Boxicity and Poset Dimension

Let G be a simple, undirected, finite graph with vertex set V (G) and edge set E(G). A k-dimensional box is a Cartesian product of closed intervals [a(1), b(1)] x [a(2), b(2)] x ... x [a(k), b(k)]. The boxicity of G, box(G), is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes; i.e., each vertex is mapped to a k-dimensional box and two vertices are adjacent in G if and only if their corresponding boxes intersect. Let P = (S, P) be a poset, where S is the ground set and P is a reflexive, antisymmetric and transitive binary relation on S. The dimension of P, dim(P), is the minimum integer t such that P can be expressed as the intersection of t total orders. Let G(P) be the underlying comparability graph of P; i.e., S is the vertex set and two vertices are adjacent if and only if they are comparable in P. It is a well-known fact that posets with the same underlying comparability graph have the same dimension. The first result of this paper links the dimension of a poset to the boxicity of its underlying comparability graph. In particular, we show that for any poset P, box(G(P))/(chi(G(P)) - 1) <= dim(P) <= 2box(G(P)), where chi(G(P)) is the chromatic number of G(P) and chi(G(P)) not equal 1. It immediately follows that if P is a height-2 poset, then box(G(P)) <= dim(P) <= 2box(G(P)) since the underlying comparability graph of a height-2 poset is a bipartite graph. The second result of the paper relates the boxicity of a graph G with a natural partial order associated with the extended double cover of G, denoted as G(c): Note that G(c) is a bipartite graph with partite sets A and B which are copies of V (G) such that, corresponding to every u is an element of V (G), there are two vertices u(A) is an element of A and u(B) is an element of B and {u(A), v(B)} is an edge in G(c) if and only if either u = v or u is adjacent to v in G. Let P(c) be the natural height-2 poset associated with G(c) by making A the set of minimal elements and B the set of maximal elements. We show that box(G)/2 <= dim(P(c)) <= 2box(G) + 4. These results have some immediate and significant consequences. The upper bound dim(P) <= 2box(G(P)) allows us to derive hitherto unknown upper bounds for poset dimension such as dim(P) = 2 tree width (G(P)) + 4, since boxicity of any graph is known to be at most its tree width + 2. In the other direction, using the already known bounds for partial order dimension we get the following: (1) The boxicity of any graph with maximum degree Delta is O(Delta log(2) Delta), which is an improvement over the best-known upper bound of Delta(2) + 2. (2) There exist graphs with boxicity Omega(Delta log Delta). This disproves a conjecture that the boxicity of a graph is O(Delta). (3) There exists no polynomial-time algorithm to approximate the boxicity of a bipartite graph on n vertices with a factor of O(n(0.5-is an element of)) for any is an element of > 0 unless NP = ZPP.

MS_RHII-RSD, a Dual-Function RNase HII-(p)ppGpp Synthetase from Mycobacterium smegmatis

In the noninfectious soil saprophyte Mycobacterium smegmatis, intracellular levels of the stress alarmones guanosine tetraphosphate and guanosine pentaphosphate, together termed (p)ppGpp, are regulated by the enzyme Rel(Msm). This enzyme consists of a single, bifunctional polypeptide chain that is capable of both synthesizing and hydrolyzing (p)ppGpp. The rel(Msm), knockout strain of M. smegmatis (Delta rel(Msm)) is expected to show a (p)ppGpp null (p)ppGpp(0)] phenotype. Contrary to this expectation, the strain is capable of synthesizing (p)ppGpp in vivo. In this study, we identify and functionally characterize the open reading frame (ORF), MSMEG_5849, that encodes a second functional (p)ppGpp synthetase in M. smegmatis. In addition to (p)ppGpp synthesis, the 567-amino-acid-long protein encoded by this gene is capable of hydrolyzing RNA(.)DNA hybrids and bears similarity to the conventional RNase HII enzymes. We have classified this protein as actRel(Msm) in accordance with the recent nomenclature proposed and have named it MS_RHII-RSD, indicating the two enzymatic activities present RHII, RNase HII domain, originally identified as (d) under bar omain of (u) under bar nknown (f) under bar unction 429 (DUF429), and RSD, RelA_SpoT nucleotidyl transferase domain, the SYNTH domain responsible for (p)ppGpp synthesis activity]. MS_RHII-RSD is expressed and is constitutively active in vivo and behaves like a monofunctional (p)ppGpp synthetase in vitro. The occurrence of the RNase HII and (p)ppGpp synthetase domains together on the same polypeptide chain is suggestive of an in vivo role for this novel protein as a link connecting the essential life processes of DNA replication, repair, and transcription to the highly conserved stress survival pathway, the stringent response.

Distinct and Contrasting Transcription Initiation Patterns at Mycobacterium tuberculosis Promoters

Although sequencing of Mycobacterium tuberculosis genome lead to better understanding of transcription units and gene functions, interactions occurring during transcription initiation between RNA polymerase and promoters is yet to be elucidated. Different stages of transcription initiation include promoter specific binding of RNAP, isomerization, abortive initiation and promoter clearance. We have now analyzed these events with four promoters of M. tuberculosis viz. P-gyrB1, P-gyrR, P-rrnPCL1 and P-metU. The promoters differed from each other in their rates of open complex formation, decay, promoter clearance and abortive transcription. The equilibrium binding and kinetic studies of various steps revealed distinct rate limiting events for each of the promoter, which also differed markedly in their characteristics from the respective promoters of Mycobacterium smegmatis. Surprisingly, the transcription at gyr promoter was enhanced in the presence of initiating nucleotides and decreased in the presence of alarmone, pppGpp, a pattern typically seen with rRNA promoters studied so far. The gyr promoter of M. smegmatis, on the other hand, was not subjected to pppGpp mediated regulation. The marked differences in the transcription initiation pathway seen with rrn and gyr promoters of M. smegmatis and M. tuberculosis suggest that such species specific differences in the regulation of expression of the crucial housekeeping genes could be one of the key determinants contributing to the differences in growth rate and lifestyle of the two organisms. Moreover, the distinct rate limiting steps during transcription initiation of each one of the promoters studied point at variations in their intracellular regulation.

Observation of the nuclear magnetic octupole moment of Yb-173 from precise measurements of the hyperfine structure in the P-3(2) state

We measure hyperfine structure in the metastable P-3(2) state of Yb-173 and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the P-3(1) and S-3(1) states. We measure frequencies of hyperfine transitions of the P-3(2) -> S-3(1) line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby P-3(1) and P-1(1) states are below 30 kHz. We obtain the hyperfine coefficients as A = -742.11(2) MHz and B = 1339.2(2) MHz, which represent a two orders-of-magnitude improvement in precision, and C = 0.54(2) MHz. From atomic structure calculations, we obtain the nuclear moments quadrupole Q = 2.46(12) b and octupole Omega = -34.4(21) b x mu(N). DOI: 10.1103/PhysRevA.87.012512

Fabrication and characterization of micro-arc oxidized fluoride containing titania films on Cp Ti

The present study is focussed at establishing an appropriate electrolyte system for developing electrochemically stable and fluorine (F) containing titania (F-TiO2) films on Cp Ti by micro-arc oxidation (MAO) technique. To fabricate the F-TiO2 films on Cp Ti, different electrolyte solutions of chosen concentrations of tri-sodium orthophosphate (TSOP, Na3PO4 center dot I2H2O), potassium hydroxide (KOH) and various F-containing compounds such as ammonium fluoride (NH4F), potassium fluoride (KF), sodium fluoride (NaF) and potassium fluorotitanate (K2TiF6) are employed. The structural and morphological characteristics, thickness and elemental composition of the developed films have been assessed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques. The in-vitro electrochemical corrosion behavior of the films was studied under Kokubo simulated body fluid (SBF) environment by potentiodynamic polarization, long term potential measurement and electrochemical impedance spectroscopy (EIS) methods. The XRD and SEM-EDS results show that the rutile content in the films vary in the range of 15-37 wt% and the F and P contents in the films is found to be in the range of 2-3 at% and 2.9-4.7 at% respectively, suggesting that the anatase to rutile phase transformation and the incorporation of F and P into the films are significantly controlled by the respective electrolyte solution. The SEM elemental mapping results show that the electrolyte borne F and P elements are incorporated and distributed uniformly in all the films. Among all the films under study, the film developed with 5 g TSOP+2 g KOH+3 g K2TiF6 electrolyte system exhibits considerably improved in-vitro corrosion resistance and therefore best suited for biomedical applications. (C) 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Internal defect and process parameter analysis during friction stir welding of Al 6061 sheets

Welding parameters like welding speed, rotation speed, plunge depth, shoulder diameter etc., influence the weld zone properties, microstructure of friction stir welds, and forming behavior of welded sheets in a synergistic fashion. The main aims of the present work are to (1) analyze the effect of welding speed, rotation speed, plunge depth, and shoulder diameter on the formation of internal defects during friction stir welding (FSW), (2) study the effect on axial force and torque during welding, (c) optimize the welding parameters for producing internal defect-free welds, and (d) propose and validate a simple criterion to identify defect-free weld formation. The base material used for FSW throughout the work is Al 6061T6 having a thickness value of 2.1 mm. Only butt welding of sheets is aimed in the present work. It is observed from the present analysis that higher welding speed, higher rotation speed, and higher plunge depth are preferred for producing a weld without internal defects. All the shoulder diameters used for FSW in the present work produced defect-free welds. The axial force and torque are not constant and a large variation is seen with respect to FSW parameters that produced defective welds. In the case of defect-free weld formation, the axial force and torque are relatively constant. A simple criterion, (a,tau/a,p)(defective) > (a,tau/a,p)(defect free) and (a,F/a,p)(defective) > (a,F/a,p)(defect free), is proposed with this observation for identifying the onset of defect-free weld formation. Here F is axial force, tau is torque, and p is welding speed or tool rotation speed or plunge depth. The same criterion is validated with respect to Al 5xxx base material. Even in this case, the axial force and torque remained constant while producing defect-free welds.

Probing hemoglobin confinement inside submicron silica tubes using synchrotron SAXS and electrochemical response

The configuration of hemoglobin in solution and confined inside silica nanotubes has been studied using synchrotron small angle X-ray scattering and electrochemical activity. Confinement inside submicron tubes of silica aid in preventing protein aggregation, which is vividly observed for unconfined protein in solution. The radius of gyration (R-g) and size polydispersity (p) of confined hemoglobin was found to be lower than that in solution. This was also recently demonstrated in case of confined hemoglobin inside layered polymer capsules. The confined hemoglobin displayed a higher thermal stability with Rg and p showing negligible changes in the temperature range 25-75 degrees C. The differences in configuration between the confined and unconfined protein were reflected in their electrochemical activity. Reversible electrochemical response (from cyclic voltammograms) obtained in case of the confined hemoglobin, in contrary to the observance of only a cathodic response for the unconfined protein, gave direct indication of the differences between the residences of the electroactive heme center in a different orientation compared to that in solution state. The confined Hb showed loss of reversibility only at higher temperatures. The electron transfer coefficient (alpha) and electron transfer rate constant (k(s)) were also different, providing additional evidence regarding structural differences between the unconfined and confined states of hemoglobin. Thus, absence of any adverse effects due to confinement of proteins inside the inorganic matrices such as silica nanotubes opens up new prospects for utilizing inorganic matrices as protein ``encapsulators'', as well as sensors at varying temperatures.

Mutation analysis of the SLC4A11 gene in Indian families with congenital hereditary endothelial dystrophy 2 and a review of the literature

Purpose: Congenital hereditary endothelial dystrophy 2 (CHED2) is an autosomal recessive disorder caused by mutations in the solute carrier family 4, sodium borate transporter, member 11 (SLC4A11) gene. The purpose of this study was to identify the genetic cause of CHED2 in six Indian families and catalog all known mutations in the SLC4A11 gene. Methods: Peripheral blood samples were collected from individuals of the families with CHED2 and used in genomic DNA isolation. PCR primers were used to amplify the entire coding region including intron-exon junctions of SLC4A11. Amplicons were subsequently sequenced to identify the mutations. Results: DNA sequence analysis of the six families identified four novel (viz., p.Thr262Ile, p.Gly417Arg, p.Cys611Arg, and p.His724Asp) mutations and one known p.Arg869His homozygous mutation in the SLC4A11 gene. The mutation p.Gly417Arg was identified in two families. Conclusions: This study increases the mutation spectrum of the SLC4A11 gene. A review of the literature showed that the total number of mutations in the SLC4A11 gene described to date is 78. Most of the mutations are missense, followed by insertions-deletions. The present study will be helpful in genetic diagnosis of the families reported here.

Experimental determination and activity coefficient based models for mixture solubilities of nitrophenol isomers in supercritical carbon dioxide

The experimental solubilities of the mixture of nitrophenol (m- and p-) isomers were determined at 308, 318 and 328 K over a pressure range of 10-17.55 MPa. Compared to the binary solubilities, the ternary solubilities of m-nitrophenol increased at 308, 318 and 328 K. The ternary solubilities of p-nitrophenol increased at 308 K, while the ternary solubilities decreased at lower pressures and increased at higher pressure at 318 and 328 K. The solubilities of the solid mixtures in supercritical carbon dioxide (SCCO2) were correlated with solution models by incorporating the non-idealities using activity coefficient based models. The Wilson and NRTL activity coefficient models were applied to determine the nature of the interactions between the molecules. The equation developed by using the NRTL model has three parameters and correlates mixture solubilities of solid solutes in terms of temperature and cosolute composition. The equation derived from the Wilson model contains five parameters and correlates solubilities in terms of temperature, density and cosolute composition. These two new equations developed in this work were used to correlate the solubilities of 25 binary solid mixtures including the current data. The average AARDs of the model equations derived using the NRTL and Wilson models for the solid mixtures were found to be 7% and 4%, respectively. (C) 2012 Elsevier B.V. All rights reserved.

Expression and function of cyclooxygenase-2 is necessary for hamster blastocyst hatching

Blastocyst hatching is critical for successful implantation leading to pregnancy. Its failure causes infertility. The phenomenon of blastocyst hatching in humans is poorly understood and the available information on this stems from studies of rodents such as mice and hamsters. We and others showed that hamster blastocyst hatching is characterized by firstly blastocyst deflation followed by a dissolution of the zona pellucida (zona) and accompanied by trophectodermal projections (TEPs). We also showed that embryo-derived cathepsins (Cat) proteases, specifically Cat-L, -B and -P act as zonalysins and are responsible for hatching. In this study, we show the expression and function of one of the potential regulators of embryogenesis, cyclooxygenase (COX)-2 during blastocyst development and hatching. The expression of COX-2 mRNA and protein was observed in 8-cell through hatched blastocyst stages and it was also localized to blastocysts TEPs. Specific COX-2 inhibitors, NS-398 and CAY-10404, inhibited blastocyst hatching; percentages achieved were only 28.4 5.3 and 32.3 5.4, respectively, compared with 90 with untreated embryos. Interestingly, inhibitor-treated blastocysts failed to deflate, normally observed during hatching. Supplementation of prostaglandins (PGs)-E-2 or -I-2 to cultured embryos reversed the inhibitors effect on hatching and also the deflation behavior. Importantly, the levels of mRNA and protein of Cat-L, -B and -P showed a significant reduction in the inhibitor-treated embryos compared with untreated embryos, although its mechanism remains to be examined. These data provide the first evidence that COX-2 is critical for blastocyst hatching in the golden hamster.

Effects of temperature on complexes I and II mediated respiration, ROS generation and oxidative stress status in isolated gill mitochondria of the mud crab Scylla serrata

Effects of fluctuations in habitat temperature (18-30 degrees) on mitochondrial respiratory behavior and oxidative metabolic responses in the euryhaline ectotherm Scylla serrate are not fully understood. In the present study, effects of different temperatures ranging from 12 to 40 degrees C on glutamate and succinate mediated mitochondrial respiration, respiratory control ratio (RCR), ATP generation rate, ratio for the utilization of phosphate molecules per atomic oxygen consumption (P/O), levels of lipid peroxidation and H2O2 in isolated gill mitochondria of S. serrata are reported. The pattern of variation in the studied parameters was similar for the two substrates at different temperatures. The values recorded for RCR ( >= 3) and P/O ratio (1.4-2.7) at the temperature range of 15-25 degrees C were within the normal range reported for other animals (3-10 for RCR and 1.5-3 for P/O). Values for P/O ratio, ATP generation rate and RCR were highest at 18 degrees C when compared to the other assay temperatures. However, at low and high extreme temperatures, i.e. at 12 and 40 degrees C, states III and IV respiration rates were not clearly distinguishable from each other indicating that mitochondria were completely uncoupled. Positive correlations were noticed between temperature and the levels of both lipid peroxidation and H2O2. It is inferred that fluctuations on either side of ambient habitat temperature may adversely influence mitochondria respiration and oxidative metabolism in S. serrata. The results provide baseline data to understand the impacts of acute changes in temperature on ectotherms inhabiting estuarine or marine environments. (C) 2014 Elsevier Ltd. All rights reserved.

Amide Functionalized Microporous Organic Polymer (Am-MOP) for Selective CO2 Sorption and Catalysis

We report the design and synthesis of an amide functionalized microporous organic polymer (Am-MOP) prepared from trimesic acid and p-phenylenediamine using thionyl chloride as a reagent. Polar amide (CONH) functional groups act as a linking unit between the node and spacer and constitute the pore wall of the continuous polymeric network. The strong covalent bonds between the building blocks (trimesic acid and p-phenylenediamine) through amide bond linkages provide high thermal and chemical stability to Am-MOP. The presence of a highly polar pore surface allows selective CO2 uptake at 195 K over other gases such as N-2, Ar, and O-2. The CO2 molecule interacts with amide functional groups via Lewis acid base type interactions as demonstrated through DFT calculations. Furthermore, for the first time Am-MOP with basic functional groups has been exploited for the Knoevenagel condensation reaction between aldehydes and active methylene compounds. Availability of a large number of catalytic sites per volume and confined microporosity gives enhanced catalytic efficiency and high selectivity for small substrate molecules.

Biogenic nanosilver incorporated reverse osmosis membrane for antibacterial and antifungal activities against selected pathogenic strains: An enhanced eco-friendly water disinfection approach

Reverse osmosis (RO) membranes have been used extensively in water desalination plants, waste water treatment in industries, agricultural farms and drinking water production applications. The objective of this work is to impart antibacterial and antifungal activities to commercially available RO membrane used in water purification systems by incorporating biogenic silver nanoparticles (AgNPs) synthesized using Rosa indica wichuriana hybrid leaf extract. The morphology and surface topography of uncoated and AgNPs-coated RO membrane were studied using Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). Elemental composition of the AgNPs-coated RO membrane was analyzed by energy-dispersive X-ray spectroscopy (EDAX). The functional groups were identified by Fourier Transform Infrared spectroscopy (FT-IR). Hydrophilicity of the uncoated and AgNPs-coated RO membrane was analyzed using water contact angle measurements. The thermal properties were studied by thermogravimetric analysis (TGA). The AgNPs incorporated RO membrane exhibited good antibacterial and antifungal activities against pathogenic bacterial strains such as E. coli, S. aureus, M. luteus, K. pneumoniae, and P. aeruginosa and fungal strains such as Candida tropicalis, C. krusei, C. glabrata, and C. albicans.

STAT-1 expression is regulated by IGFBP-3 in malignant glioma cells and is a strong predictor of poor survival in patients with glioblastoma Laboratory investigation

Object. Insulin-like growth factor binding proteins (IGEBPs) have been implicated in the pathogenesis of glioma. In a previous study the authors demonstrated that IGFBP-3 is a novel glioblastoma biomarker associated with poor survival. Since signal transducer and activator of transcription 1 (STAT-1) has been shown to be regulated by IGFBP-3 during chondrogenesis and is a prosurvival and radioresistant molecule in different tumors, the aim in the present study was to explore the functional significance of IGFBP-3 in malignant glioma cells, to determine if STAT-1 is indeed regulated by IGFBP-3, and to study the potential of STAT-1 as a biomarker in glioblastoma. Methods. The functional significance of IGFBP-3 was investigated using the short hairpin (sh)RNA gene knockdown approach on U251MG cells. STAT-1 regulation by IGFBP-3 was tested on U251MG and U87MG cells by shRNA gene knockdown and exogenous treatment with recombinant IGFBP-3 protein. Subsequently, the expression of STAT-1 was analyzed with real-time reverse transcription polymerase chain reaction (RT-PCR) and immunohistochemistry (IHC) in glioblastoma and control brain tissues. Survival analyses were done on a uniformly treated prospective cohort of adults with newly diagnosed glioblastoma (136 patients) using Kaplan-Meier and Cox regression models. Results. IGFBP-3 knockdown significantly impaired proliferation, motility, migration, and invasive capacity of U251MG cells in vitro (p < 0.005). Exogenous overexpression of IGFBP-3 in U251MG and U87MG cells demonstrated STAT-1 regulation. The mean transcript levels (by real-time RT-PCR) and the mean labeling index of STAT-1 (by IHC) were significantly higher in glioblastoma than in control brain tissues (p = 0.0239 and p < 0.001, respectively). Multivariate survival analysis revealed that STAT-1 protein expression (HR 1.015, p = 0.033, 95% CI 1.001-1.029) along with patient age (HR 1.025, p = 0.005, 95% CI 1.008-1.042) were significant predictors of shorter survival in patients with glioblastoma. Conclusions. IGFBP-3 influences tumor cell proliferation, migration, and invasion and regulates STAT-1 expression in malignant glioma cells. STAT-1 is overexpressed in human glioblastoma tissues and emerges as a novel prognostic biomarker.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.