Random Trees

Random Trees
Author: Michael Drmota
Publisher: Springer Science & Business Media
Total Pages: 466
Release: 2009-04-16
Genre: Mathematics
ISBN: 3211753575

The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.

Random Trees

Random Trees
Author: Michael Drmota
Publisher: Springer
Total Pages: 458
Release: 2009-08-29
Genre: Mathematics
ISBN: 9783211101780

The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.

Random Generation of Trees

Random Generation of Trees
Author: Laurent Alonso
Publisher: Springer Science & Business Media
Total Pages: 222
Release: 1994-12-31
Genre: Computers
ISBN: 9780792395287

Random Generation of Trees is about a field on the crossroads between computer science, combinatorics and probability theory. Computer scientists need random generators for performance analysis, simulation, image synthesis, etc. In this context random generation of trees is of particular interest. The algorithms presented here are efficient and easy to code. Some aspects of Horton--Strahler numbers, programs written in C and pictures are presented in the appendices. The complexity analysis is done rigorously both in the worst and average cases. Random Generation of Trees is intended for students in computer science and applied mathematics as well as researchers interested in random generation.

Probability on Trees and Networks

Probability on Trees and Networks
Author: Russell Lyons
Publisher: Cambridge University Press
Total Pages: 1023
Release: 2017-01-20
Genre: Mathematics
ISBN: 1316785335

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Trees of North America and Europe

Trees of North America and Europe
Author: Roger Phillips
Publisher: New York : Random House
Total Pages: 224
Release: 1978
Genre: Gardening
ISBN: 0394735412

This splendid guide to tree identification contains more than 1,000 full-color photographs. Each tree is illustrated in full detail -- by leaf, flower, fruit, bark, and mature tree shape -- and is fully described in the text. A unique leaf index makes the identification of trees simple and accurate. The trees are arranged alphabetically by Latin name and an index of common names concludes the book. An indispensable companion for both the enthusiast and the botanist.

Computational Genomics with R

Computational Genomics with R
Author: Altuna Akalin
Publisher: CRC Press
Total Pages: 463
Release: 2020-12-16
Genre: Mathematics
ISBN: 1498781861

Computational Genomics with R provides a starting point for beginners in genomic data analysis and also guides more advanced practitioners to sophisticated data analysis techniques in genomics. The book covers topics from R programming, to machine learning and statistics, to the latest genomic data analysis techniques. The text provides accessible information and explanations, always with the genomics context in the background. This also contains practical and well-documented examples in R so readers can analyze their data by simply reusing the code presented. As the field of computational genomics is interdisciplinary, it requires different starting points for people with different backgrounds. For example, a biologist might skip sections on basic genome biology and start with R programming, whereas a computer scientist might want to start with genome biology. After reading: You will have the basics of R and be able to dive right into specialized uses of R for computational genomics such as using Bioconductor packages. You will be familiar with statistics, supervised and unsupervised learning techniques that are important in data modeling, and exploratory analysis of high-dimensional data. You will understand genomic intervals and operations on them that are used for tasks such as aligned read counting and genomic feature annotation. You will know the basics of processing and quality checking high-throughput sequencing data. You will be able to do sequence analysis, such as calculating GC content for parts of a genome or finding transcription factor binding sites. You will know about visualization techniques used in genomics, such as heatmaps, meta-gene plots, and genomic track visualization. You will be familiar with analysis of different high-throughput sequencing data sets, such as RNA-seq, ChIP-seq, and BS-seq. You will know basic techniques for integrating and interpreting multi-omics datasets. Altuna Akalin is a group leader and head of the Bioinformatics and Omics Data Science Platform at the Berlin Institute of Medical Systems Biology, Max Delbrück Center, Berlin. He has been developing computational methods for analyzing and integrating large-scale genomics data sets since 2002. He has published an extensive body of work in this area. The framework for this book grew out of the yearly computational genomics courses he has been organizing and teaching since 2015.

Random Forests with R

Random Forests with R
Author: Robin Genuer
Publisher: Springer Nature
Total Pages: 107
Release: 2020-09-10
Genre: Mathematics
ISBN: 3030564851

This book offers an application-oriented guide to random forests: a statistical learning method extensively used in many fields of application, thanks to its excellent predictive performance, but also to its flexibility, which places few restrictions on the nature of the data used. Indeed, random forests can be adapted to both supervised classification problems and regression problems. In addition, they allow us to consider qualitative and quantitative explanatory variables together, without pre-processing. Moreover, they can be used to process standard data for which the number of observations is higher than the number of variables, while also performing very well in the high dimensional case, where the number of variables is quite large in comparison to the number of observations. Consequently, they are now among the preferred methods in the toolbox of statisticians and data scientists. The book is primarily intended for students in academic fields such as statistical education, but also for practitioners in statistics and machine learning. A scientific undergraduate degree is quite sufficient to take full advantage of the concepts, methods, and tools discussed. In terms of computer science skills, little background knowledge is required, though an introduction to the R language is recommended. Random forests are part of the family of tree-based methods; accordingly, after an introductory chapter, Chapter 2 presents CART trees. The next three chapters are devoted to random forests. They focus on their presentation (Chapter 3), on the variable importance tool (Chapter 4), and on the variable selection problem (Chapter 5), respectively. After discussing the concepts and methods, we illustrate their implementation on a running example. Then, various complements are provided before examining additional examples. Throughout the book, each result is given together with the code (in R) that can be used to reproduce it. Thus, the book offers readers essential information and concepts, together with examples and the software tools needed to analyse data using random forests.

Decision Trees and Random Forests

Decision Trees and Random Forests
Author: Mark Koning
Publisher: Independently Published
Total Pages: 168
Release: 2017-10-04
Genre: Computers
ISBN: 9781549893759

If you want to learn how decision trees and random forests work, plus create your own, this visual book is for you. The fact is, decision tree and random forest algorithms are powerful and likely touch your life everyday. From online search to product development and credit scoring, both types of algorithms are at work behind the scenes in many modern applications and services. They are also used in countless industries such as medicine, manufacturing and finance to help companies make better decisions and reduce risk. Whether coded or scratched out by hand, both algorithms are powerful tools that can make a significant impact. This book is a visual introduction for beginners that unpacks the fundamentals of decision trees and random forests. If you want to dig into the basics with a visual twist plus create your own algorithms in Python, this book is for you.

Probability and Real Trees

Probability and Real Trees
Author: Steven N. Evans
Publisher: Springer
Total Pages: 205
Release: 2007-09-26
Genre: Mathematics
ISBN: 3540747982

Random trees and tree-valued stochastic processes are of particular importance in many fields. Using the framework of abstract "tree-like" metric spaces and ideas from metric geometry, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behavior of such objects when the number of vertices goes to infinity. This publication surveys the relevant mathematical background and present some selected applications of the theory.