Data-driven linearization of dynamical systems.

Unlabelled: Dynamic mode decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly in others, a clarification of the assumptions under which DMD is applicable is desirable. Upon closer inspection, existing interpretations of DMD methods based on the Koopman operator are not quite satisfactory: they justify DMD under assumptions that hold only with probability zero for generic observables.

Nonlinear model reduction to fractional and mixed-mode spectral submanifolds.

A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace E of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an attracting primary SSM provides a mathematically precise reduction of the full system dynamics to a very low-dimensional, smooth model in polynomial form. A limitation of this model reduction approach has been, however, that the spectral subspace yielding the SSM must be spanned by eigenvectors of the same stability type.

[Malignant transformation of a branchial cleft cyst].

Branchial cleft cyst is the most common birth defect involving the neck. Malignant transformation is known, however, differentiating from a neck metastasis of a squamous cell carcinoma of unknown primary is challenging. Even though there are strict criterias, the diagnosis of this entity remains controversial.

Thymosin beta-4 - A potential tool in healing middle ear lesions in adult mammals.

Acute tympanic membrane perforations primarily occur due to injury or infection in humans. In acute cases, nearly 80-94 % of the perforations heal spontaneously. In chronic cases, non-surgical treatment becomes significantly limited, and the perforation can be restored only by myringoplasty.

Machine Learning-Based Characterization of the Nanostructure in a Combinatorial Co-Cr-Fe-Ni Compositionally Complex Alloy Film.

A novel artificial intelligence-assisted evaluation of the X-ray diffraction (XRD) peak profiles was elaborated for the characterization of the nanocrystallite microstructure in a combinatorial Co-Cr-Fe-Ni compositionally complex alloy (CCA) film. The layer was produced by a multiple beam sputtering physical vapor deposition (PVD) technique on a Si single crystal substrate with the diameter of about 10 cm. This new processing technique is able to produce combinatorial CCA films where the elemental concentrations vary in a wide range on the disk surface.