907 research outputs found
Multivariate Juggling Probabilities
We consider refined versions of Markov chains related to juggling introduced
by Warrington. We further generalize the construction to juggling with
arbitrary heights as well as infinitely many balls, which are expressed more
succinctly in terms of Markov chains on integer partitions. In all cases, we
give explicit product formulas for the stationary probabilities. The
normalization factor in one case can be explicitly written as a homogeneous
symmetric polynomial. We also refine and generalize enriched Markov chains on
set partitions. Lastly, we prove that in one case, the stationary distribution
is attained in bounded time.Comment: 28 pages, 5 figures, final versio
Bumping sequences and multispecies juggling
Building on previous work by four of us (ABCN), we consider further
generalizations of Warrington's juggling Markov chains. We first introduce
"multispecies" juggling, which consist in having balls of different weights:
when a ball is thrown it can possibly bump into a lighter ball that is then
sent to a higher position, where it can in turn bump an even lighter ball, etc.
We both study the case where the number of balls of each species is conserved
and the case where the juggler sends back a ball of the species of its choice.
In this latter case, we actually discuss three models: add-drop, annihilation
and overwriting. The first two are generalisations of models presented in
(ABCN) while the third one is new and its Markov chain has the ultra fast
convergence property. We finally consider the case of several jugglers
exchanging balls. In all models, we give explicit product formulas for the
stationary probability and closed form expressions for the normalisation factor
if known.Comment: 25 pages, 9 figures (v3: final version, several typos and figures
fixed
Input Redundancy under Input and State Constraints (Extended version of the submission accepted to Automatica)
For a given unconstrained dynamical system, input redundancy has been
recently redefined as the existence of distinct inputs producing identical
output for the same initial state. By directly referring to signals, this
definition readily applies to any input-to-output mapping. As an illustration
of this potentiality, this paper tackles the case where input and state
constraints are imposed on the system. This context is indeed of foremost
importance since input redundancy has been historically regarded as a way to
deal with input saturations. An example illustrating how constraints can
challenge redundancy is offered right at the outset. A more complex
phenomenology is highlighted. This motivates the enrichment of the existing
framework on redundancy. Then, a sufficient condition for redundancy to be
preserved when imposing constraints is offered in the most general context of
arbitrary constraints. It is shown that redundancy can be destroyed only when
input and state trajectories lie on the border of the set of constraints almost
all the time. Finally, those results are specialized and expanded under the
assumption that input and state constraints are linear
Implicit FEM and Fluid Coupling on GPU for Interactive Multiphysics Simulation
International audienceWe present a method to implement on the GPU an implicit FEM solver which is fast and stable enough to handle interactions and collisions. We combine this method with GPU-based fluids and collision detection to achieve interactive multiphysics simulations entirely running on the GPU
Structure Transition in PSS/Lysozyme Complexes: A Chain-Conformation-Driven Process, as Directly Seen by Small Angle Neutron Scattering
Measurements of chain conformation in proteins/polyelectrolytes complexes
(lysozyme and PSSNa) show that the crossover observed between an open structure
-a chain network crosslinked by the proteins, and a globular one - dense
globules of ~ 10 nm aggregated in a fractal way, results from a conformation
modification prior to the transition. Before showing this, we have widened the
parameters range for the observation of the transition. We had shown before
that the two structures can be formed depending on chain length (for a given
[PSS]/[lysozyme] ratio): gel for large chains, globules for short chains. We
show here that the crossover between these two regimes can also be reached as a
function of chains concentration or salinity of the buffer. Since all these
crossover parameters act on chains overlapping concentration c*, we reinforce
the idea of a transition from the dilute to the semi-dilute regime, but c* is
shifted compared to pure PSS solutions. In order to understand this, we have
measured by SANS the conformation of a single chain of PSS in presence of
proteins within the complexes. This is achieved by a specific labeling trick
where we take advantage of the fact that lysozyme and hydrogenated PSS chains
have the same neutron scattering length density. In the gel structure, the PSS
chains keep a wormlike structure as in pure solutions, but their persistence
length is strongly reduced, from 50 {\AA} without proteins to 20 {\AA} in
average with lysozyme. With this value of 20 {\AA}, we calculate new
overlapping thresholds (concentration, mass, ionic strength) in agreement with
observed ones. In a second stage, after the globular structure is formed, the
PSS chains get a third conformation, no longer wormlike, but more collapsed,
within the globules
A sparse grid approach to balance sheet risk measurement
In this work, we present a numerical method based on a sparse grid
approximation to compute the loss distribution of the balance sheet of a
financial or an insurance company. We first describe, in a stylised way, the
assets and liabilities dynamics that are used for the numerical estimation of
the balance sheet distribution. For the pricing and hedging model, we chose a
classical Black & Scholes model with a stochastic interest rate following a
Hull & White model. The risk management model describing the evolution of the
parameters of the pricing and hedging model is a Gaussian model. The new
numerical method is compared with the traditional nested simulation approach.
We review the convergence of both methods to estimate the risk indicators under
consideration. Finally, we provide numerical results showing that the sparse
grid approach is extremely competitive for models with moderate dimension.Comment: 27 pages, 7 figures. CEMRACS 201
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