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.

Pre-eruptive intracoronal resorption in "high-risk" impacted third molars: A report of four cases.

Pre-eruptive intracoronal resorption (PEIR) is usually an incidental finding as a radiolucent lesion within the coronal dentin of unerupted teeth. Through the four cases reported here, authors would demonstrate deeply impacted "high-risk" third molars with PEIR defects, showing an increased risk of inferior alveolar nerve (IAN) injury. However, follow-up or coronectomy may eliminate or reduce the risk of neurosensory disturbances, in case of PEIR lesions this can be contradictory due to the unpredictable reactions of the third molar's pulp.

Universal upper estimate for prediction errors under moderate model uncertainty.

We derive universal upper estimates for model prediction error under moderate but otherwise unknown model uncertainty. Our estimates give upper bounds on the leading-order trajectory uncertainty arising along model trajectories, solely as functions of the invariants of the known Cauchy-Green strain tensor of the model. Our bounds turn out to be optimal, which means that they cannot be improved for general systems.

Author Correction: Visualization of mucosal field in HPV positive and negative oropharyngeal squamous cell carcinomas: combined genomic and radiology based 3D model.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Visualization of mucosal field in HPV positive and negative oropharyngeal squamous cell carcinomas: combined genomic and radiology based 3D model.

The aim of this study was to visualize the tumor propagation and surrounding mucosal field in radiography-based 3D model for advanced stage HNSCC and combine it with HPV genotyping and miRNA expression characterization of the visualized area. 25 patients with T1-3 clinical stage HNSCC were enrolled in mapping biopsy sampling. Biopsy samples were evaluated for HPV positivity and miR-21-5p, miR-143, miR-155, miR-221-5p expression in Digital Droplet PCR system.

PACAP and PAC1 receptor expression in pancreatic ductal carcinoma.

Pancreatic carcinoma is one of the most malignant diseases and is associated with a poor survival rate. Pituitary adenylate cyclase activating polypeptide (PACAP) is a neuropeptide that acts on three different G protein-coupled receptors: the specific PAC1 and the VPAC1/2 that also bind vasoactive intestinal peptide. PACAP is widely distributed in the body and has diverse physiological effects.

The snowball Earth transition in a climate model with drifting parameters: Splitting of the snapshot attractor.

Using an intermediate complexity climate model (Planet Simulator), we investigate the so-called snowball Earth transition. For certain values (including its current value) of the solar constant, the climate system allows two different stable states: one of them is the snowball Earth, covered by ice and snow, and the other one is today's climate. In our setup, we consider the case when the climate system starts from its warm attractor (the stable climate we experience today), and the solar constant is changed according to the following scenario: it is decreased continuously and abruptly, over one year, to a state, where only the Snowball Earth's attractor remains stable.

Localized Amyloidosis of the Upper Aerodigestive Tract: Complex Analysis of the Cellular Infiltrate and the Amyloid Mass.

Objectives: The aim of this study was to analyse the composition of amyloid mass and the plasmacytic infiltrate of localized amyloidosis of the upper aerodigestive tract.

Methods: Biopsy materials were studied by light microscopy, immunohistochemistry (IHC), and mRNA in situ hybridization (mRNA-ISH). The amyloid mass was also analysed with high-performance liquid chromatography mass spectrometry- (HPLC-MS-) based proteomics.

Tipping phenomena in typical dynamical systems subjected to parameter drift.

Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics.

[Modern management of otologic consequences of Wegener's granulomatosis - a case report and review of the literature].

Wegener's granulomatosis - or, in other words, granulomatosis with polyangiitis - is an anti-neutrophil cytoplasmic antibody associated granuloma forming vasculitis, mainly affecting the respiratory tract and the renal system. Otologic manifestations of Wegener's disease can be otitis media with effusion or chronic silent mastoiditis with conductive hearing loss, but sensorineural hearing loss can also evolve. The diagnosis is based on the clinical appearance as well as the immunoserological and histopathological results.

Leaking in history space: A way to analyze systems subjected to arbitrary driving.

Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such systems are non-autonomous and belong to the class of non-periodically driven systems where the traditional theory of chaos (based e.g.

Death and revival of chaos.

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history.

More Cases of Benign Testicular Teratomas are Detected in Adults than in Children. A Clinicopathological Study of 543 Testicular Germ Cell Tumor Cases.

Benign testicular teratomas are always thought to be pediatric neoplasms and previously all the teratoid tumors in the adult testis regarded as malignant. Recently, three publications reported benign testicular teratomas in adulthood and the latest WHO classification refers them as "prepubertal type of teratomas" which rarely appear in adulthood. These neoplasms behave benign and seemingly analogous independently whether they appear in pre- or postpubertal patients.

Pancreatojejunostomy with modified purse-string suture technique.

Purpose: Despite many efforts, pancreatic fistula remains the most troublesome complication following pancreatic resections, especially in case of anastomosis made with soft pancreatic tissue. The purpose of the authors was to show their modification of purse-string pancreatodigestive anastomosis and the results obtained.

Methods: Between January 2013 and June 2015, the technique was applied in 49 patients; one purse-string suture and two U-shaped mattress sutures were used to create the pancreatojejunal anastomosis.