Linear Extension Research Articles

Qualitative analysis for viscous cosmologies in a non linear regime of the Israel-Stewart formalism

We explore the dynamical properties of a cosmological model that includes viscous effects in the dark matter sector of the fluid equations in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. The bulk viscous effects are described by a non linear extension of the full Israel-Stewart model, which is a fluid causal scheme. We allow the interchange of energy in the dark sector and describe this by means of the interaction term, namely Q. We establish the dynamical system corresponding to Friedmann and fluid set of equations associated to the model and study the linear stability of its critical points. From the exploration of the dynamical system, we show the appearance of a critical point characterizing a de Sitter universe within the non interacting and interacting dark sector. We focus our study to analyse the stability of this fixed point in a large region of parameter space and derive linearized solutions around it. These approximate and analytical solutions are potentially able to describe the expansion of the universe since they are close to a de Sitter stationary solution. Within this regime with Q ≠ 0, we realize the existence of regions in the space of parameters where this critical point is stable and describes the behavior of dark energy as quintessence, cosmological constant and phantom like fluids. We perform a comparison between numerical and linearized solutions nearby the critical points within the full non linear regimes and also contrast them against ΛCDM model as a fiducial model. We find that the fully non linear regime is favored by observations and closer to the concordance model due to the non-zero value of the parameter j, which controls the non linear effects of bulk viscosity. In fact, at low redshift values, the expansion rate associated to the full non linear regime is practically indistinguishable from the ΛCDM model. The deceleration parameter obtained in this regime exhibits a transition from decelerated to accelerated cosmic expansion.

Early life stages of a Mediterranean coral are vulnerable to ocean warming and acidification

Abstract. The ability of coral populations to recover from disturbance depends on larval dispersion and recruitment. While ocean warming and acidification effects on adult corals are well documented, information on early life stages is comparatively scarce. Here, we investigate whether ocean warming and acidification can affect the larval and recruit development of the Mediterranean azooxanthellate coral Astroides calycularis. Larvae and recruits were raised for 9 months at ambient (23 ∘C) and warm (26 ∘C) temperatures and ambient (8.0) and low pH (7.7, on the total scale). The timing of the larval metamorphosis, growth of the recruit polyp by linear extension and budding, and skeletal characteristics of the 9-month-old polyps were monitored. Settlement and metamorphosis were more successful and hastened under a warm temperature. In contrast, low pH delayed the metamorphosis and affected the growth of the recruits by reducing the calcified area of attachment to the substrate as well as by diminishing the skeleton volume and the number of septa. However, skeleton density was higher under low pH and ambient temperature. The warm temperature and low-pH treatment had a negative impact on the survival, settlement, and growth of recruits. This study provides evidence of the threat represented by ocean warming and acidification for the larval recruitment and the growth of recruits of A. calycularis.

Big Ramsey degrees in universal inverse limit structures

We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures, extending Zheng’s work for the profinite graph to the setting of Fraïssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that for each such Fraïssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such Fraïssé classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees.

Quantifying skeletal density at high temporal resolution in massive scleractinian corals by using two-dimensional grid-scanning gamma densitometry

The quantification of skeletal density in massive scleractinians is necessary for a better understanding of skeletal growth in reef-forming corals. However, skeletal density is difficult to quantify and requires sophisticated analytical techniques. In this study, two-dimensional grid-scanning gamma densitometry is used for the first time, to quantify skeletal density fluctuations at higher temporal (intra-annual) resolution as compared to previous annual bulk densities determined with this approach. For testing this application and to evaluate its use for being a tool in coral sclerochronology, a colony of the widespread Atlantic massive coral Orbicella faveolata from the central Belize Barrier Reef (Central America) is herein investigated. In the studied coral, temporal resolution of individual density values corresponds to an approximately bi-weekly resolution. A long-term decline in (intra-)annual skeletal density is observed combined with reduced calcification rates. This indicates a limitation in the capability for skeletal formation in O. faveolata corals within the central Belize Barrier Reef, expressed in reduced skeletal carbonate accretion. In general, time series analyses and statistical correlations of the obtained high-resolution density datasets with skeletal growth patterns (linear extension rates, calcification rates) and geochemical (δ13C, δ18O) data reveal a complex interplay of environmental parameters, which might have controlled the skeletal density in the studied coral.

Earth model-space exploration in Southern California: Influence of topography, geotechnical layer, and attenuation on wavefield accuracy

Accurately predicting the seismic wavefield is important for physics-based earthquake hazard studies and is dependent on an accurate source model, a good model of the subsurface geology, and the full physics of wave propagation. Here, we conduct numerical experiments to investigate the effect of different representations of the Southern California Earthquake Center and Harvard community velocity models on seismic waveform predictions in the vicinity of the San Andreas fault in Salton Trough. We test general preconceptions about the importance of topography, near-surface geotechnical layering, and anelastic attenuation up to a maximum frequency of 0.5 Hz. For the Southern California Earthquake Center model developed without topography, we implement 1D and linear model extensions that preserve the geologic structure and a pull-up approach that adapts the original model to topographic variations and distorts the subsurface. The Harvard model includes an elevation model, so we test the squashed topography representation, which flattens it. For both community models, we modify the top 350 m by partially applying the Ely geotechnical layer using a minimum shear wave velocity of 600 m/s and incorporate an Olsen attenuation model using a ratio of 0.05. We evaluate the resulting 24 model representations using the classical waveform misfit and five moderate-magnitude earthquakes. Only the inclusion of attenuation consistently improves the wavefield predictions. It becomes more impactful at higher frequencies, where it significantly improves the performance levels of the crude 1D and linear extension models close to that of the original version. The pull-up topography representation also enhances the waveform prediction ability of the original model. Squashing the topography of the elevation-referenced Harvard model produces better seismogram fits, suggesting that seismic imagers construct community tomographic models without topography to avoid issues related to missing model parameters near the free surface or discrepancies with a different elevation model. Although full implementation of the Ely geotechnical layer that would permit shear wave velocities as low as 90 m/s proves computationally expensive, our partial implementation provides slightly better results in some cases. Our results can serve as recommendations for implementing these community models for future validation or optimization studies.

Ethnopedological knowledge and scientific assessment of earthenware pottery-making soils of southern Botswana for natural resource management

Earthenware pottery making, a major occupation among rural dwellers in southern Botswana, has been one of the mainstay of their economy for centuries. Consequently, local potters have classified their pottery-making soils based on indigenous knowledge with no verifiable scientific support. This study explores information on the criteria used by indigenous potters in classifying pottery-making soils in southern Botswana. It also presents results on pedological parameters of the soils. Routine laboratory procedures were used to measure properties of two representative pedons. Three properties, namely colour, texture (clayeyness) and plasticity are the major factors used in classifying pottery-making soils in Botswana. Two soils were identified: seloko se se hibidu (red clay) and seloko se se sweu (white clay) as the soils used for pottery. With the exception of texture, data on scientific analysis are consistent with indigenous soil classification system. The soils had sandy clay loam texture with clay contents ranging from 25.3 to 31.8 %, while sand dominates with over 50 % composition in the two pedons. The soils have mixed clay mineralogical assemblage consisting of sepiolite, smectite, kaolinite, illite, mica and montmorillonite and vermiculite. The coefficient of linear extensibility (COLErod) of the soils are high to very high (0.10 – 0.18), implying the dorminance of 2:1 clay minerals. As the depth increased, the soil colour became more reddish (LT1; 10YR 5/3 > 10R 7/3 and LT2: 10YR 8/2 > 10R 8/2 > 10R 7/4 > 10R 7/4). Overall, the geochemical molecular ratios points to slow pedogenic processes including hydrolysis, leaching, salinization and calcification in the soils. Data on the pedological properties of the pottery-making soils would find enormous application in sustainable management of the soil resources.

The norm of linear extension operators for [formula omitted

Fix integers m≥2, n≥1. We prove the existence of a bounded linear extension operator for Cm−1,1(Rn) with operator norm at most exp⁡(γDk), where D:=(m+n−1n) is the number of multiindices of length n and order at most m−1, and γ,k>0 are absolute constants (independent of m,n,E). Upper bounds on the norm of this operator are relevant to basic questions about fitting a smooth function to data. Our results improve on a previous construction of extension operators of norm at most exp⁡(γDk2D). Along the way, we establish a finiteness theorem for Cm−1,1(Rn) with improved bounds on the involved constants.

Naruse Hook Formula for Linear Extensions of Mobile Posets


 
 
 Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like Young diagrams of straight shapes and d-complete posets have hook length product formulas to count linear extensions, whereas families like Young diagrams of skew shapes have determinant or positive sum formulas like the Naruse hook-length formula from 2014. In 2020, Garver et. al. gave determinant formulas to count linear extensions of a family of posets called mobile posets that refine d-complete posets and border strip skew shapes. We give a Naruse type hook-length formula to count linear extensions of such posets by proving a major index q-analogue. We also a inversion index q-analogue of the Naruse formula for mobile tree posets.
 
 

Modelling and Numerical Simulation of an Ultrasonic Piezo-Motor based on Piezoelectric Properties of Pb(1-x)Srx(Ti0,48Zr0,52)(1-y)NbyO3 Ceramics

Firstly, the paper presents a solid solution of piezoelectric ceramic that was synthesized according to the general formula Pb(1-x)Srx(Ti0.48Zr0.52)(1-y)NbyO3 with x = 0.05 and y = 0.02, using wet ceramic processing technology and using oxides as prime materials. The effects of dopants (Sr2+ and Nb5+) on phase constitution, on microstructure and on the dielectric and piezoelectric properties were determined. The Zr4+/Ti4+ ratio was chosen near the morphotropic phase boundary of the lead zirconate titanate (PZT) system in studied composition. The XRD data revealed that the PZT doped composition had tetragonal perovskite structure. Secondly, based on piezoelectric properties of this ceramic, the paper presents the design of the ultrasonic piezo-motor based on a surface wave, which translates the linear extension of different piezoelectric segments of a piezoelectric cylinder into a rotational bending movement. This rotational bending of the piezoelectric cylinder is then transformed into a continuous rotation of the rotor through a calculated contact. A mathematical model and the numerical simulations of ultrasonic piezo-motor is presented. The numerical simulation has been performed in two different cases: an idle-case, where no external opposition torque was applied to the rotor, and a maximum torque case, where the rotor was blocked to calculate the maximum torque that the motor could produce.

Coefficient of linear extensibility of soil can be estimated from hygroscopic water content or clay and organic carbon contents

AbstractThe determination of the coefficient of linear extensibility (COLE) of soils is crucial for enhancing structural stability in civil engineering applications. Traditional methods for measuring COLE have some practical limitations. In routine soil analyses, clay and soil organic carbon (OC) are often measured, while soil hygroscopic water content (wh) is easy to determine on several soil samples simultaneously. The aims of the study were to (1) utilise two data partitioning approaches to develop regression models that estimate the soil COLE from hygroscopic water content, clay and OC contents, and (2) compare the model performance of the developed regression models. We used two data partitioning approaches. First, the calibration models were developed on 53 soil samples from Slovakia and validated with 24 soil samples from the United States (country‐wise). Second, the calibration models were built from 67% of the entire dataset and validated with 33% (mixed data). Regression models based on hygroscopic water content accurately estimated COLE regardless of sorption direction or data partitioning approach (RMSE: 0.014–0.023 cm cm−1). The inclusion of OC in multiple linear regression models of clay only marginally improved COLE estimation compared to clay alone. For all models, the mixed data partitioning method showed better model validation performance than the country‐wise approach. The COLE classes derived from the estimated COLE values compared favourably (72%–94% accurate) to the measured data. Thus, there is a great potential to estimate the COLE from readily available (clay and OC) or easily measurable (hygroscopic water content) soil properties.HighlightsHygroscopic water content (wh) is intimately linked to soil properties that determine COLE.Regression models based on wh or clay, and organic carbon content accurately estimated COLE.Data partitioning approach for modelling significantly impacted model performanceSamples with very high COLE were better estimated bywh‐based models than by other variables

The polarized Raman spectra of N-methylpyrrolidone-an effective method for determination of intermolecular interaction and H-bond formation

The isotropic and anisotropic component Raman spectra and H NMR of N-methylpyrrolidone (NMP)/carbon tetrachloride and NMP/methanol binary mixture at different volume fractions have been collected. The polarization Raman frequencies and frequency differences of CO stretching vibration for NMP/methanol mixture show unique concentration-dependence and abrupt jump feature. It is found that the H-bond between solute and solvent does not destroy the noncoincidence (NCE) phenomenon, but has a significant synergistic effect on the NCE. Two distinctive clusters constrained by H-bond and intermolecular interactions were easily determined by means of linear extension method from abrupt jump curve. The experimental phenomena can be well explained by aggregation-induced splitting theory with the proposed dimer structure and H-bond cluster model. Applying the same methodology the conformation of NMP in water has been determined successfully. The establishment of this method will play an important role in the determination of biomolecule aggregation behavior and supramolecular self-assembly structure.

Growth as a function of sea ice cover, light and temperature in the arctic/subarctic coralline C. compactum: A year-long in situ experiment in the high arctic

Long-term, high-resolution measurements of environmental variability are sparse in the High Arctic. In the absence of such data, we turn to proxies recorded in the layered skeletons of the long-lived crustose coralline algae Clathromorphum compactum. Annual growth banding in this alga is dependent on several factors that include temperature, light availability, nutrients, salinity, and calcium carbonate saturation state. It has been observed that growth slows during winter as sunlight reaching the seafloor diminishes due to decreased insolation and the build-up of sea-ice, such that the relationship between sea-ice cover extent and algal growth has allowed for reconstructions of relative sea-ice variability through time. However, recent laboratory work has shown that C. compactum continue growing in complete darkness (sea-ice cover). Therefore, a more complete understanding of algal growth is necessary for the refinement of the sea-ice proxy. Here, we present the results of a ~year-long in-situ growth and environmental monitoring experiment in Arctic Bay, Nunavut, Canada (~73°N) which addresses, for the first time in situ, the gaps in our understanding of growth over an annual cycle in the High Arctic. Algal growth was assessed on a quasi-monthly basis, where specimens were subsampled to quantify monthly extension in the context of ocean temperature and light availability. By measuring extension rate through time, we observed that the algae grew on average 72 µm yr-1, with ~54% of annual growth occurring during the sea-ice free summer months (June-September), ~25% during the winter months (November-April), and ~21% occurring during the transition months of May and October. Although winter growth slowed, we did not observe a consistent cessation of linear extension during low-or no-light months. We posit that substantial growth during the winter months at this latitude is most likely a consequence of the mobilization of stored energy (photosynthate) produced during the photosynthetically active summer months. However, we also discuss the possibility of low light-photosynthetic activity and/or dark carbon fixation, which could also facilitate extension through time. Overall, the novel growth model presented here has implications for the use of C. compactum growth for reconstructing the environment as well as for trace-element-based (typically Mg/Ca) algal chronologies.

Gas Dynamics and Star Formation in NGC 6822

We present H i gas kinematics and star formation activities of NGC 6822, a dwarf galaxy located in the Local Group at a distance of ∼490 kpc. We perform profile decomposition of line-of-sight velocity profiles of the H i data cube (42.4″ × 12.0″ spatial, corresponding to ∼100 pc; 1.6 km s−1 spectral) taken with the Australia Telescope Compact Array. For this, we use a new tool, the so-called baygaud, which is based on Bayesian analysis techniques, allowing us to decompose a line-of-sight velocity profile into an optimal number of Gaussian components in a quantitative manner. We classify the decomposed H i gas components of NGC 6822 into cool-bulk, warm-bulk, cool-non-bulk, and warm-non-bulk motions with respect to their centroid velocities and velocity dispersions. We correlate their gas surface densities with corresponding star formation rate densities derived using both the GALEX far-ultraviolet and WISE 22 μm data to examine the resolved Kennicutt–Schmidt (K-S) law for NGC 6822. Of the decomposed H i gas components, the cool-bulk component is likely to better follow the linear extension of the K-S law for molecular hydrogen (H2) at low gas surface densities where H i is not saturated.

More on the extension of linear operators on Riesz spaces

The classical Kantorovich theorem asserts the existence and uniqueness of a linear extension of a positive additive mapping, defined on the positive cone $E^+$ of a Riesz space $E$ taking values in an Archimedean Riesz space $F$, to the entire space $E$. We prove that, if $E$ has the principal projection property and $F$ is Dedekind $\sigma$-complete then for every $e \in E^+$ every positive finitely additive $F$-valued measure defined on the Boolean algebra $\mathfrak{F}_e$ of fragments of $e$ has a unique positive linear extension to the ideal $E_e$ of $E$ generated by $e$. If, moreover, the measure is $\tau$-continuous then the linear extension is order continuous.

Effects of soil conditioner and humic acid applications on the development of some soil quality parameters

This study was conducted under greenhouse conditions in order to determine the effects of polyvinyl alcohol (PVA), polyacrylamide (PAM) and humic acid (HA) applications on the improvement of some soil quality (erosion ratio and coefficient of linear extensibility) parameters. Surface soil samples with three different textures (clay, loam and sandy loam) were used in the study. In the greenhouse, PVA, PAM and HA were applied to soil samples at doses of 500, 100 and 500 ppm, respectively, and incubated in four different periods (0, 15, 30 and 45 days). During the incubation, irrigation was performed when 50% of the available moisture in the soil samples was decreases. As a result of the analysis and evaluation made on the soil samples after the incubation, it was determined that PVA, PAM and HA applications reduced the erosion ratio and linear extensibility values in all three soil groups and that the conditioners were more effective in the soil in clay texture category. It was observed that the conditioners were ranked as PVA>PAM>HA in terms of the said effectiveness. It was observed that PVA's first period applications were more effective on erosion resistance and PVA's second period applications were more effective on coefficient of linear extensibility.

The order of the unitary subgroups of group algebras

Let [Formula: see text] be the group algebra of a finite [Formula: see text]-group [Formula: see text] over a finite field [Formula: see text] of positive characteristic [Formula: see text]. Let ⊛ be an involution of the algebra [Formula: see text] which is a linear extension of an anti-automorphism of the group [Formula: see text] to [Formula: see text]. If [Formula: see text] is an odd prime, then the order of the ⊛-unitary subgroup of [Formula: see text] is established. For the case [Formula: see text] we generalize a result obtained for finite abelian [Formula: see text]-groups. It is proved that the order of the ∗-unitary subgroup of [Formula: see text] of a non-abelian [Formula: see text]-group is always divisible by a number which depends only on the size of [Formula: see text], the order of [Formula: see text] and the number of elements of order two in [Formula: see text]. Moreover, we show that the order of the ∗-unitary subgroup of [Formula: see text] determines the order of the finite [Formula: see text]-group [Formula: see text].

Orographic Precipitation Extremes: An Application of LUME (Linear Upslope Model Extension) over the Alps and Apennines in Italy

Critical hydrometeorological events are generally triggered by heavy precipitation. In complex terrain, precipitation may be perturbed by the upslope raising of the incoming humid airflow, causing in some cases extreme rainfall. In this work, the application of LUME—Linear Upslope Model Extension—to a group of extreme events that occurred across mountainous areas of the Central Alps and Apennines in Italy is presented. Based on the previous version, the model has been “extended” in some aspects, proposing a methodology for physically estimating the time-delay coefficients as a function of precipitation efficiency. The outcomes of LUME are encouraging for the cases studied, revealing the intensification of precipitation due to the orographic effect. A comparison between the reference rain gauge data and the results of the simulations showed good agreement. Since extreme precipitation is expected to increase due to climate change, especially across the Mediterranean region, LUME represents an effective tool to investigate more closely how these extreme phenomena originate and evolve in mountainous areas that are subject to potential hydrometeorological risks.

Transparent but Accurate Evolutionary Regression Combining New Linguistic Fuzzy Grammar and a Novel Interpretable Linear Extension

Scientists must understand what machines do (systems should not behave like a black box), because in many cases how they predict is more important than what they predict. In this work, we propose a new extension of the fuzzy linguistic grammar and a mainly novel interpretable linear extension for regression problems, together with an enhanced new linguistic tree-based evolutionary multiobjective learning approach. This allows the general behavior of the data covered, as well as their specific variability, to be expressed as a single rule. In order to ensure the highest transparency and accuracy values, this learning process maximizes two widely accepted semantic metrics and also minimizes both the number of rules and the model mean squared error. The results obtained in 23 regression datasets show the effectiveness of the proposed method by applying statistical tests to the said metrics, which cover the different aspects of the interpretability of linguistic fuzzy models. This learning process has obtained the preservation of high-level semantics and less than 5 rules on average, while it still clearly outperforms some of the previous state-of-the-art linguistic fuzzy regression methods for learning interpretable regression linguistic fuzzy systems, and even to a competitive, pure accuracy-oriented linguistic learning approach. Finally, we analyze a case study in a real problem related to childhood obesity, and a real expert carries out the analysis shown.

Lens Aquaporin-5 Inserts Into Bovine Fiber Cell Plasma Membranes Via Unconventional Protein Secretion.

PurposeTo spatially map aquaporin-5 (AQP5) expression in the bovine lens, molecularly characterize cytoplasmic AQP5-containing vesicles in the outer cortex, and elucidate AQP5 membrane trafficking mechanisms.MethodsImmunofluorescence was performed on bovine lens cryosections using AQP5, TOMM20, COX IV, calnexin, LC3B, Sec22β, LIMP-2, and connexin 50 antibodies and the membrane dye CM-DiI. AQP5 plasma membrane insertion was defined via line expression profile analysis. Transmission electron microscopy (TEM) was performed on bovine lens sections to examine cytoplasmic organelle morphology and subcellular localization in cortical fiber cells. Bovine lenses were treated with 10-nM bafilomycin A1 or 0.1% dimethyl sulfoxide vehicle control for 24 hours in ex vivo culture to determine changes in AQP5 plasma membrane expression.ResultsImmunofluorescence analysis revealed cytoplasmic AQP5 expression in lens epithelial cells and differentiating fiber cells. In the lens cortex, complete AQP5 plasma membrane insertion occurs at r/a = 0.951 ± 0.005. AQP5-containing cytoplasmic vesicles are spheroidal in morphology with linear extensions, express TOMM20, and contain LC3B and LIMP-2, but not Sec22β, as fiber cells mature. TEM analysis revealed complex vesicular assemblies with congruent subcellular localization to AQP5-containing cytoplasmic vesicles. AQP5-containing cytoplasmic vesicles appear to dock with the plasma membrane. Bafilomycin A1 treatment reduced AQP5 plasma membrane expression by 27%.ConclusionsAQP5 localizes to spheroidal, linear cytoplasmic vesicles in the differentiating bovine lens fiber cells. During fiber cell differentiation, these vesicles incorporate LC3B and presumably fuse with LIMP-2–positive lysosomes. Our data suggest that AQP5 to the plasma membrane through lysosome-associated unconventional protein secretion, a novel mechanism of AQP5 trafficking.

Consequences of Warming and Acidification for the Temperate Articulated Coralline Alga, Calliarthron Tuberculosum (Florideophyceae, Rhodophyta).

Global climate changes, such as warming and ocean acidification (OA), are likely to negatively impact calcifying marine taxa. Abundant and ecologically important coralline algae may be particularly susceptible to OA; however, multi‐stressor studies and those on articulated morphotypes are lacking. Here, we use field observations and laboratory experiments to elucidate the impacts of warming and acidification on growth, calcification, mineralogy, and photophysiology of the temperate articulated coralline alga, Calliarthron tuberculosum. We conducted a 4‐week fully factorial mesocosm experiment exposing individuals from a southern CA kelp forest to current and future temperature and pH/pCO2 conditions (+2°C, −0.5 pH units). Calcification was reduced under warming (70%) and further reduced by high pCO2 or high pCO2 x warming (~150%). Growth (change in linear extension and surface area) was reduced by warming (40% and 50%, respectively), high pCO2 (20% and 40%, respectively), and high pCO2 x warming (50% and 75%, respectively). The maximum photosynthetic rate (Pmax) increased by 100% under high pCO2 conditions, but we did not detect an effect of pCO2 or warming on photosynthetic efficiency (α). We also did not detect the effect of warming or pCO2 on mineralogy. However, variation in Mg incorporation in cell walls of different cell types (i.e., higher mol % Mg in cortical vs. medullary) was documented for the first time in this species. These results support findings from a growing body of literature suggesting that coralline algae are often more negatively impacted by warming than OA, with the potential for antagonistic effects when factors are combined.