Slides of Lectures
by Arnold Neumaier
It is God's privilege to conceal things,
but the kings' pride is to research them.
(Proverbs 25:2)
A= Analysis, C = Combinatorics, F = Foundations,
L = Linear Algebra, N = Numerical Analysis, O = Optimization,
P = Physics/Chemistry, S = Statistics
In some cases, there are associated publications, see
Recent Papers and Preprints
LS.
A. Neumaier,
Estimation of accuracy in large-scale linear least squares
solutions,
Slides of a lecture given on September 13, 2019 at the
MAT TRIAD 2019, Liblice, Czech Republic
pdf file
C.
A. Neumaier and S. Penjic,
t-point counts in distance-regular graphs,
Slides of a lecture presented at the
9th Slovenian International Conference on Graph Theory
(Bled, Slovenia), 2019
pdf file
Many well-known inequalities for the intersection array can be derived
in a uniform way using t-point counts, normalized counts of
the number of ordered subsets isomorphic to a template with t vertices
and certain specified distances between them.
In this talk it is shown that by considering t-point counts with
t up to 6, the diameter bounds by Ivanov and Ivanov may be derived.
LS.
A. Neumaier and E. Groeneveld,
meBLUP = ssBLUP without relationship matrices,
Slides of a lecture given on September 20, 2018
pdf file
meBLUP is a new method for the genetic evaluation
of joint pedigree and genomic data, totally avoiding
relationship matrices or their inverse, which figure
prominently in all previous approaches.
When either the pedigree information or the genomic
information is absent, meBLUP reduces to equations
that give exactly the same BLUPs and BLUEs as the
standard formulation.
First numerical results indicate that meBLUP is
likely to be competitive with ssBLUP, the current
technique for the joint evaluation of pedigree and
genomic data.
LP.
A. Neumaier,
Invitation to Coherent Spaces,
Slides of a lecture presented at the
Conference on Quantum Harmonic Analysis and Symplectic Geometry
(Strobl, Austria), 2018
pdf file
F.
A. Neumaier,
From Informal to Formal Mathematics,
Slides of a lecture presented at VINO 2017
(Technical University Vienna, Austria)
pdf file
N.
A. Neumaier,
Concise - a synthesis of types, grammars, semantics,
Lecture, Isaac Newton Institute for Mathematical Sciences,
Cambridge 2017.
video of the lecture
N.
A. Neumaier,
The communication of mathematics,
Lecture, Isaac Newton Institute for Mathematical Sciences,
Cambridge 2017.
video of the lecture
F.
A. Neumaier,
Artificial Intelligence, Mathematics, and Consciousness,
Slides, 2016.
pdf file
P.
A. Neumaier,
Classical models for quantum light,
Slides of a lecture given on April 7, 2016 at the Zentrum für
Oberflächen- und Nanoanalytik of the University of Linz.
pdf file (350K)
In this lecture, a timeline is traced from Huygens' wave optics to the
modern concept of light according to quantum electrodynamics.
The lecture highlights the closeness of classical concepts and quantum
concepts to a surprising extent. For example, it is shown that the
modern quantum concept of a qubit was already known in 1852 in fully
classical terms.
P.
A. Neumaier,
Classical models for quantum light II,
Slides of a lecture given on April 8, 2016 at the Zentrum für
Oberflächen- und Nanoanalytik of the University of Linz.
pdf file (425K)
In this lecture the results of the historical review given in
my lecture
''Classical models for quantum light''
are utilized to reassess the meaning of observables and stochastic
processes for the classical and quantum description of light.
In particular we discuss the description of partially coherent,
fluctuating light through classical stochastic Maxwell equations
(with uncertainty in the initial conditions only), and look at a
generalization that works for all quantum aspects of arbitrary
quantum systems.
N.
A. Neumaier,
Rigorously covering all solutions of infinite-dimensional equations,
Lecture, 2014.
video of the lecture at BIRS
O.
A. Neumaier,
VXQR: Derivative-free unconstrained optimization based on QR
factorizations,
Slides, 2010.
pdf file (105K)
figures (1429K)
O.
A. Neumaier,
AD-like techniques in global optimization,
Slides, 2008
pdf file (2283K)
F.
A. Neumaier,
FMathL - Formal Mathematical Language,
Slides, 2009
pdf file (98K)
Slides for a lecture at the
AUTOMATHEŘ 2009
workshop, giving an overview of our work in the
FMathL project for creating a modeling and documentation language
for mathematics, suited to the habits of mathematicians
NO.
A. Neumaier,
Towards optimization-based error bounds for uncertain PDEs,
Slides, 2008
pdf file (347K)
Using tools from functional analysis and global optimization,
methods are presented for obtaining, given an approximate solution
of a partial differential equation, realistic error bounds for some
response functional of the solution.
The method is based on computable bounds for the inverse of linear
elliptic operators. Like in the dual weighted residual (DWR) method,
our error bounds for response functionals have the quadratic
approximation property (so that they are asymptotically optimal),
but in contrast to DWR, our bounds are rigorous and also capture
the higher order contributions to the error.
Using global optimization techniques, bounds can be found
that not only cover the errors in solving the differential equations
but also the errors caused by the uncertainty in the parameters.
This provides reliable tools for the assessment of uncertainty in the
solution of elliptic partial differential equations. Our bounds are
independent of the way the approximations are obtained, hence can be
used to independently verify the quality of an approximation computed
by an arbitrary solver.
The bounds not only account for discretization errors but also for other
numerical errors introduced through numerical integration and boundary
aproximations.
We also discuss how to represent model uncertainty in terms of
so-called clouds, which describe the rough shapes of typical samples
of various size, without fixing the details of the distribution.
Clouds use only information from 1- and 2-dimensional marginal
distributions, readily available in practice.
P.
A. Neumaier,
Optical models for quantum mechanics,
Slides of a lecture given on February 16, 2010 at the
Institute for Theoretical Physics, University of Giessen.
pdf file (156K)
This lecture (the second of three) discusses work
towards a new, classical view of quantum mechanics.
It is based on an analysis of polarized light,
of the meaning of quantum ensembles in a field theory,
of classical simulations of quantum computing algorithms,
and resulting optical models for the simulation
of quantum mechanics.
In particular, it is shown that
classical second-order stochastic optics
is precisely the quantum mechanics of a single photon,
with all its phenomenological bells and whistles.
P.
A. Neumaier,
Classical and quantum field aspects of light,
Slides of a lecture given on January 29, 2009 at the Institute of
Quantum Optics and Quantum Information of the Austrian Academy of
Sciences, Vienna.
pdf file (374K)
This lecture discusses foundational problems
on the nature of light revealed by
1. attempts to define a probability concept for photons,
2. quantum models for photons on demands (and their realization
through laser-induced emission by a calcium ion in a cavity),
3. models explaining the photo effect, and
4. Bell-type experiments for single photon nonlocality.
O.
A. Neumaier,
Global Optimization and Constraint Satisfaction,
Slides, 2006.
pdf file (173K)
O.
A. Neumaier,
Constrained global optimization,
Slides, 2005.
pdf file (225K)
O.
A. Neumaier,
Worst case analysis of mechanical structures by interval methods,
Slides, 2005.
pdf file (263K)
OS.
A. Neumaier,
Uncertainty modeling for robust verifiable design,
Slides, 2004.
pdf file (318K)
O.
A. Neumaier and J.-P. Merlet,
Constraint satisfaction and global optimization in robotics,
Slides, 2002.
pdf file (449K)
Global Optimization
Protein Folding
Interval Methods
Regularization
Mathematical Software
Computational Mathematics Links
Mathematics Links
Statistics Links
my
home page (http://arnold-neumaier.at)
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)