Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Dually discrete spaces

A neighbourhood assignment in a space X is a family O = {O-x: x is an element of X} of open subsets of X such that X is an element of O-x for any x is an element of X. A set Y subset of X is a kernel of O if O(Y) = U{O-x: x is an element of Y} = X. We obtain some new results concerning dually discrete spaces, being those spaces for which every neighbourhood assignment has a discrete kernel. This is a strictly larger class than the class of D-spaces of [E.K. van Douwen, W.F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (2) (1979) 371-377]. (c) 2008 Elsevier B.V. All rights reserved.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

Countability and star covering properties

Whenever P is a topological property, we say that a topological space is star P if whenever U is an open cover of X, there is a subspace A subset of X with property P such that X = St(A, U). We study the relationships of star P properties for P is an element of {Lindelof, sigma-compact, countable} with other Lindelof type properties. (C) 2010 Elsevier B.V. All rights reserved.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Identification of protein-coding and intronic noncoding RNAs down-regulated in clear cell renal carcinoma

The clear cell subtype of renal cell carcinoma (RCC) is the most lethal and prevalent cancer of the urinary system. To investigate the molecular changes associated with malignant transformation in clear cell RCC, the gene expression profiles of matched samples of tumor and adjacent non-neoplastic tissue were obtained from six patients. A custom-built cDNA microarray platform was used, comprising 2292 probes that map to exons of genes and 822 probes for noncoding RNAs mapping to intronic regions. Intronic transcription was detected in all normal and neoplastic renal tissues. A subset of 55 transcripts was significantly down-regulated in clear cell RCC relative to the matched nontumor tissue as determined by a combination of two statistical tests and leave-one-out patient cross-validation. Among the down-regulated transcripts, 49 mapped to untranslated or coding exons and 6 were intronic relative to known exons of protein-coding genes. Lower levels of expression of SIN3B, TRIP3, SYNJ2BP and NDE1 (P<0.02), and of intronic transcripts derived from SND1 and ACTN4 loci (P<0.05), were confirmed in clear cell RCC by Real-time RT-PCR. A subset of 25 transcripts was deregulated in additional six nonclear cell RCC samples, pointing to common transcriptional alterations in RCC irrespective of the histological subtype or differentiation state of the tumor. Our results indicate a novel set of tumor suppressor gene candidates, including noncoding intronic RNAs, which may play a significant role in malignant transformations of normal renal cells. (C) 2008 Wiley-Liss, Inc.

The iron stimulon of Xylella fastidiosa includes genes for type IV pilus and colicin V-like bacteriocins

Xylella fastidiosa is the etiologic agent of a wide range of plant diseases, including citrus variegated chlorosis (CVC), a major threat to citrus industry. The genomes of several strains of this phytopathogen were completely sequenced, enabling large-scale functional studies. DNA microarrays representing 2,608 (91.6%) coding sequences (CDS) of X. fastidiosa CVC strain 9a5c were used to investigate transcript levels during growth with different iron availabilities. When treated with the iron chelator 2,2`-dipyridyl, 193 CDS were considered up-regulated and 216 were considered down-regulated. Upon incubation with 100 mu M ferric pyrophosphate, 218 and 256 CDS were considered up- and down-regulated, respectively. Differential expression for a subset of 44 CDS was further evaluated by reverse transcription-quantitative PCR. Several CDS involved with regulatory functions, pathogenicity, and cell structure were modulated under both conditions assayed, suggesting that major changes in cell architecture and metabolism occur when X. fastidiosa cells are exposed to extreme variations in iron concentration. Interestingly, the modulated CDS include those related to colicin V-like bacteriocin synthesis and secretion and to functions of pili/fimbriae. We also investigated the contribution of the ferric uptake regulator Fur to the iron stimulon of X. fastidiosa. The promoter regions of the strain 9a5c genome were screened for putative Fur boxes, and candidates were analyzed by electrophoretic mobility shift assays. Taken together, our data support the hypothesis that Fur is not solely responsible for the modulation of the iron stimulon of X fastidiosa, and they present novel evidence for iron regulation of pathogenicity determinants.

A two-component system, an anti-sigma factor and two paralogous ECF sigma factors are involved in the control of general stress response in Caulobacter crescentus

The extracytoplasmic function sigma factor sigma(T) is the master regulator of general stress response in Caulobacter crescentus and controls the expression of its paralogue sigma(U). In this work we showed that PhyR and NepR act, respectively, as positive and negative regulators of sigma(T) expression and function. Biochemical data also demonstrated that NepR directly binds sigma(T) and the phosphorylated form of PhyR. We also described the essential role of the histidine kinase gene CC3474, here denominated phyK, for expression of sigma(T)-dependent genes and for resistance to stress conditions. Additionally, in vivo evidence of PhyK-dependent phosphorylation of PhyR is presented. This study also identified a conserved cysteine residue (C95) located in the periplasmic portion of PhyK that is crucial for the function of the protein. Furthermore, we showed that PhyK, PhyR and sigma(T) regulate the same set of genes and that sigma(T) apparently directly controls most of its regulon. In contrast, sigma(U) seems to have a very modest contribution to the expression of a subset of sigma(T)-dependent genes. In conclusion, this report describes the molecular mechanism involved in the control of general stress response in C. crescentus.

Cell-cell signal-dependent dynamic interactions between HD-GYP and GGDEF domain proteins mediate virulence in Xanthomonas campestris

RpfG is a paradigm for a class of widespread bacterial two-component regulators with a CheY-like receiver domain attached to a histidine-aspartic acid-glycine-tyrosine-proline (HD-GYP) cyclic di-GMP phosphodiesterase domain. In the plant pathogen Xanthomonas campestris pv. campestris (Xcc), a two-component system comprising RpfG and the complex sensor kinase RpfC is implicated in sensing and responding to the diffusible signaling factor (DSF), which is essential for cell-cell signaling. RpfF is involved in synthesizing DSF, and mutations of rpfF, rpfG, or rpfC lead to a coordinate reduction in the synthesis of virulence factors such as extracellular enzymes, biofilm structure, and motility. Using yeast two-hybrid analysis and fluorescence resonance energy transfer experiments in Xcc, we show that the physical interaction of RpfG with two proteins with diguanylate cyclase (GGDEF) domains controls a subset of RpfG-regulated virulence functions. RpfG interactions were abolished by alanine substitutions of the three residues of the conserved GYP motif in the HD-GYP domain. Changing the GYP motif or deletion of the two GGDEF-domain proteins reduced Xcc motility but not the synthesis of extracellular enzymes or biofilm formation. RpfG-GGDEF interactions are dynamic and depend on DSF signaling, being reduced in the rpfF mutant but restored by DSF addition. The results are consistent with a model in which DSF signal transduction controlling motility depends on a highly regulated, dynamic interaction of proteins that influence the localized expression of cyclic di-GMP.

Three-Dimensional Quantitative Structure-Activity Relationship Study of Antitumor 2-Formylpyridine Thiosemicarbazones Derivatives as Inhibitors of Ribonucleotide Reductase

In order to extend previous SAR and QSAR studies, 3D-QSAR analysis has been performed using CoMFA and CoMSIA approaches applied to a set of 39 alpha-(N)-heterocyclic carboxaldehydes thiosemicarbazones with their inhibitory activity values (IC(50)) evaluated against ribonucleotide reductase (RNR) of H.Ep.-2 cells (human epidermoid carcinoma), taken from selected literature. Both rigid and field alignment methods, taking the unsubstituted 2-formylpyridine thiosemicarbazone in its syn conformation as template, have been used to generate multiple predictive CoMFA and CoMSIA models derived from training sets and validated with the corresponding test sets. Acceptable predictive correlation coefficients (Q(cv)(2) from 0.360 to 0.609 for CoMFA and Q(cv)(2) from 0.394 to 0.580 for CoMSIA models) with high fitted correlation coefficients (r` from 0.881 to 0.981 for CoMFA and r(2) from 0.938 to 0.993 for CoMSIA models) and low standard errors (s from 0.135 to 0.383 for CoMFA and s from 0.098 to 0.240 for CoMSIA models) were obtained. More precise CoMFA and CoMSIA models have been derived considering the subset of thiosemicarbazones (TSC) substituted only at 5-position of the pyridine ring (n=22). Reasonable predictive correlation coefficients (Q(cv)(2) from 0.486 to 0.683 for CoMFA and Q(cv)(2) from 0.565 to 0.791 for CoMSIA models) with high fitted correlation coefficients (r(2) from 0.896 to 0.997 for CoMFA and r(2) from 0.991 to 0.998 for CoMSIA models) and very low standard errors (s from 0.040 to 0.179 for CoMFA and s from 0.029 to 0.068 for CoMSIA models) were obtained. The stability of each CoMFA and CoMSIA models was further assessed by performing bootstrapping analysis. For the two sets the generated CoMSIA models showed, in general, better statistics than the corresponding CoMFA models. The analysis of CoMFA and CoMSIA contour maps suggest that a hydrogen bond acceptor near the nitrogen of the pyridine ring can enhance inhibitory activity values. This observation agrees with literature data, which suggests that the nitrogen pyridine lone pairs can complex with the iron ion leading to species that inhibits RNR. The derived CoMFA and CoMSIA models contribute to understand the structural features of this class of TSC as antitumor agents in terms of steric, electrostatic, hydrophobic and hydrogen bond donor and hydrogen bond acceptor fields as well as to the rational design of this key enzyme inhibitors.