Images acquired from histological sections of liver tissue are used as a case study to demonstrate the effectiveness of the approach. The histological landscape consists of hepatocytes and non‐parenchymal cells. The accuracy of the proposed methodology is verified against an automated workflow created by the output of a conventional filter bank (validated by experts) and the supervised training of a random forest classifier. The results are obtained on a per‐object basis. The proposed workflow successfully detected both hepatocyte and non‐parenchymal cell nuclei with an accuracy of 84.6%, and hepatocyte cell nuclei only with an accuracy of 86.2%. A public histological dataset with supplied ground‐truth data is also used for evaluating the performance of the proposed approach (accuracy: 94.5%). Further validations are carried out with a publicly available dataset and ground‐truth data from the Gland Segmentation in Colon Histology Images Challenge (GlaS) contest. The proposed method is useful for obtaining unsupervised robust initial segmentations that can be further integrated in image/data processing and management pipelines. The development of a fully automated system supporting a human expert provides tangible benefits in the context of clinical decision‐making. Symbol. No caption available. Symbol. No caption available.

Interpreting Neural Networks in the Frame of the Logic of Lukasiewicz

A new regression method based on the aggregating algorithm for regression (AAR) is presented. The proposal shows how ridge regression can be modified in order to reduce the number of operations by avoiding the inverse matrix calculation only considering a sliding window of the last input values. This modification allows algorithm expression in a recursive way and therefore its use in an online context. Ridge regression, AAR and our proposal were compared using the closing stock prices of 45 stocks from the technology market from 2000 to 2012. Empirical results show that our proposal performs better than the other two methods in 28 of 45 stocks analyzed, due to the lower MSE error.

Design of a system for image registration and compensation based on spectral analysis

For functions f whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of w(y) := |f( + iy)| for y > 0 ( � 1 fixed).