6,071 research outputs found
Strong convergence rates of probabilistic integrators for ordinary differential equations
Probabilistic integration of a continuous dynamical system is a way of
systematically introducing model error, at scales no larger than errors
introduced by standard numerical discretisation, in order to enable thorough
exploration of possible responses of the system to inputs. It is thus a
potentially useful approach in a number of applications such as forward
uncertainty quantification, inverse problems, and data assimilation. We extend
the convergence analysis of probabilistic integrators for deterministic
ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\
Comput.}, 2017), to establish mean-square convergence in the uniform norm on
discrete- or continuous-time solutions under relaxed regularity assumptions on
the driving vector fields and their induced flows. Specifically, we show that
randomised high-order integrators for globally Lipschitz flows and randomised
Euler integrators for dissipative vector fields with polynomially-bounded local
Lipschitz constants all have the same mean-square convergence rate as their
deterministic counterparts, provided that the variance of the integration noise
is not of higher order than the corresponding deterministic integrator. These
and similar results are proven for probabilistic integrators where the random
perturbations may be state-dependent, non-Gaussian, or non-centred random
variables.Comment: 25 page
Invariants of differential equations defined by vector fields
We determine the most general group of equivalence transformations for a
family of differential equations defined by an arbitrary vector field on a
manifold. We also find all invariants and differential invariants for this
group up to the second order. A result on the characterization of classes of
these equations by the invariant functions is also given.Comment: 13 page
Ordinary differential equations which linearize on differentiation
In this short note we discuss ordinary differential equations which linearize
upon one (or more) differentiations. Although the subject is fairly elementary,
equations of this type arise naturally in the context of integrable systems.Comment: 9 page
Mitotic Regulators Govern Progress through Steps in the Centrosome Duplication Cycle
Centrosome duplication is marked by discrete changes in centriole structure that occur in lockstep with cell cycle transitions. We show that mitotic regulators govern steps in centriole replication in Drosophila embryos. Cdc25string, the expression of which initiates mitosis, is required for completion of daughter centriole assembly. Cdc20fizzy, which is required for the metaphase-anaphase transition, is required for timely disengagement of mother and daughter centrioles. Stabilization of mitotic cyclins, which prevents exit from mitosis, blocks assembly of new daughter centrioles. Common regulation of the nuclear and centrosome cycles by mitotic regulators may ensure precise duplication of the centrosome
Non-Newtonian gravity in finite nuclei
In this talk, we report our recent study of constraining the non-Newtonian
gravity at femtometer scale. We incorporate the Yukawa-type non-Newtonian
gravitational potential consistently to the Skyrme functional form using the
exact treatment for the direct contribution and density-matrix expansion method
for the exchange contribution. The effects from the non-Newtonian potential on
finite nuclei properties are then studied together with a well-tested Skyrme
force. Assuming that the framework without non-Newtonian gravity can explain
the binding energies and charge radii of medium to heavy nuclei within 2%
error, we set an upper limit for the strength of the non-Newtonian
gravitational potential at femtometer scale.Comment: Talk given at the 11th International Conference on Nucleus-Nucleus
Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear
in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS
Composition algebras and the two faces of
We consider composition and division algebras over the real numbers: We note
two r\^oles for the group : as automorphism group of the octonions and
as the isotropy group of a generic 3-form in 7 dimensions. We show why they are
equivalent, by means of a regular metric. We express in some diagrams the
relation between some pertinent groups, most of them related to the octonions.
Some applications to physics are also discussed.Comment: 11 pages, 3 figure
Particle detection experiment for Applications Technology Satellite 1 /ATS-1/ Final report
Applications technology satellite particle detection experiment for measuring energy spectra of earth magnetic fiel
Gauge Theory for Quantum Spin Glasses
The gauge theory for random spin systems is extended to quantum spin glasses
to derive a number of exact and/or rigorous results. The transverse Ising model
and the quantum gauge glass are shown to be gauge invariant. For these models,
an identity is proved that the expectation value of the gauge invariant
operator in the ferromagnetic limit is equal to the one in the classical
equilibrium state on the Nishimori line. As a result, a set of inequalities for
the correlation function are proved, which restrict the location of the ordered
phase. It is also proved that there is no long-range order in the
two-dimensional quantum gauge glass in the ground state. The phase diagram for
the quantum XY Mattis model is determined.Comment: 15 pages, 2 figure
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