Search result: Catalogue data in Spring Semester 2019

Statistics Master Information
The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.
Core Courses
In each subject area, the core courses offered are normally mathematical as well as application-oriented in content. For each subject area, only one of these is recognised for the Master degree.
Does not take place this semester.
W8 credits4Gnot available
AbstractIn regression, the dependency of a random response variable on other variables is examined. We consider the theory of linear regression with one or more covariates, high-dimensional linear models, nonlinear models and generalized linear models, robust methods, model choice and nonparametric models. Several numerical examples will illustrate the theory.
ObjectiveIntroduction into theory and practice of a broad and popular area of statistics, from a modern viewpoint.
ContentIn der Regression wird die Abhängigkeit einer beobachteten quantitativen Grösse von einer oder mehreren anderen (unter Berücksichtigung zufälliger Fehler) untersucht. Themen der Vorlesung sind: Einfache und multiple Regression, Theorie allgemeiner linearer Modelle, Hoch-dimensionale Modelle, Ausblick auf nichtlineare Modelle. Querverbindungen zur Varianzanalyse, Modellsuche, Residuenanalyse; Einblicke in Robuste Regression. Durchrechnung und Diskussion von Anwendungsbeispielen.
Lecture notesLecture notes
Prerequisites / NoticeCredits cannot be recognised for both courses 401-3622-00L Regression and 401-0649-00L Applied Statistical Regression in the Mathematics Bachelor and Master programmes (to be precise: one course in the Bachelor and the other course in the Master is also forbidden).
Analysis of Variance and Design of Experiments
No offering in this semester yet
Multivariate Statistics
401-6102-00LMultivariate StatisticsW4 credits2GN. Meinshausen
AbstractMultivariate Statistics deals with joint distributions of several random variables. This course introduces the basic concepts and provides an overview over classical and modern methods of multivariate statistics. We will consider the theory behind the methods as well as their applications.
ObjectiveAfter the course, you should be able to:
- describe the various methods and the concepts and theory behind them
- identify adequate methods for a given statistical problem
- use the statistical software "R" to efficiently apply these methods
- interpret the output of these methods
ContentVisualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis
Lecture notesNone
LiteratureThe course will be based on class notes and books that are available electronically via the ETH library.
Prerequisites / NoticeTarget audience: This course is the more theoretical version of "Applied Multivariate Statistics" (401-0102-00L) and is targeted at students with a math background.

Prerequisite: A basic course in probability and statistics.

Note: The courses 401-0102-00L and 401-6102-00L are mutually exclusive. You may register for at most one of these two course units.
401-0102-00LApplied Multivariate StatisticsW5 credits2V + 1UF. Sigrist
AbstractMultivariate statistics analyzes data on several random variables simultaneously. This course introduces the basic concepts and provides an overview of classical and modern methods of multivariate statistics including visualization, dimension reduction, supervised and unsupervised learning for multivariate data. An emphasis is on applications and solving problems with the statistical software R.
ObjectiveAfter the course, you are able to:
- describe the various methods and the concepts behind them
- identify adequate methods for a given statistical problem
- use the statistical software R to efficiently apply these methods
- interpret the output of these methods
ContentVisualization, multivariate outliers, the multivariate normal distribution, dimension reduction, principal component analysis, multidimensional scaling, factor analysis, cluster analysis, classification, multivariate tests and multiple testing
Lecture notesNone
Literature1) "An Introduction to Applied Multivariate Analysis with R" (2011) by Everitt and Hothorn
2) "An Introduction to Statistical Learning: With Applications in R" (2013) by Gareth, Witten, Hastie and Tibshirani

Electronic versions (pdf) of both books can be downloaded for free from the ETH library.
Prerequisites / NoticeThis course is targeted at students with a non-math background.

1) Introductory course in statistics (min: t-test, regression; ideal: conditional probability, multiple regression)
2) Good understanding of R (if you don't know R, it is recommended that you study chapters 1,2,3,4, and 5 of "Introductory Statistics with R" from Peter Dalgaard, which is freely available online from the ETH library)

An alternative course with more emphasis on theory is 401-6102-00L "Multivariate Statistics" (only every second year).

401-0102-00L and 401-6102-00L are mutually exclusive. You can register for only one of these two courses.
Time Series and Stochastic Processes
401-6624-11LApplied Time SeriesW5 credits2V + 1UM. Dettling
AbstractThe course starts with an introduction to time series analysis (examples, goal, mathematical notation). In the following, descriptive techniques, modeling and prediction as well as advanced topics will be covered.
ObjectiveGetting to know the mathematical properties of time series, as well as the requirements, descriptive techniques, models, advanced methods and software that are necessary such that the student can independently run an applied time series analysis.
ContentThe course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis.
Lecture notesA script will be available.
Prerequisites / NoticeThe course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis.
Mathematical Statistics
No offering in this semester yet
Specialization Areas and Electives
Statistical and Mathematical Courses
401-4632-15LCausality Information W4 credits2GC. Heinze-Deml
AbstractIn statistics, we are used to search for the best predictors of some random variable. In many situations, however, we are interested in predicting a system's behavior under manipulations. For such an analysis, we require knowledge about the underlying causal structure of the system. In this course, we study concepts and theory behind causal inference.
ObjectiveAfter this course, you should be able to
- understand the language and concepts of causal inference
- know the assumptions under which one can infer causal relations from observational and/or interventional data
- describe and apply different methods for causal structure learning
- given data and a causal structure, derive causal effects and predictions of interventional experiments
Prerequisites / NoticePrerequisites: basic knowledge of probability theory and regression
401-3632-00LComputational StatisticsW8 credits3V + 1UM. H. Maathuis
AbstractWe discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R.
ObjectiveThe student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R.
ContentSee the class website
Prerequisites / NoticeAt least one semester of (basic) probability and statistics.

Programming experience is helpful but not required.
401-3602-00LApplied Stochastic Processes Information W8 credits3V + 1UV. Tassion
AbstractPoisson processes; renewal processes; Markov chains in discrete and in continuous time; some applications.
ObjectiveStochastic processes are a way to describe and study the behaviour of systems that evolve in some random way. In this course, the evolution will be with respect to a scalar parameter interpreted as time, so that we discuss the temporal evolution of the system. We present several classes of stochastic processes, analyse their properties and behaviour and show by some examples how they can be used. The main emphasis is on theory; in that sense, "applied" should be understood to mean "applicable".
LiteratureR. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online:
R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online:
M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online:
S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005)
Prerequisites / NoticePrerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L).
401-3642-00LBrownian Motion and Stochastic Calculus Information W10 credits4V + 1UW. Werner
AbstractThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
ObjectiveThis course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
Lecture notesLecture notes will be distributed in class.
Literature- J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).
- I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991).
- D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005).
- L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000).
- D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006).
Prerequisites / NoticeFamiliarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in
- J. Jacod, P. Protter, Probability Essentials, Springer (2004).
- R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010).
401-6228-00LProgramming with R for Reproducible Research Information W1 credit1GM. Mächler
AbstractDeeper understanding of R: Function calls, rather than "commands".
Reproducible research and data analysis via Sweave and Rmarkdown.
Limits of floating point arithmetic.
Understanding how functions work. Environments, packages, namespaces.
Closures, i.e., Functions returning functions.
Lists and [mc]lapply() for easy parallelization.
Performance measurement and improvements.
Lecture notesMaterial available from
LiteratureNorman Matloff (2011) The Art of R Programming - A tour of statistical software design.
no starch press, San Francisco. on stock at Polybuchhandlung (CHF 42.-).
Prerequisites / NoticeR Knowledge on the same level as after *both* parts of the ETH lecture
401-6217-00L Using R for Data Analysis and Graphics
401-4627-00LEmpirical Process Theory with Applications in Statistics and Machine Learning Information W4 credits2VS. van de Geer
AbstractEmpirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc.
ContentIn this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.
401-3629-00LQuantitative Risk ManagementW4 credits2V + 1UP. Cheridito
AbstractThis course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas, dependence structures and operational risk.
ObjectiveThe goal is to learn the most important methods from probability theory and statistics used in financial risk modeling.
Content1. Introduction
2. Basic Concepts in Risk Management
3. Empirical Properties of Financial Data
4. Financial Time Series
5. Extreme Value Theory
6. Multivariate Models
7. Copulas and Dependence
8. Operational Risk
Lecture notesCourse material is available on
LiteratureQuantitative Risk Management: Concepts, Techniques and Tools
AJ McNeil, R Frey and P Embrechts
Princeton University Press, Princeton, 2015 (Revised Edition)
Prerequisites / NoticeThe course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance.
401-4658-00LComputational Methods for Quantitative Finance: PDE Methods Information Restricted registration - show details W6 credits3V + 1UL. Herrmann, K. Kirchner
AbstractIntroduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming
and knowledge of numerical mathematics at ETH BSc level.
ObjectiveIntroduce the main methods for efficient numerical valuation of derivative contracts in a
Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility
models. Develop implementation of pricing methods in MATLAB.
Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation.
Content1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic
volatility models.
2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees.
European contracts.
3. Finite Difference methods for Asian, American and Barrier type contracts.
4. Finite element methods for European and American style contracts.
5. Pricing under local and stochastic volatility in Black-Scholes Markets.
6. Finite Element Methods for option pricing under Levy processes. Treatment of
integrodifferential operators.
7. Stochastic volatility models for Levy processes.
8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and
stochastic volatility models in Black Scholes and Levy markets.
9. Introduction to sparse grid option pricing techniques.
Lecture notesThere will be english, typed lecture notes as well as MATLAB software for registered participants in the course.
LiteratureR. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004.

Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005.

D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008.

J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000.

N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013.
401-2284-00LMeasure and Integration Information W6 credits3V + 2UJ. Teichmann
AbstractIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
ObjectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Lecture notes
Literature- D. A. Salamon, Measure and Integration, EMS 2016
- W. Rudin, Real and Complex Analysis, McGraw-Hill 1987
- P. R. Halmos, Measure Theory, Springer 1950
401-3903-11LGeometric Integer ProgrammingW6 credits2V + 1UR. Weismantel, J. Paat, M. Schlöter
AbstractInteger programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
ObjectiveThe purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
ContentKey topics are:
- lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension,
- the theory of integral generating sets and its connection to totally dual integral systems,
- finite cutting plane algorithms based on lattices and integral generating sets.
Lecture notesnot available, blackboard presentation
LiteratureBertsimas, Weismantel: Optimization over Integers, Dynamic Ideas 2005.
Schrijver: Theory of linear and integer programming, Wiley, 1986.
Prerequisites / Notice"Mathematical Optimization" (401-3901-00L)
401-4904-00LCombinatorial Optimization Information W6 credits2V + 1UR. Zenklusen
AbstractCombinatorial Optimization deals with efficiently finding a provably strong solution among a finite set of options. This course discusses key combinatorial structures and techniques to design efficient algorithms for combinatorial optimization problems. We put a strong emphasis on polyhedral methods, which proved to be a powerful and unifying tool throughout combinatorial optimization.
ObjectiveThe goal of this lecture is to get a thorough understanding of various modern combinatorial optimization techniques with an emphasis on polyhedral approaches. Students will learn a general toolbox to tackle a wide range of combinatorial optimization problems.
ContentKey topics include:
- Polyhedral descriptions;
- Combinatorial uncrossing;
- Ellipsoid method;
- Equivalence between separation and optimization;
- Design of efficient approximation algorithms for hard problems.
Lecture notesLecture notes will be available online.
Literature- Bernhard Korte, Jens Vygen: Combinatorial Optimization. 5th edition, Springer, 2012.
- Alexander Schrijver: Combinatorial Optimization: Polyhedra and Efficiency, Springer, 2003. This work has 3 volumes.
Prerequisites / NoticePrior exposure to Linear Programming can greatly help the understanding of the material. We therefore recommend that students interested in Combinatorial Optimization get familiarized with Linear Programming before taking this lecture.
261-5110-00LOptimization for Data Science Information W8 credits3V + 2U + 2AB. Gärtner, D. Steurer
AbstractThis course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science.
ObjectiveUnderstanding the theoretical and practical aspects of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science.
ContentThis course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science.

In the first part of the course, we will discuss how classical first and second order methods such as gradient descent and Newton's method can be adapated to scale to large datasets, in theory and in practice. We also cover some new algorithms and paradigms that have been developed specifically in the context of data science. The emphasis is not so much on the application of these methods (many of which are covered in other courses), but on understanding and analyzing the methods themselves.

In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation.
Prerequisites / NoticeAs background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary.
252-0526-00LStatistical Learning Theory Information W7 credits3V + 2U + 1AJ. M. Buhmann
AbstractThe course covers advanced methods of statistical learning :
Statistical learning theory;variational methods and optimization, e.g., maximum entropy techniques, information bottleneck, deterministic and simulated annealing; clustering for vectorial, histogram and relational data; model selection; graphical models.
ObjectiveThe course surveys recent methods of statistical learning. The fundamentals of machine learning as presented in the course "Introduction to Machine Learning" are expanded and in particular, the theory of statistical learning is discussed.
Content# Theory of estimators: How can we measure the quality of a statistical estimator? We already discussed bias and variance of estimators very briefly, but the interesting part is yet to come.

# Variational methods and optimization: We consider optimization approaches for problems where the optimizer is a probability distribution. Concepts we will discuss in this context include:

* Maximum Entropy
* Information Bottleneck
* Deterministic Annealing

# Clustering: The problem of sorting data into groups without using training samples. This requires a definition of ``similarity'' between data points and adequate optimization procedures.

# Model selection: We have already discussed how to fit a model to a data set in ML I, which usually involved adjusting model parameters for a given type of model. Model selection refers to the question of how complex the chosen model should be. As we already know, simple and complex models both have advantages and drawbacks alike.

# Statistical physics models: approaches for large systems approximate optimization, which originate in the statistical physics (free energy minimization applied to spin glasses and other models); sampling methods based on these models
Lecture notesA draft of a script will be provided;
transparencies of the lectures will be made available.
LiteratureHastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001.

L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996
Prerequisites / NoticeRequirements:

knowledge of the Machine Learning course
basic knowledge of statistics, interest in statistical methods.

It is recommended that Introduction to Machine Learning (ML I) is taken first; but with a little extra effort Statistical Learning Theory can be followed without the introductory course.
636-0702-00LStatistical Models in Computational BiologyW6 credits2V + 1U + 2AN. Beerenwinkel
AbstractThe course offers an introduction to graphical models and their application to complex biological systems. Graphical models combine a statistical methodology with efficient algorithms for inference in settings of high dimension and uncertainty. The unifying graphical model framework is developed and used to examine several classical and topical computational biology methods.
ObjectiveThe goal of this course is to establish the common language of graphical models for applications in computational biology and to see this methodology at work for several real-world data sets.
ContentGraphical models are a marriage between probability theory and graph theory. They combine the notion of probabilities with efficient algorithms for inference among many random variables. Graphical models play an important role in computational biology, because they explicitly address two features that are inherent to biological systems: complexity and uncertainty. We will develop the basic theory and the common underlying formalism of graphical models and discuss several computational biology applications. Topics covered include conditional independence, Bayesian networks, Markov random fields, Gaussian graphical models, EM algorithm, junction tree algorithm, model selection, Dirichlet process mixture, causality, the pair hidden Markov model for sequence alignment, probabilistic phylogenetic models, phylo-HMMs, microarray experiments and gene regulatory networks, protein interaction networks, learning from perturbation experiments, time series data and dynamic Bayesian networks. Some of the biological applications will be explored in small data analysis problems as part of the exercises.
Lecture notesno
Literature- Airoldi EM (2007) Getting started in probabilistic graphical models. PLoS Comput Biol 3(12): e252. doi:10.1371/journal.pcbi.0030252
- Bishop CM. Pattern Recognition and Machine Learning. Springer, 2007.
- Durbin R, Eddy S, Krogh A, Mitchinson G. Biological Sequence Analysis. Cambridge university Press, 2004
701-0104-00LStatistical Modelling of Spatial DataW3 credits2GA. J. Papritz
AbstractIn environmental sciences one often deals with spatial data. When analysing such data the focus is either on exploring their structure (dependence on explanatory variables, autocorrelation) and/or on spatial prediction. The course provides an introduction to geostatistical methods that are useful for such analyses.
ObjectiveThe course will provide an overview of the basic concepts and stochastic models that are used to model spatial data. In addition, participants will learn a number of geostatistical techniques and acquire familiarity with R software that is useful for analyzing spatial data.
ContentAfter an introductory discussion of the types of problems and the kind of data that arise in environmental research, an introduction into linear geostatistics (models: stationary and intrinsic random processes, modelling large-scale spatial patterns by linear regression, modelling autocorrelation by variogram; kriging: mean square prediction of spatial data) will be taught. The lectures will be complemented by data analyses that the participants have to do themselves.
Lecture notesSlides, descriptions of the problems for the data analyses and solutions to them will be provided.
LiteratureP.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer.

Bivand, R. S., Pebesma, E. J. & Gómez-Rubio, V. 2013. Applied Spatial Data Analysis with R. Springer.
Prerequisites / NoticeFamiliarity with linear regression analysis (e.g. equivalent to the first part of the course 401-0649-00L Applied Statistical Regression) and with the software R (e.g. 401-6215-00L Using R for Data Analysis and Graphics (Part I), 401-6217-00L Using R for Data Analysis and Graphics (Part II)) are required for attending the course.
401-6222-00LRobust and Nonlinear Regression Information Restricted registration - show details
Does not take place this semester.
W2 credits1V + 1U
AbstractIn a first part, the basic ideas of robust fitting techniques are explained theoretically and practically using regression models and explorative multivariate analysis.

The second part addresses the challenges of fitting nonlinear regression functions and finding reliable confidence intervals.
ObjectiveParticipants are familiar with common robust fitting methods for the linear regression models as well as for exploratory multivariate analysis and are able to assess their suitability for the data at hand.

They know the challenges that arise in fitting of nonlinear regression functions, and know the difference between classical and profile based methods to determine confidence intervals.

They can apply the discussed methods in practise by using the statistics software R.
ContentRobust fitting: influence function, breakdown point, regression M-estimation, regression MM-estimation, robust inference, covariance estimation with high breakdown point, application in principal component analysis and linear discriminant analysis.

Nonlinear regression: the nonlinear regression model, estimation methods, approximate tests and confidence intervals, estimation methods, profile t plot, profile traces, parameter transformation, prediction and calibration
Lecture notesLecture notes are available
Prerequisites / NoticeIt is a block course on three Mondays in June
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