Secant varieties of P^2 x P^n embedded by O(1,2)

We describe the defining ideal of the rth secant variety of P^2 x P^n embedded by O(1,2), for arbitrary n and r at most 5. We also present the Schur module decomposition of the space of generators of each such ideal. Our main results are based on a more general construction for producing explicit matrix equations that vanish on secant varieties of products of projective spaces. This extends previous work of Strassen and Ottaviani.Comment: 21 page

Hilbert schemes of 8 points

The Hilbert scheme H^d_n of n points in A^d contains an irreducible component R^d_n which generically represents n distinct points in A^d. We show that when n is at most 8, the Hilbert scheme H^d_n is reducible if and only if n = 8 and d >= 4. In the simplest case of reducibility, the component R^4_8 \subset H^4_8 is defined by a single explicit equation which serves as a criterion for deciding whether a given ideal is a limit of distinct points. To understand the components of the Hilbert scheme, we study the closed subschemes of H_n^d which parametrize those ideals which are homogeneous and have a fixed Hilbert function. These subschemes are a special case of multigraded Hilbert schemes, and we describe their components when the colength is at most 8. In particular, we show that the scheme corresponding to the Hilbert function (1,3,2,1) is the minimal reducible example.Comment: 28 pages; Rewrote introduction and reorganized parts of the paper, some minor errors have been fixe

Preliminary analysis of amplitude and phase fluctuations in the JAPE multiple tone data to distances of 500 meters

The JAPE short range data provide a good opportunity for studying phase and amplitude fluctuations of acoustic signals in the atmosphere over distances of several hundred meters. Several factors contribute to the usefulness of these data: extensive meteorological measurements were made, controlled sources were used, the data were recorded with a high dynamic range digital system that preserved phase information and a significant number of measurement points were obtained allowing both longitudinal and transverse studies. Further, Michigan Tech, in cooperation with the U.S. Army TARDEC, has developed phase tracking algorithms for studying vehicle acoustic signals. These techniques provide an excellent tool for analyzing the amplitude and phase fluctuations of the JAPE data. The results of studies such as those reported here have application at several levels: the mechanisms of signal amplitude and phase fluctuations in propagating acoustic signals are not well understood nor are the mathematical models highly developed, acoustic arrays depend strongly on signal coherence and signal amplitude stability in order to perform to their design specifications and active noise control implementation in regions considerably removed from the primary and secondary sources depends upon signal amplitude and phase stability. Work reported here is preliminary in nature but it does indicate the utility of the phase tracking and amplitude detection algorithms. The results obtained indicate that the phase fluctuations of the JAPE continuous multiple tone data (simultaneous transmission of 80, 200 and 500 Hz) are in general agreement with existing theories but the amplitude fluctuations are seen to be less well behaved and show less consistency

Monthly average daily global and diffuse solar radiation based on sunshine duration and clearness index for Brasov, Romania

The main objective of this study is to develop single location appropriate models for the estimation of the monthly average daily global and diffuse horizontal solar radiation for Brasov, Romania. The study focuses particularly on models based on the sunshine duration and clearness index. The data used for the calibration of the models were collected during a period of 4 yr, between November 2008 and October 2012, at the Transilvania University of Brasov. The testing and validation of the models was carried out using data from the online SoDa database for Brasov for the year 2005. Different statistical error tests were applied to evaluate the accuracy of the models. The predicted values are also compared with values from three other known models concerning the global and diffuse solar radiation. A new mixed model was developed for the estimation of monthly average daily global horizontal solar radiation. The data processing was performed by means of a real-time interface developed with LabVIEW graphical programming language. The parameters taken into account were the relative sunshine, the clearness index, the extraterrestrial radiation, the latitude and the longitude. The methodology is simple and effective and may be applied for any region. Its effectiveness was proven through comparison with global models

PfeIK1, a eukaryotic initiation factor 2α kinase of the human malaria parasite Plasmodium falciparum, regulates stress-response to amino-acid starvation

<p>Abstract</p> <p>Background</p> <p>Post-transcriptional control of gene expression is suspected to play an important role in malaria parasites. In yeast and metazoans, part of the stress response is mediated through phosphorylation of eukaryotic translation initiation factor 2α (eIF2α), which results in the selective translation of mRNAs encoding stress-response proteins.</p> <p>Methods</p> <p>The impact of starvation on the phosphorylation state of PfeIF2α was examined. Bioinformatic methods were used to identify plasmodial eIF2α kinases. The activity of one of these, PfeIK1, was investigated using recombinant protein with non-physiological substrates and recombinant PfeIF2α. Reverse genetic techniques were used to disrupt the <it>pfeik1 </it>gene.</p> <p>Results</p> <p>The data demonstrate that the <it>Plasmodium falciparum </it>eIF2α orthologue is phosphorylated in response to starvation, and provide bioinformatic evidence for the presence of three eIF2α kinases in <it>P. falciparum</it>, only one of which (PfPK4) had been described previously. Evidence is provided that one of the novel eIF2α kinases, PfeIK1, is able to phosphorylate the <it>P. falciparum </it>eIF2α orthologue <it>in vitro</it>. PfeIK1 is not required for asexual or sexual development of the parasite, as shown by the ability of <it>pfeik1</it>^-parasites to develop into sporozoites. However, eIF2α phosphorylation in response to starvation is abolished in <it>pfeik1</it>^-asexual parasites</p> <p>Conclusion</p> <p>This study strongly suggests that a mechanism for versatile regulation of translation by several kinases with a similar catalytic domain but distinct regulatory domains, is conserved in <it>P. falciparum</it>.</p

Baker's conjecture for functions with real zeros

Baker's conjecture states that a transcendental entire functions of order less than 1/2 has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou components and so it remains to show that they can also have no unbounded wandering domains. Here we introduce completely new techniques to show that the conjecture holds in the case that the transcendental entire function is real with only real zeros, and we prove the much stronger result that such a function has no orbits consisting of unbounded wandering domains whenever the order is less than 1. This raises the question as to whether such wandering domains can exist for any transcendental entire function with order less than 1. Key ingredients of our proofs are new results in classical complex analysis with wider applications. These new results concern: the winding properties of the images of certain curves proved using extremal length arguments, growth estimates for entire functions, and the distribution of the zeros of entire functions of order less than 1

Expansion of a single transposable element family is associated with genome-size increase and radiation in the genus Hydra

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.Transposable elements are one of the major contributors to genome-size differences in metazoans. Despite this, relatively little is known about the evolutionary patterns of element expansions and the element families involved. Here we report a broad genomic sampling within the genus Hydra, a freshwater cnidarian at the focal point of diverse research in regeneration, symbiosis, biogeography, and aging. We find that the genome of Hydra is the result of an expansion event involving long interspersed nuclear elements and in particular a single family of the chicken repeat 1 (CR1) class. This expansion is unique to a subgroup of the genus Hydra, the brown hydras, and is absent in the green hydra, which has a repeat landscape similar to that of other cnidarians. These features of the genome make Hydra attractive for studies of transposon-driven genome expansions and speciation

A syzygetic approach to the smoothability of zero-dimensional schemes

We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this question for zero-dimensional schemes of regularity two. This invariant imposes obstructions for smoothability in general, and it completely answers the question of smoothability for certain zero-dimensional schemes of low degree. The tools of this paper also lead to other results about Hilbert schemes of points, including a characterization of nonsmoothable zero-dimensional schemes of minimal degree in every embedding dimension d\geq 4.Comment: 22 pages, 1 figure. Corrected typos. Included Macaulay2 code for computations cited in the paper at the end of the laTex version of the documen