Branching structures such as vascular networks are representative morphological patterns in living systems, and they often arise from collective cell migration. Angiogenesis, the sprouting of new blood vessels from pre-existing ones, is a fundamental process in development. Experimental and theoretical studies have demonstrated that sprout formation depends on the collective movements and shapes of endothelial cells, as well as the remodelling of the extracellular matrix. Many discrete models have been proposed to describe cell dynamics, successfully reproducing vascular patterns and collective behaviours. In this study, we present a two-dimensional mathematical model that represents each endothelial cell as an ellipse and incorporates the effects of the extracellular matrix. We performed computer simulations under two scenarios: invasion from a pre-formed sprout and collective advancement into an extracellular matrix region. The results show that the extracellular matrix helps maintain linear sprout extension and suppresses the formation of dispersed or curved branches, while elongated cell shapes promote sprouting more effectively than round cells. The model also reproduces experimentally observed behaviours such as tip-cell replacement and the mixing of cells within sprouts. These findings highlight the importance of integrating cell shape and extracellular matrix remodelling to understand early blood vessel formation.

Linear stroke extension of quasi-zero stiffness isolators through displacement scaling principle targeted on large amplitude excitation

This paper presents a rigorous, application-oriented survey of separation theorems and supporting functionals for convex sets in normed and Banach spaces. Emphasizing geometric version of the Hahn-Banach theorem, this work develops clean conditions for strict and non-strict separation, existence of supporting hyperplanes, and links to dual cones and polar sets. We highlight the role of weak and weak-star topologies in separation and illustrate how these results undergird feasibility, sensitivity, and duality principles in convex optimization. Short, self-contained proofs and examples are provided to keep the exposition accessible while maintaining mathematical precision. The paper thereby complements classical treatments of linear functional extension by focusing on geometric separation mechanisms and their applied consequences, especially in linear programming, convex feasibility, and basic duality frameworks. This comprehensive investigation into separation theorems reveals fundamental geometric structures that underpin both theoretical functional analysis and practical optimization applications, providing a unified framework for understanding convex separation phenomena across diverse mathematical contexts.

This study presents the design, control, and flight experiments of a motor-directly-driven flapping-wing micro air vehicle with extension springs (MDD-FWMAVES). The flapping wing actuation utilizes the resonance of a linear extension spring and a flapping wing. The analysis results of the proposed MDD-FWMAVES revealed a resonant frequency of 19.59 Hz for the flapping-wing mechanism, and actual flapping experiments confirmed this to be 20 Hz. Using a six-axis load cell, we demonstrated the ability to generate roll, pitch, and yaw moments for attitude control based on wing flapping variations. All roll, pitch, and yaw moments were linearly proportional to the wing flapping variations. MEMS gyroscopes and accelerometers were used to measure roll, pitch, and yaw angular velocities and the gravity. A complementary filter was applied to these measurements to obtain the roll and pitch angles required for attitude control. A microprocessor, two motor drive circuits, one MEMS gyroscope/accelerometer, and one EEPROM for flight data storage were implemented on a single, ultra-compact electronic control board and mounted on the MDD-FWMAVES. Simple roll and pitch PD controllers were implemented on this electronic control board, and the controlled flight feasibility of the MDD-FWMAVES was explored. Flight tests demonstrated stable hovering for approximately 6 s. While yaw control was not achieved, the onboard feedback control system demonstrated stable roll and pitch control. Therefore, the MDD-FWMAVES holds the potential to be developed into a high-performance flapping-wing micro air vehicle if its flight system and controller are improved.

Horizontal vibration of car is a critical issue affecting the stability and ride comfort of high-speed elevators. This phenomenon primarily caused by the uncertain nonlinear disturbances induced by guide rails, guide shoes, and other various internal and external perturbations. To mitigate these vibrations, a novel output feedback stabilization control strategy based on nonlinear extension state observer (NLESO) is proposed. First, an eight-degree-of-freedom dynamics model considering the uncertain nonlinear disturbances was established for the horizontal vibrations. Second, NLESOs were developed to observe and compensate for the internal and external perturbations of elevator car system. Subsequently, a stabilization controller with NLESOs was designed based on the output feedback of the dynamics model using a finite-time stabilization control law. The finite-time stability of NLESOs was proven using Lyapunov’s theorem. Finally, numerical simulations for the proposed method were conducted under two typical rail excitations using MATLAB/Simulink and compared with higher-order sliding mode control (HOSMC), linear extension state observer (LESO), and passive control schemes. The results indicate that the proposed method significantly reduces the displacement acceleration and angular deflection acceleration of horizontal vibrations, with root mean square values decreasing by more than 68% and 67%, respectively, compared to passive control. This demonstrates the superior stability and finite-time convergence of the proposed method, effectively suppressing horizontal vibrations during high-speed elevator operation.

In recent years, questions about the construction of special orderings of a given graph search were studied by several authors. On the one hand, the so called end-vertex problem introduced by Corneil et al. in 2010 asks for search orderings ending in a particular vertex. On the other hand, the problem of finding orderings that induce a given search tree was introduced already in the 1980s by Hagerup and received new attention most recently. Here, we consider a generalization of some of these problems by studying the question whether there is a search ordering that is a linear extension of a given partial order on a graph's vertex set. We show that this problem can be solved in polynomial time for Generic Search on general graphs as well as for searches called forgetful and partial orders of bounded width. Furthermore, we present polynomial-time algorithms on the classes of chordal bipartite graphs and split graphs for some searches including (Lexicographic) Breadth First Search. These algorithms generalize known algorithmic results for the End-Vertex Problem and the Search Tree Recognition Problem.

Relevance of Mathematical Optimization as a Tool for Diet Modeling in the Development of Food-Based Dietary Recommendations in Sub-Saharan Africa: A Scoping Review.

Remote reefs offer insights into natural coral dynamics, influenced by regional environmental factors and climate change fluctuations. Clipperton Atoll is the eastern tropical Pacific’s most isolated reef, where coral reef growth and life strategies have been poorly studied so far. Recognizing the coral species’ growth response might help understand ecological dynamics and the impacts of anthropogenic stressors on coastal reefs. The present study evaluates annual coral growth parameters of the most abundant coral reef-building species, Porites australiensis, Porites arnaudi, Porites lutea, and Porites lobata. The results showed that during 2015–2019, corals exhibited the lowest annual linear extension (0.65 ± 0.29 cm yr−1), skeletal density (1.14 ± 0.32 g cm−3), and calcification rates (0.78 ± 0.44 g cm−2 yr−1) for the genera along the Pacific. Differences in growth patterns among species were observed, with Porites lutea and Porites lobata showing a higher radial extension, developing massive-hemispherical morphologies, and acting as structural stabilizers; meanwhile, P. arnaudi and P. australiensis exhibited more skeletal compaction but also with a high plasticity on their morphologies, contributing to benthic heterogeneity. These differences are particularly important as each species fulfills different ecological functions within the reef, contributing to the ecosystem balance and enhancing the relevance of the massive species in the physical structure of remote reef systems, such as Clipperton Atoll.

Abstract Linear Standard Model (SM) extensions, defined as new particles that can couple linearly to SM fields, form a motivated and finite set of simplified models for exploring phenomenology Beyond the SM (BSM). Heavy BSM particles may be integrated out to obtain their low-energy effects in the SM Effective Field Theory (SMEFT) parametrised by the Wilson coefficients of higher-dimensional operators. We compute and map the dimension-6 SMEFT operator structure of all scalar and fermion linear SM extensions up to one-loop order, thus extending the existing tree-level dictionary of results. Explicit analytic matching expressions for the Wilson coefficients are provided as both Python and Mathematica code in a GitHub repository accessible through links embedded in our main table for each coefficient and within a Python package. We apply our map to highlight the sensitivity to heavy new physics of a Z-pole run at a future Tera-Z factory; at one loop, with unit couplings, all linear SM extensions can be indirectly probed by electroweak precision measurements up to $$ \mathcal{O}(10) $$ O 10 TeV.

Accurate retail demand forecasting is integral to the operational efficiency of any retail business. As demand is described over time, the prediction of demand is a time-series forecasting problem which may be addressed in a univariate manner, via statistical methods and simplistic machine learning approaches, or in a multivariate fashion using generic deep learning forecasters that are well-established in other fields. This study analyzes, optimizes, trains and tests such forecasters, namely the Temporal Fusion Transformer and the Temporal Convolutional Network, alongside the recently proposed Time-Series Mixer, to accurately forecast retail demand given a dataset of historical sales in 45 stores with their accompanied features. Moreover, the present work proposes a novel extension of the Time-Series Mixer architecture, the LSTMixer, which utilizes an additional Long Short-Term Memory block to achieve better forecasts. The results indicate that the proposed LSTMixer model is the better predictor, whilst all the other aforementioned models outperform the common statistical and machine learning methods. An ablation test is also performed to ensure that the extension within the LSTMixer design is responsible for the improved results. The findings promote the use of deep learning models for retail demand forecasting problems and establish LSTMixer as a viable and efficient option.

The fossil record of past climate transitions offers insights into future biotic responses to climate change. Here, we compare shell growth dynamics, specifically linear extension and net calcification rates, of the bivalve Chamelea gallina between Northern Adriatic Sea assemblages from the Holocene Climate Optimum (HCO, 9 − 5 cal. kyr B.P.) and today. This species is a valuable economic resource, currently threatened by climate change and numerous anthropogenic stressors. During the HCO, regional sea surface temperatures were warmer than today, making it a potential analog for exploring ecological responses to increasing seawater temperatures predicted in the coming decades. By combining standard aging methods with reconstructed sea surface temperatures, we observed a significant reduction in linear extension and net calcification rates in warmer HCO assemblages. During the HCO, immature C. gallina specimens developed a denser shell at the expense of a linear extension rate, which was significantly lower than modern specimens. This resulted in an average delay of 3 months in reaching sexual maturity, which is currently reached after 13–14 months or at a length of ~ 18 mm. This study sheds light on the natural range of variability of C. gallina over longer time scales and its potential responses to near-future global warming.

Climate change and anthropogenic stressors are accelerating coral reef degradation, prompting urgent restoration strategies. This study evaluates the performance of two coral nursery types, floating mid-water nurseries (FNs) and bottom-attached table nurseries (TNs), at two contrasting reef environments in Mauritius: the degraded, high sedimentation site of Flic-en-Flac (FEF) and the more pristine Pointe aux Feuilles (PAF). Coral fragments from Millepora sp., Acropora muricata, Acropora selago, and Pocillopora damicornis were monitored over three years for survivorship, growth, and linear extension rate (LER). Survivorship exceeded 88% in all cases, with Millepora sp. in PAF–TN achieving the highest rate (99.8%) and P. damicornis in FEF–FN the lowest (88%). Growth was greatest at PAF–TN, where Millepora sp. reached a mean length of 27.25 cm and LER of 9.66 mm y−1. In contrast, the same species in FEF–TN averaged only 3.64 cm in length and 3.44 mm y−1 in LER. Environmental conditions including higher turbidity, nitrate, and phosphate at FEF, and higher phytoplankton density at PAF significantly influenced coral performance. We propose a site-specific nursery selection framework, including FNs for high-sediment areas and TNs for protected and biodiverse sites, to support more effective coral farming outcomes in island restoration programs.

Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular in systems biology due to their ability to model long-term biological phenotypes within a qualitative, predictive framework. Boolean networks model phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable hypercubes in the system’s state space). In biological applications, attractors and minimal trap spaces are typically in one-to-one correspondence. However, this correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside minimal trap spaces are possible. MAAs are rare and poorly understood, despite recent efforts. In this contribution to the BMB & JMB Special Collection “Problems, Progress and Perspectives in Mathematical and Computational Biology”, we summarize the current state of knowledge regarding MAAs and present several novel observations regarding their response to node deletion reductions and linear extensions of edges. We conduct large-scale computational studies on an ensemble of 14 000 models derived from published Boolean models of biological systems, and more than 100 million Random Boolean Networks. Our findings quantify the rarity of MAAs; in particular, we only observed MAAs in biological models after applying standard simplification methods, highlighting the role of network reduction in introducing MAAs into the dynamics. We also show that MAAs are fragile to linear extensions: in sparse networks, even a single linear node can disrupt virtually all MAAs. Motivated by this observation, we improve the upper bound on the number of delays needed to disrupt a motif-avoidant attractor.

Bayesian inference for partial orders from random linear extensions: Power relations from 12th century royal acta

Enhancing the applied force and range of axial optical tweezers

Nearshore reefs, at the interface of land-sea interactions, provide essential ecosystem services, but are susceptible to multiple global and local stressors. These stressors can detrimentally impact coral growth and the continuity of the reef framework. Here, we analyse coral growth records (1998 – 2016) of massive Porites spp. colonies from nearshore reefs in Fiji. Our aim is to assess the role of thermal stress and turbidity on coral growth across a range of environments. Our findings reveal a negative linear relationship between linear extension and seawater turbidity across locations (GLM, R2 = 0.42, p < 0.001), indicating that average coral growth is significantly influenced by local environmental conditions. On interannual timescales, all locations experienced a 14% to 30% decrease in linear extension in response to acute thermal stress during the 2013 – 2016 period. This finding highlights the existence of compounding effects between water quality and thermal stress. We suggest that inshore, long-lived massive hard corals in areas of high turbidity are more vulnerable to increasing SSTs due to an already reduced mean growth. Integrated management strategies in these regions that considers managing for multiple, interacting local stressors are warranted to enhance resilience.

Diaryl urea-based compounds have attracted the attention of many researchers due to their potential as anticancer agents. Following our previous study on a series of diaryl urea compounds and implementation of the obtained structure activity relationship (SAR) analysis, a new set of derivatives were designed and synthesized. The synthesized compounds were subjected to evaluation for their in vitro antiproliferative activities against A549 and HT-29 cell lines. Among all, 6a emerged as the most potent antiproliferative agent with an IC50 value of 15.28 and 2.566 µM against HT-29 and A549 cells, respectively. Comparing the activity of the newly designed and synthesized diaryl urea compounds 4a-b and 6a-e with those for the previously reported compounds 8a-b and 9a-f confirmed the importance of the substitution of amide groups instead of ester between the central and distal benzene rings of diaryl urea scaffold. The results of current study revealed that the substitution of proximal and distal benzene rings with chlorine and methyl groups, alongside the linear extension of molecules through the introduction of a methylene spacer group could enhance antiproliferative activity, which is in agreement with previously reported SAR analysis. Molecular docking simulations demonstrated that all designed compounds exhibit binding affinity to VEGFR-2 similar to that observed experimentally for sorafenib. The findings of this study may offer valuable insights for the further development of diaryl urea-based anticancer agents.Graphical

The third fossil minute-clubbed beetle of the extant genus Europs Wollaston, 1854 (Coleoptera: Monotomidae), E. carsteni sp. nov., is described, diagnosed and illustrated from Eocene Baltic amber. This Palaeogene species can be distinguished from the known Eocene congeners by triangular femoral lines with long longitudinal linear extension produced beyond the middle of abdominal ventrite 1 and by the finely setose dorsum.

Addressing the human peopling of South America requires an understanding of the case of North America, including the alternative routes suggested by different dispersal models. Accordingly, it is useful to evaluate both the assumptions and implications behind current peopling models, even when South America is rarely mentioned. One result of this discussion is that the dispersal of humans into South America should not be viewed as a linear extension of the peopling of North America, given that both innovations and divergences are expected for populations that have previously interacted with different geographies and resources. The scarcity of basic information at the crucial entry places makes it difficult to evaluate and improveme those models. The age of the peopling process is one of the most debated issues, for which the strength and quality of the available evidence is central. We also discuss some methodological factors implicated in the construction of the different temporal frameworks and the controversies surrounding them.

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the inequalities, and the computational complexity aspects of the results.