NA Digest, V. 16, # 45

NA Digest Tuesday, December 13, 2016 Volume 16 : Issue 45

Today's Editor:

Daniel M. Dunlavy
Sandia National Labs

Today's Topics: Subscribe, unsubscribe, change address, or for na-digest archives:

Submissions for NA Digest:

From: David Binner
Date: December 12, 2016
Subject: Optimization Routine UNCMND: Call for Users

I am translating the optimization routine UNCMND from FORTRAN into C++
and am almost finished. However, I have reached a point which has me
baffled, so I come to this group seeking users of this routine.
(Alternately, the single-precision version UNCMIN.)

Does anybody in this group presently use this routine (or has used
it?) If not, could anybody here refer me to somebody who does?

Any old test data or examples--including the error codes
returned--that could be shared with me would be greatly
appreciated. Specifically, I am looking for trials that return with
the error code 0.

In addition to replying through this group, please feel free to
contact me directly via the email address above.

Reference: "Numerical Methods and Software" by D. Kahaner, C. Moler,
S. Nash, Prentice Hall, 1988

Excerpt: "UNCMND minimizes a smooth nonlinear function of n

From: George Anastassiou
Date: December 12, 2016
Subject: New Book, Discrete Approximation Theory


In this monograph chapters are self-contained and can be read
independently and advanced courses can be taught out of this book. An
extensive list of references is given per chapter. Here our
generalized discrete singular operators are of types: Picard,
Gauss-Weierstrass and Poisson-Cauchy operators. We treat both the
unitary and non-unitary, univariate and multivariate cases of these
operators, which are not necessarily positive operators. Our study is
extremely rare in the literature, the first book of this kind, filling
a very important gap in the bibliography. The book's results are
expected to find applications in many areas of pure and applied
mathematics, and statistics. As such this monograph is suitable for
researchers, graduate students, and seminars of the above subjects,
also to be in all science libraries.


ISBN: 978-981-3145-83-2 (hardcover)
ISBN: 978-981-3145-85-6 (ebook)

From: Bruce Bailey
Date: December 08, 2016
Subject: New Book, Dynamic Mode Decomposition

Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems,
by J. Nathan Kutz, Steven L. Brunton, Bingni W. Brunton, Joshua
L. Procto, xvi + 234 pages / Softcover / 978-1-611974-49-2 / List Price
$69.00 / SIAM Member Price $48.30 / OT149

Data-driven dynamical systems is a burgeoning field-it connects how
measurements of nonlinear dynamical systems and/or complex systems can
be used with well-established methods in dynamical systems theory.
The recently developed dynamic mode decomposition (DMD) is an
innovative tool for integrating data with dynamical systems
theory. The DMD has deep connections with traditional dynamical
systems theory and many recent innovations in compressed sensing and
machine learning. This is the first book to address the DMD
algorithm; it presents a pedagogical and comprehensive approach to all
aspects of DMD currently developed or under development and blends
theoretical development, example codes, and applications to showcase
the theory and its many innovations and uses

To order or for more about this book, including links to its table of
contents, preface, and index, please visit .

From: Jean-Michel Muller
Date: December 12, 2016
Subject: New Book, Elementary Functions: Algorithms and Implementation

Birkhauser has just released the 3rd edition of the following book:

Elementary Functions: Algorithms and Implementation
Jean-Michel Muller

From: Anja Milde
Date: December 08, 2016
Subject: Advanced Process Control of Batch Processes, Germany, Feb 2017

KoMSO Challenge Workshop on "Challenges for Mathematical Modeling,
Simulation and Optimization for Advanced Process Control of Batch
Processes", February 9-10, 2017
Interdisciplinary Center for Scientific Computing (IWR)
Heidelberg University, Mathematikon
Im Neuenheimer Feld 205, 69120 Heidelberg, Germany

Batch processes are an important way of manufacturing chemicals. They
are particularly important for the production of specialty chemicals
due to their flexibility, simplicity and low investment costs. This
workshop treats opportunities and challenges to improve the operation
of batch processes in the framework of Real Time Optimization and of
Nonlinear Model Predictive Control. This includes newly developed
models of reaction kinetics, new sensors and new fast mathematical
optimization methods for process operation. The effects of model-based
optimizing control are demonstrated by presenting problems from
several application areas, e.g. polymerization processes. The aim of
this workshop is to bring together representatives from both academia
and industry in order to determine mathematical challenges of common
interest, to improve and integrate process control solutions for
applications across various industries, and to foster synergies and
collaborations. Participation in the workshop is free of charge. It
is, however, mandatory to register in advance. Registration for the
workshop is on a first come, first served basis and SPACE IS LIMITED!

From: Dmitri Kvasov
Date: December 10, 2016
Subject: Learning and Intelligent Optimization, Russia, Jun 2017

LION11 - 11th Learning and Intelligent Optimization Conference, Nizhny
Novgorod (Russia):
Submission deadline is approaching: December 18, 2016.

The LION conferences explore the intersections and uncharted
territories between machine learning, artificial intelligence,
mathematical programming and algorithms for hard optimization

In addition to scientific papers the following aspects should be
highlighted: Contests in continuous and discrete optimization.
Sessions dedicated to commercial software and open source initiatives.
Parallel computing, supercomputing, and cloud for "big optimization".
Elevator pitches about new and crazy ideas (also by PhD students).
Tutorials about methods and software.

Conference proceedings will be published by Springer in LNCS series.

Collocated with Net2017 conference to be held in the same city in the
period June 22-24, 2017.

From: Paul Constantine
Date: December 12, 2016
Subject: SIAM Parameter Space Dimension Reduction, USA, Jul 2017

SIAM Workshop on Parameter Space Dimension Reduction (DR17)
July 9-10, Pittsburgh, PA

The DR17 workshop brings together researchers across mathematics,
statistics, and engineering to explore a range of emerging techniques
for parameter space dimension reduction. Topics of interest include:
active subspaces; basis adaptation; inverse regression; sufficient
dimension reduction; sloppy models; sensitivity analysis; ridge
recovery and approximation; deterministic and statistical parameter
estimation; and applications with science and engineering simulations
or data sets.

The submission deadline is February 27. Submitted abstracts will be
considered for a 20-minute presentation or poster. More details on the

Some travel support is available for students and early-career
researchers. Deadline to apply for travel support is January 20.

From: H. Metin Aktulga
Date: December 08, 2016
Subject: Faculty Position, Numerical Linear Algebra, Michigan State Univ

The Department of Computational Mathematics, Science, and Engineering
(CMSE) at Michigan State University invite applications for a
tenure-system position in the area of Numerical Linear
Algebra. Candidates must have a PhD in Mathematics, Statistics,
Computer Science, or a related field. The position will be filled at
the assistant, associate, or full professor level depending on the
qualifications and record of the successful candidate. The candidate
is expected to establish a sustainable research program, make
significant scholarly contributions to their discipline, be an
effective teacher and mentor of both undergraduate and graduate
students, and engage in institutional and professional service. The
Department of CMSE is particularly interested in candidates whose
research efforts focus on numerical linear algebra as applied to
large-scale and high performance computing, including linear solvers,
nonlinear solvers, eigensolvers, preconditioning techniques for
massively parallel applications, and fast direct solvers, as well as
novel numerical methods designed to achieve high performance on
heterogeneous computing platforms and next-generation High Performance
Computing hardware.

Interested individuals should submit an application for this position
through: and should refer to position
#4449. Applicants must submit a detailed resume, a cover letter
summarizing their qualifications, vision statements for teaching and
research, and the names and contact information for at least three
references. For full consideration, applications should be received
before January 11th, 2017. Applications will be reviewed on a
continuing basis thereafter until the position is filled. Nominations
or questions are welcome by contacting the search committee chair
through email at The position is available on August
16, 2017.

From: Stig Larsson
Date: December 08, 2016
Subject: Senior Lecturer Position, Chalmers Univ of Technology, Sweden

The Department of Mathematical Sciences at Chalmers University of
Technology, Gothenburg, Sweden, invites applications for a Senior
Lecturer position. Applications from all mathematical and applied
mathematical research areas will be considered.

See Ref No 20160477 at

Deadline: January 16, 2017.

From: Hartwig Anzt
Date: December 06, 2016
Subject: Postdoc Position, Karlsruhe Institute of Technology (KIT), Germany

We are looking for a highly motivated candidate to instruct and carry
out research at the edge of numerical mathematics and High Performance
Computing. Particular focus is on sparse linear algebra, iterative
methods, and preconditioning. Candidates with interest in Big Data,
Machine Learning, or Graph Theory are also invited to apply.

Candidates are expected to have A PhD degree or equivalent in
Mathematics, Computer Science, or a related field; A publication
record reflecting excellent research; Motivation to inspire and
supervise students; A solid background in numerical mathematics and
High Performance Computing; Experience in software development on HPC
architectures; Interest in inter-disciplinary research with
application specialists.

The initial appointment is for 2 years, and offers a competitive
salary plus an additional budget for relocation. Close cooperation
with international partner institutions is anticipated, including
research visits to US universities.

The candidate is expected to start in summer/fall 2017.

Interested candidates should get in contact with
Hartwig Anzt,

From: Carola Schönlieb
Date: December 09, 2016
Subject: Postdoc Position, Maths & Stats for Medical Imaging, UK

We invite applications for at least one Post Doctoral Research
Associate position to work in the EPSRC Centre for Mathematical and
Statistical Analysis of Multimodal Clinical Imaging (CMIH) at the
University of Cambridge. The centre is a collaboration between
mathematics, engineering, physics and biomedical scientists and
clinicians, and aims to achieve synergies between applied mathematics
and statistics through the focus on the analysis of clinical imaging,
particularly that arising in neurological, cardiovascular and oncology
imaging. The research activity of the successful candidate will take
place within one or more multidisciplinary projects joint between
investigators within the centre. Preference will be given to
applicants interested in working on projects involving Electronic
Health Records and Imaging, joint reconstruction of multimodal
imaging, dynamic image reconstruction and analysis, and/or image
distortion correction. For further information concerning the types of
project the centre is likely to undertake and a list of investigators,
please visit The PDRAs will join a cohort of
researchers in the mathematical and statistical analysis of clinical
imaging who are already working in the centre. Applicants must have
(or be about to receive) a PhD degree in mathematics or statistics (or
closely related discipline). The ideal candidate will be experienced
in one or more of the following areas: statistical imaging /
statistical shape analysis, functional data analysis, spatial
statistics, inverse problems, computational analysis, optimisation,
variational methods in image processing, data science. Experience in
parallel computing and C programming skills are desirable.

Informal inquiries can be made by contacting

Applications should be made at the following website where a number of
postdoctoral positions across the faculty can be applied for -

Application deadline is the 10th of January 2017.
Limit of tenure: 2 years.

The University values diversity and is committed to equality of
opportunity. The University has a responsibility to ensure that all
employees are eligible to live and work in the UK.

From: Marie E. Rognes
Date: December 12, 2016
Subject: Postdoc Position, NA/Scientific Computing, Simula, Norway

Applications are invited for a Postdoc position in Numerical
Analysis/Scientific Computing at Simula Research Laboratory within The
Numerical Waterscape of the Brain (Waterscape) Project. The position
is initially for 2 years. The official announcement with full details
of the position and online application instructions can be found here:

Waterscape is an RCN FRINATEK project (2016-2019) aiming to develop a
numerical and technological foundation for in silico studies of fluid
flow and solute transport within brain tissue for both normal and
pathological conditions. For more information about the project, see

Applicants are evaluated on a rolling basis, with preference to
applications submitted before January 15 2017.

From: Bryan Quaife
Date: December 12, 2016
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,
Stokes equations, and HPC.

Please contact Bryan Quaife at for more details.

The full posting can be found at

From: Carola Schönlieb
Date: December 07, 2016
Subject: Postdoc Positions, Mathematics of Information, Cambridge, UK

We are pleased to advertise three positions for Postdoctoral Research
Fellows affiliated with the new Cantab Capital Institute for the
Mathematics of Information (CCIMI, The Fellow will be free to pursue
independent research related to fundamental mathematical problems and
methodology for understanding, analysing, processing and simulating
data. The Fellowship is available for three years. Appointment will be
made at an appropriate point on the University's Postdoctoral Research
Associate scale or the Senior Research Associate scale as
appropriate. The Fellow will also receive an annual allowance for
research expenses. Applicants should have a PhD in Mathematics,
Statistics or closely related discipline before commencing the
Fellowship. Senior Research Associates will have commensurately more
experience, including at least three years postdoctoral experience.
Duties would include developing and conducting individual and
collaborative research objectives, proposals and projects. The role
holder will be expected to plan and manage their own research and
administration, with guidance if required, and to assist in the
preparation of proposals and applications to external bodies. You must
be able to communicate material of a technical nature and be able to
build internal and external contacts. You may be asked to assist in
the supervision of student projects, the development of student
research skills, provide instruction or plan/deliver seminars relating
to the research area of the CCIMI. To apply online for this vacancy,
and to find out further information, please visit

The closing date for applications is the 10th of January 2017.

Informal enquiries about the positions may be made to:

The University of Cambridge values diversity and is committed to
equality of opportunity. The Department would particularly welcome
applications from women, since women are, and have historically been,
underrepresented on our research staff. The University has a
responsibility to ensure that all employees are eligible to live and
work in the UK.

From: Tim Burns
Date: December 07, 2016
Subject: Postdoc Positions, NIST

The Applied and Computational Mathematics Division (ACMD) of the
National Institute of Standards and Technology (NIST) invites
applications for two-year NRC postdoctoral research positions at NIST
Laboratories in Gaithersburg, Maryland, and Boulder, Colorado. NIST is
a Federal government research laboratory specializing in measurement
science. ACMD consists of some 47 full-time professional staff, along
with part-time faculty appointees and guest researchers. Staff members
engage in collaborative research with scientists throughout NIST,
providing expertise in applied mathematics, mathematical modeling, and
computational science and engineering. Research areas of interest
include combinatorial and discrete algorithms, computational materials
science, computational fluid dynamics, computational electromagnetics,
computational biology, orthogonal polynomials and special functions,
applied optimization and simulation, combinatorial software testing,
data mining, immersive visualization, parallel and distributed
algorithms, quantum information science, and statistics for quantum
systems. Of particular interest are candidates whose interests also
overlap with the thrusts of recent Federal initiatives, including the
National Strategic Computing Initiative
high-performance-computing) and the Materials Genome Initiative
(, especially in the area of uncertainty
quantification for modeling and simulation.

Candidates and their research proposals are evaluated in a competitive
process managed by the National Research Council (NRC) Associateship
Programs. The current stipend is $67,588 per year. For further
details, see
opportunities.cfm. Application deadlines are February 1 and August 1.
Appointments commence within one year of selection. For questions,
contact Tim Burns,

NIST is an equal opportunity/affirmative action employer. The NRC
Associateship Program at NIST is restricted to US citizens.

From: Yves Lucet
Date: December 08, 2016
Subject: PhD/MSc Positions, Optimization, UBC

COCANA (Centre for Optimization Convex Analysis and Nonsmooth
Analysis, invites applications for PhD/MSc
positions starting September 2017.

The positions will be based at the UBC Okanagan campus
( The PhD positions are fully funded for 4 years
while the MSc positions are fully funded for 2 years (The MSc in
Computer Science program mandate a minimum funding of $17,500/year.)

The first project is on road design optimization. The research is
industry sponsored and include the opportunity to develop
patents. Good programming skills (C/C++ preferred) are required, and
optimization or operations research skills are desired.

The second project is on computational convex analysis and involves
the creation of new algorithms to compute mathematical objects
regularly used in convex analysis. The background required is in
algorithms with good programming skills in high level languages
(MATLAB, Scilab, or Octave), and a desire to learn convex analysis.

Historically students with a computer science background have been
very successful in our program (and found positions at Google, Amazon,
or Microsoft), as well as students with a mathematical background and
strong programming skills.

Interested candidates should contact Dr. Yves Lucet, Professor,
Computer Science, Associate Head Computer Science/Data Science at The deadline for funded applications is January 31,

From: Hartwig Anzt
Date: December 06, 2016
Subject: PhD Position, Karlsruhe Institute of Technology (KIT), Germany

We are looking for a highly motivated candidate to carry out research
at the edge of numerical mathematics and High Performance Computing
(HPC). Particular focus is on sparse linear algebra, iterative
methods, and preconditioning. Candidates with interest in Big Data,
Machine Learning, or Graph Theory are also invited to apply.

Candidates are expected to have A master's degree or equivalent in
Mathematics, Computer Science, or a related field; A solid background
in numerical mathematics; Experience in parallel programming and/or
scientific computing; An academic record demonstrating excellent oral
and written communication skills in English.

The position comes with a competitive 3-year funding plus an
additional budget for relocation. Close cooperation with international
partner institutions is anticipated, which also offers the possibility
of an extended research stay in the US.

The candidate is expected to start in summer/fall 2017.

Interested candidates should get in contact with
Hartwig Anzt,

From: Johan Hoffman
Date: December 08, 2016
Subject: PhD Position, Scientific Computing, KTH

KTH Royal Institute of Technology in Stockholm is Sweden,s largest
technical research and learning institution and home to students,
researchers and faculty from around the world. This PhD position is
based at the department of Computational Science and Technology.

As doctoral student you will conduct research in the area of numerical
methods with particular focus on adaptive finite element methods,
efficient algorithms for high performance computing and data
assimilation, with applications in biomechanics and aerodynamics,
including patient-specific simulation of the human heart, virtual
prototyping of renewable energy technology, and forecasting of urban
air quality. The work will involve mathematical analysis, programming
and modelling, and will be a combination of independent work and
collaboration with other researchers within the different projects at
the department, including the FEniCS open source project
( and the cloud computing project MSO4SC

For more information:

From: Matthias J. Ehrhardt
Date: December 07, 2016
Subject: CFP, Inverse Problems, Special issue

Special issue on Joint Reconstruction and
Multi-Modality/Multi-Spectral Imaging

Inverse Problems is pleased to announce the following upcoming
special issue, which is now open for submissions via our
submissions page. We also kindly ask you to distribute this call
among all colleagues who might be interested in submitting their work.

Abstract: Multi-channel (either multi-modality or multi-spectral)
imaging has become increasingly interesting in many areas like medical
imaging, remote sensing, photography and geophysics to name just a
few. It includes methods where a subject is imaged on two or more
channels either sequentially or simultaneously, as well as coupled
techniques where user-controlled probes generate stimulated signals
read by a complementary measurement system. Examples include Positron
Emission Tomography/Magnetic Resonance Imaging (PET-MRI),
multi-spectral CT, and joint DC resistivity/bore hole tomography for
oil-exploration. Relevant topics: Multimodality systems such as
Positron Emission Tomography plus X-Ray Computed Tomography (PET-CT),
Single Photon Emission Computed Tomography plus CT (SPECT-CT), PET
plus Magnetic Resonance Imaging (PET-MRI), EEG +MEG, etc.; Combining
ill-posed and (almost) well-posed imaging systems such as DOT+MRI,
EIT+CT, EEG+fMRI, etc.; Multi- and hyperspectral imaging systems,
joint reconstruction of spectral or colour data; Multi-parameter MRI
(e.g. fingerprinting) or fMRI time series; Coupled Physics Imaging
such as Photoacoustic Tomography (PAT)-plus-Ultrasound (US), ShearWave
Elastography (SWE) plus US, etc.; Design of priors promoting joint
statistical and/or geometrical similarity such as joint sparsity or
joint edges; Algorithms for solving inverse problems with joint
priors; Analysis of joint reconstruction approaches (uniqueness,
improvement in resolution etc.).

Potential authors are invited to contact one of the editors to discuss
suitability prior to submission.

From: Nicholas Valente
Date: December 06, 2016
Subject: Contents, Advances in Computational Mathematics, 42 (6)

MATHEMATICS, VOL. 42, NO. 6, 2016

Dimensions of spline spaces over non-rectangular T-meshes, Chao Zeng,
Meng Wu, Fang Deng & Jiansong Deng

Fixed point algorithm based on adapted metric method for convex
minimization problem with application to image deblurring, Dai-Qiang
Chen, Yan Zhou & Li-Juan Song

Unconditional convergence and optimal error estimates of the Euler
semi-implicit scheme for a generalized nonlinear Schrödinger equation,
Wentao Cai, Jian Li & Zhangxin Chen

Convergence analysis of a minimax method for finding multiple
solutions of hemivariational inequality in Hilbert space, Xudong Yao

Asymptotically compatible schemes for the approximation of fractional
Laplacian and related nonlocal diffusion problems on bounded domains,
Xiaochuan Tian, Qiang Du & Max Gunzburger

One condition for solution uniqueness and robustness of both l1-
synthesis and l1-analysis minimizations, Hui Zhang, Ming Yan & Wotao

A comparison of Rosenbrock and ESDIRK methods combined with iterative
solvers for unsteady compressible flows, David S. Blom, Philipp
Birken, Hester Bijl, Fleur Kessels, Andreas Meister & Alexander H. van

Bell-shaped nonstationary refinable ripplets, Francesca Pitolli

Superconvergence of three dimensional Morley elements on cuboid meshes
for biharmonic equations, Jun Hu, Zhongci Shi & Xueqin Yang

A weak Galerkin finite element method for the Oseen equations, Xin
Liu, Jian Li & Zhangxin Chen

Variational Laplacians for semidiscrete surfaces, Wolfgang Carl &
Johannes Wallner

From: Chi-Wang Shu
Date: December 06, 2016
Subject: Contents, Journal of Scientific Computing, 69 (3)

Journal of Scientific Computing
Volume 69, Number 3, December 2016

Fully Discretized Energy Stable Schemes for Hydrodynamic Equations
Governing Two-Phase Viscous Fluid Flows, Yuezheng Gong, Xinfeng Liu
and Qi Wang

Stabilized Times Schemes for High Accurate Finite Differences
Solutions of Nonlinear Parabolic Equations, Matthieu Brachet and
Jean-Paul Chehab`

Minimizing Eigenvalues for Inhomogeneous Rods and Plates, Weitao Chen,
Ching-Shan Chou and Chiu-Yen Kao

A Two-Stage Low Rank Approach for Calibrationless Dynamic Parallel
Magnetic Resonance Image Reconstruction, Likun Hou, Hao Gao and
Xiaoqun Zhang

Application of WENO-Positivity-Preserving Schemes to Highly
Under-Expanded Jets, Stefano Zaghi, Andrea Di Mascio and Bernardo

On the Numerical Solution of the Stationary Power-Law Stokes
Equations: A Penalty Finite Element Approach, J.K. Djoko, J.M. Lubuma
and M. Mbehou

A Second-Order, Weakly Energy-Stable Pseudo-spectral Scheme for the
Cahn-Hilliard Equation and Its Solution by the Homogeneous Linear
Iteration Method, Kelong Cheng, Cheng Wang, Steven M. Wise and Xingye

Tracing Multiple Solution Branches for Nonlinear Ordinary Differential
Equations: Chebyshev and Fourier Spectral Methods and a
Degree-Increasing Spectral Homotopy [DISH], John P. Boyd

A Weighted ADI Scheme for Subdiffusion Equations, Hong-lin Liao, Ying
Zhao and Xing-hu Teng

A Low Complexity Algorithm for Non-Monotonically Evolving Fronts,
Alexandra Tcheng and Jean-Christophe Nave

A Priori and a Posteriori Error Analyses of an Augmented HDG Method
for a Class of Quasi-Newtonian Stokes Flows, Gabriel N. Gatica and
Filander A. Sequeira

A Superconvergent C0 Discontinuous Galerkin Method for Kirchhoff
Plates: Error Estimates, Hybridization and Postprocessing, Xuehai
Huang and Jianguo Huang

An Adaptive Finite Element Method for the Transmission Eigenvalue
Problem, Jiayu Han and Yidu Yang

Local Linear Convergence of a Primal-Dual Algorithm for the Augmented
Convex Models, Tao Sun, Roberto Barrio, Hao Jiang and Lizhi Cheng

A High-Order Level-Set Method with Enhanced Stability for Curvature
Driven Flows and Surface Diffusion Motion, Yujie Zhang and Wenjing Ye

An h-Adaptive RKDG Method for the Vlasov-Poisson System, Hongqiang
Zhu, Jianxian Qiu and Jing-Mei Qiu

Capacity of the Adini Element for Biharmonic Equations Jun Hu, Xueqin
Yang and Shuo Zhang

A High Order HDG Method for Curved-Interface Problems Via
Approximations from Straight Triangulations, Weifeng Qiu, Manuel
Solano and Patrick Vega

End of Digest