Abstract: The study of quantum correlations started with John Bell's discovery of nonlocality and has led to real-world applications in cryptography, randomness certification and other fields. However, the structure of the set of quantum correlations is not well understood. Even to determine if a given correlation is quantum can be difficult in general. In this talk, I am going to introduce tools from semidefinite programming which can be used to determine if a given correlation is in the quantum set or an extreme point of the quantum set. Related basic concepts of semidefinite programming and quantum correlation will also be covered.
Abstract: I will connect continued fractions with even or odd partial quotients to geodesic flows on modular surfaces. The connection between geodesics on the modular surface PSL(2,Z)\H and regular continued fractions was established by Series, and we extend this to the odd and grotesque continued fractions and even continued fractions. This is joint work with Florin Boca.
Abstract: The Virtual Element Method (VEM), is a very recent technology introduced in [Beirao da Veiga, Brezzi, Cangiani, Manzini, Marini, Russo, 2013, M3AS] for the discretization of partial differential equations, that has shared a good success in recent years. The VEM can be interpreted as a generalization of the Finite Element Method that allows to use general polygonal and polyhedral meshes, still keeping the same coding complexity and allowing for arbitrary degree of accuracy. In addition to the possibility to handle general polytopal meshes, the flexibility of the above construction yields other interesting properties with respect to more standard Galerkin methods. For instance, the VEM easily allows to build discrete spaces of arbitrary C^k regularity, or to satisfy exactly the divergence-free constraint for incompressible fluids.
The present talk is an introduction to the VEM, aiming at showing the main ideas of the method. We consider for simplicity a simple elliptic model problem but set ourselves in the more involved 3D setting. In the first part we introduce the adopted Virtual Element space and the associated degrees of freedom, first by addressing the faces of the polyhedrons (i.e. polygons) and then building the space in the full volumes. We then describe the construction of the discrete bilinear form and the ensuing discretization of the problem. Furthermore, we show a set of theoretical and numerical results. In the very final part, we will give a glance at a pair of more involved problems.
Abstract: Toroidal magnetic fields can confine charged particles, which can be exploited for basic physics studies or potentially for fusion energy. The magnetic field should lack axisymmetry (continuous rotational symmetry), or else a large electric current is needed inside the confinement region. However, the magnetic field should possess two properties that could be termed âhidden symmetriesâ. The first, integrability, means the field lines should lie on nested toroidal surfaces, without regions of islands or chaos. The second, called `quasi-symmetryâ, generalizes the conservation of canonical angular momentum in the presence of strong magnetic fields. This second property arises because the Lagrangian for particle motion in strong magnetic fields can be expressed in terms of the strength of the field, independent of its direction. Magnetic fields with these properties can be found using optimization or using a new constructive procedure.
Abstract: The question of reproducibility of research outcomes is discussed now in the open press with a potential negative
impact on science as a whole. In dealing with this question, from a statistical view point, several methodological
advances have been proposed (like FDR) and several clarification attempts have been published (like the ASA
statement on the p value). These attempts seem to only partially address the rising concerns of the public and
research funding agencies.
Kenett and Shmueli in Clarifying the terminology that describes scientific reproducibility, Nature Methods, 12(8), p
699, 2015, review the terminology used in this debate and refer to generalizability, as a dimension that can clarify
what are research claims that should be scrutinize as reproducible. Generalizability is one of the eight dimensions
of the information quality (InfoQ) framework presented in Kenett and Shmueli, On information quality: The
Potential of Data and Analytics to Generate Knowledge, John Wiley and Sons, 2016.
In this talk, we expand on the idea of generalizability of research findings by referring to Type S errors proposed in
Gelman and Carlin (2014) [Beyond power calculations: Assessing Type S (sign) and Type M (magnitude) errors,
Perspectives on Psychological Science, Vol. 9(6), pp. 641â651]. The talk will first discuss methods for setting up a
boundary of meaning used in generalizing research findings. It will then show how Type S errors and directional
FDR methods fit with this generalizability approach. An example from research in localized colon cancer
diagnostics will be used to demonstrate the approach.
4176 Campus Drive - William E. Kirwan Hall
College Park, MD 20742-4015
P: 301.405.5047 | F: 301.314.0827