Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Monoclonal antibody against carcinoembryonic antigen (CEA) identifies two new forms of crossreacting antigens of molecular weight 90,000 and 160,000 in normal granulocytes.

Two new forms of non-specific crossreacting antigens (NCAs) were identified in the Nonidet P40 (NP-40) extracts of normal granulocytes by precipitation with the monoclonal antibody (MAb) 192 directed against carcinoembryonic antigen (CEA) and already known to crossreact with the perchloric acid soluble NCA-55. The NP-40 soluble NCAs recognized by MAb 192 have apparent mol. wts of 90,000 and 160,000 in sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Both NCAs appear to consist of a single monomeric polypeptide chain, since they have the same electrophoretic mobility in SDS-PAGE under reduced and non-reduced conditions. When granulocytes were extracted with perchloric acid instead of NP-40, only the 55,000 mol. wt antigen, corresponding to the previously described NCA-55, was precipitated by MAb 192. Furthermore, it was shown that NCA-55 is not a degradation product of NCA-90 or NCA-160 due to the perchloric acid treatment because exposure to perchloric acid of NCA preparations purified from NP-40 extracts did not change their apparent mol. wts in SDS-PAGE. It was also shown that NCA-160 is not a granulocytic form of CEA because it was not precipitated by the MAb 35 reacting exclusively with CEA. Immunocytochemical studies of granulocytes and macrophages showed that MAb 192 stained both types of cells whereas MAb 47 stained only the granulocytes and MAb 35 none of these cells. In granulocytes both MAbs reacted with antigens associated with granules and also present at the periphery of the nucleus as well as in the Golgi apparatus. The NCA-90 identified by MAb 192 was found by sequential immunodepletion to be antigenically distinct from the NCA-95 precipitated by MAb 47. The epitope recognized by MAb 192 on CEA and NCA molecules appears to be on the peptidic moiety because the antigens deglycosylated by the enzyme Endo F were still precipitated by this MAb. Taken together, the results indicate that MAb 192 identifies two novel forms of NCA (NCA-90 and NCA-160) in NP-40 extracts of granulocytes, which are distinct from CEA and the previously described NCA-55 and NCA-95 identified by MAbs 192 and 47, respectively, in perchloric acid extracts of granulocytes.

‘A tiger that wants to become a lion’: Violent forms of agency among youth in Cape Verde

Cape Verdean prison population raised 100% in the last ten years: in this paper I offer an interpretation of this disturbing figure, addressing the issue of young offenders and children in conflict with the law, the perception of youth crime in Cape Verde, and how the government has recently dealt with these issues. Cape Verde currently deploys a repressive approach to the issue of youth crime: in this draconian context, I will follow the application of policies and laws targeting juvenile delinquents as well as the public and media discourse on the issue. At the same time, through interviews with younger inmates in prisons and institutions, I will relocate young offenders’ behavior and activity within their wider social context, providing urgently needed data on the cultural and social dimensions of juvenile offending and violence.

ParA2, a Vibrio cholerae chromosome partitioning protein, forms left-handed helical filaments on DNA.

Most bacterial chromosomes contain homologs of plasmid partitioning (par) loci. These loci encode ATPases called ParA that are thought to contribute to the mechanical force required for chromosome and plasmid segregation. In Vibrio cholerae, the chromosome II (chrII) par locus is essential for chrII segregation. Here, we found that purified ParA2 had ATPase activities comparable to other ParA homologs, but, unlike many other ParA homologs, did not form high molecular weight complexes in the presence of ATP alone. Instead, formation of high molecular weight ParA2 polymers required DNA. Electron microscopy and three-dimensional reconstruction revealed that ParA2 formed bipolar helical filaments on double-stranded DNA in a sequence-independent manner. These filaments had a distinct change in pitch when ParA2 was polymerized in the presence of ATP versus in the absence of a nucleotide cofactor. Fitting a crystal structure of a ParA protein into our filament reconstruction showed how a dimer of ParA2 binds the DNA. The filaments formed with ATP are left-handed, but surprisingly these filaments exert no topological changes on the right-handed B-DNA to which they are bound. The stoichiometry of binding is one dimer for every eight base pairs, and this determines the geometry of the ParA2 filaments with 4.4 dimers per 120 A pitch left-handed turn. Our findings will be critical for understanding how ParA proteins function in plasmid and chromosome segregation.

Two functional forms of the Xenopus laevis estrogen receptor translated from a single mRNA species.

Steroid receptors are nuclear proteins that regulate gene transcription in a ligand-dependent manner. Over-expression of the Xenopus estrogen receptor in a vaccinia virus-derived expression system revealed that the receptor localized exclusively in the nucleus of the infected cells, irrespective of the presence or absence of the ligand. Furthermore, two forms of the receptor were produced, a full-length and a N-terminal truncated version, which are translated from a single mRNA species by the use of two AUG within the same reading frame. These 66- and 61-kDa receptors were also observed after in vitro translation of the mRNA as well as in primary Xenopus hepatocytes. Both forms are potent estrogen-dependent transcriptional activators in transient transfection experiments, as well as in in vitro transcription assays.

Congruences between modular forms and lowering the level mod l^n

In this article we study the behavior of inertia groups for modularGalois mod l^n representations and in some cases we give a generalizationof Ribet s lowering the level result (cf. [Rib90]).

Developmental time of immature forms of Sabethes aurescens Lutz (Diptera, Culicidae) from artificially perforated bamboo in the rain forest of southern Brazil

The development time of the immature forms of Sabethes aurescens Lutz, 1905, from perforated bamboo in the southern Brazil rain forest was studied under laboratory conditions. Mean development periods were 5±2.23, 10±5.20, 14±8.26, 36±13.90 and 9±2.43 days, respectively, for the four larval instars and pupae. The 4th instar of females was longer than that of males. Implications of the long development time of the immature forms of Sa. aurescens are discussed.

Amyloid and non-amyloid forms of 5q31-linked corneal dystrophy resulting from kerato-epithelin mutations at Arg-124 are associated with abnormal turnover of the protein.

Mutations in kerato-epithelin are responsible for a group of hereditary cornea-specific deposition diseases, 5q31-linked corneal dystrophies. These conditions are characterized by progressive accumulation of protein deposits of different ultrastructure. Herein, we studied the corneas with mutations at kerato-epithelin residue Arg-124 resulting in amyloid (R124C), non-amyloid (R124L), and a mixed pattern of deposition (R124H). We found that aggregated kerato-epithelin comprised all types of pathological deposits. Each mutation was associated with characteristic changes of protein turnover in corneal tissue. Amyloidogenesis in R124C corneas was accompanied by the accumulation of N-terminal kerato-epithelin fragments, whereby species of 44 kDa were the major constituents of amyloid fibrils. R124H corneas with prevailing non-amyloid inclusions showed accumulation of a new 66-kDa species altogether with the full-size 68-kDa form. Finally, in R124L cornea with non amyloid deposits, we found only the accumulation of the 68-kDa form. Two-dimensional gels revealed mutation-specific changes in the processing of the full-size protein in all affected corneas. It appears that substitutions at the same residue (Arg-124) result in cornea-specific deposition of kerato-epithelin via distinct aggregation pathways each involving altered turnover of the protein in corneal tissue.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

The meiosis-specific recombinase hDmc1 forms ring structures and interacts with hRad51.

Eukaryotic cells encode two homologs of Escherichia coli RecA protein, Rad51 and Dmc1, which are required for meiotic recombination. Rad51, like E.coli RecA, forms helical nucleoprotein filaments that promote joint molecule and heteroduplex DNA formation. Electron microscopy reveals that the human meiosis-specific recombinase Dmc1 forms ring structures that bind single-stranded (ss) and double-stranded (ds) DNA. The protein binds preferentially to ssDNA tails and gaps in duplex DNA. hDmc1-ssDNA complexes exhibit an irregular, often compacted structure, and promote strand-transfer reactions with homologous duplex DNA. hDmc1 binds duplex DNA with reduced affinity to form nucleoprotein complexes. In contrast to helical RecA/Rad51 filaments, however, Dmc1 filaments are composed of a linear array of stacked protein rings. Consistent with the requirement for two recombinases in meiotic recombination, hDmc1 interacts directly with hRad51.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.