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

Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are current interest but have not yet been explored cases with chaotic internal dynamics. Based on example a paradigmatic low-dimensional dissipative system different scenarios drifts non-negligible rates, we show that number novel types tippings can be observed due topological complexity underlying general systems. Tippings from and into several coexisting...

Abstract Based on the theory of “snapshot/pullback attractors”, we show that important features climate change are observing can be understood by imagining many replicas Earth not interacting with each other. Their systems evolve in parallel, but same way, although they all obey physical laws, harmony chaotic-like nature dynamics. These parallel realizations evolving time considered as members an ensemble. We argue contingency our Earth’s system is characterized multiplicity rather than...

An extended turbulent state can coexist with the stable laminar in pipe flows. We focus here on short pipes additional discrete symmetries imposed. In this case, boundary between coexisting basins of attraction, often called edge chaos, is manifold an state, which a lower-branch travelling wave solution. show that low-dimensional submanifold chaos be constructed from velocity data using recently developed theory spectral submanifolds (SSMs). These manifolds are unique smoothest nonlinear...

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

We use video footage of a water-tunnel experiment to construct 2-D reduced-order model the flapping dynamics an inverted flag in uniform flow. The is obtained as reduced on attracting spectral submanifold (SSM) that emanates from two slowest modes unstable fixed point flag. Beyond and limit cycle expected observations, our SSM-reduced also confirms existence points for flag, which were found by previous studies. Importantly, correctly reconstructs small number general trajectories no further...

The dynamics in a primary spectral submanifold (SSM) constructed over the slowest modes of dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling trajectories further away from SSM, however, is difficult if linear part exhibits strong non-normal behavior. Such non-normality implies that simply projecting onto SSMs along directions normal to slow will not pair those correctly with their reduced counterparts on SSMs. In principle, well-defined nonlinear...

Transitions among various states of complex fluid flows are intrinsically nonlinear phenomena. Using the recent theory data-driven spectral submanifolds, we derive here first low-dimensional reduced model that successfully predicts transitions from a laminar base state to other steady or time-periodic in plane Couette flow.

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

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

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

Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such are non-autonomous and belong the class of non-periodically driven where traditional theory chaos (based e.g., on periodic orbits) does not hold. We demonstrate that even such possess an topological horseshoe-like structure at least for finite period time. This result based specifically developed method which allows compute corresponding time-dependent stable unstable foliations. These can...

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces the closest first integral field. Such approximate enable effective and efficient visualization vortical regions in flows. Here we propose variational construction these to remove limitation Fourier series representation earlier work. Specifically, use finite-element methods solve partial differential equation that describes best for given We several examples demonstrate power our...

Pancreatic carcinoma is one of the most malignant diseases and associated with a poor survival rate. Pituitary adenylate cyclase activating polypeptide (PACAP) neuropeptide that acts on three different G protein‑coupled receptors: specific PAC1 VPAC1/2 also bind vasoactive intestinal peptide. PACAP widely distributed in body has diverse physiological effects. Among other things, it as trophic factor influences proliferation differentiation several cells both under normal circumstances...

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

For an arbitrary velocity field $\mathbf{v}$ defined on a finite, fixed spatial domain, we find the closest rigid-body $\mathbf{v}_{RB}$ to in $L^2$ norm. The resulting deformation component, $\mathbf{v}_{d}=\mathbf{v-\mathbf{v}}_{RB}$, turns out be frame-indifferent and physically observable. Specifically, if $\mathbf{Q}_{\text{RB}}(t)$ is rotation tensor describing motion of rigid body frame, then seen as $\mathbf{Q}_{\text{RB}}^{T}\mathbf{v}_{d}$ by observer that frame. As consequence,...

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

We derive universal upper estimates for model prediction error under moderate but otherwise unknown uncertainty. Our give bounds on the leading-order trajectory uncertainty arising along trajectories, solely as functions of invariants known Cauchy-Green strain tensor model. turn out to be optimal, which means that they cannot improved general systems. The quantity relating trajectory-uncertainty is sensitivity (MS), we find a useful tool quick global assessment impact modeling uncertainties...

The aim of this study was to analyse the composition amyloid mass and plasmacytic infiltrate localized amyloidosis upper aerodigestive tract.Biopsy materials were studied by light microscopy, immunohistochemistry (IHC), mRNA in situ hybridization (mRNA-ISH). also analysed with high-performance liquid chromatography spectrometry- (HPLC-MS-) based proteomics.Nodular diffuse forms deposition detected. IHC analysis revealed λ-light chain (LC) two cases, κ-LC one case. remaining positive both....

Abstract Pituitary adenylate cyclase activating polypeptide (PACAP) is a neuropeptide with widespread occurrence and diverse functions. PACAP binds to specific PAC1 non-specific VPAC1/2 receptors. considered as growth factor, it plays important roles during development participates in reparative processes. Highest concentrations are found the nervous system endocrine glands, where several functions known, including actions tissue growth, differentiation tumour development. Therefore, we have...

We use video footage of a water tunnel experiment to construct two-dimensional reduced-order model the flapping dynamics an inverted flag in uniform flow. The is obtained as reduced on attracting spectral submanifold (SSM) that emanates from two slowest modes unstable fixed point flag. Beyond and limit cycle expected observations, our SSM-reduced also confirms existence points for flag, which were found by previous studies. Importantly, correctly reconstructs small number general...