Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
Not a member yet
2063 research outputs found
Sort by
Statistical and Computational Aspects of Learning with Complex Structure
No full textThe recent explosion of data that is routinely collected has led scientists to contemplate more and more sophisticated structural assumptions. Understanding how to harness and exploit such structure is key to improving the prediction accuracy of various statistical procedures. The ultimate goal of this line of research is to develop a set of tools that leverage underlying complex structures to pool information across observations and ultimately improve statistical accuracy as well as computational efficiency of the deployed methods. The workshop focused on recent developments in regression and matrix estimation under various complex constraints such as physical, computational, privacy, sparsity or robustness. Optimal-transport based techniques for geometric data analysis were also a main topic of the workshop
Moist Processes in the Atmosphere
No full textProcesses related to water in the atmosphere lead to severe uncertainties in weather
forecasting and climate research. Atmospheric water vapor and cloud water strongly
influence the Earth's energy budget through, e.g., energy conversions associated
with phase changes, fluid dynamical effects associated with buoyancy, and through their
influence on radiative transfer properties of the atmosphere. Given the critical green-house
effect of water vapor, it seems astounding that climate modellers cannot with certainty state
whether the Earth's cloud system has a positive or negative influence on the global mean
temperature. The formation of clouds involves small-scale processes currently unresolved by
climate models, and thus cloud cover is one of the main sources of uncertainty. This large
uncertainty has its roots in the extremely wide range of length and time scales associated
with moist processes, which pose an equally wide range of challenges to mathematical and
computational modelling.
New and innovative methods, modeling frameworks, efficient computational techniques, and complex statistical data analysis procedures as well as their mathematical analysis are urgently needed in order to make progress in this new field -- from the mathematicians point of view. One of the main goals of this workshop is to show the path forward for current and future applied mathematical scientists, to work hand in hand across the disciplines of mathematics, physics, and atmospheric science, in order to tackle the complex problem of dynamical and thermodynamical processes associated with clouds and moisture, both from the theoretical and the applied view points
Algebra, matrices, and computers
No full textWhat part does algebra play in representing the real
world abstractly? How can algebra be used to solve
hard mathematical problems with the aid of modern
computing technology? We provide answers to these
questions that rely on the theory of matrix groups
and new methods for handling matrix groups in a
computer
Combinatorics, Probability and Computing
No full textThe main theme of this workshop was the use of probabilistic
methods in combinatorics and theoretical computer science. Although
these methods have been around for decades, they are being refined all
the time: they are getting more and more sophisticated and powerful.
Another theme was the study of random combinatorial structures,
either for their own sake, or to tackle extremal questions. The workshop
also emphasized connections between probabilistic combinatorics and
discrete probability
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
No full textWe study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball is, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems
A Cheeger Type Inequality in Finite Cayley Sum Graphs
No full textLet be a finite group and be a symmetric generating set of with . We show that if the undirected Cayley sum graph is an expander graph and is non-bipartite, then the spectrum of its normalised adjacency operator is bounded away from . We also establish an explicit lower bound for the spectrum of these graphs, namely, the non-trivial eigenvalues of the normalised adjacency operator lies in the interval , where denotes the (vertex) Cheeger constant of the -regular graph and . Further, we improve upon a recently obtained bound on the non-trivial spectrum of the normalised adjacency operator of the non-bipartite Cayley graph
A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables
No full textFor compact sets , we introduce a subalgebra of , which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
No full textThroughout the history of dynamical systems, instruments
have been used to calculate and visualize (approximate)
solutions of differential equations. Here
we describe the approach of a group of physicists and
engineers in the period 1948–1964, and we give examples
of the specific (analogue) mathematical instruments
they conceived and used. These examples
also illustrate how their analogue culture and practices
faced the advent of the digital computer, which
appeared at that time as a new instrument, full of
promises