New and Old Results in Resultant Theory

Resultants are getting increasingly important in modern theoretical physics: they appear whenever one deals with non-linear (polynomial) equations, with non-quadratic forms or with non-Gaussian integrals. Being a subject of more than three-hundred-year research, resultants are of course rather well studied: a lot of explicit formulas, beautiful properties and intriguing relationships are known in this field. We present a brief overview of these results, including both recent and already classical. Emphasis is made on explicit formulas for resultants, which could be practically useful in a future physics research.Comment: 50 pages, 15 figure

Creation of a recombinant Komagataella phaffii strain, a producer of proteinase K from Tritirachium album

The objects of the study were recombinant clones of Komagataella phaffii K51 carrying the heterologous proteinase K (PK-w) gene from Tritirachium album integrated into their genome as well as samples of recombinant proteinase K isolated from these clones. The aims of this work were i) to determine whether it is possible to create recombinant K. phaffii K51 clones overexpressing functionally active proteinase K from T. album and ii) to analyze the enzymatic activity of the resulting recombinant enzyme. The following methods were used: computational analysis of primary structure of the proteinase K gene, molecular biological methods (PCR, electrophoresis of DNA in an agarose gel, electrophoresis of proteins in an SDS polyacrylamide gel under denaturing conditions, spectrophotometry, and quantitative assays of protease activity), and genetic engineering techniques (cloning and selection of genes in bacterial cells Escherichia coli TOP10 and in the methylotrophic yeast K. phaffii K51). The gene encoding natural proteinase K (PK-w) was designed and optimized for expression in K. phaffii K51. The proteinase K gene was synthesized and cloned within the plasmid pPICZα-A vector in E. coli TOP10 cells. The proteinase K gene was inserted into pPICZα-A in such a way that – at a subsequent stage of transfection into yeast cells – it was efficiently expressed under the control of the promoter and terminator of the AOX1 gene, and the product of the exogenous gene contained the signal peptide of the Saccharomyces cerevisiae a-factor to ensure the protein’s secretion into the culture medium. The resultant recombinant plasmid (pPICZα-A/PK-w) was transfected into K. phaffii K51 cells. A recombinant K. phaffii K51 clone was obtained that carried the synthetic proteinase K gene and ensured its effective expression and secretion into the culture medium. An approximate productivity of the yeast recombinant clones for recombinant proteinase K was 25 μg/ mL after 4 days of cultivation. The resulting recombinant protease has a high specific proteolytic activity: ~5000 U/mg

Rationality of the moduli spaces of plane curves of sufficiently large degree

We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.Comment: 18 pages; 1 figure; Macaulay2 scripts used can be found at http://www.uni-math.gwdg.de/bothmer/rationality/ or at the end of the latex source fil

Introduction to Integral Discriminants

The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J_{n|r}(S) = \int e^{-S(x_1 ... x_n)} dx_1 ... dx_n. Actually, S-dependence remains the same if e^{-S} in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate J_{n|r} in a number of non-Gaussian cases. Using Ward identities -- linear differential equations, satisfied by integral discriminants -- we calculate J_{2|3}, J_{2|4}, J_{2|5} and J_{3|3}. In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.Comment: 36 pages, 19 figure

The maternal and early embryonic transcriptome of the milkweed bug Oncopeltus fasciatus

<p>Abstract</p> <p>Background</p> <p>Most evolutionary developmental biology ("evo-devo") studies of emerging model organisms focus on small numbers of candidate genes cloned individually using degenerate PCR. However, newly available sequencing technologies such as 454 pyrosequencing have recently begun to allow for massive gene discovery in animals without sequenced genomes. Within insects, although large volumes of sequence data are available for holometabolous insects, developmental studies of basally branching hemimetabolous insects typically suffer from low rates of gene discovery.</p> <p>Results</p> <p>We used 454 pyrosequencing to sequence over 500 million bases of cDNA from the ovaries and embryos of the milkweed bug <it>Oncopeltus fasciatus</it>, which lacks a sequenced genome. This indirectly developing insect occupies an important phylogenetic position, branching basal to Diptera (including fruit flies) and Hymenoptera (including honeybees), and is an experimentally tractable model for short-germ development. 2,087,410 reads from both normalized and non-normalized cDNA assembled into 21,097 sequences (isotigs) and 112,531 singletons. The assembled sequences fell into 16,617 unique gene models, and included predictions of splicing isoforms, which we examined experimentally. Discovery of new genes plateaued after assembly of ~1.5 million reads, suggesting that we have sequenced nearly all transcripts present in the cDNA sampled. Many transcripts have been assembled at close to full length, and there is a net gain of sequence data for over half of the pre-existing <it>O. fasciatus </it>accessions for developmental genes in GenBank. We identified 10,775 unique genes, including members of all major conserved metazoan signaling pathways and genes involved in several major categories of early developmental processes. We also specifically address the effects of cDNA normalization on gene discovery in <it>de novo </it>transcriptome analyses.</p> <p>Conclusions</p> <p>Our sequencing, assembly and annotation framework provide a simple and effective way to achieve high-throughput gene discovery for organisms lacking a sequenced genome. These data will have applications to the study of the evolution of arthropod genes and genetic pathways, and to the wider evolution, development and genomics communities working with emerging model organisms.</p> <p>[The sequence data from this study have been submitted to GenBank under study accession number SRP002610 (<url>http://www.ncbi.nlm.nih.gov/sra?term=SRP002610</url>). Custom scripts generated are available at <url>http://www.extavourlab.com/protocols/index.html</url>. Seven Additional files are available.]</p

Molecular identification of Palearctic members of Anopheles maculipennis in northern Iran

BACKGROUND: Members of Anopheles maculipennis complex are effective malaria vectors in Europe and the Caspian Sea region in northern Iran, where malaria has been re-introduced since 1994. The current study has been designed in order to provide further evidence on the status of species composition and to identify more accurately the members of the maculipennis complex in northern Iran. METHODS: The second internal transcribed spacer of ribosomal DNA (rDNA-ITS2) was sequenced in 28 out of 235 specimens that were collected in the five provinces of East Azerbayjan, Ardebil, Guilan, Mazandaran and Khorassan in Iran. RESULTS: The length of the ITS2 ranged from 283 to 302 bp with a GC content of 49.33 – 54.76%. No intra-specific variations were observed. Construction of phylogenetic tree based on the ITS2 sequence revealed that the six Iranian members of the maculipennis complex could be easily clustered into three groups: the An. atroparvus – Anopheles labranchiae group; the paraphyletic group of An. maculipennis, An. messeae, An. persiensis; and An. sacharovi as the third group. CONCLUSION: Detection of three species of the An. maculipennis complex including An. atroparvus, An. messae and An. labranchiae, as shown as new records in northern Iran, is somehow alarming. A better understanding of the epidemiology of malaria on both sides of the Caspian Sea may be provided by applying the molecular techniques to the correct identification of species complexes, to the detection of Plasmodium composition in Anopheles vectors and to the status of insecticide resistance by looking to related genes

Gene expression patterns associated with blood-feeding in the malaria mosquito Anopheles gambiae

BACKGROUND: Blood feeding, or hematophagy, is a behavior exhibited by female mosquitoes required both for reproduction and for transmission of pathogens. We determined the expression patterns of 3,068 ESTs, representing ~2,000 unique gene transcripts using cDNA microarrays in adult female Anopheles gambiae at selected times during the first two days following blood ingestion, at 5 and 30 min during a 40 minute blood meal and at 0, 1, 3, 5, 12, 16, 24 and 48 hours after completion of the blood meal and compared their expression to transcript levels in mosquitoes with access only to a sugar solution. RESULTS: In blood-fed mosquitoes, 413 unique transcripts, approximately 25% of the total, were expressed at least two-fold above or below their levels in the sugar-fed mosquitoes, at one or more time points. These differentially expressed gene products were clustered using k-means clustering into Early Genes, Middle Genes, and Late Genes, containing 144, 130, and 139 unique transcripts, respectively. Several genes from each group were analyzed by quantitative real-time PCR in order to validate the microarray results. CONCLUSION: The expression patterns and annotation of the genes in these three groups (Early, Middle, and Late genes) are discussed in the context of female mosquitoes' physiological responses to blood feeding, including blood digestion, peritrophic matrix formation, egg development, and immunity

Provability logic

The idea of provability logic seems to originate in a short paper [Gödel, 1933]. K. Gödel was motivated by the question of providing Brouwer’s intuitionistic logic, as formalized by Heyting, with an adequate semantics. According to Brouwer, intuitionistic truth means provability. Here is