3,935 research outputs found
Automatic Computation of Feynman Diagrams
Quantum corrections significantly influence the quantities observed in modern
particle physics. The corresponding theoretical computations are usually quite
lengthy which makes their automation mandatory. This review reports on the
current status of automatic calculation of Feynman diagrams in particle
physics. The most important theoretical techniques are introduced and their
usefulness is demonstrated with the help of simple examples. A survey over
frequently used programs and packages is provided, discussing their abilities
and fields of applications. Subsequently, some powerful packages which have
already been applied to important physical problems are described in more
detail. The review closes with the discussion of a few typical applications for
the automated computation of Feynman diagrams, addressing current physical
questions like properties of the and Higgs boson, four-loop corrections to
renormalization group functions and two-loop electroweak corrections.Comment: Latex, 62 pages. Typos corrected, references updated and some
comments added. Vertical offset changed. The complete paper is also available
via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or
via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints
The computational challenge of enumerating high-dimensional rook walks
We provide guessed recurrence equations for the counting sequences of rook
paths on d-dimensional chess boards starting at (0..0) and ending at (n..n),
where d=2,3,...,12. Our recurrences suggest refined asymptotic formulas of
these sequences. Rigorous proofs of the guessed recurrences as well as the
suggested asymptotic forms are posed as challenges to the reader
Track 3: Computations in theoretical physics -- techniques and methods
Here, we attempt to summarize the activities of Track 3 of the 17th
International Workshop on Advanced Computing and Analysis Techniques in Physics
Research (ACAT 2016).Comment: 10 pages, 3 figures, to appear in the proceedings of ACAT 201
Report on "Geometry and representation theory of tensors for computer science, statistics and other areas."
This is a technical report on the proceedings of the workshop held July 21 to
July 25, 2008 at the American Institute of Mathematics, Palo Alto, California,
organized by Joseph Landsberg, Lek-Heng Lim, Jason Morton, and Jerzy Weyman. We
include a list of open problems coming from applications in 4 different areas:
signal processing, the Mulmuley-Sohoni approach to P vs. NP, matchgates and
holographic algorithms, and entanglement and quantum information theory. We
emphasize the interactions between geometry and representation theory and these
applied areas
On Characterizing the Data Access Complexity of Programs
Technology trends will cause data movement to account for the majority of
energy expenditure and execution time on emerging computers. Therefore,
computational complexity will no longer be a sufficient metric for comparing
algorithms, and a fundamental characterization of data access complexity will
be increasingly important. The problem of developing lower bounds for data
access complexity has been modeled using the formalism of Hong & Kung's
red/blue pebble game for computational directed acyclic graphs (CDAGs).
However, previously developed approaches to lower bounds analysis for the
red/blue pebble game are very limited in effectiveness when applied to CDAGs of
real programs, with computations comprised of multiple sub-computations with
differing DAG structure. We address this problem by developing an approach for
effectively composing lower bounds based on graph decomposition. We also
develop a static analysis algorithm to derive the asymptotic data-access lower
bounds of programs, as a function of the problem size and cache size
Automatic Classification of Restricted Lattice Walks
We propose an experimental mathematics approach leading to the
computer-driven discovery of various structural properties of general counting
functions coming from enumeration of walks
- …