Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

SCC antigen and ApoC-II as serum biomarkers of cervical cancer

There are currently no reliable, established serum biomarkers to predict the prognosis of radiotherapy for advanced cervical cancer. We aimed to identify serum biomarkers for survival after radiotherapy for cervical cancer. In this multicenter prospective cohort study, the usefulness of pre- and posttreatment serum protein levels of potential biomarkers, including squamous cell carcinoma antigen (SCC-Ag), apolipoprotein C-II (ApoC-II), matrix metalloproteinase (MMP)1, and MMP2, were evaluated together with clinical factors in 145 cervical cancer patients in order to determine their suitability to predict survival. Progression-free survival (PFS) was the primary endpoint, and overall survival (OS), pelvic PFS (PPFS), and distant metastasis-free survival (DMFS) were the secondary endpoints. Blood samples were collected before and 1 month after radiotherapy to measure serum biomarker levels. ApoC-II was measured using a monoclonal antibody-based enzyme-linked immunosorbent assay, which was developed for this purpose. Kaplan-Meier method, log-rank test, and univariate and multivariate Cox proportional hazards models were used for statistical analyses. In multivariate analysis, larger tumor size was independently associated with shorter PFS, OS, PPFS, and DMFS, while longer overall treatment time was independently associated with shorter PPFS. Higher pretreatment SCC-Ag (P 25.8 μg/ml (P = 0.023, log-rank test). Pre- and posttreatment serum SCC-Ag and pretreatment serum ApoC-II levels may be important biomarkers to predict survival outcomes of patients with cervical cancer after radiotherapy. Pre- and posttreatment SCC-Ag and pretreatment ApoC-II might be useful in clinical settings for screening patients to improve treatment strategies in cervical cancer

Expression and trans-specific polymorphism of self-incompatibility RNases in Coffea (Rubiaceae)

Self-incompatibility (SI) is widespread in the angiosperms, but identifying the biochemical components of SI mechanisms has proven to be difficult in most lineages. Coffea (coffee; Rubiaceae) is a genus of old-world tropical understory trees in which the vast majority of diploid species utilize a mechanism of gametophytic self-incompatibility (GSI). The S-RNase GSI system was one of the first SI mechanisms to be biochemically characterized, and likely represents the ancestral Eudicot condition as evidenced by its functional characterization in both asterid (Solanaceae, Plantaginaceae) and rosid (Rosaceae) lineages. The S-RNase GSI mechanism employs the activity of class III RNase T2 proteins to terminate the growth of "self" pollen tubes. Here, we investigate the mechanism of Coffea GSI and specifically examine the potential for homology to S-RNase GSI by sequencing class III RNase T2 genes in populations of 14 African and Madagascan Coffea species and the closely related self-compatible species Psilanthus ebracteolatus. Phylogenetic analyses of these sequences aligned to a diverse sample of plant RNase T2 genes show that the Coffea genome contains at least three class III RNase T2 genes. Patterns of tissue-specific gene expression identify one of these RNase T2 genes as the putative Coffea S-RNase gene. We show that populations of SI Coffea are remarkably polymorphic for putative S-RNase alleles, and exhibit a persistent pattern of trans-specific polymorphism characteristic of all S-RNase genes previously isolated from GSI Eudicot lineages. We thus conclude that Coffea GSI is most likely homologous to the classic Eudicot S-RNase system, which was retained since the divergence of the Rubiaceae lineage from an ancient SI Eudicot ancestor, nearly 90 million years ago.United States National Science Foundation [0849186]; Society of Systematic Biologists; American Society of Plant Taxonomists; Duke University Graduate Schoolinfo:eu-repo/semantics/publishedVersio

Peculiaritats al·lèliques del locus <em>S</em> de les cultivars mallorquines d’ametller

The examination of the allelic diversity of the locus <em>S</em> in ten almond cultivars from Majorca has shown the presence of the <em>S_f</em> allele in four of them, as well as the presence of five new alleles non identified so far. Although the <em>S_f</em> allele has been described as responsible for the expression of self-compatibility in almond, it has been recently shown that this allele has two different phenotypic expressions. As a consequence, this allele cannot be always considered an index for self-compatibility of the genotypes harbouring it. The study of the four Majorcan cultivars possessing this allele has confirmed their selfincompatibility, showing that this allele is in its phenotypically active form, as it has been also observed in a group of cultivars from southern Italy, a fact possibly suggesting a connexion between these two Mediterranean almond populations.<br><br>El examen de la diversidad alélica del locus <em>S</em> en diez cultivares mallorquines de almendro ha mostrado la presencia del alelo <em>S_f</em> en cuatro de ellos, así como la presencia de cinco nuevos alelos no identificados hasta ahora. Aunque el alelo <em>S_f</em> se ha descrito como responsable de la expresión de la autocompatibilidad del almendro, recientemente se ha descubierto que tiene dos expresiones fenotípicas diferentes, por lo que no siempre se puede considerar un índice de la autocompatibilidad de los genotipos que lo presentan. El estudio de los cuatro cultivares mallorquines que presentan este alelo ha confirmado su autoincompatibilidad, de manera que este alelo se expresa en estos cultivares en su forma fenotípicamente activa, como también se ha comprobado en un grupo de cultivares del sur de Italia, lo que podría indicar una conexión entre estas dos poblaciones mediterráneas de almendro. [ca] L’examen de la diversitat al·lèlica del locus <em>S</em> en deu cultivars mallorquines d’ametller ha mostrat la presència de l’al·lel <em>S_f</em> en quatre, així com la presència de cinc al·lels nous fins ara no identificats. Encara que l’al·lel <em>S_f</em> s’ha descrit com a responsable de l’expressió de l’autocompatibilitat de l’ametller, fa poc que s’ha descobert que té dues expressions fenotípiques diferents, pel que no sempre es pot considerar un índex de l’autocompatibilitat dels genotips que el tenen. L’estudi de les quatre cultivars mallorquines que presenten aquest al·lel ha confirmat la seva autoincompatibilitat, de manera que aquest al·lel s’hi expressa en la seva forma fenotípicament activa, com també s’ha comprovat en un grup de cultivars del sud d’Itàlia, fet que podria indicar una connexió entre aquestes dues poblacions mediterrànies d’ametller

Computational Micromodel for Epigenetic Mechanisms

Characterization of the epigenetic profile of humans since the initial breakthrough on the human genome project has strongly established the key role of histone modifications and DNA methylation. These dynamic elements interact to determine the normal level of expression or methylation status of the constituent genes in the genome. Recently, considerable evidence has been put forward to demonstrate that environmental stress implicitly alters epigenetic patterns causing imbalance that can lead to cancer initiation. This chain of consequences has motivated attempts to computationally model the influence of histone modification and DNA methylation in gene expression and investigate their intrinsic interdependency. In this paper, we explore the relation between DNA methylation and transcription and characterize in detail the histone modifications for specific DNA methylation levels using a stochastic approach

Mechanical properties of Ti-6Al-4V selectively laser melted parts with body-centred-cubic lattices of varying cell size

Significant weight savings in parts can be made through the use of additive manufacture (AM), a process which enables the construction of more complex geometries, such as functionally graded lattices, than can be achieved conventionally. The existing framework describing the mechanical properties of lattices places strong emphasis on one property, the relative density of the repeating cells, but there are other properties to consider if lattices are to be used effectively. In this work, we explore the effects of cell size and number of cells, attempting to construct more complete models for the mechanical performance of lattices. This was achieved by examining the modulus and ultimate tensile strength of latticed tensile specimens with a range of unit cell sizes and fixed relative density. Understanding how these mechanical properties depend upon the lattice design variables is crucial for the development of design tools, such as finite element methods, that deliver the best performance from AM latticed parts. We observed significant reductions in modulus and strength with increasing cell size, and these reductions cannot be explained by increasing strut porosity as has previously been suggested. We obtained power law relationships for the mechanical properties of the latticed specimens as a function of cell size, which are similar in form to the existing laws for the relative density dependence. These can be used to predict the properties of latticed column structures comprised of body-centred-cubic (BCC) cells, and may also be adapted for other part geometries. In addition, we propose a novel way to analyse the tensile modulus data, which considers a relative lattice cell size rather than an absolute size. This may lead to more general models for the mechanical properties of lattice structures, applicable to parts of varying size

Quantification and characterisation of porosity in selectively laser melted Al–Si10–Mg using x-ray computed tomography

We used X-ray computed tomography (CT), microscopy and hardness measurements to study Al–Si10–Mg produced by selective laser melting (SLM). Specimens were subject to a series of heat treatments including annealing and precipitation hardening. The specimen interiors were imaged with X-ray CT, allowing the non-destructive quantification and characterisation of pores, including their spatial distribution. The specimens had porosities less than 0.1%, but included some pores with effective cross-sectional diameters up to 260 μm. The largest pores were highly anisotropic, being flat and lying in the plane normal to the build direction. Annealing cycles caused significant coarsening of the microstructure and a reduction of the hardness from (114 ± 3) HV, in the as-built state, to (45 ± 1) HV, while precipitation hardening increased this to a final hardness of (59 ± 1) HV. The pore size and shape distributions were unaffected by the heat treatments. We demonstrate the applicability of CT measurements and quantitative defect analysis for the purposes of SLM process monitoring and refinement