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

Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles

An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self 4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed respectively in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system

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

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

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

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

Tools for crushing diatoms – opal teeth in copepods feature a rubber-like bearing composed of resilin

Diatoms are generally known for superior mechanical properties of their mineralised shells. Nevertheless, many copepod crustaceans are able to crush such shells using their mandibles. This ability very likely requires feeding tools with specific material compositions and properties. For mandibles of several copepod species silica-containing parts called opal teeth have been described. The present study reveals the existence of complex composite structures, which contain, in addition to silica, the soft and elastic protein resilin and form opal teeth with a rubber-like bearing in the mandibles of the copepod Centropages hamatus. These composite structures likely increase the efficiency of the opal teeth while simultaneously reducing the risk of mechanical damage. They are supposed to have coevolved with the diatom shells in the evolutionary arms race, and their development might have been the basis for the dominance of the copepods within today's marine zooplankton

Large scale patterns in vertical distribution and behavior of mesopelagic scattering layers

Recent studies suggest that previous estimates of mesopelagic biomasses are severely biased, with the new, higher estimates underlining the need to unveil behaviourally mediated coupling between shallow and deep ocean habitats. We analysed vertical distribution and diel vertical migration (DVM) of mesopelagic acoustic scattering layers (SLs) recorded at 38 kHz across oceanographic regimes encountered during the circumglobal Malaspina expedition. Mesopelagic SLs were observed in all areas covered, but vertical distributions and DVM patterns varied markedly. The distribution of mesopelagic backscatter was deepest in the southern Indian Ocean (weighted mean daytime depth: WMD 590 m) and shallowest at the oxygen minimum zone in the eastern Pacific (WMD 350 m). DVM was evident in all areas covered, on average ~50% of mesopelagic backscatter made daily excursions from mesopelagic depths to shallow waters. There were marked differences in migrating proportions between the regions, ranging from ~20% in the Indian Ocean to ~90% in the Eastern Pacific. Overall the data suggest strong spatial gradients in mesopelagic DVM patterns, with implied ecological and biogeochemical consequences. Our results suggest that parts of this spatial variability can be explained by horizontal patterns in physical-chemical properties of water masses, such as oxygen, temperature and turbidity.En prensa2,927

Classical Morphology of Plants as an Elementary Instance of Classical Invariant Theory

It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT). Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential “accurate morphological method”. However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers). We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the “theory of axilar bud” is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent