NA Digest, V. 18, # 20

## NA Digest Sunday, May 20, 2018 Volume 18 : Issue 20

Today's Editor:

Daniel M. Dunlavy
Sandia National Labs
dmdunla@sandia.gov

Today's Topics: Subscribe, unsubscribe, change address, or for na-digest archives: http://www.netlib.org/na-digest-html/faq.html

### Submissions for NA Digest:

http://icl.utk.edu/na-digest/

From: John C. Nash profjcnash@gmail.com
Date: May 15, 2018
Subject: histoRicalg: Documentation and Transfer of Knowledge about Algorithms

For approximately the last year I have been developing ideas for ways
to document and transfer knowledge of older algorithms used by
R. These are mainly in Fortran, but some are in C, with the original
codes possibly in other programming languages. My efforts were
prompted by possibility of bugs in codes, which could be either from
the original programs or else the implementations. Two examples in
particular -- in nlm() and in optim::L-BFGS-B -- gave impetus to the
project, which I call histoRicalg. The R Consortium has awarded this
project some modest funding.

A preliminary web-site is at https://gitlab.com/nashjc/histoRicalg.
As a first task, I am hoping to establish a "Working Group on
Algorithms Used in R" to identify and prioritize issues and to develop
procedures for linking older and younger workers to enable the
transfer of knowledge. Expressions of interest are welcome.

While active membership of the Working Group is desirable, given the
nature of this project, I anticipate that most members will contribute
mainly by providing timely and pertinent ideas. Some may not even be R
users, since the underlying algorithms are used by other computing
systems and the documentation effort has many common features. We will
also need participation of younger workers willing to learn about the
methods that underly the computations in R.

From: Peter Jimack p.k.jimack@leeds.ac.uk
Date: May 15, 2018
Subject: SIAG/CSE Early Career Prize

I'd like to bring to your attention that the call for nominations is
open for the SIAM Activity Group on Computational Science and
Engineering (SIAG/CSE) Early Career Prize:
http://www.siam.org/prizes/nominations/nom_siag_cseearlycareer.php

The prize is awarded every two years to one post-PhD early career
researcher in the field of computational science and engineering for
outstanding, influential, and potentially long-lasting contributions
to the field. For the 2019 award, the candidate must have been awarded
their PhD no earlier than January 1, 2012 and no later than the
nomination deadline, which is July 31, 2018.

From: Lars Elden lars.elden@liu.se
Date: May 17, 2018
Subject: 2018 Froberg Prize Awarded

The 2018 Carl-Erik Froberg Prize has been awarded to Dr Georg
Muntingh, SINTEF, Oslo, for the paper

Symbols and exact regularity of symmetric pseudo-splines of any arity,
BIT Numerical Mathematics 57(2017), 867-900, DOI
https://doi.org/10.1007/s10543-017-0656-y

The prize is given in even numbered years to a young author of a
distinguished paper published in BIT Numerical Mathematics. The paper
must have been published in the most recent two-year period prior to
the year of the award. At the beginning of that period the age of the
author must have been 35 years or less.

The prize is open to young BIT authors of all nationalities. The sum
for the 2016 prize is EUR 5000.
http://projects.mai.liu.se/BIT/BIT_CEF_prize.html

Carl-Erik Froberg was one of the cofounders of the journal BIT, and he
was its first editor-in-chief.

Gunilla Kreiss and Lars Elden, editors-in-chief, BIT Numerical
Mathematics

From: JS Hysing jshysing@featool.com
Date: May 16, 2018
Subject: FEATool 1.8 with OpenFOAM GUI and Matlab CFD Interface

The FEATool Multiphysics MATLAB and Octave FEM Simulation Toolbox
version 1.8 is now available. In addition to being a fully integrated
FEA multiphysics toolbox, and interfacing with the FEniCS FEM solver
and external mesh generators such as DistMesh, GiD, Gmsh, and
Triangle, the highlight of the new version is introducing a fully
integrated and cross-platform OpenFOAM CFD GUI interface for MATLAB
and GNU Octave.

The new OpenFOAM MATLAB CFD interface allows one to conveniently setup
both laminar and fully turbulent incompressible Navier-Stokes CFD
problems all within an easy to use graphical user interface
automatic mesh generation (with automatic 2D to 3D mesh conversion and
extrusion for 2D problems), FEATool to OpenFOAM case file conversion,
solver selection and control, as well as solution import with
postprocessing and visualization. As with all the FEATool MATLAB GUI
functionality, models can also be saved and exported as m-file CLI
functions where custom scripting and support for all MATLAB and Octave
functions and toolboxes is supported. With the added support for the
popular OpenFOAM CFD solver and FEniCS, high-performance multiphysics,
multi-simulation, and CFD modeling can now be all be conveniently done
within a single software interface.

From: Matthias Maier msmaier@umn.edu
Date: May 14, 2018
Subject: deal.II Version 9.0.0 released

Version 9.0.0 of deal.II, the object-oriented finite element library
awarded the J. H. Wilkinson Prize for Numerical Software, has been
the deal.II homepage at https://www.dealii.org/

The major changes of this release are:
- Improved support for curved geometries
- Support for particle-in-cell methods
- Dedicated support for automatic differentiation
- Interfaces to more external libraries and programs: Assimp, Gmsh,
nanoflann, ROL, ScaLAPACK and Sundials.
- C++11 is now both required and used
- Support for GPU computations via CUDA
- Support for face integrals and significant improvements of the
matrix-free framework

The main features of deal.II are:
- Extensive documentation and 57 working example programs
- Support for dimension-independent programming
- Locally refined adaptive meshes and multigrid support
- A zoo of different finite elements
- Built-in support for shared memory and distributed parallel
computing, scaling from laptops to clusters with 100,000+ of
processor cores
- Interfaces to Trilinos, PETSc, METIS, UMFPACK and other external
software

From: Frank Kunkle kunkle@siam.org
Date: May 14, 2018
Subject: New Book, A Software Repository for Orthogonal Polynomials

A SOFTWARE REPOSITORY FOR ORTHOGONAL POLYNOMIALS BY WALTER GAUTSCHI
2018 / viii + 60 pages / ebook / eISBN 978-1-611975-22-2 / List Price
$24.00 / SIAM Member Price$16.80 / Order Code: SE28
http://bookstore.siam.org/se28/

Keywords: orthogonal polynomials; Matlab software; classical weight
functions; quasi-classical weight functions; nonclassical weight
functions

This is the first book that provides graphs and references to online
datasets that enable the generation of a large number of orthogonal
polynomials with classical, quasi-classical, and nonclassical weight
functions. Useful numerical tables are also included.

Audience: The book will be of interest to scientists, engineers,
applied mathematicians, and statisticians.

About the Author: Walter Gautschi has held postdoctoral positions at
the Istituto per le Applicazioni del Calcolo "Mauro Picone" in Rome
and at Harvard University. He was Research Mathematician at the
National Bureau of Standards in Washington, D.C. for four years and at
Oak Ridge National Laboratory for three years before taking on a full
professorship at Purdue University, where he remained until his
retirement in 2000. Elected Corresponding Member of the Bavarian
Sciences, Gautschi has served on the editorial committees of several
journals and was chairman of the Mathematics of Computation editorial
board. He has published extensively in the areas of computational
mathematics, orthogonal polynomials, and history, including two books.

From: Frank Kunkle kunkle@siam.org
Date: May 14, 2018
Subject: New Book, Elementary Numerical Analysis: An Algorithmic Approach

ELEMENTARY NUMERICAL ANALYSIS: AN ALGORITHMIC APPROACH
BY S. D. CONTE AND CARL DE BOOR
2017 / xxiv + 456 pages / softcover / ISBN 978-1-611975-19-2 / List
Price $76.00 / SIAM Member Price$53.20 / Order Code: CL78

Keywords: elementary, algorithmic, numerical analysis, scientific
computation

This book provides a thorough and careful introduction to the theory
and practice of scientific computing at an elementary, yet rigorous,
level, from theory via examples and algorithms to computer
programs. The intended audience is upper-division undergraduates in
engineering, mathematics, and the sciences, including computer
science. The book has served well as a text book. The original FORTRAN
programs have been rewritten in MATLAB and now appear in a new
appendix and online, offering a modernized version of this classic
reference for basic numerical algorithms.

About the Authors: Samuel D. Conte was a Professor of Computer Science
and Mathematics at Purdue University. Starting in 1962, he led the
Purdue Department of Computer Science for its first 17 years. Prior to
that, Professor Conte served as the manager of the Math and
Programming Department of the Aerospace Corporation, taught at Wayne
State University, and was head of the Mathematics and Programming
Departments at TRW Inc. Carl de Boor is presently Professor emeritus
of Mathematics and Computer Science at the University of
Wisconsin-Madison and Affiliated Professor of Applied Mathematics at
the University of Washington. His early work at the Mathematics
Department of GM Research at Warren, MI led to his lifelong
preoccupation with spline functions. He is the author of A Practical
Guide to Splines and co-author of Box Splines. He is the recipient of
the 2003 National Medal of Science in Mathematics and Computer Science
in recognition of his contributions to scientific computing.

From: Frank Kunkle kunkle@siam.org
Date: May 14, 2018
Subject: New Book, Mathematical Models and Their Analysis

MATHEMATICAL MODELS AND THEIR ANALYSIS
BY FREDERIC Y. M. WAN
2018 / xx + 402 pages / softcover / ISBN 978-1-611975-26-0 / List Price
$74.00 / SIAM Member Price$51.80 / Order Code: CL79
http://bookstore.siam.org/cl79/

A great deal can be learned through modeling and mathematical analysis
about real-life phenomena, even before numerical simulations are used
to accurately portray the specific configuration of a situation.
Scientific computing also becomes more effective and efficient if it
is preceded by some preliminary analysis. These important advantages
of mathematical modeling are demonstrated by models of historical
importance in an easily understandable way.

The organization of Mathematical Models and Their Analysis groups
models by the issues that need to be addressed about the phenomena.
The new approach shows how mathematics effective for one modeled
phenomenon can be used to analyze another unrelated problem. For
instance, the mathematics of differential equations useful in
understanding the classical physics of planetary models, fluid motion,
and heat conduction is also applicable to the seemingly unrelated
phenomena of traffic flow and congestion, offshore sovereignty, and
regulation of overfishing and deforestation. The formulation and
in-depth analysis of these and other models on modern social issues,
such as the management of exhaustible and renewable resources in
response to consumption demands and economic growth, are of increasing
concern to students and researchers of our time.

graduate students, or anyone with a strong background in calculus and
ordinary differential equations, for use in mathematical modeling and
introduction to applied mathematics courses.

About the Author: Frederic Y. M. Wan has been a Professor of
Mathematics at the University of California, Irvine since 1995, where
he was also Chancellor for Research and Dean of Graduate Studies,
1995-2000. He has previously held positions on the mathematics faculty
at MIT and as the founding Director of the Institute of Applied
Mathematics and Statistics at the University of British Columbia,
President of the American Academy of Mechanics (AAM), President of the
Canadian Applied Mathematics Society (CAMS/SCMA), and founding Chair
of the Department of Applied Mathematics at the University of
Washington. He was Chair of the Committee of Pure and Applied
Mathematics of the Natural Science and Engineering Council of Canada
and Director of the National Science Foundation's Division of
Mathematical Sciences, the only person to have held both positions. He
is a fellow of AAM, ASME, AAAS, and SIAM.

From: Emmanuil Georgoulis georgoulis@math.ntua.gr
Date: May 17, 2018
Subject: NA for Deterministic and Stochastic Differential Equations, Greece, Jul 2018

The Department of Mathematics of the School of Applied Mathematical
and Physical Sciences of the National Technical University of Athens
(NTUA) is organizing a summer school on: Numerical analysis for
deterministic and stochastic differential equations

The school will take place between10--13 July 2018, at the Zografou
Campus of the NTUA in Athens, Greece. The targeted audience are
school will consist of three mini-courses, instructed by

1) Charalambos Makridakis (Crete (FORTH, UC) and Sussex) on
"Approximations of Nonlinear Problems: Adaptive Algorithms and
Analysis"

2) Grigorios Pavliotis (Imperial College London) on "Sampling from
probability measures using stochastic differential equations"

3) Daniel Peterseim (University of Augsburg) on "Numerical
homogenization beyond periodicity and scale separation"

There will also be a small number of research talks. The language of
the summer school is English. There is no registration fee, however
the number of participants is limited. Please apply by 31 May 2018 via
the registration form at the summer school website:

http://sites.math.ntua.gr/summer-school-2018/

Financial support in the form of board and lodging will be available
for selected participants. We regret we cannot offer any financial
assistance with travel costs or with visa arrangements.

From: Pau Farre pau.farre@bsc.es
Date: May 16, 2018
Subject: PUMPS+AI Summer School, Spain, Jul 2018

On its ninth edition, the Programming and tUning Massively Parallel
Systems summer school (PUMPS) premiers a brand-new "+AI" design,
offering researchers and graduate students a unique opportunity to
improve their skills with cutting-edge techniques and hands-on
experience in developing and tuning applications for many-core
processors with massively parallel computing resources like GPU
accelerators, with more content devoted to artificial intelligence.

http://pumps.bsc.es

- PUMPS 2018 Distinguished Lecturers:
Wen-mei Hwu (Univ. of Illinois) and David Kirk (NVIDIA)
- BSC/UPC Lecturers:
Antonio J. Pena, Xavier Martorell, Xavier Teruel

The summer school is oriented towards advanced programming and
optimizations, and thus previous experience in basic GPU programming
will be considered in the selection process. We will also consider the
current parallel applications, numerical methods, and AI techniques
you are familiar with, and the specific optimizations you would like
to discuss.

Some of the topics that will be covered during the course are: AI /
DEEP Learning; High-level programming models on GPUs: OmpSs, OpenACC;
CUDA Algorithmic Optimization Strategies; Dealing with Sparse and
Dynamic data; Efficiency in Large Data Traversal; Reducing Output
Interference; Controlling Load Imbalance and Divergence; Acceleration
of Collective Operations; Dynamic Parallelism and HyperQ; Debugging
and Profiling CUDA Code; Multi-GPU and multi-node Execution;
Architecture Trends and Implications.

will learn to program and optimize applications in languages such as
CUDA and OmpSs. Teaching Assistants will be available to help with
your hands-on lab assignments. At poster and code clinic sessions you
may show your current work and applications you are optimizing. NVIDIA
will award the best poster presentation and course achievements.

Applications due: May 31, 2018
Notification of acceptance: June 12, 2018
Summer school: July 16-20, 2018

Complete information, program and registration: http://pumps.bsc.es
Contact: pumps@bsc.es

From: Volker Schulz volker.schulz@uni-trier.de
Date: May 17, 2018
Subject: European Conference on Computational Optimization, Germany, Sep 2018

With this email, we would like to draw your attention to the 5th
European Conference on Computational Optimization - EUCCO 2018, taking
place in Trier in from September 10 - 12, 2018. The deadline for paper
submission (May 30th) is approaching.

The scope of this conference series is quite broad as it aims to bring
together scientists from a diversity of subdisciplines, such as
computational optimization, algorithms and applications. The upcoming
conference will place special emphasis on certain aspects of
optimization, found in the focus sessions, while still keeping its
more traditional focus on large scale optimization, optimization with
partial differential equations, and numerical optimization algorithms
https://alop.uni-trier.de/eucco2018/

Furthermore, there is a special travel fund available for enroled
Master students in mathematics:
https://alop.uni-trier.de/EUCCO2018/student- travel-fund-application/

From: Panagiota Tsompanopoulou yota@uth.gr
Date: May 16, 2018
Subject: International Conference on Tools with Artificial Intelligence, Greece, Nov 2018

The 30th International Conference on Tools with Artificial
Intelligence, ICTAI 2018, will take place in Volos, Greece,
November 5-7, 2018.

Paper submission due: June 1, 2018 (time: 23:59 PST)
Notification fo Acceptance: July 16, 2018

http://ictai2018.org/

From: Zhen Wang TODDWZ@GMAIL.COM
Date: May 18, 2018
Subject: Software R&D Engineer II Position, ANSYS, Pittsburgh

The Twin Builder development team has an exciting opportunity for a
R&D Engineer to help build and extend our state of art system
simulation products for system validation and operational
analysis. The successful candidate will drive research and development
of our simulators, develop of new features and innovative algorithms,
participate in defining requirements and specifications, and be
responsible for design, development, and maintenance of features and
algorithms. Join us in building and extending the first of its kind
offering that combines the Electro-Mechanical, Fluid-Mechanical and
Control worlds to enable true system simulation.

ANSYS is an Equal Opportunity Employer. All qualified applicants will
receive consideration for employment without regard to race, color,
religion, sex, sexual orientation, gender identity, national origin,
disability, veteran status, and other protected characteristics.

Anyone with computer engineering, electrical engineering, mathematics
or related background and C++ experience is welcome to apply. More
details can be found at https://www.linkedin.com/jobs/view/666556063/

From: Tiangang Cui tiangang.cui@monash.edu
Date: May 17, 2018
Subject: Faculty Positions, Applied and Computational Mathematics, Monash Univ

The School of Mathematical Sciences at Monash University invites
applications for a number of continuing academic positions in Applied
Mathematics at all levels. The school is currently going through a
phase of significant growth that will reinforce its position as a

Research areas of interest include Mathematical Biology, Computational
Mathematics, and related areas in Applied Mathematics. We are
interested in outstanding academics who apply their mathematics
research to problems in science, engineering, technology, and the
biomedical sciences. These are continuing positions subject to
the details at the end of this email.

Monash University is a leading Australian research university that
ranks in the top-100 globally. Monash University is located in
Melbourne, which is a major cosmopolitan centre and has been named the
world's most liveable city for five years in a row.

Application deadline is 8 July 2018.

Professor/Associate Professor in Applied Mathematics (Mathematical
Biology or Computational Mathematics)
http://careers.pageuppeople.com/513/cw/en/job/576574/professor-associate-professor-in-
applied-mathematics

Lecturer/Senior Lecturer in Applied Mathematics (Mathematical Biology or Computational
Mathematics)
http://careers.pageuppeople.com/513/cw/en/job/576575/lecturersenior-lecturer-in-applied-
mathematics-mathematical-biology-or-computational-mathematics

Lecturer/Senior Lecturer in Applied Mathematics (Female Only)
http://careers.pageuppeople.com/513/cw/en/job/576578/lecturersenior-lecturer-in-applied-
mathematics-female-only

From: Volker Mehrmann mehrmann@math.tu-berlin.de
Date: May 16, 2018
Subject: Junior Professorship Position, Modeling, Simulation and Optimization, TU Berlin

Technische Universitat Berlin, Faculty II - Mathematics and Natural
Sciences, Institute of Mathematics, calls for applications for a
position of a Junior Professor - salary grade W1 with W3 tenure track
option for the field of Mathematics - Modeling, Simulation and
Optimization of Real world Processes

With this position, TU Berlin addresses especially young
scientists. For that reason, this position will be a temporary W1
junior professorship with an evaluation after 3 years. In case of a
second successful evaluation, this position will lead toa permanent
W3professorship after 6 years.

Working field: The position requires research and teaching in the area
of Mathematical Modeling, Simulation, and Optimization with a strong
interdisciplinary orientation. As research topics the following areas
will be considered:
- Modelling with Differential Equations
- Model Reduction
- Multiscale and Inverse Problems
- Sparsity/Low Order Modelling
- Data assimilation

From: Guowei Wei wei@math.msu.edu
Date: May 15, 2018
Subject: Postdoc Position, Computational Hemodynamics, Hemostasis, and Thrombosis

I am seeking for an experienced postdoc to work on computational
modeling of hemodynamics, hemostasis and/or thrombosis and their
interactions with intervention drugs. The ideal candidate will hold a
Ph.D. degree in computational biomechanics, or bioengineering, or
mathematics, or computer science, or computational biophysics, or
bioinformatics, have extensive experience in code development and have
demonstrated the potential for excellence in research. Applications
consisting of a letter of application, current vita, and descriptions
of research plans and teaching experience should be submitted via
www.mathjobs.org/jobs (Michigan State University). In addition,
candidates should arrange for at least three letters of
recommendations, which may be submitted on the same website. To
by June 20, 2018, but applications will be accepted until the position
is filled. Please send an email to wei@math.msu.edu to acknowledge
your application. Depending on experience, the annual salary is at
least \$48,000, in additional to standard faculty benefits.

From: Bryan Quaife bquaife@fsu.edu
Date: May 17, 2018
Subject: Postdoc Position, Scientific Computing, Florida State Univ

The Department of Scientific Computing at Florida State University
invites applications for a postdoctoral position.

The research will focus on developing efficient integral equation
methods for simulating complex Stokesian fluids. Possible applications
include porous media flow, erosion, sedimentation, particulate flows,
and boundary layers. An ideal candidate will have experience with
numerical methods for integral equation methods applied to fluid
dynamics.

The full posting can be found at

From: Colin Cotter colin.cotter@imperial.ac.uk
Date: May 15, 2018
Subject: Postdoc Position, Time-parallel Methods for Weather Prediction

A postdoc position in time-parallel methods for numerical weather
prediction is available to work with Dr Colin Cotter in the Department
of Mathematics at Imperial College London.

https://www.imperial.ac.uk/jobs/description/NAT00175/research-associate-mathematics

From: Paul Mycek mycek@cerfacs.fr
Date: May 16, 2018
Subject: PhD Position, Scientific Computing, Cerfacs, Toulouse, France

We are looking for a PhD student within the "Parallel Algorithms" team
at Cerfacs, Toulouse, France. The work concerns parallel domain
decomposition methods for uncertain elliptic PDEs and is at the
interface of high performance computing, numerical linear algebra and
uncertainty quantification. This PhD thesis will be developed in the
framework of a scientific collaboration between Cerfacs, LIMSI-CNRS
and Inria Bordeaux.

PhD position description:
https://cerfacs.fr/en/offer/phd-stochastic-dd/

Working at Cerfacs: https://cerfacs.fr/en/jobs-at-cerfacs/

From: Bruno Carpentieri bruno.carpentieri@unibz.it
Date: May 15, 2018
Subject: PhD Positions, Computational Mathematics, Free Univ of Bozen-Bolzano

The Computational Mathematics Group of the Computer Science Faculty at
the Free University of Bozen-Bolzano offers to well- motivated,
enthusiastic mathematically talented candidates the opportunity for
fully-funded PhD positions in Computer Science with focus on
Computational Mathematics. Research areas of the group include
modelling, algorithms and their analysis in the fields of high-
performance computing, numerical linear algebra, partial differential
and integral equations. Topics of interest range from the development
of parallel and scalable iterative matrix solvers for large linear
systems and graph analytics (vertex- and linear-algebra-centric
formulation), to scalable and applied machine learning in
high-performance computing, to performance modelling, simulation and
optimization for extreme-scale scientific computing applications on
massively parallel computing systems (e.g, GPUs).

Further details are available on
https://www.unibz.it/en/faculties/computer-science/phd-computer-science/

Applications for PhDs are open until the 9th of July 2018 and can be

Informal enquiries about the post prior to formal application are
encouraged; they may be made to Prof. Bruno Carpentieri
(bruno.carpentieri@unibz.it).

From: Hans Munthe-Kaas hans.munthe-kaas@uib.no
Date: May 16, 2018
Subject: PhD Positions, Math, Univ Bergen Norway

Two PhD positions Department of Mathematics University of Bergen,

Pure mathematics:
https://www.jobbnorge.no/en/available-jobs/job/150784/phd-position-in-pure-mathematics

Pure or applied mathematics:
https://www.jobbnorge.no/en/available-jobs/job/150750/phd-position-in-mathematics-
pure-or-applied

The positions are open for any direction of interest to the
department. I would like to attract students who are interested in
working in any of the following areas:
* Geometric integration of differential equations
* Algebraic, combinatorial and differential geometric aspects of
computational differential equations, including stochastic
differential equations, rough paths and regularity structures.

Contact: hans.munthe-kaas@uib.no

From: Edward B. Saff Constr.Approx@vanderbilt.edu
Date: May 15, 2018
Subject: Contents, Constructive Approximation, 47 (3)

Constructive Approximation
Volume 47, Issue 3, June 2018

Observations on Interpolation by Total Degree Polynomials in Two
Variables, Jesus Carnicer, Tomas Sauer

Convergences of Alternating Projections in CAT(\kappa) Spaces, Byoung
Jin Choi, Un Cig Ji, Yongdo Lim

Zeros of Orthogonal Polynomials Near an Algebraic Singularity of the

On the Christoffel Function for the Generalized Jacobi Measures on a

Approximation and Entropy Numbers of Embeddings Between Approximation
Spaces, Fernando Cobos, Oscar Dominguez, Thomas Kuehn

Singular Values for Products of Two Coupled Random Matrices: Hard Edge
Phase Transition, Dang-Zheng Liu

Rahman's Biorthogonal Rational Functions and Superconformal Indices,
Hjalmar Rosengren

End of Digest
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