73 research outputs found
Singular perturbations and a theorem of Kisynski
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31989/1/0000031.pd
Existence of the Bogoliubov S(g) operator for the quantum field theory
We prove the existence of the Bogoliubov S(g) operator for the
quantum field theory for coupling functions of compact support in space and
time. The construction is nonperturbative and relies on a theorem of
Kisy\'nski. It implies almost automatically the properties of unitarity and
causality for disjoint supports in the time variable.Comment: LaTeX, 24 pages, minor modifications, typos correcte
Lower Complexity Bounds for Lifted Inference
One of the big challenges in the development of probabilistic relational (or
probabilistic logical) modeling and learning frameworks is the design of
inference techniques that operate on the level of the abstract model
representation language, rather than on the level of ground, propositional
instances of the model. Numerous approaches for such "lifted inference"
techniques have been proposed. While it has been demonstrated that these
techniques will lead to significantly more efficient inference on some specific
models, there are only very recent and still quite restricted results that show
the feasibility of lifted inference on certain syntactically defined classes of
models. Lower complexity bounds that imply some limitations for the feasibility
of lifted inference on more expressive model classes were established early on
in (Jaeger 2000). However, it is not immediate that these results also apply to
the type of modeling languages that currently receive the most attention, i.e.,
weighted, quantifier-free formulas. In this paper we extend these earlier
results, and show that under the assumption that NETIME =/= ETIME, there is no
polynomial lifted inference algorithm for knowledge bases of weighted,
quantifier- and function-free formulas. Further strengthening earlier results,
this is also shown to hold for approximate inference, and for knowledge bases
not containing the equality predicate.Comment: To appear in Theory and Practice of Logic Programming (TPLP
Necessary conditions for variational regularization schemes
We study variational regularization methods in a general framework, more
precisely those methods that use a discrepancy and a regularization functional.
While several sets of sufficient conditions are known to obtain a
regularization method, we start with an investigation of the converse question:
How could necessary conditions for a variational method to provide a
regularization method look like? To this end, we formalize the notion of a
variational scheme and start with comparison of three different instances of
variational methods. Then we focus on the data space model and investigate the
role and interplay of the topological structure, the convergence notion and the
discrepancy functional. Especially, we deduce necessary conditions for the
discrepancy functional to fulfill usual continuity assumptions. The results are
applied to discrepancy functionals given by Bregman distances and especially to
the Kullback-Leibler divergence.Comment: To appear in Inverse Problem
The time singular limit for a fourth-order damped wave equation for MEMS
We consider a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the electrostatic potential. We first review some recent results on existence and non-existence of steady-states as well as on local and global well-posedness of the dynamical problem, the main focus being on the possible touchdown behavior of the elastic plate. We then investigate the behavior of the solutions in the time singular limit when the ratio between inertial and damping effects tends to zero
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