Stable Pairs Research Articles

Human musical capacity and products should have been induced by the hominin-specific combination of several biosocial features: A three-phase scheme on socio-ecological, cognitive, and cultural evolution.

Various selection pressures have shaped human uniqueness, for instance, music. When and why did musical universality and diversity emerge? Our hypothesis is that "music" initially originated from manipulative calls with limited musical elements. Thereafter, vocalizations became more complex and flexible along with a greater degree of social learning. Finally, constructed musical instruments and the language faculty resulted in diverse and context-specific music. Music precursors correspond to vocal communication among nonhuman primates, songbirds, and cetaceans. To place this scenario in hominin history, a three-phase scheme for music evolution is presented herein. We emphasize (1) the evolution of sociality and life history in australopithecines, (2) the evolution of cognitive and learning abilities in early/middle Homo, and (3) cultural evolution, primarily in Homo sapiens. Human musical capacity and products should be due to the hominin-specific combination of several biosocial features, including bipedalism, stable pair bonding, alloparenting, expanded brain size, and sexual selection.

A nascent riboswitch helix orchestrates robust transcriptional regulation through signal integration

Widespread manganese-sensing transcriptional riboswitches effect the dependable gene regulation needed for bacterial manganese homeostasis in changing environments. Riboswitches – like most structured RNAs – are believed to fold co-transcriptionally, subject to both ligand binding and transcription events; yet how these processes are orchestrated for robust regulation is poorly understood. Through a combination of single-molecule and bulk approaches, we discover how a single Mn2+ ion and the transcribing RNA polymerase (RNAP), paused immediately downstream by a DNA template sequence, are coordinated by the bridging switch helix P1.1 in the representative Lactococcus lactis riboswitch. This coordination achieves a heretofore-overlooked semi-docked global conformation of the nascent RNA, P1.1 base pair stabilization, transcription factor NusA ejection, and RNAP pause extension, thereby enforcing transcription readthrough. Our work demonstrates how a central, adaptable RNA helix functions analogous to a molecular fulcrum of a first-class lever system to integrate disparate signals for finely balanced gene expression control.

Cholesterol sulfate-mediated ion-pairing facilitates the self-nanoassembly of hydrophilic cationic mitoxantrone

HypothesisHydrophilic cationic drugs such as mitoxantrone hydrochloride (MTO) pose a significant delivery challenge to the development of nanodrug systems. Herein, we report the use of a hydrophobic ion-pairing strategy to enhance the nano-assembly of MTO. ExperimentsWe employed biocompatible sodium cholesteryl sulfate (SCS) as a modification module to form stable ion pairs with MTO, which balanced the intermolecular forces and facilitated nano-assembly. PEGylated MTO-SCS nanoassemblies (pMS NAs) were prepared via nanoprecipitation. We systematically evaluated the effect of the ratio of the drug module (MTO) to the modification module (SCS) on the nanoassemblies. FindingsThe increased lipophilicity of MTO-SCS ion pair could significantly improve the encapsulation efficiency (∼97 %) and cellular uptake efficiency of MTO. The pMS NAs showed prolonged blood circulation, maintained the same level of tumor antiproliferative activity, and exhibited reduced toxicity compared with the free MTO solution. It is noteworthy that the stability, cellular uptake, cytotoxicity, and in vivo pharmacokinetic behavior of the pMS NAs increased in proportion to the molar ratio of SCS to MTO. This study presents a self-assembly strategy mediated by ion pairing to overcome the challenges commonly associated with the poor assembly ability of hydrophilic cationic drugs.

Many-to-one matching based cooperative spectrum sharing in overlay cognitive radio networks

Cooperative Spectrum Sharing (CSS) is a Dynamic Spectrum Access mechanism aimed at providing incentives for both primary users (PUs) and secondary users (SUs) through cooperative communication. This paper addresses the pairing problem among multiple PUs and SUs to allocate optimal fractions of spectrum resources in terms of access time, using the CSS technique. Inspired by Matching Theory, we model the CSS between PUs and SUs as a Two-sided Matching Market and explore different market equilibria. Cooperative strategies among SUs are employed to maximize the gross utility of cooperative SUs and overall utility of the secondary network, in exchange for relay services rendered to PUs. We propose a polynomial-time based many-to-one matching scheme that favors groups of collaborative SUs to attract favorable PUs from the opposite side, leading to optimal matching for SUs. On the other hand, each PU achieves stable matching when paired with a group of cooperative SUs. We provide necessary proofs for the achieved matching equilibrium. Furthermore, we formulate an optimization framework for the optimal usage of PU access time among stable PU-SU pairs and propose a near-optimal solution, achieving 96% accuracy compared to the optimal allocation yield from the benchmark method (analytical). Our proposed many-to-one matching scheme outperforms similar existing schemes and the one-to-one matching scheme in terms of SU utility, satisfaction, participation, and throughput fairness index.

Identification of potent schistosomicidal compounds predicted as type II-kinase inhibitors against Schistosoma mansoni c-Jun N-terminal kinase SMJNK

IntroductionSchistosomiasis has for many years relied on a single drug, praziquantel (PZQ) for treatment of the disease. Immense efforts have been invested in the discovery of protein kinase (PK) inhibitors; however, given that the majority of PKs are still not targeted by an inhibitor with a useful level of selectivity, there is a compelling need to expand the chemical space available for synthesizing new, potent, and selective PK inhibitors. Small-molecule inhibitors targeting the ATP pocket of the catalytic domain of PKs have the potential to become drugs devoid of (major) side effects, particularly if they bind selectively. This is the case for type II PK inhibitors, which cause PKs to adopt the so-called DFG-out conformation, corresponding to the inactive state of the enzyme.MethodsThe goal was to perform a virtual screen against the ATP pocket of the inactive JNK protein kinase. After virtually screening millions of compounds, Atomwise provided 85 compounds predicted to target c-Jun N-terminal kinase (JNK) as type II inhibitors. Selected compounds were screened in vitro against larval stage (schistosomula) of S. mansoni using the XTT assay. Adult worms were assessed for motility, attachment, and pairing stability. Active compounds were further analyzed by molecular docking against SmJNK.ResultsIn total, 33 compounds were considered active in at least one of the assays, and two compounds were active in every in vitro screening assay. The two most potent compounds presented strong effects against both life stages of the parasite, and microscopy analysis showed phenotypic alterations on the tegument, in the gonads, and impairment of cell proliferation.ConclusionThe approach to screen type II kinase inhibitors resulted in the identification of active compounds that will be further developed against schistosomiasis.

Chiral spin textures creation and dynamics in a rectangular nanostructure

Abstract Controlled creation of stable chiral spin textures is required to use them as an energy-efficient information carrier in spintronics. Here we have studied the stable creation of isolated chiral spin texture (skyrmion and antiskyrmion) and its pair through the magnetization reversal of a rectangular nanostructure using spin-polarized currents. An isolated spin texture is created through a negative current pulse. Dynamics of the stable spin texture are explored under external magnetic fields, and the resonant frequencies are calculated. A stable skyrmion pair is created using an asymmetric current pulse, and their interaction is studied using the Thiele equation. The stability of isolated or paired spin texture depends on the Dzyaloshinskii–Moriya interaction strength, spin-polarized current density, and pulse duration. In addition, the stability of the skyrmion pair depends on their initial separation, and a threshold for the separation between skyrmions of 78 nm is observed.

Identification of qualitative characteristics of immunosuppression in sepsis based on immune-related genes and immune infiltration features

ObjectiveSepsis is linked to high morbidity and mortality rates. Consequently, early diagnosis is crucial for proper treatment, reducing hospitalization, and mortality rates. Additionally, over one-fifth of sepsis patients still face a risk of death. Hence, early diagnosis, and effective treatment play pivotal roles in enhancing the prognosis of patients with sepsis. MethodThe study analyzed whole blood data obtained from patients with sepsis and control samples sourced from three datasets (GSE57065, GSE69528, and GSE28750). Commonly dysregulated immune-related genes (IRGs) among these three datasets were identified. The differential characteristics of these common IRGs in the sepsis and control samples were assessed using the REO-based algorithm. Based on these differential characteristics, samples from eight Gene Expression Omnibus (GEO) databases (GSE57065, GSE69528, GSE28750, GSE65682, GSE69063, GSE95233, GSE131761, and GSE154918), along with three ArrayExpress databases (E-MTAB-4421, E-MTAB-4451, and E-MTAB-7581), were categorized and scored. The effectiveness of these differential characteristics in distinguishing sepsis samples from control samples was evaluated using the AUC value derived from the receiver operating characteristic curve (ROC) curve. Furthermore, the expression of IRGs was validated in peripheral blood samples obtained from patients with sepsis through qRT-PCR. ResultsAmong the three training datasets, a total of 84 common dysregulated immune-related genes (IRGs) were identified. Utilizing a within-sample relative expression ordering (REOs)-based algorithm to analyze these common IRGs, differential characteristics were observed in three reverse stable pairs (ELANE-RORA, IL18RAP-CD247, and IL1R1-CD28). In the eight GEO datasets, the expression of ELANE, IL18RAP, and IL1R1 demonstrated significant upregulation, while RORA, CD247, and CD28 expression exhibited notable downregulation during sepsis. These three pairs of immune-related marker genes displayed accuracies of 95.89% and 97.99% in distinguishing sepsis samples among the eight GEO datasets and the three independent ArrayExpress datasets, respectively. The area under the receiver operating characteristic curve ranged from 0.81 to 1.0. Additionally, among these three immune-related marker gene pairs, mRNA expression levels of ELANE and IL1R1 were upregulated, whereas the levels of CD247 and CD28 mRNA were downregulated in blood samples from patients with sepsis compared to normal controls. ConclusionThese three immune-related marker gene pairs exhibit high predictive performance for blood samples from patients with sepsis. They hold potential as valuable auxiliary clinical blood screening tools for sepsis.

Real-time measurements of breathing dissipative soliton pairs in mode-locked fiber lasers

The emergence of breathing solitons, as well as the breathing soliton molecules undergoing periodic evolution in peak power and spectral width has attracted growing research attentions in dissipative systems. Beyond the intense pulse interactions within tightly-bound states with picoseconds interval, the long-range interplay between pulses separated by nanosecond-scale starts to be investigated in recent years, thus filling the long-standing academic gap between the bound solitons and independent multiple pulses. In this work, we report on the real-time observations of breathing dissipative soliton pairs with nanoseconds’ separations in a fiber laser operating under the threshold of stationary mode locking. Compared with conventional soliton counterpart, here the breathing soliton pair exhibit even more fascinating inter-pulse nonlinear dynamics due to the intriguing self-excited periodic evolutions. The shot-to-shot measurements of pulse intensity profiles, associated with dispersive Fourier transform clearly uncover not only the different breathing phase synchronization and pulse separations among different pulses but also the hysteresis behaviors of the breathing ratio by continuously varying the laser parameters. Moreover, we observed various transient stages in this unstable lasing regime, including the transition between stable single soliton and breathing soliton pair, as well as their long-range breather interaction. These results reveal the breathing multi-pulse state and the instantaneous non-equilibrium dynamics involving the breather pairs, enriching the framework of breathing solitons and opening a novel possibility to explore the internal motions of breathing soliton complex in nonlinear systems.

The W(E6)$W(E_6)$‐invariant birational geometry of the moduli space of marked cubic surfaces

AbstractThe moduli space of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth‐century work of Cayley and Salmon. Modern interest in was restored in the 1980s by Naruki's explicit construction of a ‐equivariant smooth projective compactification of , and in the 2000s by Hacking, Keel, and Tevelev's construction of the Kollár–Shepherd‐Barron–Alexeev (KSBA) stable pair compactification of as a natural sequence of blowups of . We describe generators for the cones of ‐invariant effective divisors and curves of both and . For Naruki's compactification , we further obtain a complete stable base locus decomposition of the ‐invariant effective cone, and as a consequence find several new ‐equivariant birational models of . Furthermore, we fully describe the log minimal model program for the KSBA compactification , with respect to the divisor , where is the boundary and is the sum of the divisors parameterizing marked cubic surfaces with Eckardt points.

Construction of Ag/CdZnS QDs nanocomposite for enhanced visible light photoinactivation of Staphylococcus aureus

With increasing use of antibiotics, the development of antibiotic-resistant pathogens poses a serious threat to human health and the environment. Photocatalytic inactivation of these harmful pathogens is one of the novel and non-antibiotic treatments. The study fabricated Ag NPs decorated CdZnS QDs via a facile and biological co-precipitation method using L. camara plant extract as a green alternative to treat the toxic chemicals. The fabricated Ag/CdZnS QDs (NCs) were prepared for the efficient treatment of antibiotic-resistant pathogens as they raise a major global concern. The fabricated NCs were characterized with various characterization techniques to verify its physicochemical properties. The fabricated NCs have shown excellent photo-sterilization performance of 97 % against S. aureus. The excellent activity was attributed to the decoration of Ag NPs on CdZnS QDs as it helped in shortening band gap, improved visible light absorption ability, increased active sites, and boosted photogenerated electron/hole pairs stability. Radical trapping experiment and ESR analysis indicated the involvement of •OH and h+ in the photoinactivation of bacteria. The photo sterilization reaction of NCs was carried out under different environmental conditions, including light and dark conditions and different pH conditions. The experiment was carried out in sewage-treated water in order to test the real-time application, and the fabricated NCs achieved excellent 95.9 % photo-inactivation of S. aureus cells in sewage treated water and the Chemical Oxygen Demand (COD) of the system was increased after photo inactivation treatment. The fabricated NCs have also shown excellent reusable efficiency of 95% after six runs and the photostability and anti-corrosive nature of NCs were confirmed. The study provides an insight for the employment of photocatalysis for the sterilization of pathogens in real time aquatic environment across the globe.

Anion Competition at Positively Charged Surfactant Monolayers.

Interactions of anions with hydrophobic surfaces of proteins and water-soluble polymers depend on the ability of the ions to shed their hydration shells. At positively charged surfactant monolayers, the interactions of anions are less well understood. Due to the interplay of electrostatic surface forces, hydration effects, and ion-ion interactions in the electrostatic double layer, a comprehensive microscopic picture remains elusive. Herein, we study the interactions of chloride, bromide, and a mixture of these two anions at the aqueous interface of dihexadecyldimethylammonium (DHDA+) and dioctadecyldimethylammonium (DODA+) cationic monolayers. Using molecular dynamics simulations and three surface-sensitive X-ray scattering techniques, we demonstrate that bromide interacts preferentially over chloride with both monolayers. The structure of the two monolayers and their interfacial electron density profiles obtained from the simulations quantitatively reproduce the experimental data. We observe that chloride and bromide form contact ion pairs with the quaternary ammonium groups on both monolayers. However, ion pairing with bromide leads to a greater reduction in the number of water molecules hydrating the anion, resulting in more energetically stable ion pairs. This leads to long-range (>3 nm) lateral correlations between bromide ions on the structured DODA+ monolayer. These observations indicate that ion hydration is the dominant factor determining the interfacial electrolyte structure.

Multiple behavioral mechanisms shape development in a highly social cichlid fish

Early-life social experiences shape adult phenotype, yet the underlying behavioral mechanisms remain poorly understood. We manipulated early-life social experience in the highly social African cichlid fish Astatotilapia burtoni to investigate the effects on behavior and stress axis function in juveniles. Juveniles experienced different numbers of social partners in stable pairs (1 partner), stable groups (6 fish; 5 partners), and socialized pairs (a novel fish was exchanged every 5 days; 5 partners). Treatments also differed in group size (groups vs. pairs) and stability (stable vs. socialized). We then measured individual behavior and water-borne cortisol to identify effects of early-life experience. We found treatment differences in behavior across all assays: open field exploration, social cue investigation, dominant behavior, and subordinate behavior. Treatment did not affect cortisol. Principal components (PC) analysis revealed robust co-variation of behavior across contexts, including with cortisol, to form behavioral syndromes sensitive to early-life social experience. PC1 (25.1 %) differed by social partner number: juveniles with more partners (groups and socialized pairs) were more exploratory during the social cue investigation, spent less time in the territory, and were more interactive as dominants. PC5 (8.5 %) differed by stability: socialized pairs were more dominant, spent less time in and around the territory, were more socially investigative, and had lower cortisol than stable groups or pairs. Observations of the home tanks provided insights into the social experiences that may underlie these effects. These results contribute to our understanding of how early-life social experiences are accrued and exert strong, lasting effects on phenotype.

A case study: lessons learned from online tutorial to improve practice readiness for family medicine residents in Palestine

BackgroundGeopolitical and socioeconomic challenges limit faculty development and clinical teaching in Palestine and many other developing countries. The first, and still only, Family Medicine (FM) residency program is a four-year program based out of An-Najah University in the West Bank. Training in primary care clinics occurs in the final two years and there are many challenges to adequate supervision in the clinical setting that were exacerbated during the pandemic. To improve the readiness for practice skills of 13 Palestinian FM residents a three-month tutorial program was organized in 2020. A nongovernmental organization (NGO) that has worked to support Family Medicine development in the region engaged experienced British and American General Practitioners trained as tutors to offer online tutorials. We examined the program as a case study to understand the factors that facilitated or impaired a positive virtual learning environment in a middle/low income country.MethodsThe tutors and residents were divided into groups and met virtually between June and September 2020. Evaluations and session reports collected during the program, the text of an online chat, and responses to an online survey two years later were collected. Using thematic analysis techniques, we evaluated the value for the residents at the time and two years later and identified factors that facilitated or impaired a positive virtual learning environment.ResultsThemes of knowledge, skills, attitudes, cultural disconnects, and tutorial logistics emerged. The group with the most stable tutor pairing, including one Arabic-speaker familiar with the context, was the most engaged. The all-female group formed a chat group to share real-time case questions during clinical practice and focused on skills (e.g. conducting a thorough medication review) and attitudes (e.g. open to sharing and discussing uncertainties). Other groups were less cohesive.ConclusionsTransnational tutorials that focused on clinical thinking and decision-making skills were most successful when the tutorial pair was stable, offered familiarity with the language and addressed cultural differences. Intrinsic factors such as lacking the motivation to participate and extrinsic factors such as unstable internet and rolling electric cuts, and clinical structures that made applying new skills challenging were more difficult to address but must be considered.

Self-ordering and organization of a staggered oblate particle pair in three-dimensional square ducts

We numerically investigate the formation and ordering of staggered oblate particle pairs in three-dimensional straight ducts with a square cross section. The lattice Boltzmann method is employed to simulate rigid particle pairs in a Newtonian liquid. The effects of initial axial spacing, Reynolds number, blockage ratio, and particle aspect ratio on the formation process, migration behavior, and interparticle spacing are explored in detail. Current results indicate that the process from initial to final steady state can be divided into two stages. The first stage is rapid migration from initial positions toward equilibrium positions under shear-induced lift force and wall-induced repulsive force. The second stage is the slow self-assembly of stable particle pairs in the axial direction due to the interparticle interaction. Interestingly, initial axial spacing significantly affects the formation process of particle pairs but does not affect the final steady state. It is found that the equilibrium positions of staggered particle pairs move slightly toward the duct walls, and the axial spacing increases with increasing Reynolds number or particle aspect ratio, or decreasing blockage ratio. For a staggered particle pair, the second particle will occupy the eddy center induced by the first focusing particle. Based on the existing data, a correlation is put forward to predict the axial interparticle spacing of staggered oblate particle pairs in duct flows. The present results may give insights into manipulating and comprehending non-spherical particle dynamics in microfluidic applications.

Establishing New Isosexual Pairs in Adult Male Guinea Pigs (Cavia porcellus) to Facilitate Social Housing.

Guinea pigs (Cavia porcellus) are a commonly used species in biomedical research. As social creatures, compatible guinea pigs should be housed together unless scientific objectives or veterinary care require otherwise. Extensive literature suggests that adult male guinea pigs are highly aggressive in the presence of females, but data are lacking regarding the compatibility of cohoused adult males in the absence of females. Most studies that use adult males do not report housing densities. We used serial wound scoring and observations of behavior to determine whether unfamiliar adult male guinea pigs will develop stable, prosocial isosexual pairs. Wound scoring was performed before and 24 h after pairing. Serial behavioral observations assessed affiliative and agonistic behaviors at 0.5, 2, 24, and 48 h after pairing. Wound scoring and behavioral observations continued weekly for 1 mo and monthly thereafter. Wound scores were significantly higher at 24 h after pairing as compared with baseline and all other time points. Wounding was rare after week 2, indicating reduced aggression. Furthermore, affiliative behaviors significantly increased over time while agonistic behaviors were rare. Together, these data suggest that unfamiliar adult male guinea pigs establish stable prosocial pairs after an acclimation period. As was done in the present study, providing ample space, separate shelters for each animal, and the absence of female guinea pigs will likely facilitate successful pairing. We recommend consideration of a social housing program for adult male guinea pigs to provide companionship and enrich their housing environment.

Finite element simulations of Herschel–Bulkley visco-plastic materials over a cylinder: Drag and lift correlation analysis

This study employs a two-dimensional and incompressible flow of Herschel–Bulkley visco-plastic materials in order to investigate the hydrodynamic forces that are acting on a barrier that is located close to the inlet of a channel. As the benchmark configuration, the flow domain that has been selected is a channel that still contains the impediment. The two important parameters of the Herschel–Bulkley Model (HBM) are the yield stress [Formula: see text] and power law index n. Obtaining special situations within the HBM, such as Newtonian, power-law, and Bingham fluids, can be accomplished by assigning certain values to these parameters at the appropriate times. Utilizing a numerical strategy grounded in the Finite Element Method (FEM), we tackle the nonlinearity of the governing equations as well as the viscosity models. As a result of this nonlinearity, FEM becomes an essential tool. The generation of a refined hybrid mesh is done in order to guarantee accuracy in the computations. The stable finite element pair ([Formula: see text]) has been selected for discretization purposes. The discretized nonlinear system is linearized with Newton’s method and subsequently, a direct linear solver PARDISO has been employed in the inner iterations. The pressure, velocity, and viscosity profiles are plotted for various values of n and Bingham number (Bn). In addition, the velocity behavior is observed along the y-direction in a channel through line graphs. Code validation is done as a special case [Formula: see text] and a good agreement is found with the results available in the literature. Finally, a correlation analysis has been performed for the drag coefficient [Formula: see text] and lift coefficient [Formula: see text].

Stabilization of Naphthalene Diimide Anions by Ion Pair Formation in Nonaqueous Organic Redox Flow Batteries.

In redox flow batteries, a compelling strategy for enhancing the charge capacity of redox-active organic molecules involves storing multiple electrons within a single molecule. However, this approach poses unique challenges such as chemical instability by forming radicals, elevated energy requirements, and unsustainable charge concentration. Ion pairing is a possible solution to achieve charge neutrality and engineer redox potential shifts but has received limited attention. In this study, we demonstrate that Li+ can stabilize naphthalene diimide (NDI) anions dissolved in acetonitrile and significantly shift the second cathodic potential close to the first. Our findings, supported by density functional theory calculations and Fourier transform infrared spectroscopy, indicate that dimeric NDI species form stable ion pairs with Li+. Conversely, K+ ions exhibit weak interactions, and cyclic voltammograms confirm significant potential shifts when stronger Lewis acids and solvents with lower donor numbers are employed. Galvanostatic examinations reveal a single voltage plateau with Li+, which indicates a rapid redox process involving doubly charged NDI2- with Li+. These aggregated ion pairs offer the additional benefits of hindering crossover events, contributing to excellent cyclability, and suppressing undesirable side reactions even after 1000 redox cycles.

The Complete Mitochondrial Genomes of Aelia sibirica and A. fieberi (Hemiptera, Pentatomidae), and Phylogenetic Implications

Species of genus Aelia are important pests of wheat crops in arid areas. In this study, the mitogenomes of A. sibirica and A. fieberi were sequenced using high-throughput sequencing technology. The mitochondrial genome characteristics of both Aelia species were compared and analyzed, and the phylogenetic relationships of Pentatomidae were constructed based on protein-coding genes. In addition, the taxonomic status of the genus Aelia was confirmed. The results showed that the total length of the mitogenome sequences of A. sibirica and A. fieberi were 15,372 bp and 15,450 bp, respectively, including 13 protein-coding genes, 22 tRNA genes, 2 rRNA genes, and a control region. By comparing the mitochondrial genome structure, base composition, codon usage, RNA secondary structure, and other characteristics, it was found that the mitochondrial genome characteristics of the two species were similar. Phylogenetic analysis showed that Phyllocephalinae and Asopinae both formed monophyletic groups, but the relationship between Podopinae and Pentatominae was not resolved. Within the subfamily Pentatominae, (Nezarini + Antestiini), (Aeliini + Carpocorini), and (Strachiini + Pentatoma) formed stable clades. Aelia sibirica and A. fieberi were found to be a stable sibling pair, and the clade was closely related to Dolycoris baccarum.

A parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress

In this paper, we design and analyze a parameter-free mixed method of arbitrary polynomial orders for the Stokes equations and linear elasticity problem, where the symmetry of stress is strongly imposed. Equal-order polynomials are exploited for the stress and velocity spaces in which the stress is approximated by discontinuous polynomials. In contrast, the velocity is approximated by an H(div;Ω) conforming space. As a consequence, the proposed scheme yields divergence-free velocity approximations and is pressure-robust for the Stokes equations. The stable Stokes pair are integrated to facilitate the proof of the inf-sup condition. The comprehensive convergence error estimates for all the variables are explored for the Stokes equations and linear elasticity problem. In particular, we explicitly track the dependence of the error estimates on the physical parameters and illustrate the locking-free property of the proposed scheme, which is non-trivial under the proposed formulation. The judicious balancing of the mixed formulation and the equivalent primal formulation enable us to achieve the robust error estimates for the linear elasticity problem. Several numerical experiments for the Stokes equations and linear elasticity problem are carried out to verify the proposed theories.

Compact moduli of K3 surfaces with a nonsymplectic automorphism

We construct a modular compactification via stable slc pairs for the moduli spaces of K3 surfaces with a nonsymplectic group of automorphisms under the assumption that some combination of the fixed loci of automorphisms defines an effective big divisor, and prove that it is semitoroidal.