Automated Classification of Histopathology Images Using Transfer Learning

There is a strong need for automated systems to improve diagnostic quality and reduce the analysis time in histopathology image processing. Automated detection and classification of pathological tissue characteristics with computer-aided diagnostic systems are a critical step in the early diagnosis and treatment of diseases. Once a pathology image is scanned by a microscope and loaded onto a computer, it can be used for automated detection and classification of diseases. In this study, the DenseNet-161 and ResNet-50 pre-trained CNN models have been used to classify digital histopathology patches into the corresponding whole slide images via transfer learning technique. The proposed pre-trained models were tested on grayscale and color histopathology images. The DenseNet-161 pre-trained model achieved a classification accuracy of 97.89% using grayscale images and the ResNet-50 model obtained the accuracy of 98.87% for color images. The proposed pre-trained models outperform state-of-the-art methods in all performance metrics to classify digital pathology patches into 24 categories

A presentation of PGL(2,Q)

We give a conjectural presentation of the infinitely generated group PGL(2,Q) with an infinite list of relators.Comment: 9 page

Supports of Weighted Equilibrium Measures and Examples

We analyze the supports of weighted equilibrium measures in $\mathbb{C}^n$. We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight $w$. These examples also give new constructions of plurisubharmonic functions in the Lelong class. We also include a list of open problems on the support of extremal measures which are related to solutions of Monge-{A}mp\`ere equations.Comment: 17 page

Smooth finite abelian uniformizations of projective spaces and Calabi-Yau Orbifolds

We give a classification of smooth complex manifolds with a finite abelian group action, such that the quotient is isomorphic to a projective space. The case where the manifold is a Calabi-Yau is studied in detail.Comment: 14 page

An Analytical Approach to Exponent-Restricted Multiple Counting Sequences

This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I also studied matrix representations and obtained generalized Binet formulas for defined sequences. As a result of multiple-counting sequence explanation, this study leads to a better understanding for distribution of composite numbers between consecutive bases

Weighted θ\theta-Incomplete Pluripotential Theory

Weighted pluripotential theory is a rapidly developing area; and Callaghan \cite{Callaghan} recently introduced $\theta$-incomplete polynomials in \cd for $d>1$. In this paper we combine these two theories by defining weighted $\theta$-incomplete pluripotential theory. We define weighted $\theta$-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of $\theta$-incomplete polynomials. Finally we prove that the extremal functions can be recovered using orthonormal polynomials and we demonstrate a result on strong asymptotics of Bergman functions in the spirit of \cite{BermanCn}.Comment: 27 Pages, A new theorem added, Some corrections mad

On Branched Galois Coverings (B1)n→Pn(B_1)^n\to {\mathbb P}^n

For any $n>1$, we construct examples branched Galois coverings from $M$ to the nth projective space ${\mathbb P}^n$ where $M$ is one of $({\mathbb P}^1)^n$, ${\mathbb C}^n$ or $(B_1)^n$, and $B_1$ is the 1-ball. In terms of orbifolds, this amounts to giving examples of orbifolds over ${\mathbb P}^n$ uniformized by $M$.We also discuss the related "orbifold braid groups".Comment: 13 pages, no figure

Covering relations between ball-quotient orbifolds

Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding lattices are all arithmetic and commensurable. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which the projective plane is uniformized by the product of two 1-balls.Comment: 18 pages, 13 figure

Hypergeometric Galois Actions

We outline a project to study the Galois action on a class of modular graphs (special type of dessins) which arise as the dual graphs of the sphere triangulations of non-negative curvature, classified by Thurston. Because of their connections to hypergeometric functions, there is a hope that these graphs will render themselves to explicit calculation for a study of Galois action on them, unlike the case of a general dessin.Comment: 37 pages,12 figure

Spatiotemporal Assessment of So2, SO4 and AOD from over MENA Domain from 2006 to 2016 Using multiple satellite Data and Reanalysis MERRA2 Data

The sulfur pollutants are the source of a sizeable portion of the air pollution. In this work, the spatial distribution and temporal trend of the mass concentration of two of the critical sulfur pollutants, SO2 and SO4, in addition to the aerosol optical properties (AOD) were analyzed over the region of the Middle East and North Africa (MENA) from multiple satellite resources and Modern Era Retrospective Analysis for Research and Applications version 2 (MERRA2) reanalysis data. The So2 and So4 data used in these analyses are obtained from (MERRA2) with a resolution of 0.5 x 0.625 deg throughout a period of 10 years (2005 to 2015). On the other hand, the temporal trend and spatial distribution of AOD was identified from four different satellite data. (1) moderate resolution imaging spectroradiometer (MODIS) Level 3 AOD data at 550 nm wavelengths from Collection 6 algorithm (combined dark target and deep blue algorithms) are used for 10 years temporal analysis (2006 to 2015). Data were obtained for the period 2006 to 2015 (2) Multi angle imaging spectroradiometer (MISR) with 0.5 deg spatial resolution for the same 10 years (2006 to 2015). (3) Sea Viewing Wide Field of View Sensor (SeaWIFS) with 0.5 deg for the period (2005 to 2010). (4) Ozone Monitoring Instrument (OMI) AOD at 500 nm wavelength with resolution 1 degree.Comment: 28 Page , 10 Figures , 7 Table