- Table View
- List View
Analysis in Euclidean Space (Dover Books on Mathematics)
by Kenneth HoffmanDeveloped for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.
Analysis kompakt fur Dummies (Für Dummies)
by Mark RyanAn der Analysis kommen Sie nicht vorbei: Sei es nun in der Schule oder wenn Sie Natur-, Ingenieurs-, oder Wirtschaftswissenschaften studieren. Dieses Buch hilft Ihnen, wenn Sie sich einen schnellen Überblick über das Thema verschaffen wollen. Mark Ryan erklärt Ihnen leicht verständlich, was Sie über Grenzwerte und Funktionen unbedingt wissen sollten. So ist dies Ihr perfekter Nachhilfelehrer für die Tasche: freundlich, kompetent, günstig.
Analysis, Modelling, Optimization, and Numerical Techniques: ICAMI, San Andres Island, Colombia, November 2013 (Springer Proceedings in Mathematics & Statistics #121)
by Gerard Olivar Tost Olga VasilievaThis book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applicabilitions to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.
Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Candace M. Kent David M. ChanIn the 1960s and 1970s, mathematical biologists Sir Robert M. May, E.C. Pielou, and others utilized difference equations as models of ecological and epidemiological phenomena. Since then, with or without applications, the mathematics of difference equations has evolved into a field unto itself. Difference equations with the maximum (or the minimum or the "rank-type") function were rigorously investigated from the mid-1990s into the 2000s, without any applications in mind. These equations often involved arguments varying from reciprocal terms with parameters in the numerators to other special functions. Recently, the authors of Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy and their colleagues investigated the first known application of a "max-type" difference equation. Their equation is a phenomenological model of epileptic seizures. In this book, the authors expand on that research and present a more comprehensive development of mathematical, numerical, and biological results. Additionally, they describe the first documented instance of a novel dynamical behavior that they call rippled almost periodic behavior, which can be described as an unpredictable pseudo-periodic behavior. Features: Suitable for researchers in mathematical neuroscience and potentially as supplementary reading for postgraduate students Thoroughly researched and replete with references
Analysis of Arithmetic for Mathematics Teaching
by Gaea LeinhardtThis volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.
Analysis of Binary Data (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #32)
by D.R. CoxThe first edition of this book (1970) set out a systematic basis for the analysis of binary data and in particular for the study of how the probability of 'success' depends on explanatory variables. The first edition has been widely used and the general level and style have been preserved in the second edition, which contains a substantial amount of new material. This amplifies matters dealt with only cryptically in the first edition and includes many more recent developments. In addition the whole material has been reorganized, in particular to put more emphasis on m.aximum likelihood methods.There are nearly 60 further results and exercises. The main points are illustrated by practical examples, many of them not in the first edition, and some general essential background material is set out in new Appendices.
Analysis of Biomarker Data
by Stephen W. Looney Joseph L. HaganA "how to" guide for applying statistical methods to biomarker data analysisPresenting a solid foundation for the statistical methods that are used to analyze biomarker data, Analysis of Biomarker Data: A Practical Guide features preferred techniques for biomarker validation. The authors provide descriptions of select elementary statistical methods that are traditionally used to analyze biomarker data with a focus on the proper application of each method, including necessary assumptions, software recommendations, and proper interpretation of computer output. In addition, the book discusses frequently encountered challenges in analyzing biomarker data and how to deal with them, methods for the quality assessment of biomarkers, and biomarker study designs. Covering a broad range of statistical methods that have been used to analyze biomarker data in published research studies, Analysis of Biomarker Data: A Practical Guide also features:A greater emphasis on the application of methods as opposed to the underlying statistical and mathematical theoryThe use of SAS®, R , and other software throughout to illustrate the presented calculations for each exampleNumerous exercises based on real-world data as well as solutions to the problems to aid in reader comprehensionThe principles of good research study design and the methods for assessing the quality of a newly proposed biomarkerA companion website that includes a software appendix with multiple types of software and complete data sets from the book's examplesAnalysis of Biomarker Data: A Practical Guide is an ideal upper-undergraduate and graduate-level textbook for courses in the biological or environmental sciences. An excellent reference for statisticians who routinely analyze and interpret biomarker data, the book is also useful for researchers who wish to perform their own analyses of biomarker data, such as toxicologists, pharmacologists, epidemiologists, environmental and clinical laboratory scientists, and other professionals in the health and environmental sciences.
Analysis of Categorical Data from Historical Perspectives: Essays in Honour of Shizuhiko Nishisato (Behaviormetrics: Quantitative Approaches to Human Behavior #17)
by Eric J. Beh Rosaria Lombardo Jose G. ClavelThis collection of essays is in honor of Shizuhiko Nishisato on his 88th birthday and consists of invited contributions only. The book contains essays on the analysis of categorical data, which includes quantification theory, cluster analysis, and other areas of multidimensional data analysis, covering more than half a century of research by the 41 interdisciplinary and international researchers who are contributors. Thus, it offers the wisdom and experience of work past and present and attracts a new generation of researchers to this field. Central to this wisdom and experience is that of Prof. Nishisato, who has spent much of the past 60 years mentoring and providing leadership in the research of quantification theory, especially that of “dual scaling”. The book includes contributions by leading researchers who have worked alongside Prof. Nishisato, published with him, been mentored by him, or whose work has been influenced by the research he has undertaken over his illustrious career. This book inspires researchers young and old as it highlights the significant contributions, past and present, that Prof. Nishisato has made in his field.
Analysis of Categorical Data with R (Chapman & Hall/CRC Texts in Statistical Science)
by Christopher R. Bilder Thomas M. LoughinAnalysis of Categorical Data with R, Second Edition presents a modern account of categorical data analysis using the R software environment. It covers recent techniques of model building and assessment for binary, multicategory, and count response variables and discusses fundamentals, such as odds ratio and probability estimation. The authors give detailed advice and guidelines on which procedures to use and why to use them.The second edition is a substantial update of the first based on the authors’ experiences of teaching from the book for nearly a decade. The book is organized as before, but with new content throughout, and there are two new substantive topics in the advanced topics chapter—group testing and splines. The computing has been completely updated, with the "emmeans" package now integrated into the book. The examples have also been updated, notably to include new examples based on COVID-19, and there are more than 90 new exercises in the book. The solutions manual and teaching videos have also been updated.Features: Requires no prior experience with R, and offers an introduction to the essential features and functions of R Includes numerous examples from medicine, psychology, sports, ecology, and many other areas Integrates extensive R code and output Graphically demonstrates many of the features and properties of various analysis methods Offers a substantial number of exercises in all chapters, enabling use as a course text or for self-study Supplemented by a website with data sets, code, and teaching videos Analysis of Categorical Data with R, Second Edition is primarily designed for a course on categorical data analysis taught at the advanced undergraduate or graduate level. Such a course could be taught in a statistics or biostatistics department, or within mathematics, psychology, social science, ecology, or another quantitative discipline. It could also be used by a self-learner and would make an ideal reference for a researcher from any discipline where categorical data arise.
Analysis of Correlated Data with SAS and R
by Mohamed M. ShoukriAnalysis of Correlated Data with SAS and R: 4th edition presents an applied treatment of recently developed statistical models and methods for the analysis of hierarchical binary, count and continuous response data. It explains how to use procedures in SAS and packages in R for exploring data, fitting appropriate models, presenting programming codes and results. The book is designed for senior undergraduate and graduate students in the health sciences, epidemiology, statistics, and biostatistics as well as clinical researchers, and consulting statisticians who can apply the methods with their own data analyses. In each chapter a brief description of the foundations of statistical theory needed to understand the methods is given, thereafter the author illustrates the applicability of the techniques by providing sufficient number of examples. The last three chapters of the 4th edition contain introductory material on propensity score analysis, meta-analysis and the treatment of missing data using SAS and R. These topics were not covered in previous editions. The main reason is that there is an increasing demand by clinical researchers to have these topics covered at a reasonably understandable level of complexity. Mohamed Shoukri is principal scientist and professor of biostatistics at The National Biotechnology Center, King Faisal Specialist Hospital and Research Center and Al-Faisal University, Saudi Arabia. Professor Shoukri’s research includes analytic epidemiology, analysis of hierarchical data, and clinical biostatistics. He is an associate editor of the 3Biotech journal, a Fellow of the Royal Statistical Society and an elected member of the International Statistical Institute.
The Analysis of Covariance and Alternatives
by Bradley E. HuitemaA complete guide to cutting-edge techniques and best practices for applying covariance analysis methods The Second Edition of Analysis of Covariance and Alternatives sheds new light on its topic, offering in-depth discussions of underlying assumptions, comprehensive interpretations of results, and comparisons of distinct approaches. The book has been extensively revised and updated to feature an in-depth review of prerequisites and the latest developments in the field. The author begins with a discussion of essential topics relating to experimental design and analysis, including analysis of variance, multiple regression, effect size measures and newly developed methods of communicating statistical results. Subsequent chapters feature newly added methods for the analysis of experiments with ordered treatments, including two parametric and nonparametric monotone analyses as well as approaches based on the robust general linear model and reversed ordinal logistic regression. Four groundbreaking chapters on single-case designs introduce powerful new analyses for simple and complex single-case experiments. This Second Edition also features coverage of advanced methods including: Simple and multiple analysis of covariance using both the Fisher approach and the general linear model approach Methods to manage assumption departures, including heterogeneous slopes, nonlinear functions, dichotomous dependent variables, and covariates affected by treatments Power analysis and the application of covariance analysis to randomized-block designs, two-factor designs, pre- and post-test designs, and multiple dependent variable designs Measurement error correction and propensity score methods developed for quasi-experiments, observational studies, and uncontrolled clinical trials Thoroughly updated to reflect the growing nature of the field, Analysis of Covariance and Alternatives is a suitable book for behavioral and medical scineces courses on design of experiments and regression and the upper-undergraduate and graduate levels. It also serves as an authoritative reference work for researchers and academics in the fields of medicine, clinical trials, epidemiology, public health, sociology, and engineering.
Analysis of Data from Randomized Controlled Trials: A Practical Guide
by Jos W.R. TwiskThis book provides a practical guide to the analysis of data from randomized controlled trials (RCT). It gives an answer to the question of how to estimate the intervention effect in an appropriate way. This problem is examined for different RCT designs, such as RCTs with one follow-up measurement, RCTs with more than one follow-up measurement, cluster RCTs, cross-over trials, stepped wedge trials, and N-of-1 trials. The statistical methods are explained in a non-mathematical way and are illustrated by extensive examples. All datasets used in the book are available for download, so readers can reanalyse the examples to gain a better understanding of the methods used. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other fields.
Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays (SpringerBriefs in Electrical and Computer Engineering)
by Mehmet Eren Ahsen Hitay Özbay Silviu-Iulian NiculescuThis brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.
Analysis of Distributional Data
by Paula BritoIn a time when increasingly larger and complex data collections are being produced, it is clear that new and adaptive forms of data representation and analysis have to be conceived and implemented. Distributional data, i.e., data where a distribution rather than a single value is recorded for each descriptor, on each unit, come into this framework. Distributional data may result from the aggregation of large amounts of open/collected/generated data, or it may be directly available in a structured or unstructured form, describing the variability of some features. This book provides models and methods for the representation, analysis, interpretation, and organization of distributional data, taking into account its specific nature, and not relying on a reduction to single values, to be conform to classical paradigms.Conceived as an edited book, gathering contributions from multiple authors, the book presents alternative representations and analysis’ methods for distributional data of different types, and in particular,-Uni- and bi-variate descriptive statistics for distributional data-Clustering and classification methodologies-Methods for the representation in low-dimensional spaces-Regression models and forecasting approaches for distribution-valued variables Furthermore, the different chapters -Feature applications to show how the proposed methods work in practice, and how results are to be interpreted, -Often provide information about available software. The methodologies presented in this book constitute cutting-edge developments for stakeholders from all domains who produce and analyse large amounts of complex data, to be analysed in the form of distributions. The book is hence of interest for companies operating not only in the area of data analytics, but also on logistics, energy and finance. It also concerns national statistical institutes and other institutions at European and international level, where microdata is aggregated to preserve confidentiality and allow for analysis at the appropriate regional level. Academics will find in the analysis of distributional data a challenging up-to-date field of research.
Analysis of Doubly Truncated Data: An Introduction (SpringerBriefs in Statistics)
by Achim Dörre Takeshi EmuraThis book introduces readers to statistical methodologies used to analyze doubly truncated data. The first book exclusively dedicated to the topic, it provides likelihood-based methods, Bayesian methods, non-parametric methods, and linear regression methods. These procedures can be used to effectively analyze continuous data, especially survival data arising in biostatistics and economics. Because truncation is a phenomenon that is often encountered in non-experimental studies, the methods presented here can be applied to many branches of science. The book provides R codes for most of the statistical methods, to help readers analyze their data. Given its scope, the book is ideally suited as a textbook for students of statistics, mathematics, econometrics, and other fields.
Analysis of Electrical Circuits with Variable Load Regime Parameters: Projective Geometry Method (Power Systems)
by A. PeninThis book introduces electric circuits with variable loads and voltage regulators. It allows to define invariant relationships for various parameters of regime and circuit sections and to prove the concepts characterizing these circuits. Generalized equivalent circuits are introduced. Projective geometry is used for the interpretation of changes of operating regime parameters. Expressions of normalized regime parameters and their changes are presented. Convenient formulas for the calculation of currents are given. Parallel voltage sources and the cascade connection of multi-port networks are described. The two-value voltage regulation characteristics of loads with limited power of voltage source is considered. The book presents the fundamentals of electric circuits and develops circuit theorems. It is useful to engineers, researchers and graduate students who are interested in the basic electric circuit theory and the regulation and monitoring of power supply systems.
Analysis of Epidemiologic Data Using R (Synthesis Lectures on Mathematics & Statistics)
by Robert HirschThis book addresses the description and analysis of occurrence data frequently encountered in epidemiological studies. With the occurrence of Covid-19, people have been exposed to the analysis and interpretation of epidemiological data. To be informed consumers of this information, people need to understand the nature and analysis of these data. Effort is made to emphasize concepts rather than mathematics. Subjects range from description of the frequencies of disease to the analysis of associations between the occurrence of disease and exposure. Those analyses begin with simple associations and work up to complex relationships that involve the control of extraneous characteristics. Analyses rely on the statistical software R, which is freeware in wide use by professional epidemiologists and other scientists.
Analysis of Failure and Survival Data (Chapman & Hall/CRC Texts in Statistical Science)
by Peter J. Smith<p>Analysis of Failure and Survival Data is an essential textbook for graduate-level students of survival analysis and reliability and a valuable reference for practitioners. It focuses on the many techniques that appear in popular software packages, including plotting product-limit survival curves, hazard plots, and probability plots in the context of censored data. <p>The author integrates S-Plus and Minitab output throughout the text, along with a variety of real data sets so readers can see how the theory and methods are applied. He also incorporates exercises in each chapter that provide valuable problem-solving experience. In addition to all of this, the book also brings to light the most recent linear regression techniques. Most importantly, it includes a definitive account of the Buckley-James method for censored linear regression, found to be the best performing method when a Cox proportional hazards method is not appropriate. <p>Applying the theories of survival analysis and reliability requires more background and experience than students typically receive at the undergraduate level. Mastering the contents of this book will help prepare students to begin performing research in survival analysis and reliability and provide seasoned practitioners with a deeper understanding of the field.</p>
Analysis of Financial Time Series
by Ruey S. TsayThis book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described. The author begins with basic characteristics of financial time series data before covering three main topics: Analysis and application of univariate financial time series The return series of multiple assets Bayesian inference in finance methods Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.
Analysis of Finite Difference Schemes: For Linear Partial Differential Equations with Generalized Solutions (Springer Series in Computational Mathematics #46)
by Endre Süli Boško S. JovanovićThis book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary - and initial - value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Analysis of Genetic Association Studies (Statistics for Biology and Health)
by Gang Zheng Xiaofeng Zhu Yaning Yang Robert C. ElstonAnalysis of Genetic Association Studies is both a graduate level textbook in statistical genetics and genetic epidemiology, and a reference book for the analysis of genetic association studies. Students, researchers, and professionals will find the topics introduced in Analysis of Genetic Association Studies particularly relevant. The book is applicable to the study of statistics, biostatistics, genetics and genetic epidemiology. In addition to providing derivations, the book uses real examples and simulations to illustrate step-by-step applications. Introductory chapters on probability and genetic epidemiology terminology provide the reader with necessary background knowledge. The organization of this work allows for both casual reference and close study.
Analysis of Heat Equations on Domains
by El Maati OuhabazThis is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics. This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade. The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.
Analysis of Heat Equations on Domains. (LMS-31)
by El-Maati OuhabazThis is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics.This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade.The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.
The Analysis of Household Surveys: A Microeconometric Approach to Development Policy (World Bank Ser.)
by Angus DeatonTwo decades after its original publication, The Analysis of Household Surveys is reissued with a new preface by its author, Sir Angus Deaton, recipient of the 2015 Nobel Prize in Economic Sciences. This classic work remains relevant to anyone with a serious interest in using household survey data to shed light on policy issues. The book reviews the analysis of household survey data, including the construction of household surveys, the econometric tools useful for such analysis, and a range of problems in development policy for which this survey analysis can be applied. Chapter 1 describes the features of survey design that need to be understood in order to undertake appropriate analysis. Chapter 2 discusses the general econometric and statistical issues that arise when using survey data for estimation and inference. Chapter 3 covers the use of survey data to measure welfare, poverty, and distribution. Chapter 4 focuses on the use of household budget data to explore patterns of household demand. Chapter 5 discusses price reform, its effects on equity and efficiency, and how to measure them. Chapter 6 addresses the role of household consumption and saving in economic development. The book includes an appendix providing code and programs using STATA, which can serve as a template for users' own analysis.
Analysis of Images, Social Networks and Texts: 11th International Conference, AIST 2023, Yerevan, Armenia, September 28–30, 2023, Revised Selected Papers (Lecture Notes in Computer Science #14486)
by Dmitry I. Ignatov Michael Khachay Andrey Kutuzov Habet Madoyan Ilya Makarov Irina Nikishina Alexander Panchenko Maxim Panov Panos M. Pardalos Andrey V. Savchenko Evgenii Tsymbalov Elena Tutubalina Sergey ZagoruykoThis book constitutes revised selected papers from the thoroughly refereed proceedings of the 11th International Conference on Analysis of Images, Social Networks and Texts, AIST 2023, held in Yerevan, Armenia, during September 28-30, 2023. The 24 full papers included in this book were carefully reviewed and selected from 93 submissions. They were organized in topical sections as follows: natural language processing; computer vision; data analysis and machine learning; network analysis; and theoretical machine learning and optimization. The book also contains one invited talk in full paper length.