Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

CA : A Cancer Journal for Clinicians

http://www.numdam.org/item/PMIHES_1981__53__53_0.pdf

Groups of polynomial growth and expanding maps

Visual inspection of histopathology slides is one of the main methods used by pathologists to assess the stage, type and subtype of lung tumors. Adenocarcinoma (LUAD) and squamous cell carcinoma (LUSC) are the most prevalent subtypes of lung cancer, and their distinction requires visual inspection by an experienced pathologist. In this study, we trained a deep convolutional neural network (inception v3) on whole-slide images obtained from The Cancer Genome Atlas to accurately and automatically classify them into LUAD, LUSC or normal lung tissue. The performance of our method is comparable to that of pathologists, with an average area under the curve (AUC) of 0.97. Our model was validated on independent datasets of frozen tissues, formalin-fixed paraffin-embedded tissues and biopsies. Furthermore, we trained the network to predict the ten most commonly mutated genes in LUAD. We found that six of them—STK11, EGFR, FAT1, SETBP1, KRAS and TP53—can be predicted from pathology images, with AUCs from 0.733 to 0.856 as measured on a held-out population. These findings suggest that deep-learning models can assist pathologists in the detection of cancer subtype or gene mutations. Our approach can be applied to any cancer type, and the code is available at https://github.com/ncoudray/DeepPATH
 .

/pdf/classification-and-mutation-prediction-from-non-small-cell-9iqvajuj7y.pdf

Classification and mutation prediction from non-small cell lung cancer histopathology images using deep learning.

The theory of 3-manifolds has been revolutionised in the last few years by work of Thurston [66-70]. He has shown that geometry has an important role to play in the theory in addition to the use of purely topological methods. The basic aim of this article is to discuss the various geometries which arise and explain their significance for the theory of 3-manifolds. The idea is that many 3-manifolds admit 'nice' metrics which give one new insight into properties of the manifolds. For the purposes of this article, the nicest metrics are those of constant curvature. An observer in a manifold with a constant curvature metric will see the same picture wherever he stands and in whichever direction he looks. Such manifolds have special topological properties. However, we will also need to consider nice metrics which are not of constant curvature. In this article, I will explain what is meant by a 'nice' metric and describe their classification in dimension three which is due to Thurston. Then I will discuss some of the 3-manifolds which admit these nice metrics and the relationship between their geometric and topological properties. In this introduction all manifolds and metrics will be assumed to be smooth so that the objects of interest are all Riemannian manifolds. It has been known since the nineteenth century that in dimension two there is a very close relationship between geometry and topology. I will start by describing some basic facts about closed surfaces. I will discuss these in more detail in §1. Each

/pdf/the-geometries-of-3-manifolds-nexnn41bw1.pdf

The geometries of 3-manifolds

From the Publisher:
This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to mathematicians and computer scientists and includes open problems that will dominate the research for years to come.

Word processing in groups

/pdf/curves-on-2-manifolds-and-isotopies-4hp702pues.pdf

Curves on 2-manifolds and isotopies

On introduit une methode pour diviser une variete hyperbolique non compacte de volume fini en morceaux euclidiens canoniques

/pdf/euclidean-decompositions-of-noncompact-hyperbolic-manifolds-n6nfylit58.pdf

Euclidean decompositions of noncompact hyperbolic manifolds

Definition. A (topological) n-manifold M is a Hausdorff topological space with a countable basis of open sets, such that each point of M lies in an open set homeomorphic to R or R+ = {(x1, . . . , xn) ∈ R n : xn ≥ 0}. The boundary ∂M of M is the set of points not having neighbourhoods homeomorphic to R. The set M − ∂M is the interior of M , denoted int(M). If M is compact and ∂M = ∅, then M is closed.

Three-dimensional manifolds

A device disposed between a carburetor and the intake manifold of an internal combustion engine has a passage aligned with the carburetor and intake manifold opening into which secondary-air is admitted radially from a valve system connected to the accelerator pedals of the vehicle.

David B. A. Epstein

Papers

Word processing in groups

Curves on 2-manifolds and isotopies

Euclidean decompositions of noncompact hyperbolic manifolds

Three-dimensional manifolds

The simplicity of certain groups of homeomorphisms