Data-driven linearization of dynamical systems.

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. Here, we give a justification for DMD as a local, leading-order reduced model for the dominant system dynamics under conditions that hold with probability one for generic observables and non-degenerate observational data. We achieve this for autonomous and for periodically forced systems of finite or infinite dimensions by constructing linearizing transformations for their dominant dynamics within attracting slow spectral submanifolds (SSMs). Our arguments also lead to a new algorithm, data-driven linearization (DDL), which is a higher-order, systematic linearization of the observable dynamics within slow SSMs. We show by examples how DDL outperforms DMD and EDMD on numerical and experimental data. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-024-10026-x.

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. A further limitation has been that in some problems, the nonlinear behavior of interest may be far away from the smoothest nonlinear continuation of the invariant subspace E. Here, we remove both of these limitations by constructing a significantly extended class of SSMs that also contains invariant manifolds with mixed internal stability types and of lower smoothness class arising from fractional powers in their parametrization. We show on examples how fractional and mixed-mode SSMs extend the power of data-driven SSM reduction to transitions in shear flows, dynamic buckling of beams, and periodically forced nonlinear oscillatory systems. More generally, our results reveal the general function library that should be used beyond integer-powered polynomials in fitting nonlinear reduced-order models to data.

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. The quantity relating the leading-order trajectory-uncertainty to the model uncertainty is the model sensitivity (MS), which we find to be a useful tool for a quick global assessment of the impact of modeling uncertainties in various domains of the phase space. By examining the expectation that finite-time Lyapunov exponents capture sensitivity to modeling errors, we show that this does not generally follow. However, we find that certain important features of the finite-time Lyapunov exponent persist in the MS field.

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. This induces an inevitable transition or climate tipping from the warm climate. The reverse transition is also discussed. Increasing the solar constant back to its original value in a similar way, in individual simulations, depending on the rate of the solar constant reduction, we find that either the system stays stuck in the snowball state or returns to warm climate. However, using ensemble methods, i.e., using an ensemble of climate realizations differing only slightly in their initial conditions we show that the transition from the snowball Earth to the warm climate is also possible with a certain probability, which depends on the specific scenario used. From the point of view of dynamical systems theory, we can say that the system's snapshot attractor splits between the warm climate's and the snowball Earth's attractor.

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., on periodic orbits) does not hold. We demonstrate that even such systems possess an underlying topological horseshoe-like structure at least for a finite period of time. This result is based on a specifically developed method which allows to compute the corresponding time-dependent stable and unstable foliations. These structures can be made visible by prescribing a certain type of history for an ensemble of trajectories in phase space and by analyzing the trajectories fulfilling this constraint. The process can be considered as a leaking in history space-a generalization of traditional leaking, a method that has become widespread in traditional chaotic systems, to leaks depending on time.

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. In case of soft pancreatic parenchyma, an external stent was temporarily left in the main pancreatic duct. The most frequent pathology was pancreatic cancer, and a pylorus-preserving Whipple procedure was mostly done. RESULTS: Postoperative early morbidity rate was 35 %. There were two fistulas, one grade A fistula from a fibrotic pancreas (4.2 %) and one grade B in case of a soft pancreas (4 %). However, there was no reoperation and mortality. CONCLUSIONS: According to favorable results, the modification of the purse-string suture technique makes this method even safer.

[Malignant transformation of a branchial cleft cyst]. / Rosszindulatúan elfajult nyaki branchiogen cysta.

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. We present the case of a 69-year-old woman, who presented with a swelling under the left side of the mandible. After diagnostic workup, fine-needle aspiration biopsy raised the suspicion of a cystic squamous cell carcinoma metastasis, therefore we performed panendoscopy and modified radical neck dissection. The pathological examination confirmed branchial cleft cyst carcinoma. After surgery, the patient received adjuvant radiation and chemotherapy. During the case workup, we present the difficulties of the diagnostic process, differential diagnostic problems, and the review of the international literature. In the case of a solitary, cystic mass on the neck without a primary tumor, we should consider the possibility of a branchiogenic carcinoma. Orv Hetil. 2023; 164(10): 388-392.

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. In addition to classical grafts such as the fascia or cartilage, promising results have been reported with various biological materials including silk or acellular collagen. However, despite of all the efforts, healing remains insufficient. Consequentially, a need for substances which actively promote tympanic cell migration and proliferation is deemed essential. In our study, we utilized Thymosin beta-4 (TB4), a 43aa peptide possessing many regenerative properties in various organ systems. Our aim was to reveal the impact of externally administered TB4 regarding impairments of the middle ear, particularly the tympanic membrane. We harvested tympanic membranes from adult mice and treated these with TB4 or PBS on both collagen gel matrixes and in the form of floating, ex vivo explants. Cell migration and proliferation was measured, while immunocytochemical analyses were performed to determine cell type and the nature of the targeted molecules. We discovered the peptide affects the behavior of epidermal and epithelial cells of the tympanic membrane in vitro. Moreover, as our initial results imply, it is not the differentiated, yet most likely the local epidermal progenitor cells which are the primary targets of the molecule. Our present results unveil a new, thus far undiscovered field regarding clinical utilization for TB4 in the future.

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. Cases show the important role of preoperative imaging in the diagnostics and management of deeply impacted PEIR third molars and highlight the need for investigations regarding coronectomy in such cases.

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. The most important benefit of the combinatorial sample is that it can be used for the study of the correlation between the chemical composition and the microstructure on a single specimen. The microstructure can be characterized quickly in many points on the disk surface using synchrotron XRD. However, the evaluation of the diffraction patterns for the crystallite size and the density of lattice defects (e.g., dislocations and twin faults) using X-ray line profile analysis (XLPA) is not possible in a reasonable amount of time due to the large number (hundreds) of XRD patterns. In the present study, a machine learning-based X-ray line profile analysis (ML-XLPA) was developed and tested on the combinatorial Co-Cr-Fe-Ni film. The new method is able to produce maps of the characteristic parameters of the nanostructure (crystallite size, defect densities) on the disk surface very quickly. Since the novel technique was developed and tested only for face-centered cubic (FCC) structures, additional work is required for the extension of its applicability to other materials. Nevertheless, to the knowledge of the authors, this is the first ML-XLPA evaluation method in the literature, which can pave the way for further development of this methodology.

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. Significant miRNA expression differences of HPV positive tumor tissue biopsies were found for miR-21-5p, miR-143 and miR-221-5p compared to the HPV negative tumor biopsy series. Peritumoral mucosa showed patchy pattern alterations of miR-21-5p and miR-155 in HPV positive cases, while gradual change of miR-21-5p and miR-221-5p was seen in HPV negative tumors. In our study we found differences of the miRNA expression patterns among the HPV positive and negative tumorous tissues as well as the surrounding mucosal fields. The CT based 3D models of the cancer field and surrounding mucosal surface can be utilized to improve proper preoperative planning. Complex evaluation of HNSCC tissue organization field can elucidate the clinical and molecular differentiation of HPV positive and negative cases, and enhance effective organ saving therapeutic strategies.

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. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.

[Modern management of otologic consequences of Wegener's granulomatosis - a case report and review of the literature]. / Wegener-granulomatosis talaján kialakult krónikus gennyes középfülgyulladás komplex kezelése.

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. It is of paramount importance to begin a combined immunosuppressive treatment immediately, besides eradicating the otologic manifestations. The intractable cases of chronic otitis media due to Wegener's granulomatosis are challenging any ear surgeons. Subtotal petrosectomy has proved to be an effective solution in such cases to create a dry ear and to provide a safe surgical field for hearing restoration. The authors reviewed the literature and report a case history to present the modern management of Wegener's granulomatosis with otologic manifestation. Orv Hetil. 2019; 160(4): 151-157.

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. RESULTS: Nodular and diffuse forms of amyloid deposition were detected. IHC analysis revealed λ-light chain (LC) in two cases, κ-LC in one case. The remaining two were positive with both. Proteins, well known from other amyloidoses like amyloid A (AA), prealbumin/transthyretin (PA), apolipoprotein A-I (ApoAI), and amyloid P component (APC), and also keratin were found with variable intensities in the cases. HPLC-MS revealed dozens of proteins with both LCs in all the lesions but sometimes with surprisingly small intensities. mRNA-ISH analysis revealed identical λ and κ dominance and only one normal κ/λ cell ratio. CONCLUSION: Cellular infiltrate and protein components in the amyloid showed congruent results in all but one case. The only exception with normal cell ratio and λ-dominant amyloid could be originated from the different protein-secreting activity of plasma cell clones. HPLC-MS analysis explored both LCs in all the amyloid in variable amount, but other proteins with much higher intensities like keratins, apolipoprotein A-IV (ApoAIV), were also detected. Proteins like AA, PA, ApoAI, and APC, previously known about amyloid-forming capability, also appeared. This indicates that localized amyloid in the upper aerodigestive tract is not a homogenous immunoglobulin mass but a mixture of proteins. The sometimes very low light chain intensities might also suggest that not all the localized amyloidosis cases of the upper aerodigestive tract are of convincingly AL type, and the analysis of the cellular infiltrate might indicate that not all are monoclonal.

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. Among other things, it acts as a trophic factor and influences proliferation and differentiation of several different cells both under normal circumstances and tumourous transformation. Changes of PACAP and its receptors have been shown in various tumour types. However, it is not known whether PACAP and its specific receptor are altered in pancreatic cancer. Perioperative data of patients with pancreas carcinoma was investigated over a five-year period. Histological results showed Grade 2 or Grade 3 adenocarcinoma in most cases. PACAP and PAC1 receptor expression were investigated by immunohistochemistry. Staining intensity of PAC1 receptor was strong in normal tissues both in the exocrine and endocrine parts of the pancreas, the receptor staining was markedly weaker in the adenocarcinoma. PACAP immunostaining was weak in the exocrine part and very strong in the islets and nerve elements in non-tumourous tissues. The PACAP immunostaining almost disappeared in the adenocarcinoma samples. Based on these findings a decrease or lack of the PAC1 receptor/PACAP signalling might have an influence on tumour growth and/or differentiation.

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. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.