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Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
This paper studies a dynamic ordered logit model for panel data with fixed effects. The main contribution of the paper is to construct a set of valid moment conditions that are free of the fixed effects. The moment functions can be computed…
We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…
We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
A practical challenge for structural estimation is the requirement to accurately minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions…
In some high-dimensional and semiparametric inference problems involving two populations, the parameter of interest can be characterized by two-sample U-statistics involving some nuisance parameters. In this work we first extend the…
The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…
We describe some recent approaches to likelihood based inference in the presence of nuisance parameters. Our approach is based on plotting the likelihood function and the $p$-value function, using recently developed third order…