Critical Loci Research Articles

Peculiar behavior of the critical loci of azeotropic binary mixtures: Case of perfluoromethylcyclohexane-isomeric hexane systems

In a previous publication [A. Abbaci, H.R. van den Berg, E. Sakonidou, J.V. Sengers, Int. J. Thermophys. 13, 1043 (1992)], a study of ethane-carbon dioxide mixture critical locus as a function of the mole fraction was presented in order to show the evidence of an abnormal behavior in the critical density curve. An update on the evaluation of the critical parameters of this same mixture was published by [J.V. Sengers, G.X. Jin, Int. J. Thermophys. 28, 1181 (2007)]. In this work, we generalize the study to the critical loci of five selected azeotropic mixtures of perfluoromethylcyclohexane-isomeric hexane systems that have been correlated using simple polynomials. It is generally assumed that an azeotropic mixture is a synonym of a peculiar behavior of the critical density of this mixture as a function of the mole fraction. The purpose of this correlation is to show that this is not the case. Finally, we show the consequences of this abnormal behavior if it exists on the behavior of certain thermodynamic properties of such mixtures.

Characterization of chromosomal abnormalities in pregnancy losses reveals critical genes and loci for human early development.

Detailed characterization of chromosomal abnormalities, a common cause for congenital abnormalities and pregnancy loss, is critical for elucidating genes for human fetal development. Here, 2,186 product-of-conception samples were tested for copy-number variations (CNVs) at two clinical diagnostic centers using whole-genome sequencing and high-resolution chromosomal microarray analysis. We developed a new gene discovery approach to predict potential developmental genes and identified 275 candidate genes from CNVs detected from both datasets. Based on Mouse Genome Informatics (MGI) and Zebrafish model organism database (ZFIN), 75% of identified genes could lead to developmental defects when mutated. Genes involved in embryonic development, gene transcription, and regulation of biological processes were significantly enriched. Especially, transcription factors and gene families sharing specific protein domains predominated, which included known developmental genes such as HOX, NKX homeodomain genes, and helix-loop-helix containing HAND2, NEUROG2, and NEUROD1 as well as potential novel developmental genes. We observed that developmental genes were denser in certain chromosomal regions, enabling identification of 31 potential genomic loci with clustered genes associated with development.

𝜆-lemma for families of Riemann surfaces and the critical loci of complex Hénon maps

We prove a version of the classical λ \lambda -lemma for holomorphic families of Riemann surfaces. We then use it to show that critical loci for complex Hénon maps that are small perturbations of quadratic polynomials with Cantor Julia sets are all quasiconformally equivalent.

Critical behaviour of spanning forests on random planar graphs**Dedicated to Tony Guttmann on the occasion of his 70th birthday.

As a follow-up of previous work of the authors, we analyse the statistical mechanics model of random spanning forests on random planar graphs. Special emphasis is given to the analysis of the critical behaviour.Exploiting an exact relation with a model of -loops and dimers, previously solved by Kostov and Staudacher, we identify critical and multicritical loci, and find them consistent with recent results of Bousquet-Mélou and Courtiel. This is also consistent with the KPZ relation, and the Berker–Kadanoff phase in the anti-ferromagnetic regime of the Potts Model on periodic lattices, predicted by Saleur. To our knowledge, this is the first known example of KPZ appearing explicitly to work within a Berker–Kadanoff phase.We set up equations for the generating function, at the value t = −1 of the fugacity, which is of combinatorial interest, and we investigate the resulting numerical series, a favourite problem of Tony Guttmann’s.

Experimental determination of the critical loci for R-23 + (n-propane or n-hexane) and R-116 + n-propane binary mixtures

Isothermal VLE for the (R-23+n-propane) system was measured using a static-analytic apparatus at temperatures between T=(293.18 and 353.15)K. The critical loci for the systems {R-23+(n-propane or n-hexane)} and (R-116+n-propane) were measured using a critical point determination apparatus. The method of Ungerer et al. was used to extrapolate the isothermal VLE data to the isothermal critical locus. These extrapolated critical loci were compared with experimental data. The Redlich-Kister type correlations were used to correlate the critical loci of the systems. A critical locus curve for the (R-23+n-hexane) system which was calculated by the method of Heidemann and Khalil was compared with the experimental critical loci. The systems were classified according to the van Konynenburg and Scott classification system.

Noncritical holomorphic functions on Stein spaces

In this paper we prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, every closed discrete subset of a reduced Stein space X is the critical locus of a holomorphic function on X . We also show that for every complex analytic stratification with nonsingular strata on a reduced Stein space there exists a holomorphic function whose restriction to every stratum is noncritical. These result provide some information on critical loci of holomorphic functions on desingularizations of Stein spaces. In particular, every 1-convex manifold admits a holomorphic function that is noncritical outside the exceptional variety.

Quantitative comparison between predicted and experimental binary n-alkane + benzene phase behaviors using cubic and PC-SAFT EOS

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state correctly predicts Type I phase behavior for binary n-alkane + aromatic and naphthenic mixtures, while cubic equations of state (Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK)) predict a transition from Type I to Type II phase behavior within these families of mixtures, unless unconventional large and negative interaction parameters (kij) are used. In this work, bubble pressures and L = V critical loci are evaluated for 13 binary n-alkane + benzene mixtures, including new data obtained for benzene + n-C20, n-C24, n-C28 and n-C36 binary mixtures. Computed bubble pressures for the Peng-Robinson (PR), Soave-Redlich-Kwong (SRK) and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state are compared with one another and with experimental measurements. The PC-SAFT EOS, with pure component parameters rescaled to conform with critical temperatures and pressures following the recommendation of Alfradique and Castier (2007), and interaction parameter values set to zero, yield accurate bubble pressures and critical loci for all benzene + n-alkane mixtures. By contrast, the PR and SRK EOS require mixture specific kij values in order to provide quantitative bubble pressure and critical loci estimates, and best-fit kij values exhibit significant temperature dependence. In the absence of experimental bubble pressures, options for estimating interaction parameters for cubic EOS for binary benzene + n-alkane mixtures, and for aromatic or naphthenic + alkane mixtures more broadly are discussed. While subject to further testing, selection of interaction parameter values for cubic EOS such that computed bubble pressures closely mimic bubble pressures predicted by the scaled PC-SAFT EOS is recommended.

Isothermal vapour-liquid equilibrium data for the binary systems of (CHF3 or C2F6) and n-heptane

Isothermal vapour-liquid equilibrium (VLE) values for two binary systems; trifluoromethane and n-heptane at temperatures between T=(272.9 and 313.2)K, and hexafluoroethane and n-heptane at temperatures between T=(293.0 and 313.2)K were measured with a static-analytic apparatus. Bubble pressures at temperatures between T=(293.0 and 313.2)K, at several compositions, were also measured with a variable-volume static-synthetic apparatus. Vapour-liquid-liquid equilibrium (VLLE) was found to occur for certain isotherms for both of the systems. The PR EOS, with the Mathias-Copeman (MC) alpha function, combined with either the classical mixing rule or the Wong-Sandler (WS) mixing rule was used to correlate the experimental results. Either the NRTL or the UNIQUAC activity coefficient model was used within the WS mixing rule.The indirect extended scaling laws of Ungerer et al. were used to extrapolate critical loci from the experimental coexistence data, and the calculation procedure of Heidemann and Khalil was employed to calculate the mixture critical locus curves at temperatures close to the refrigerant critical temperatures. At lower temperatures on the mixture critical curve, gas-liquid critical points occurred, whereas, at higher temperatures, the critical points occurred along a liquid-liquid locus curve. The two systems were categorised according to the van Konynenburg and Scott classification.

QuIN: A Web Server for Querying and Visualizing Chromatin Interaction Networks.

Recent studies of the human genome have indicated that regulatory elements (e.g. promoters and enhancers) at distal genomic locations can interact with each other via chromatin folding and affect gene expression levels. Genomic technologies for mapping interactions between DNA regions, e.g., ChIA-PET and HiC, can generate genome-wide maps of interactions between regulatory elements. These interaction datasets are important resources to infer distal gene targets of non-coding regulatory elements and to facilitate prioritization of critical loci for important cellular functions. With the increasing diversity and complexity of genomic information and public ontologies, making sense of these datasets demands integrative and easy-to-use software tools. Moreover, network representation of chromatin interaction maps enables effective data visualization, integration, and mining. Currently, there is no software that can take full advantage of network theory approaches for the analysis of chromatin interaction datasets. To fill this gap, we developed a web-based application, QuIN, which enables: 1) building and visualizing chromatin interaction networks, 2) annotating networks with user-provided private and publicly available functional genomics and interaction datasets, 3) querying network components based on gene name or chromosome location, and 4) utilizing network based measures to identify and prioritize critical regulatory targets and their direct and indirect interactions. AVAILABILITY: QuIN’s web server is available at http://quin.jax.org QuIN is developed in Java and JavaScript, utilizing an Apache Tomcat web server and MySQL database and the source code is available under the GPLV3 license available on GitHub: https://github.com/UcarLab/QuIN/.

Delayed Microvascular Shear Adaptation in Pulmonary Arterial Hypertension. Role of Platelet Endothelial Cell Adhesion Molecule-1 Cleavage.

Altered pulmonary hemodynamics and fluid flow-induced high shear stress (HSS) are characteristic hallmarks in the pathogenesis of pulmonary arterial hypertension (PAH). However, the contribution of HSS to cellular and vascular alterations in PAH is unclear. We hypothesize that failing shear adaptation is an essential part of the endothelial dysfunction in all forms of PAH and tested whether microvascular endothelial cells (MVECs) or pulmonary arterial endothelial cells (PAECs) from lungs of patients with PAH adapt to HSS and if the shear defect partakes in vascular remodeling in vivo. PAH MVEC (n = 7) and PAH PAEC (n = 3) morphology, function, protein, and gene expressions were compared with control MVEC (n = 8) under static culture conditions and after 24, 72, and 120 hours of HSS. PAH MVEC showed a significantly delayed morphological shear adaptation (P = 0.03) and evidence of cell injury at sites of nonuniform shear profiles that are critical loci for vascular remodeling in PAH. In clear contrast, PAEC isolated from the same PAH lungs showed no impairments. PAH MVEC gene expression and transcriptional shear activation were not altered but showed significant decreased protein levels (P = 0.02) and disturbed interendothelial localization of the shear sensor platelet endothelial cell adhesion molecule-1 (PECAM-1). The decreased PECAM-1 levels were caused by caspase-mediated cytoplasmic cleavage but not increased cell apoptosis. Caspase blockade stabilized PECAM-1 levels, restored endothelial shear responsiveness in vitro, and attenuated occlusive vascular remodeling in chronically hypoxic Sugen5416-treated rats modeling severe PAH. Delayed shear adaptation, which promotes shear-induced endothelial injury, is a newly identified dysfunction specific to the microvascular endothelium in PAH. The shear response is normalized on stabilization of PECAM-1, which reverses intimal remodeling in vivo.

On Segre Numbers of Homogeneous Map Germs

Segre numbers and Segre cycles of ideals were independently introduced by Tworzewski, by Achilles and Manaresi and by Gaffney and Gassler. They are generalization of the Lê numbers and Lê cycles, introduced by Massey. In this article we give Lê-Iomdine type formulas for these cycles and numbers of arbitrary ideals. As a consequence we give a Plücker type formula for the Segre numbers of ideals generated by weighted homogeneous functions, in terms of their weights and degree. As an application of these results, we compute, in a purely combinatorial manner, the Segre numbers of the ideal which defines the critical loci of a map germ defined by a sequence of central hyperplane arrangements in $\mathsf{C}^{n+1}$.

Specific behavior of excess enthalpy of binary fluid mixtures near critical loci

The excess enthalpies for model fluid mixture interacting through the Lennard-Jones potential were calculated using the Percus–Yevick integral equation over wide ranges of temperature and pressure and over the entire mole fraction range. The calculated results near the critical locus reproduced the several specific behaviors founded experimentally in many fluid mixtures, and all these specific behaviors were explained by the phenomena due to the change of the combination of the states of the mixture and its component fluids. Based on this result, the excess enthalpies of the model mixture and the mixture composed of ethane and ethene measured by Gruszkiewcz et al. (J. Chem. Thermodynamics, 27, 1995, 507–524) were divided into two contributions, that is, the contribution due to the difference of the states between the mixture and its component fluids and the contribution which reflects the details of the molecular interactions for each mixture. The following results were found from these considerations. The specific behaviors of excess enthalpies near the critical locus are determined by the first contribution, and the excess enthalpies at states far from the critical locus are determined by the second contribution. In intermediate region, the new type specific behavior may arise because of the compensation of these two contributions with similar magnitude.

Ezh2 regulates differentiation and function of natural killer cells through histone methyltransferase activity

Changes of histone modification status at critical lineage-specifying gene loci in multipotent precursors can influence cell fate commitment. The contribution of these epigenetic mechanisms to natural killer (NK) cell lineage determination from common lymphoid precursors is not understood. Here we investigate the impact of histone methylation repressive marks (H3 Lys27 trimethylation; H3K27(me3)) on early NK cell differentiation. We demonstrate that selective loss of the histone-lysine N-methyltransferase Ezh2 (enhancer of zeste homolog 2) or inhibition of its enzymatic activity with small molecules unexpectedly increased generation of the IL-15 receptor (IL-15R) CD122(+) NK precursors and mature NK progeny from both mouse and human hematopoietic stem and progenitor cells. Mechanistic studies revealed that enhanced NK cell expansion and cytotoxicity against tumor cells were associated with up-regulation of CD122 and the C-type lectin receptor NKG2D. Moreover, NKG2D deficiency diminished the positive effects of Ezh2 inhibitors on NK cell commitment. Identification of the contribution of Ezh2 to NK lineage specification and function reveals an epigenetic-based mechanism that regulates NK cell development and provides insight into the clinical application of Ezh2 inhibitors in NK-based cancer immunotherapies.

Determination of critical properties for binary and ternary mixtures containing propanol and alkanes using a flow view-type apparatus

The critical temperatures and pressures of eight binary systems and two ternary systems (1-propanol+cyclohexane, 1-propanol+n-hexane, 1-propanol+n-heptane, 1-propanol+n-octane, 1-propanol+n-decane, 2-propanol+cyclohexane, cyclohexane+n-hexane, cyclohexane+n-heptane, 1-propanol+cyclohexane+n-heptane and 1-propanol+n-octane+n-decane) were measured using an efficient and accurate low residence time flow apparatus. The uncertainties of the critical temperature and the pressure were estimated to be less than 0.4K and 0.01MPa, respectively. All the critical loci of binary systems belong to the type I or type II as defined by Scott and van Konynenburg. The curves of critical temperatures for the six binary mixtures containing 1-propanol or 2-propanol are non-ideal. Maximum average absolute deviations of the Redlich–Kister equations from the experimental results for the critical temperatures and the critical pressures of all the binary systems are 0.05% and 0.07%, respectively. Moreover, the two ternary systems were correlated by Cibulka's and Singh's expressions with maximum average absolute deviations 0.06% for critical temperatures and 0.83% for critical pressures.

Isothermal (vapour + liquid) equilibrium data for binary systems of (n-hexane + CO2 or CHF3)

The (vapour+liquid) equilibrium (VLE) was measured for the (carbon dioxide+n-hexane) binary system at temperatures between T=(303.1 and 323.1)K. In addition, VLE and (vapour+liquid+liquid) equilibria (VLLE) were determined for the (trifluoromethane+n-hexane) binary system at temperatures between T=(272.9 and 313.3)K and pressures in the range of P=(1.0 to 5.7)MPa. Measurements were undertaken in a static-analytic apparatus, with verification of experimental values undertaken using a static-synthetic equilibrium cell to measure bubble point pressures at several compositions.The phase equilibrium results were modelled with the Peng–Robinson equation of state with the Mathias–Copeman alpha function, coupled with the Wong–Sandler mixing rules. Regression of the data was performed with the NRTL and the UNIQUAC activity coefficient models with the Wong–Sandler mixing rules, and the performance of the models was compared. Critical loci for both systems were estimated, using the calculation procedures of Ungerer et al. and Heidemann and Khalil.For the (trifluoromethane+n-hexane) system, liquid–liquid immiscibility was experienced at the lowest temperature measured (T=272.9K). At higher temperatures, no immiscibility was visible during the measurements; however, the models continued to predict a miscibility gap.

Regulation of Retinal Development via the Epigenetic Modification of Histone H3.

We are interested in the roles of epigenetic mechanisms in retinal development. By ChIP-qPCR using whole retinal extracts at various developmental stages, we found that the levels of methylation of histones H3K27 and H3K4 and acetylation of histone H3 at specific loci in various genes, which play critical roles in retinal proliferation and differentiation, changed dramatically during retinal development. We next focused on the roles of H3K27 trimethylation in retinal development. Ezh1 and Ezh2 are methyltransferases that act on H3K27, while Jmjd3 and Utx are demethylases. We found that Ezh2 and Jmjd3 were mainly expressed during retinal development, and a loss-of-function of these genes revealed a role for H3K27me3 in the maturation of subsets of bipolar cells. Furthermore, Ezh2 and Jmjd3 regulate H3K27 trimethylation at specific loci within Bhlhb4 and Vsx1, which play critical roles in the differentiation of subsets of bipolar cells. Utx is expressed weakly in retina, and the down-regulation of Utx by sh-RNA in retinal explants suggested that Utx also participates in the maturation of bipolar cells. Ezh1 is expressed weakly in postnatal retina, and the phenotype of Ezh2-knockout retina suggested that Ezh1 plays a role in the methylation of H3K27 in the late phase of retinal differentiation. Taken together, we found that these four genes, which exhibit temporally and spatially unique expression patterns during retinal development, play critical roles in the differentiation of retinal subsets through the regulation of histone H3K27 methylation at critical genetic loci.

A classical model for derived critical loci

Let $f:U\to{\mathbb A}^1$ be a regular function on a smooth scheme $U$ over a field $\mathbb K$. Pantev, Toen, Vaquie and Vezzosi (arXiv:1111.3209, arXiv:1109.5213) define the critical Crit$(f)$, an example of a new class of spaces in derived geometry, which they call symplectic derived They show that intersections of Lagrangians in a smooth symplectic $\mathbb K$-scheme, and stable moduli schemes of coherent sheaves on a Calabi-Yau 3-fold over $\mathbb K$, are also $-1$-shifted symplectic derived schemes. Thus, their theory may have applications in symplectic geometry, and in Donaldson-Thomas theory of Calabi-Yau 3-folds. This paper defines and studies a new class of spaces we call algebraic loci, which should be regarded as classical truncations of $-1$-shifted symplectic derived schemes. They are simpler than their derived analogues. We also give a analytic version of the theory, complex analytic loci, and an extension to Artin stacks, d-critical In the sequels arXiv:1305.6302, arXiv:1211.3259, arXiv:1305.6428, arXiv:1312.0090 we will define truncation functors from $-1$-shifted symplectic derived schemes or stacks to loci or stacks, and we will apply loci to motivic and categorified Donaldson-Thomas theory, and to intersections of (derived) Lagrangians in symplectic manifolds. We will show that the important structures one wants to associate to a derived critical locus -- virtual cycles, perverse sheaves and mixed Hodge modules of vanishing cycles, and motivic Milnor fibres -- can be defined for oriented loci and oriented stacks.

Lack of association between RAD50-IL13 polymorphisms and pediatric asthma susceptibility in Northeastern Han Chinese

Objective: RAD50-IL13 region has been recently identified as one of critical asthma susceptibility loci in genome-wide association studies, yet the role of these genetic variants or single-nucleotide polymorphisms (SNPs) in the risk of developing asthma in Northeastern Han Chinese remains largely unknown. Methods: We conducted an association study by genotyping four SNPs (rs2244012 and rs6871536 in RAD50 as well as rs1295686 and rs1800925 in IL13) in 652 asthmatic children and age-matched 752 healthy controls from Northeastern Han Chinese to evaluate the asthma susceptibility with each individual SNP using SNaPshot genotyping method. Results: We did not find the allele or genotype frequency distribution of four SNPs in RAD50-IL13 region which was significantly different between asthmatic children and controls (p > 0.05). Conclusions: Our findings first suggested that the variants in RAD50-IL13 region were not associated with asthma risk in Northeastern Han Chinese children.

Chern–Simons functions on toric Calabi–Yau threefolds and Donaldson–Thomas theory

In this paper, we give a construction of the global Chern-Simons functions for toric Calabi-Yau stacks of dimension three using strong exceptional collections. The moduli spaces of sheaves on such stacks can be identified with critical loci of these functions. We give two applications of these functions. First, we prove Joyce's integrality conjecture of generalized DT invariants on local surfaces. Second, we prove a dimension reduction formula for virtual motives, which leads to two recursion formulas for motivic Donaldson-Thomas invariants.

Reprogramming and transdifferentiation for cardiovascular development and regenerative medicine: where do we stand?

Heart disease remains a leading cause of mortality and a major worldwide healthcare burden. Recent advances in stem cell biology have made it feasible to derive large quantities of cardiomyocytes for disease modeling, drug development, and regenerative medicine. The discoveries of reprogramming and transdifferentiation as novel biological processes have significantly contributed to this paradigm. This review surveys the means by which reprogramming and transdifferentiation can be employed to generate induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) and induced cardiomyocytes (iCMs). The application of these patient-specific cardiomyocytes for both in vitro disease modeling and in vivo therapies for various cardiovascular diseases will also be discussed. We propose that, with additional refinement, human disease-specific cardiomyocytes will allow us to significantly advance the understanding of cardiovascular disease mechanisms and accelerate the development of novel therapeutic options.