Horrocks Correspondence on a Quadric Surface

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.Comment: 19 page

Horrocks Correspondence on ACM Varieties

We describe a vector bundle \sE on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants H^i_*(\sE), $1\leq i \leq n-1$, and certain graded modules of "socle elements" built from \sE. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\mathbb P^{n+1}$ and the Veronese surface in $\mathbb P^5$ are considered in more detail.Comment: 18 pages, not figure

Rank two bundles on P^n with isolated cohomology

The purpose of this paper is to study minimal monads associated to a rank two vector bundle $\mathcal E$ on $\mathbb P^n$. In particular, we study situations where $\mathcal E$ has $H^i_*(\mathcal E) =0$ for $1<i<n-1$, except for one pair of values $(k,n-k)$. We show that on $\mathbb P^8,$ if $H^3_*(\mathcal E)=H^4_*(\mathcal E)=0$, then $\mathcal E$ must be decomposable. More generally, we show that for $n\geq 4k$, there is no indecomposable bundle $\mathcal E$ for which all intermediate cohomology modules except for $H^1_*, H^k_*, H^{n-k}_*, H^{n-1}_*$ are zero.Comment: 14 pages, no figure

Spacecraft charging and ion wake formation in the near-Sun environment

A three-dimensional (3-D), self-consistent code is employed to solve for the static potential structure surrounding a spacecraft in a high photoelectron environment. The numerical solutions show that, under certain conditions, a spacecraft can take on a negative potential in spite of strong photoelectron currents. The negative potential is due to an electrostatic barrier near the surface of the spacecraft that can reflect a large fraction of the photoelectron flux back to the spacecraft. This electrostatic barrier forms if (1) the photoelectron density at the surface of the spacecraft greatly exceeds the ambient plasma density, (2) the spacecraft size is significantly larger than local Debye length of the photoelectrons, and (3) the thermal electron energy is much larger than the characteristic energy of the escaping photoelectrons. All of these conditions are present near the Sun. The numerical solutions also show that the spacecraft's negative potential can be amplified by an ion wake. The negative potential of the ion wake prevents secondary electrons from escaping the part of spacecraft in contact with the wake. These findings may be important for future spacecraft missions that go nearer to the Sun, such as Solar Orbiter and Solar Probe Plus.Comment: 25 pages, 7 figures, accepted for publication in Physics of Plasma

SSADH variation in primates: Intra- and interspecific data on a gene with a potential role in human cognitive functions

In the present study we focus on the nucleotide and the inferred amino acid variation occurring in humans and other primate species for mitochondrial NAD(+)-dependent succinic semialdehyde dehydrogenase, a gene recently supposed to contribute to cognitive performance in humans. We determined 2527 bp of coding, intronic, and flanking sequences from chimpanzee, bonobo, gorilla, orangutan, gibbon, and macaque. We also resequenced the entire coding sequence on 39 independent chromosomes from Italian families. Four variable coding sites were genotyped in additional populations from Europe, Africa, and Asia. A test for constancy of the nonsynonymous vs. synonymous rates of nucleotide changes revealed that primates are characterized by largely variable d(N)/d(S) ratios. On a background of strong conservation, probably controlled by selective constraints, the lineage leading to humans showed a ratio increased to 0.42. Human polymorphic levels fall in the range reported for other genes, with a pattern of frequency and haplotype structure strongly suggestive of nonneutrality. The comparison with the primate sequences allowed inferring the ancestral state at all variable positions, suggesting that the c.538(C) allele and the associated functional variant is indeed a derived state that is proceeding to fixation. The unexpected pattern of human polymorphism compared to interspecific findings outlines the possibility of a recent positive selection on some variants relevant to new cognitive capabilities unique to humans

Visual evoked potentials in succinate semialdehyde dehydrogenase (SSADH) deficiency

In mammals, increased GABA in the central nervous system has been associated with abnormalities of visual evoked potentials (VEPs), predominantly manifested as increased latency of the major positive component P100. Accordingly, we hypothesized that patients with a defect in GABA metabolism, succinate semialdehyde dehydrogenase (SSADH) deficiency (in whom supraphysiological levels of GABA accumulate), would manifest VEP anomalies. We evaluated VEPs on two patients with confirmed SSADH deficiency. Whereas the P100 latencies and amplitudes for binocular VEP analyses were within normal ranges for both patients, the P100 latencies were markedly delayed for left eye (OS) (and right eye (OD), patient 1) and monocular OS (patient 2): 134-147 ms; normal <118 ms. We hypothesize that elevated GABA in ocular tissue of SSADH patients leads to a use-dependent downregulation of the major GABAergic receptor in eye, GABA(C), and that the VEP recordings' abnormalities, as evidenced by P100 latency and/or amplitude measurements, may be reflective of abnormalities within visual systems. This is a preliminary finding that may suggest the utility of performing VEP analysis in a larger sample of SSADH-deficient patients, and encourage a neurophysiological assessment of GABA(C) receptor function in Aldh5a1(-/-) mice to reveal new pathophysiological mechanisms of this rare disorder of GABA degradation

Late Pleistocene-Holocene palaeoenvironmental evolution of the Makgadikgadi Basin, central Kalahari, Botswana: new evidence from shallow sediments and ostracod fauna

The Makgadikgadi Basin in Botswana hosts a system of salt lakes, which developed from the Upper Pleistocene onwards due to gradual shrinking of the giant Lake Palaeo-Makgadikgadi. Stratigraphic and palaeoclimatic studies of this area are complicated by influence of several factors, such as a complex history of regional tectonic activities, as well as climatic changes coupled with dryland diagenetic processes. This lake, in the central Kalahari is the key to understand the climatic variability in the southern Africa in the Quaternary and holds important role for the evolution of numerous taxa, including our own. Here, detailed sedimentological analyses (grain size and major elements distribution) of shallow sediments from the Makgadikgadi Pans were combined with the first comprehensive study of the encountered ostracod fauna in order to establish trends in the environmental changes in the area from the Late Quaternary. Ostracod fossil assemblages from the cores of the Makgadikgadi Pans are dominated by the Limnocythere ssp., an opportunistic taxa commonly colonizing the littoral areas of shallow evaporative, ephemeral lakes, together with the subordinate occurrences of Sarcypridopsis ochracea, Sclerocypris cf. bicornis, Candonopsis spp. and Ilyocypris spp. The sediments from the pans show fluctuations in the Cl/K and Ca/Cl ratios, often in phase with the relative abundance of Limnocythere suggesting a cyclicity induced by changes of salinity and alkalinity in the water. This multi-proxy study of the cores collected from the pans suggests a Late Pleistocene shallow, playa lake environment with strongly alkaline water, interrupted by a prolonged drought with sustained aeolian conditions between ~16 and 2 ka BP. An increasing diversity of ostracod fauna in the top 20-30 cm of the cores indicates that a temporary shift toward higher humidity occurred around 2 – 1.5 ka BP and lasted through the Medieval Warm Period. This humid period was followed by an overall desiccation trend that started with the Little Ice Age and continues until the present day

Mutational spectrum of the succinate semialdehyde dehydrogenase (ALDH5A1) gene and functional analysis of 27 novel disease-causing mutations in patients with SSADH deficiency

Succinate semialdehyde dehydrogenase (SSADH; ALlDH5A1) deficiency, a rare metabolic disorder that disrupts the normal degradation of GABA, gives rise to a highly heterogeneous neurological phenotype ranging from mild to very severe. The nature of the mutation has so far been reported in patients from six families world wide and eight different mutations were described. Here we report the mutational spectrum in 48 additional unrelated families of different geographic origin. We detected 27 novel mutations at the cDNA level, of which 26 could be attributed to changes at the genomic level. Furthermore, six mutations were detected that did not strongly affect SSADH activity when expressed in HEK 293 cells and are considered nonpathogenic allelic variants. Twenty of the mutations were only found in one family. The spectrum of disease-causing mutations from all patients sequenced thus far consists of 25 point mutations, four small insertions, and five small deletions. Seven of these mutations affect splice junctions, seven are nonsense mutations, and 12 are missense mutations. Although there were no mutational hotspots or prevalent mutations responsible for a significant number of cases, 14 out of 37 (38%) of the missense alleles were present in exon 4 or 5. With one exception, the missense mutations we consider to be causative of SSADH deficiency reduced the SSADH activity to less than 5% of the normal activity in our in vitro expression system. This indicates that residual expression is not likely to be an important factor contributing to the large phenotypic differences observed among different families and even among siblings, suggesting that other modifying factors are of great importance in disease pathology. (C) 2003 Wiley,Liss, Inc

Off-line radiometric analysis of Planck/LFI data

The Planck Low Frequency Instrument (LFI) is an array of 22 pseudo-correlation radiometers on-board the Planck satellite to measure temperature and polarization anisotropies in the Cosmic Microwave Background (CMB) in three frequency bands (30, 44 and 70 GHz). To calibrate and verify the performances of the LFI, a software suite named LIFE has been developed. Its aims are to provide a common platform to use for analyzing the results of the tests performed on the single components of the instrument (RCAs, Radiometric Chain Assemblies) and on the integrated Radiometric Array Assembly (RAA). Moreover, its analysis tools are designed to be used during the flight as well to produce periodic reports on the status of the instrument. The LIFE suite has been developed using a multi-layered, cross-platform approach. It implements a number of analysis modules written in RSI IDL, each accessing the data through a portable and heavily optimized library of functions written in C and C++. One of the most important features of LIFE is its ability to run the same data analysis codes both using ground test data and real flight data as input. The LIFE software suite has been successfully used during the RCA/RAA tests and the Planck Integrated System Tests. Moreover, the software has also passed the verification for its in-flight use during the System Operations Verification Tests, held in October 2008.Comment: Planck LFI technical papers published by JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/1748-022