Linear Extension Research Articles

Counting Cherry Reduction Sequences in Phylogenetic Tree-Child Networks is Counting Linear Extensions

Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries and reticulated cherries. As it is the case with phylogenetic trees, the number of ways in which this can be done gives information about the topology of the network. Here, we show that the problem of computing this number in tree-child networks is akin to that of finding the number of linear extensions of the poset induced by each network, and give an algorithm based on this reduction whose complexity is bounded in terms of the level of the network.

Ecophenotypic variation in a cosmopolitan reef-building coral suggests reduced deep-sea reef growth under ocean change

Sensitivity of reef-building corals to environmental factors has far-reaching ecosystem implications, especially in the limited number of cold-water coral (CWC) species that form reefs in the deep sea. Understanding CWC responses to large-scale oceanographic variation in their natural habitat can elucidate their sensitivity to global anthropogenic stressors. Here, we use skeletal samples to analyse fine-scale phenotypic variation in the widespread reef-building CWC Desmophyllum pertusum (Lophelia pertusa) in relation to broad physicochemical gradients in different sites across the Atlantic Ocean and Mediterranean Sea. We find evidence, amidst local and regional differentiation, of species-wide growth responses to physicochemical factors, mainly affecting corallite length, width and their ratio (slenderness). Our results suggest that higher temperature and lower oxygen levels negatively affect skeletal linear extension and budding rate of polyps. As also hinted by the reduced corallite length and slenderness in less developed reefs, these widespread responses may lead to a general decline in CWC reef growth rates as a long-term consequence of ocean warming and deoxygenation. Given this relevance, such responses can be used to model reef growth in a changing ocean.

Synthesis and Characterization of Polyimides with Rigid Folded Fragments

The macromolecular chain of conventional polyimide (PI) is a predominant linear extension, which is anticipated to uphold robust interchain interactions essential for preserving overall mechanical and thermal performance. This study is dedicated to the design and synthesis for the novel PIs containing folded chains, with a particular emphasis on modifying the chain conformational behavior with respect to the structure of the aggregation state and the corresponding gas separation properties. First, two unidirectional diamine monomers, dibenzo [c, g] phenanthrene-9,12-diamine (NPDA) and anthracene-1,8-diamine (ADA), were meticulously synthesized through a sequence of chemical reactions, including Witting olefination and photocyclization. These monomers possess distinctive spatial characteristics: NPDA adopts a helical conformation, while ADA maintains a planar structure. Subsequently, the corresponding folded chain-containing PIs, denoted as NPI and API, were successfully achieved by copolymerizing one of the unidirectional monomers with the 6FDA-TPDA system. API and NPI generally exhibit a propensity for enhanced molecular chain stacking, while retaining their good solubility and processability. Drawing from both experimental data and simulation results, it was ascertained that the inclusion of these two monomers produces a rearrangement of pore sizes with a decrease in large-size micropores and an increase in the percentage of ultra-micropores. Moreover, the PI membranes with the folded fragments have a much better CO2 plasticization resistance.

Second Order Extended Ensemble Filter for Non-linear Filtering

Whenever the state of a system must be estimated from noisy information, a state estimator is employed to fuse the data with the model to produce an accurate estimate of the state. When the system dynamics and observation models are linear, the Kalman Filter which is optimal, is used. However, in most applications of interest the system dynamics and observations equations are not- linear and suitable extensions of the Kalman Filter have been developed; for example, the Extended Kalman Filter(EKF). The Extended Kalman Filter is based on linearization by the Taylor series expansion about the mean of the state. This filtering process is however computationally expensive especially in high dimensional data. The cause for this is the high cost of integrating the equation of evolution of covariances. Due to this complexity in integration, new methods were sought known as the particle filters. It replaces linearization of non-linearities with Monte Carlo methods. The particle filter formed a basis for Ensemble Kalman Filter (EnKF) an extension of Kalman filter to non-linear filtering. The EnKF reduced the computational cost but its innovation process does not capture information sufficiently hence there is need to improve its performance. This study has developed a new filter, Second order Extended Ensemble Filter (SoEEF).We derived it from stochastic state models by expansion of expected values to the second order by use of Taylor series together with Monte Carlo method and Matlab. We used Lorenz 63 system of ordinary equations and differential Matlab to test the performance of the new filter. Then we compared its performance with four other filters like Bootstrap Particle Filter (BPF), First order Kalman Bucy Filter (FoEKBF),Second order Kalman Bucy Filter (SoKBF) and First order Extended Ensemble Filter (FoEEF). SoEEKF performs much better than the other four filters.

Seabird nutrients increase coral calcification rates and boost reef carbonate production

While excessive anthropogenic nutrient loads are harmful to coral reefs, natural nutrient flows can boost coral growth and reef functions. Here we investigate if seabird-derived nutrient subsidies benefit the growth of two dominant corals on lagoonal reefs, submassive Isopora palifera and corymbose Acropora vermiculata, and if enhanced colony-level calcification rates can increase reef-scale carbonate production. I. palifera and A. vermiculata colonies close to an island with high seabird densities displayed 1.4 and 3.2-times higher linear extension rates, 1.8 and 3.9-times faster planar area increase, and 1.6 and 2.7-times higher calcification rates compared to colonies close to a nearby island with low seabird densities, respectively. While benthic ReefBudget surveys in combination with average coral growth rates did not indicate differences in reef-scale carbonate production across sites, coral carbonate production was 2.2-times higher at the seabird-rich island when using site-specific linear growth rates and skeletal densities. This study shows that seabird-derived nutrients benefit fast-growing branching as well as previously unstudied submassive coral taxa. It also demonstrates that nutrient subsidies benefit colony-scale and reef-scale calcification rates, which underpin important geo-ecological reef functions. Restoring natural nutrient pathways should thus be a priority for island and reef management.

Fluvial-lacustrine influences on linear dune erosion at Lake Caroline in the Simpson Desert of Australia

Linear dunes are frequently examined with regard to their formation and maintenance; however, erosion or degradation of these landforms is less commonly addressed, due in part to the lack of observable changes in the geologic record. This study investigates the significant erosion of linear dunes along Lake Caroline, a playa in the northern Simpson Desert of central Australia. Field observations, laboratory analyses, and remote sensing imagery document recent fluvial and lacustrine interactions at Lake Caroline. Compositional and geochemical sediment analyses from three ∼2 m deep hand-augured sample sites indicate that the playa is primarily filled with sand from linear dunes, but also contains evaporite minerals and weathered local bedrock. Satellite images show that the playa has flooded at least 58 times since 2001. Our results indicate that present-day aeolian processes are sufficient to mobilize and transport sediment but are dominated by fluvial-lacustrine processes, resulting in the playa-adjacent dunes becoming isolated and starved of local sediment. As a result, the dunes are currently eroding into the playa which supports the conclusion that long-distance sediment transport is not responsible for the formation or maintenance of linear dunes as suggested by the linear due extension hypothesis. Burial dates from optically stimulated luminescence (OSL) indicate the linear dunes have been eroding for as much as 24 ka, and sediment samples from the playa near one linear dune suggest an onset of dune formation in the area before 58 ka. This work documents an instance in geologic time during the late Quaternary when aeolian, fluvial, and lacustrine processes are competing with one another, offering new insights into the dynamics of linear dunes in the arid Simpson Desert.

Synchronized magnet-induced displacement detection in non-magnetic plates via smart materials near-field sensing

Accurate monitoring of small displacements in non-magnetic thin-walled plates is essential for assessing their manufacturing precision and vibrational characteristics. Optical techniques are limited by environmental disturbances and spatial constraints, while contact methods are compromised by mechanical forces and wear. A synchronized magnet-induced displacement detection method (SMDDM) using heteropolar permanent magnets (HPMs) and smart materials for non-magnetic plates is proposed. Supported by a magnetic-mechanical–electrical coupling model and a joint algorithm with dynamic linear extension and analytic hierarchy process (DLE-AHP), the prototype’s parameters are refined through experimental design, neural networks, and multi-objective optimization. Comprehensive tests show that SMDDM achieves an accuracy of 2 μm and a resolution of 1 μm, with smaller measurement errors observed in low-frequency, small-displacement tests. This validates the method’s effectiveness in multi-scale displacement measurement and vibration testing, highlighting its potential for in-situ monitoring in thin-plate applications.

Research on the Performance and Control Strategy of Electro-Hydraulic Servo System for Selective Hole Digging Tree Planter

Compared to agricultural environments, afforestation sites are more complex, often presenting issues such as undulating and uneven terrain. These conditions lead to instability in hole digging depth and plant spacing during continuous movement, and the hole shape may not meet expectations. Additionally, the hydraulic system exhibits slow response speed and long steady-state time, affecting the quality of sapling planting. To address these issues, this paper designs an intelligent planting control system for intermittent hole digging under continuous dynamic movement, based on a large tree planter. The focus is on studying the dynamic accuracy of the hole digging cylinder to resolve the instability of plant spacing and planting depth in actual planting processes. Firstly, a motion trajectory model of the intermittent hole digging mechanism is established to obtain the relationship between the displacement trajectory of the rotating cutter and the displacements of the floating cylinder and the hole digging cylinder. Secondly, a mathematical model of the electro-hydraulic servo system is established to control the dynamic accuracy of the hole digging operation. Finally, a Simulink simulation model of the system is established to analyze the performance indicators of the hydraulic system during operation using step and sinusoidal excitation signals. The test results show that the displacement of the hydraulic piston rod can ensure a linear extension trend within the range of 0 to 0.4 m, and the extension distance of the hole digging cylinder in the planting system is 0 to 0.35 m, ensuring linear change within this stroke. When the system’s extension command is 1 V, the actual output is 0.6 m, with a relative error of less than 10% compared to the simulation value, indicating that the control strategy can effectively improve the dynamic performance of the system. When the hydraulic system is in a steady-state extension state at 50 to 58.6 s, the relative error with the simulation value is 7.3%, meeting the “double ten indicators” requirement. The research results clearly verify the superior performance of the proposed intelligent control system, and the proposed control strategy has great potential in practical applications, promising to improve afforestation quality by stabilizing planting spacing and planting depth.

Linear Operating Range and Extension of Three-Dimensional Active Zero-State PWM for Open-End Winding Drive

Linear Operating Range and Extension of Three-Dimensional Active Zero-State PWM for Open-End Winding Drive

Postnatal Skull Development Reveals a Conservative Pattern in Living and Fossil Vizcachas Genus Lagostomus (Rodentia, Chinchillidae).

The plains vizcacha, Lagostomus maximus, is the only living species in the genus, being notably larger than fossil congeneric species, such as Lagostomus incisus, from the Pliocene of Argentina and Uruguay. Here, we compare the skull growth allometric pattern and sexual dimorphism of L. maximus and L. incisus, relating shape and size changes with skull function. We also test whether the ontogenetic trajectories and allometric trends between both sexes of L. maximus follow the same pattern. A common allometric pattern between both species was the elongation of the skull, a product of the lengthening of rostrum, and chondrogenesis on the spheno-occipitalis synchondrosis and coronalis suture. We also detected a low proportion of skull suture fusion. In some variables, older male specimens did not represent a simple linear extension of female trajectory, and all dimorphic traits were related to the development of the masticatory muscles. Sexual dimorphism previously attributed to L. incisus would indicate that this phenomenon was present in the genus since the early Pliocene and suggests social behaviors such as polygyny and male-male competition. Ontogenetic changes in L. incisus were similar to L. maximus, showing a conservative condition of the genus. Only two changes were different in the ontogeny of both species, which appeared earlier in L. incisus compared to L. maximus: the development of the frontal process of the nasals in a square shape, and the straight shape of the occipital bone in lateral view. Juveniles of L. maximus were close to adult L. incisus in the morphospace, suggesting a peramorphic process. The sequence of suture and synchondroses fusion showed minor differences in temporozygomatica and frontonasalis sutures, indicating major mechanical stress in L. maximus related to size. We suggest a generalized growth path in Chinchillidae, but further analyses are necessary at an evolutionary level, including Lagidium and Chinchilla.

Soil quality assessment and mapping in basaltic terrain of Central India for sustainable soil and crop management using integrated PCA and GIS

The cereal-based cropping system plays a vital role in ensuring food security in the Indian subcontinent. However, the productivity of these systems has seen a continuous decline due to the degradation of soil quality. This study aims to develop a Soil Quality Index (SQI) for such cropping systems. A detailed survey was conducted in the Bareli watershed of Seoni district, Madhya Pradesh, at a 1:10000 scale using high-resolution satellite data and Geographic Information System (GIS) technology. The survey identified and mapped 5 soil series: Diwartola, Diwara, Bareli-1, Bareli-2 and Bareli-3. Soil quality was evaluated based on morphological, physical and chemical properties as well as fertility parameters. Key indicators for soil quality assessment included sand, silt, clay content, bulk density, hydraulic conductivity, available water capacity and coefficient of linear extensibility (COLE). Additionally, pH, electrical conductivity, organic carbon, cation exchange capacity and nutrients like N, P, K, Fe, Mn, Cu and Zn were considered. The SQI was calculated using integrated principal component analysis, which involved selecting a minimum data set (MDS), assigning weights and scoring indicators. The results revealed that Diwartola soils had high quality (242.7 ha, 13.5 % TGA), Bareli-1 and Bareli-3 soils were of medium quality (462.8 ha, 25.7 % TGA), while Diwara and Bareli-2 soils were of low quality (966.1 ha, 53.8 % TGA). Agro-interventions such as agri-horticulture, agro-forestry, silvi-pasture, intensive cultivation and soil and water conservation measures were recommended based on the different mapping units.

Growth rates of five coral species across a strong environmental gradient in the Colombian Caribbean

Coral calcification is critical for reef growth and highly dependent on environmental conditions. Yet, little is known about how corals calcify under sub-optimal conditions (e.g., turbid waters, high nutrients, sedimentation) or coral growth in understudied regions such as the Colombian Caribbean. We therefore assessed the calcification and linear extension rates of five coral species across an inshore-to-offshore gradient in the Colombian Caribbean. A suite of environmental variables (temperature, light intensity, visibility, pH, nutrients) measured during the rainy season (May – November 2022) demonstrated more sub-optimal conditions inshore compared to offshore. Across all species, calcification rates were 59% and 37% lower inshore compared to the offshore and midshore sites, respectively. Across all sites, massive corals calcified up to 92% more than branching species but were more susceptible to heat stress and sub-optimal inshore conditions. However, branching species had reduced survival due to extreme climatic events (i.e., bleaching, hurricanes). A comparison with published rates for the wider Caribbean revealed that massive species in the Colombian Caribbean grow up to 11 times more than those in the wider Caribbean while branching species generally have similar growth rates, but this finding may have been influenced by fragment size and/or heat stress. Our findings indicate that present-day environmental conditions, coupled with more frequent extreme climatic events, will favor massive over branching species in midshore areas of the Colombian Caribbean. This suggests a possible shift towards faster calcifying massive species in future coral communities, possibly exacerbating the ongoing regional decline in branching species over the last decades.

Relationships between linear extension, calcification rate, skeletal density, and nutrients with coral bioerosion: A case study in the Persian Gulf

The balance between reef growth and physical and biological erosion that underlies the coral reef framework can be disrupted by environmental disturbances. The variation in macroborer assemblages and the bioerosion intensity in four scleractinian corals (Porites harrisoni, Platygyra daedalea, Cyphastrea microphtalma and Dipsastraea pallida) were investigated at Kharg and Khargo islands in the northern Persian Gulf. Macroborers in five-mm-thick sections of the longest central axis of each coral colony in each species were identified and counted. Five groups of macroborers were identified including bivalves, polychaetes, sponges, barnacles and vermetid snails. Boring bivalves accounting for 63.3% of the total internal macrobioerosion and were the most abundant macrobioeroder group in all coral species. There were significant differences in macrobioerosion intensity among coral species and locations (P≤0.05). Barnacles were only detected in P. daedalea. Boring sponges were marginally found in P. harrisoni, C. microphtalama and D. pallida. Polychaetes were the second-most important macroborers after bivalves, particularly in C. microphtalma and P. harrisoni. Vermetid snails were recorded from all four coral species but to lesser extend in P. harrisoni. Higher linear extension rate was positively correlated to higher bioerosion intensity, but was significant only in C. microphthalma. We detected no significant correlation between coral calcification rate and macrobioerosion intensity. Skeletal density was negatively correlated with the bioerosion intensity in all coral species. Macrobioerosion was most abundant at the site with highest pollution levels and increased with nutrients. Nutrients and skeletal density were the most important factors influencing macrobioerosion intensity. We found that northwestern part of the Persian Gulf experienced high bioerosion intensity compared to other parts. We concluded that Khargo Island possessed higher water quality compared to Kharg Island.

The extremals of the Kahn-Saks inequality

A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distinguished elements differ by k is log-concave as a function of k. The log-concave sequences that can arise in this manner prove to exhibit a much richer structure, however, than is evident from log-concavity alone. The main result of this paper is a complete characterization of the extremals of the Kahn-Saks inequality: we obtain a detailed combinatorial understanding of where and what kind of geometric progressions can appear in these log-concave sequences. This settles a partial conjecture of Chan-Pak-Panova, while the analysis uncovers new extremals that were not previously conjectured. The proof relies on a much more general geometric mechanism—a hard Lefschetz theorem for nef classes that was obtained in the setting of convex polytopes by Shenfeld and Van Handel—which forms a model for the investigation of such structures in other combinatorial problems.

Hurricane Irma Linked to Coral Skeletal Density Shifts on the Florida Keys Reef Tract.

Coral reefs are at risk due to various global and local anthropogenic stressors that impact the health of reef ecosystems worldwide. The most recent climate models predict that climate change will increase the frequency and intensity of tropical storms. This increased storm occurrence and strength will likely compromise coral reef structures and habitats for reef-dwelling organisms, including across the Florida Keys Reef Tract (FKRT), the most extensive tropical reef system along the US coast. While several recent studies reveal the chronic impacts of tropical storms on corals, relatively little is known about the effects of major storm events on coral growth and how these effects vary over spatiotemporal scales. Here, I characterize the skeletal growth of two common Caribbean reef-building coral species, Siderastrea siderea and Pseudodiploria strigosa, before and after Hurricane Irma to investigate the storm's impact on coral skeletal growth on inner and outer reefs of the FKRT. Coral cores were extracted from both species at four inner and four outer reef sites in May 2015, before Hurricane Irma struck the Florida Keys in September 2017. Subsequently, 33 micro-cores were collected in May 2019, two years after the storm traversed our previously cored coral colonies. A three-way ANOVA model with storm, species, and reef location as the three factors was used to assess the impact of the storm on each of three growth parameters: skeletal density, linear extension, and calcification rates. Results reveal no difference in the coral annual skeletal growth parameters pre- and post-Hurricane Irma, although previously quantified differences in these growth parameters across species and location were observed. However, analysis of the "yearly" change in annual skeletal growth parameters showed significant differences in skeletal density across groups before and after Hurricane Irma, but not for linear extension and calcification rates. Our findings improve an understanding of the impacts of tropical storms on coral skeletal growth and offer new insights into how we can employ corals' innate growth capacities to help conserve coral reefs under climate change.

Advancing estimation techniques and their applications in engineering and medical data analysis through novel continuous and discrete linear failure rate distribution extension

In this paper, we present a new heavy-tailed distribution called the heavy-tailed linear failure rate (HTLFR) distribution. Various statistical properties of the proposed distribution are derived, including the quantile function, the median, the ordinary moments, the moment generating function, the incomplete moments and the conditional moments. Some actuarial measures such as value at risk, expected shortfall, tail value at risk, tail variance and tail variance premium are calculated. Three different methods of estimation such as the maximum likelihood method, the maximum product spacing method and the Bayesian method as well as some simulation results for the model parameters of the HTLFR distribution under complete samples are examined. The results of the real data set show that the proposed distribution has greater flexibility and has been empirically evaluated under complete data. Discrimination analysis was employed to ensure fairness, equity, and accuracy in decision-making processes for selecting the best model, comparing the proposed distribution with known distributions. A discrete analog of the HTLFR distribution is proposed.

Evaluating Linear Coral Growth Estimation Using Photogrammetry and Alternative Point Cloud Comparison Methods

Abstract. Corals are critical reef-building organisms, providing essential habitat and ecosystem services. Tracking coral growth over time indicates coral reef health, which can be measured using various established techniques. Several coral growth-related studies have successfully applied photogrammetry to a particular coral of various types. While the focus of previous work was on standardised data processing and, to a certain degree, on the assessment of different point cloud comparison methods (Lange et al. 2022), little attention has been given to the impact of camera calibration. This study measured the annual linear extension of five Acropora spp. colonies using photogrammetry and evaluated all stages of imagery processing. A high focus was given to the analysis of the camera calibration method and the validation of camera parameters derived using an in-situ calibration of coral images with scale bars placed in the camera's field of view. We demonstrate that this method is as reliable as the calibration using a calibration frame. This study also examined the impact of the different point cloud comparison methods for Acropora spp. More specifically, the derived point clouds are compared by applying the point-to-point and point-to-model methods and manually selecting 12 coral branch tips. Histograms derived from the comparison methods were analysed and deemed a suitable and efficient alternative approach for measuring the maximum growth rate of mature colonies over shorter time periods (1 year or less).

On dynamical system modeling of learned primal-dual with a linear operator K : stability and convergence properties

Learned Primal-Dual (LPD) is a deep learning based method for composite optimization problems that is based on unrolling/unfolding the primal-dual hybrid gradient algorithm. While achieving great successes in applications, the mathematical interpretation of LPD as a truncated iterative scheme is not necessarily sufficient to fully understand its properties. In this paper, we study the LPD with a general linear operator. We model the forward propagation of LPD as a system of difference equations and a system of differential equations in discrete- and continuous-time settings (for primal and dual variables/trajectories), which are named discrete-time LPD and continuous-time LPD, respectively. Forward analyses such as stabilities and the convergence of the state variables of the discrete-time LPD to the solution of continuous-time LPD are given. Moreover, we analyze the learning problems with/without regularization terms of both discrete-time and continuous-time LPD from the optimal control viewpoint. We prove convergence results of their optimal solutions with respect to the network state initialization and training data, showing in some sense the topological stability of the learning problems. We also establish convergence from the solution of the discrete-time LPD learning problem to that of the continuous-time LPD learning problem through a piecewise linear extension, under some appropriate assumptions on the space of learnable parameters. This study demonstrates theoretically the robustness of the LPD structure and the associated training process, and can induce some future research and applications.

An example related to Whitney’s extension problem for L 2,p (R2) when 1 < p < 2

Abstract In this paper, we prove the existence of a bounded linear extension operator T : L 2 , p ( E ) → L 2 , p ( R 2 ) $T:{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2, where E ⊂ R 2 $E\subset {\mathbb{R}}^{2}$ is a certain discrete set with fractal structure. Our proof makes use of a theorem of Fefferman–Klartag (“Linear extension operators for Sobolev spaces on radially symmetric binary trees,” Adv. Nonlinear Stud., vol. 23, no. 1, p. 20220075, 2023) on the existence of linear extension operators for radially symmetric binary trees.

Millennial calcification trends in Porites corals: Resilient skeletal density and vulnerable linear extension in response to environmental change

Global coral reefs are currently facing widespread declines in calcification rates, a trend that underscores the need to understand variations between calcification in contemporary and ancient corals. This study investigates the changes in coral calcification over the last millennium by analyzing 21 subfossil and 11 modern coral samples from a marginal reef in the northern South China Sea. Our results reveal that although coral skeletal density has remained relatively stable, significant differences are evident in linear extension rates between the Medieval Climate Anomaly (MCA, 900–1300 CE) and the Little Ice Age (LIA, 1550–1850 CE), as well as between the pre- and post-industrial periods. This finding suggests that inshore Porites corals have greater resilience in their skeletal density compared to linear extension rates when responding to environmental changes. Our analysis indicates that sea surface temperature (SST) is the primary environmental driver influencing coral calcification, with a positive correlation observed between SST and both modern coral linear extension and calcification rates. In contrast, factors such as seawater pH, salinity, and total solar irradiance appear to have minimal impact on coral skeletal growth. Therefore, the lower linear extension and calcification rates observed in the LIA corals, as compared to the MCA corals, are likely due to the cooler temperatures during the LIA. We also hypothesize that the extended period of cold SST from the LIA to the early 20th century may have led to the reduced linear extension and calcification rates in modern corals, with recent warming insufficient to facilitate a return to the optimal skeletal growth observed during the MCA.