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This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as…
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain…
In unsupervised domain adaptation, existing theory focuses on situations where the source and target domains are close. In practice, conditional entropy minimization and pseudo-labeling work even when the domain shifts are much larger than…
We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin (charge) domain-derived scattering potential $V_{s}$ ($V_{c}$). We show that the charge domain-derived scattering is less…
Stripe domains are studied in perpendicular magnetic anisotropy films nanostructured with a periodic thickness modulation that induces the lateral modulation of both stripe periods and inplane magnetization. The resulting system is the 2D…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…
Domain adaptation aims to learn models on a supervised source domain that perform well on an unsupervised target. Prior work has examined domain adaptation in the context of stationary domain shifts, i.e. static data sets. However, with…
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in…
We consider an aggregation model with nonlinear diffusion in domains with boundaries and investigate the zero diffusion limit of its solutions. We establish the convergence of weak solutions for fixed times, as well as the convergence of…
In recent decades novel solid substrates have been designed which change their wettability in response to light or an electrostatic field. Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimium…
Current unsupervised domain adaptation methods can address many types of distribution shift, but they assume data from the source domain is freely available. As the use of pre-trained models becomes more prevalent, it is reasonable to…
We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this…
We propose associative domain adaptation, a novel technique for end-to-end domain adaptation with neural networks, the task of inferring class labels for an unlabeled target domain based on the statistical properties of a labeled source…
Real-world machine learning applications often involve deploying neural networks to domains that are not seen in the training time. Hence, we need to understand the extrapolation of nonlinear models -- under what conditions on the…
We prove that if $\Omega$ is a simply connected quadrature domain for a distribution with compact support and the infinity point belongs the boundary, then the boundary has an asymptotic curve that is either a straight line or a parabola or…
Deep Neural Networks have exhibited considerable success in various visual tasks. However, when applied to unseen test datasets, state-of-the-art models often suffer performance degradation due to domain shifts. In this paper, we introduce…
We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…
Using the mean field theory in the slave-boson approach we analyzed the electron correlation effects in the stripe phases. One finds that a finite next-nearest neighbor hopping $t'$ plays an important role in the low doping regime, where it…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…