2,894 research outputs found
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
We prove combinatorially the explicit relation between genus filtrated
-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
given by for
. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure
Proving Non-Termination via Loop Acceleration
We present the first approach to prove non-termination of integer programs
that is based on loop acceleration. If our technique cannot show
non-termination of a loop, it tries to accelerate it instead in order to find
paths to other non-terminating loops automatically. The prerequisites for our
novel loop acceleration technique generalize a simple yet effective
non-termination criterion. Thus, we can use the same program transformations to
facilitate both non-termination proving and loop acceleration. In particular,
we present a novel invariant inference technique that is tailored to our
approach. An extensive evaluation of our fully automated tool LoAT shows that
it is competitive with the state of the art
Differential Invariants of Conformal and Projective Surfaces
We show that, for both the conformal and projective groups, all the
differential invariants of a generic surface in three-dimensional space can be
written as combinations of the invariant derivatives of a single differential
invariant. The proof is based on the equivariant method of moving frames.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
The Cauchy-Lagrangian method for numerical analysis of Euler flow
A novel semi-Lagrangian method is introduced to solve numerically the Euler
equation for ideal incompressible flow in arbitrary space dimension. It
exploits the time-analyticity of fluid particle trajectories and requires, in
principle, only limited spatial smoothness of the initial data. Efficient
generation of high-order time-Taylor coefficients is made possible by a
recurrence relation that follows from the Cauchy invariants formulation of the
Euler equation (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430).
Truncated time-Taylor series of very high order allow the use of time steps
vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the
accuracy of the solution. Tests performed on the two-dimensional Euler equation
indicate that the Cauchy-Lagrangian method is more - and occasionally much more
- efficient and less prone to instability than Eulerian Runge-Kutta methods,
and less prone to rapid growth of rounding errors than the high-order Eulerian
time-Taylor algorithm. We also develop tools of analysis adapted to the
Cauchy-Lagrangian method, such as the monitoring of the radius of convergence
of the time-Taylor series. Certain other fluid equations can be handled
similarly.Comment: 30 pp., 13 figures, 45 references. Minor revision. In press in
Journal of Scientific Computin
Summary-based inference of quantitative bounds of live heap objects
This article presents a symbolic static analysis for computing parametric upper bounds of the number of simultaneously live objects of sequential Java-like programs. Inferring the peak amount of irreclaimable objects is the cornerstone for analyzing potential heap-memory consumption of stand-alone applications or libraries. The analysis builds method-level summaries quantifying the peak number of live objects and the number of escaping objects. Summaries are built by resorting to summaries of their callees. The usability, scalability and precision of the technique is validated by successfully predicting the object heap usage of a medium-size, real-life application which is significantly larger than other previously reported case-studies.Fil: Braberman, Victor Adrian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garbervetsky, Diego David. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hym, Samuel. Universite Lille 3; FranciaFil: Yovine, Sergio Fabian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Differential equations on unitarity cut surfaces
We reformulate differential equations (DEs) for Feynman integrals to avoid
doubled propagators in intermediate steps. External momentum derivatives are
dressed with loop momentum derivatives to form tangent vectors to unitarity cut
surfaces, in a way inspired by unitarity-compatible IBP reduction. For the
one-loop box, our method directly produces the final DEs without any
integration-by-parts reduction. We further illustrate the method by deriving
maximal-cut level differential equations for two-loop nonplanar five-point
integrals, whose exact expressions are yet unknown. We speed up the computation
using finite field techniques and rational function reconstruction.Comment: 17 pages, 3 figures; v2: added more results and references, final
journal versio
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