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The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued…
Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance…
Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…
The data supporting neutrino oscillations are reexamined empirically, ignoring the phase space of the usual theory. An absolutely minimum description can be constructed easily without assuming oscillations. An empirical fit to a simplified…
We obtain explicit upper and lower bounds on the norms of the spectral projections of the non-self-adjoint harmonic oscillator. Some of our results apply to a variety of other families of orthogonal polynomials.
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…
We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
We give the first super-polynomial (in fact, mildly exponential) lower bounds for tolerant testing (equivalently, distance estimation) of monotonicity, unateness, and juntas with a constant separation between the "yes" and "no" cases.…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
We obtain a lower bound for the period of periodic solutions of semilinear evolution equations for the full range of nonlinear terms for which standard local existence theory applies. This lower bound depends on the Lipschitz constant of…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…