188 research outputs found
\epsilon-regularity for systems involving non-local, antisymmetric operators
We prove an epsilon-regularity theorem for critical and super-critical
systems with a non-local antisymmetric operator on the right-hand side.
These systems contain as special cases, Euler-Lagrange equations of
conformally invariant variational functionals as Rivi\`ere treated them, and
also Euler-Lagrange equations of fractional harmonic maps introduced by Da
Lio-Rivi\`ere.
In particular, the arguments presented here give new and uniform proofs of
the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and
also the integrability results by Sharp-Topping and Sharp, not discriminating
between the classical local, and the non-local situations
Artificial co-drivers as a universal enabling technology for future intelligent vehicles and transportation systems
This position paper introduces the concept of artificial
“co-drivers” as an enabling technology for future intelligent
transportation systems. In Sections I and II, the design
principles of co-drivers are introduced and framed within general human–robot interactions. Several contributing theories and technologies are reviewed, specifically those relating to relevant cognitive architectures, human-like sensory-motor strategies, and
the emulation theory of cognition. In Sections III and IV, we
present the co-driver developed for the EU project interactIVe
as an example instantiation of this notion, demonstrating how
it conforms to the given guidelines. We also present substantive experimental results and clarify the limitations and performance of the current implementation. In Sections IV and V, we analyze the impact of the co-driver technology. In particular, we identify a range of application fields, showing how it constitutes a universal enabling technology for both smart vehicles and cooperative systems, and naturally sets out a program for future research
Global Existence Results and Uniqueness for Dislocation Equations
We are interested in nonlocal Eikonal Equations arising in the study of the
dynamics of dislocations lines in crystals. For these nonlocal but also non
monotone equations, only the existence and uniqueness of Lipschitz and
local-in-time solutions were available in some particular cases. In this paper,
we propose a definition of weak solutions for which we are able to prove the
existence for all time. Then we discuss the uniqueness of such solutions in
several situations, both in the monotone and non monotone case
Artificial co-drivers as a universal enabling technology for future intelligent vehicles and transportation systems
This position paper introduces the concept of artificial “co-drivers” as an enabling technology for future intelligent transportation systems. In Sections I and II, the design principles of co-drivers are introduced and framed within general human–robot interactions. Several contributing theories and technologies are reviewed, specifically those relating to relevant cognitive architectures, human-like sensory-motor strategies, and the emulation theory of cognition. In Sections III and IV, we present the co-driver developed for the EU project interactIVe as an example instantiation of this notion, demonstrating how it conforms to the given guidelines. We also present substantive experimental results and clarify the limitations and performance of the current implementation. In Sections IV and V, we analyze the impact of the co-driver technology. In particular, we identify a range of application fields, showing how it constitutes a universal enabling technology for both smart vehicles and cooperative systems, and naturally sets out a program for future research
The value function of an asymptotic exit-time optimal control problem
We consider a class of exit--time control problems for nonlinear systems with
a nonnegative vanishing Lagrangian. In general, the associated PDE may have
multiple solutions, and known regularity and stability properties do not hold.
In this paper we obtain such properties and a uniqueness result under some
explicit sufficient conditions. We briefly investigate also the infinite
horizon problem
The Tychonoff uniqueness theorem for the G-heat equation
In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat
equation
Global results on reset-induced periodic trajectories of planar systems
We study the existence of asymptotically stable periodic trajectories induced
by reset feedback. The analysis is developed for a planar system. Casting the
problem into the hybrid setting, we show that a periodic orbit arises from the
balance between the energy dissipated during flows and the energy restored by
resets, at jumps. The stability of the periodic orbit is studied with hybrid
Lyapunov tools. The satisfaction of the so-called hybrid basic conditions
ensures the robustness of the asymptotic stability. Extensions of the approach
to more general mechanical systems are discussed.Work supported in part by ANR under project LimICoS, contract number 12 BS03 005 01, by the iCODE institute, research project of the Idex ParisSaclay, and by the University of Trento, grant OptHySYS.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by IEEE
Quadratic BSDEs with convex generators and unbounded terminal conditions
In a previous work, we proved an existence result for BSDEs with quadratic
generators with respect to the variable z and with unbounded terminal
conditions. However, no uniqueness result was stated in that work. The main
goal of this paper is to fill this gap. In order to obtain a comparison theorem
for this kind of BSDEs, we assume that the generator is convex with respect to
the variable z. Under this assumption of convexity, we are also able to prove a
stability result in the spirit of the a priori estimates stated in the article
of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can
derive the nonlinear Feynman--Kac formula in this context
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
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