While the basic laws of Newtonian mechanics are well understood, explaining a physical scenario still requires manually modeling the problem with suitable equations and associated parameters. In order to adopt such models for artificial intelligence, researchers have handcrafted the relevant states, and then used neural networks to learn the state transitions using simulation runs as training d...

[1] Increasingly accurate remote sensing techniques are available today, and methods such as modal analysis are used to transform, interpolate, and regularize the measured velocity fields. Until recently, the modes used did not incorporate flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline. Previous modal ...

Let C(R) be the space of functions on R whose m derivatives are Lipschitz 1. For E ⊂ R, let C(E) be the space of all restrictions to E of functions in C(R). We show that there exists a bounded linear operator T : C(E)→ C(R) such that, for any f ∈ C(E), we have Tf = f on E.

We consider strongly coupled quasilinear reaction-diiusion systems subject to nonlinear boundary conditions. Our aim is to develop a geometric theory for this type of equations. Such a theory is necessary in order to describe the dynamical behavior of solutions. In our main result we establish the existence and attractivity of center manifolds under suitable technical assumptions. The technical...

We consider strongly coupled quasilinear reaction-di↵usion systems subject to nonlinear boundary conditions. Our aim is to develop a geometric theory for these types of equations. Such a theory is necessary in order to describe the dynamical behavior of solutions. In our main result we establish the existence and attractivity of center manifolds under suitable technical assumptions. The technic...

The reconstruction of signals or images from incomplete or noisy data is a recurring problem in signal theory, with important practical applications. The band-limited interpolation and extrapola-tion problems, in which the signals or images are assumed to be band-limited, are among the most often studied reconstruction problems. We discuss certain aspects of these problems, concentrating on the...

In this paper, we compare different models for the interpolation and extrapolation of the SAR (Specific Absorption Rate) in biological tissues produced by an electromagnetic source. The configuration under study is a spherical benchmark at 900 MHz. The spatial distribution of the SAR is well-known [1] for this configuration. Based on these data, one can do a virtual measurement on a realistical...

We present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra. This approach minimizes a cost function derived from Bayes’ theorem. The method is suitable for line spectra since a “long tailed” distribution is used to model the prior distribution of spectral amplitudes. An important aspect of this method is that since the data...

Abstraction was investigated by examining extrapolation behavior in a function-learning task. During training, participants associated stimulus and response magnitudes (in the form of horizontal bar lengths) that covaried according to a linear, exponential, or quadratic function. After training, novel stimulus magnitudes were presented as tests of extrapolation and interpolation. Participants e...