4,412 research outputs found
[Book Review of] \u3cem\u3eLoving and Curing the Neurotic\u3c/em\u3e, by Dr. Anna Terruwe and Dr. Conrad Baars
Geometry of curved Yang-Mills-Higgs gauge theories
This is my Ph.D. thesis defended at 31 May 2021, and it is devoted to the
study of the geometry of curved Yang-Mills-Higgs gauge theory (CYMH GT), a
theory introduced by Alexei Kotov and Thomas Strobl. This theory reformulates
classical gauge theory, in particular, the Lie algebra (and its action) is
generalized to a Lie algebroid , equipped with a connection , and
the field strength has an extra term . In the classical situation is
an action Lie algebroid, is then the canonical flat connection with
respect to such an , and . The shortened main results of this
Ph.D.thesis are the following; see the abstract in the thesis itself for more
information: 1. Reformulating curved Yang-Mills-Higgs gauge theory, also
including a thorough introduction and a coordinate-free formulation. Especially
the infinitesimal gauge transformation will be generalized to a derivation on
vector bundle -valued functionals, induced by a Lie algebroid connection. 2.
We will discuss what type of connection for the definition of the infinitesimal
gauge transformation should be used, and this is argued by studying the
commutator of two infinitesimal gauge transformations, viewed as derivations on
-valued functionals. We take the connection on then in such a way that
the commutator is again an infinitesimal gauge transformation. 3. Defining an
equivalence of CYMH GTs given by a field redefinition. In order to preserve the
physics, this equivalence is constructed in such a way that the Lagrangian of
the studied theory is invariant under this field redefinition. It is then
natural to study whether there are equivalence classes admitting
representatives with flat and/or zero , and we will do so
especially for Lie algebra bundles, tangent bundles and their direct products
as Lie algebroids.Comment: This is my Ph.D. thesis which I have defended on 31 May 2021, in
total 293 pages; the thesis lists a more detailed abstract about my main
results; newer versions with several corrected typos, clarified texts et
Scalable visualisation methods for modern Generalized Additive Models
In the last two decades the growth of computational resources has made it
possible to handle Generalized Additive Models (GAMs) that formerly were too
costly for serious applications. However, the growth in model complexity has
not been matched by improved visualisations for model development and results
presentation. Motivated by an industrial application in electricity load
forecasting, we identify the areas where the lack of modern visualisation tools
for GAMs is particularly severe, and we address the shortcomings of existing
methods by proposing a set of visual tools that a) are fast enough for
interactive use, b) exploit the additive structure of GAMs, c) scale to large
data sets and d) can be used in conjunction with a wide range of response
distributions. All the new visual methods proposed in this work are implemented
by the mgcViz R package, which can be found on the Comprehensive R Archive
Network
Hypercontractive semigroups and two dimensional self-coupled Bose fields
AbstractWe present an abstract perturbation theory for operators of the form H0 + V obeying four properties: (1) H0 is a positive self-adjoint operator on L2(M, μ) with μ a probability measure so that e−tH0 is a contraction on L1 for each t > 0; (2) e−TH0 is a bounded map of L2 to L4 for some T; (3) V ϵ Lp(M, μ) for some p > 2; (4) e−tV ϵ L1 for all t > 0. We then show that spatially cutoff Bose fields in two-dimensional space-time fit into this framework. Finally, we discuss some details of two-dimensional Bose fields in the abstract including coupling constant analyticity in the spatially cutoff case
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