Nadel's Subschemes of Fano Manifolds X with a Picard Group Pic(X) Isomorphic to Z

∗The author supported by Contract NSFR MM 402/1994.

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Instantons on Calabi–Yau cones

The Hermitian Yang–Mills equations on certain vector bundles over Calabi–Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.

A novel T-DNA vector design for selection of transgenic lines with simple transgene integration and stable transgene expression

Plants transformed with Agrobacterium frequently contain T-DNA concatamers with direct-repeat (d/r) or inverted-repeat (i/r) transgene integrations, and these repetitive T-DNA insertions are often associated with transgene silencing. To facilitate the selection of transgenic lines with simple T-DNA insertions, we constructed a binary vector (pSIV) based on the principle of hairpin RNA (hpRNA)-induced gene silencing. The vector is designed so that any transformed cells that contain more than one insertion per locus should generate hpRNA against the selective marker gene, leading to its silencing. These cells should, therefore, be sensitive to the selective agent and less likely to regenerate. Results from Arabidopsis and tobacco transformation showed that pSIV gave considerably fewer transgenic lines with repetitive insertions than did a conventional T-DNA vector (pCON). Furthermore, the transgene was more stably expressed in the pSIV plants than in the pCON plants. Rescue of plant DNA flanking sequences from pSIV plants was significantly more frequent than from pCON plants, suggesting that pSIV is potentially useful for T-DNA tagging. Our results revealed a perfect correlation between the presence of tail-to-tail inverted repeats and transgene silencing, supporting the view that read-through hpRNA transcript derived from i/r T-DNA insertions is a primary inducer of transgene silencing in plants. © CSIRO 2005.

Stable feature selection with support vector machines

The support vector machine (SVM) is a popular method for classification, well known for finding the maximum-margin hyperplane. Combining SVM with l1-norm penalty further enables it to simultaneously perform feature selection and margin maximization within a single framework. However, l1-norm SVM shows instability in selecting features in presence of correlated features. We propose a new method to increase the stability of l1-norm SVM by encouraging similarities between feature weights based on feature correlations, which is captured via a feature covariance matrix. Our proposed method can capture both positive and negative correlations between features. We formulate the model as a convex optimization problem and propose a solution based on alternating minimization. Using both synthetic and real-world datasets, we show that our model achieves better stability and classification accuracy compared to several state-of-the-art regularized classification methods.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bioelectrical impedance vector analysis (BIVA) in stable preterm newborns

Objective: To observe the behavior of the plotted vectors on the RXc (R - resistance - and Xc - reactance corrected for body height/length) graph through bioelectrical impedance analysis (BIVA) and phase angle (PA) values in stable premature infants, considering the hypothesis that preterm infants present vector behavior on BIVA suggestive of less total body water and soft tissues, compared to reference data for term infants. Methods: Cross-sectional study, including preterm neonates of both genders, in-patients admitted to an intermediate care unit at a tertiary care hospital. Data on delivery, diet and bioelectrical impedance (800 mA, 50 kHz) were collected. The graphs and vector analysis were performed with the BIVA software. Results: A total of 108 preterm infants were studied, separated according to age (< 7 days and >= 7 days). Most of the premature babies were without the normal range (above the 95% tolerance intervals) existing in literature for term newborn infants and there was a tendency to dispersion of the points in the upper right quadrant, RXc plan. The PA was 4.92 degrees (+/- 2.18) for newborns < 7 days and 4.34 degrees (+/- 2.37) for newborns >= 7 days. Conclusion: Premature infants behave similarly in terms of BIVA and most of them have less absolute body water, presenting less fat free mass and fat mass in absolute values, compared to term newborn infants.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

Stable and efficient gene transfer into the retina using an HIV-based lentiviral vector

The development of methods for efficient gene transfer to terminally differentiated retinal cells is important to study the function of the retina as well as for gene therapy of retinal diseases. We have developed a lentiviral vector system based on the HIV that can transduce terminally differentiated neurons of the brain in vivo. In this study, we have evaluated the ability of HIV vectors to transfer genes into retinal cells. An HIV vector containing a gene encoding the green fluorescent protein (GFP) was injected into the subretinal space of rat eyes. The GFP gene under the control of the cytomegalovirus promoter was efficiently expressed in both photoreceptor cells and retinal pigment epithelium. However, the use of the rhodopsin promoter resulted in expression predominantly in photoreceptor cells. Most successfully transduced eyes showed that photoreceptor cells in >80% of the area of whole retina expressed the GFP. The GFP expression persisted for at least 12 weeks with no apparent decrease. The efficient gene transfer into photoreceptor cells by HIV vectors will be useful for gene therapy of retinal diseases such as retinitis pigmentosa.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

High level stable expression of rat brain type IIA sodium channel ?-subunit in CHO cells

The neuronal sodium channels are responsible for the rising phase of action potential and are composed of three subunits, of which the alpha-subunit has been shown to be adequate for most of its functional properties. We have stably expressed the rat brain type IIA sodium channel alpha-subunit in CHO cell tine using a CMV promoter-based vector. The expression was confirmed by detecting a 6.5 kb RNA corresponding to sodium channel alpha-subunit using Northern hybridization. The cells stably expressing the alpha-subunit, yield isolated sodium currents of amplitudes greater than 4nA when studied in whole-cell configuration of the patch-clamp technique. The sodium currents are characterized by activation and inactivation properties similar to neuronal sodium channels, and are blocked by the voltage gated sodium channel blocker tetrodotoxin (TTX).

Highly fluorescent GFPm2+-based genome integration-proficient promoter probe vector to study Mycobacterium tuberculosis promoters in infected macrophages

Study of activity of cloned promoters in slow-growing Mycobacterium tuberculosis during long-term growth conditions in vitro or inside macrophages, requires a genome-integration proficient promoter probe vector, which can be stably maintained even without antibiotics, carrying a substrate-independent, easily scorable and highly sensitive reporter gene. In order to meet this requirement, we constructed pAKMN2, which contains mycobacterial codon-optimized gfpm2+ gene, coding for GFPm2+ of highest fluorescence reported till date, mycobacteriophage L5 attP-int sequence for genome integration, and a multiple cloning site. pAKMN2 showed stable integration and expression of GFPm2+ from M. tuberculosis and M. smegmatis genome. Expression of GFPm2+, driven by the cloned minimal promoters of M. tuberculosis cell division gene, ftsZ (MtftsZ), could be detected in the M. tuberculosis/pAKMN2-promoter integrants, growing at exponential phase in defined medium in vitro and inside macrophages. Stable expression from genome-integrated format even without antibiotic, and high sensitivity of detection by flow cytometry and fluorescence imaging, in spite of single copy integration, make pAKMN2 useful for the study of cloned promoters of any mycobacterial species under long-term in vitro growth or stress conditions, or inside macrophages.

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Construction of shuttle, expression vector of human tumor necrosis factor alpha (hTNF-alpha) gene and its expression in a cyanobacterium, Anabaena sp. PCC 7120

The construction of the shuttle, expression vector of human tumor necrosis factor alpha (hTNF-alpha) gene and its expression in a cyanobacterium Anabaena sp. PCC 7120 was reported. The 700-bp hTNF cDNA fragments have been recovered from plasmid pRL-rhTNF, then inserted downstream of the promoter PpsbA in the plasmid pRL439. The resultant intermediary plasmid pRL-TC has further been combined with the shuttle vector pDC-8 to get the shuttle, expression vector pDC-TNF. The expression of the rhTNF gene in Escherichia coil has been analyzed by SDS-PAGE and thin-layer scanning, and the results show that the expressed TNF protein with these two vectors is 16.9 percent (pRL-TC) and 15.0 percent (pDC-TNF) of the total proteins in the cells, respectively, while the expression level of TNF gene in plasmid pRL-rhTNF is only 11.8 percent. Combined with the participation of the conjugal and helper plasmids, pDC-TNF has been introduced into Anabaena sg PCC 7120 by triparental conjugative transfer, and the stable transgenic strains have been obtained. The existence of the introduced plasmid pDC-TNF in recombinant cyanobacterial cells has been demonstrated by the results of the agarose electrophoresis with the extracted plasmid samples and Southern blotting with alpha-(32)p labeled hTNF cDNA probes, while the expression of the hTNF gene in Anabaena sp. PCC 7120 has been confirmed by the results of Western blotting with extracted protein samples and human TNF-alpha monoclonal antibodies. The cytotoxicity assays using the mouse cancer cell line L929 proved the cytotoxicity of the TNF in the crude extracts from the transgenic cyanobacterium Anabaena sp. PCC 7120.

Modeling trophic positions of the alpine meadow ecosystem combining stable carbon and nitrogen isotope ratios

Stable carbon and nitrogen isotope ratios of single tissues or whole bodies were analyzed to establish trophic positions of main consumers living at the alpine meadow ecosystem in the Tibetan Plateau. The results demonstrated that delta C-13 and delta N-15 values of vertebrates showed great variations and ranged from -26.83 to -22.51 parts per thousand and from 2.33 to 8.44 parts per thousand, respectively. Plateau pika, root vole, plateau hare, infants of rodents and hatchlings of passerine bird species had the lowest delta C-13 and delta N-15 values. delta C-13 and delta N-15 values of omnivorous and insectivorous birds and amphibians showed intermediate. Carnivorous species, steppe polecat and Upland buzzard, and omnivorous Robin accentor and White wagtail possessed extremely higher VC and delta N-15 values. Omnivorous birds captured in earlier year had significantly less negative delta C-13 and greater delta N-15 values than those captured later. Based on steady angular enrichment between trophic levels, an "alpha and vector model" combing delta C-13 and delta N-15 values was introduced to reveal trophic positions, the results indicated that Tibetan sheep, Tibetan yak, plateau pika, root vole, plateau hare, infants of small rodents showed the lowest trophic positions (TP 1.81-2.38). While omnivorous and insectivorous birds, their hatchlings and amphibians showed intermediate trophic positions (TP 2.06-2.89), carnivorous species steppe polecat and Upland buzzard, migrant birds possessed extremely higher trophic positions (TP 2.89-3.05). The isotopic investigation of organisms and the introduced "alpha and vector model" successfully demonstrated the same trophic positions and diet prediction of consumers as nitrogen enrichment model at the alpine meadow ecosystem. Besides of this information, the "alpha and vector model" can also be incorporated into multiple isotope signatures to infer trophic relationships. This angular enrichment model has the potential to address basic ecological questions, such as trophic structure, trophic dynamics, and energy flow in other terrestrial ecosystems of properly handled. (C) 2005 Elsevier B.V. All rights reserved.