This work analyzes the effect of wall geometry when a reaction-diffusion system is confined to a narrow channel. In particular, we study the entropy production density in the reversible Gray-Scott system. Using an effective diffusion equation that considers modifications by the channel characteristics, we find that the entropy density changes its value but not its qualitative behavior, which helps explore the structure-formation space.

Introduction: European mistletoe (Viscum album L.) has been gaining increasing interest in the field of oncology as a clinically relevant adjunctive treatment in many forms of cancer. In the field of phytopharmacology, harvesting time is pivotal. In the last century, a form of metabolomic fingerprinting based on pattern formation was proposed as a way to determine optimal harvesting times to ensure high quality of mistletoe as raw material for pharmaceutical use. In order to further evaluate the information obtained with this metabolomic fingerprinting method, we analysed a large time series of previously undigitised daily mistletoe chromatograms dating back to the 1950s. Methods: These chromatograms were scanned and evaluated using computerized image analysis, resulting in 12 descriptors for each individual chromatogram. We performed a statistical analysis of the data obtained, investigating statistical distributions, cross-correlations and time self-correlations. Results: The analysed dataset spanning about 27 years, contains 19,037 evaluable chromatograms in daily resolution. Based on the distribution and cross-correlation analyses, the 12 descriptors could be clustered into six independent groups describing different aspects of the chromatograms. One descriptor was found to mirror the annual rhythm being well correlated with temperature and a phase shift of 10 days. The time self-correlation analysis showed that most other descriptors had a characteristic self-correlation of ∼50 days, which points to further infradian rhythms (i.e., more than 24 h). Discussion: To our knowledge, this dataset is the largest of its type. The combination of this form of metabolomic fingerprinting with the proposed computer analysis seems to be a promising tool to characterise biological variations of mistletoe. Additional research is underway to further analyse the different rhythms present in this dataset.

Decline of the dissolved oxygen in the ocean is a growing concern, as it may eventually lead to global anoxia, an elevated mortality of marine fauna and even a mass extinction. Deoxygenation of the ocean often results in the formation of oxygen minimum zones (OMZ): large domains where the abundance of oxygen is much lower than that in the surrounding ocean environment. Factors and processes resulting in the OMZ formation remain controversial. We consider a conceptual model of coupled plankton-oxygen dynamics that, apart from the plankton growth and the oxygen production by phytoplankton, also accounts for the difference in the timescales for phyto- and zooplankton (making it a \"slow-fast system\") and for the implicit effect of upper trophic levels resulting in density dependent (nonlinear) zooplankton mortality. The model is investigated using a combination of analytical techniques and numerical simulations. The slow-fast system is decomposed into its slow and fast subsystems. The critical manifold of the slow-fast system and its stability is then studied by analyzing the bifurcation structure of the fast subsystem. We obtain the canard cycles of the slow-fast system for a range of parameter values. However, the system does not allow for persistent relaxation oscillations; instead, the blowup of the canard cycle results in plankton extinction and oxygen depletion. For the spatially explicit model, the earlier works in this direction did not take into account the density dependent mortality rate of the zooplankton, and thus could exhibit Turing pattern. However, the inclusion of the density dependent mortality into the system can lead to stationary Turing patterns. The dynamics of the system is then studied near the Turing bifurcation threshold. We further consider the effect of the self-movement of the zooplankton along with the turbulent mixing. We show that an initial non-uniform perturbation can lead to the formation of an OMZ, which then grows in size and spreads over space. For a sufficiently large timescale separation, the spread of the OMZ can result in global anoxia.

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

We use data produced by industrial wood grading machines to train a machine learning model for predicting strength-related properties of wood lamellae from colour images of their surfaces. The focus was on samples of Norway spruce (Picea abies) wood, which display visible fibre pattern formations on their surfaces. We used a pre-trained machine learning model based on the residual network ResNet50 that we trained with over 15 000 high-definition images labelled with the indicating properties measured by the grading machine. With the help of augmentation techniques, we were able to achieve a coefficient of determination (R2) value of just over 0.9. Considering the ever-increasing demand for construction-grade wood, we argue that computer vision should be considered a viable option for the automatic sorting and grading of wood lamellae in the future.

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz\'s theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

By masterfully balancing directed growth and passive mechanics, plant roots are remarkably capable of navigating complex heterogeneous environments to find resources. Here, we present a theoretical and numerical framework which allows us to interrogate and simulate the mechanical impact of solid interfaces on the growth pattern of plant organs. We focus on the well-known waving, coiling, and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined surfaces, serving as a minimal model of the intricate interplay with solid substrates. By modeling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations verify hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane responses. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling, and skewing patterns with substrate tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico plant organs behavior in relation to their environment.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing\'s reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

The milestone of compound leaf development is the generation of separate leaflet primordia during the early stages, which involves two linked but distinct morphogenetic events: leaflet initiation and boundary establishment for leaflet separation. Although some progress in understanding the regulatory pathways for each event have been made, it is unclear how they are intrinsically coordinated. Here, we identify the PINNATE-LIKE PENTAFOLIATA2 (PINNA2) gene encoding a newly identified GRAS transcription factor in Medicago truncatula. PINNA2 transcripts are preferentially detected at organ boundaries. Its loss-of-function mutations convert trifoliate leaves into a pinnate pentafoliate pattern. PINNA2 directly binds to the promoter region of the LEAFY orthologue SINGLE LEAFLET1 (SGL1), which encodes a key positive regulator of leaflet initiation, and downregulates its expression. Further analysis revealed that PINNA2 synergizes with two other repressors of SGL1 expression, the BEL1-like homeodomain protein PINNA1 and the C2H2 zinc finger protein PALMATE-LIKE PENTAFOLIATA1 (PALM1), to precisely define the spatiotemporal expression of SGL1 in compound leaf primordia, thereby maintaining a proper pattern of leaflet initiation. Moreover, we showed that the enriched expression of PINNA2 at the leaflet-to-leaflet boundaries is positively regulated by the boundary-specific gene MtNAM, which is essential for leaflet boundary formation. Together, these results unveil a pivotal role of the boundary-expressed transcription factor PINNA2 in regulating leaflet initiation, providing molecular insights into the coordination of intricate developmental processes underlying compound leaf pattern formation.

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing\'s reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.