A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Ageing in the critical contact process: a Monte Carlo study

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.Comment: 18 pages, 7 figures, Latex2e with IOP macros; final for

Stein--Sahi complementary series and their degenerations

The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n,n).Comment: 40pp, 7fig, revised versio

The deformation quantizations of the hyperbolic plane

We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative harmonic analytical techniques on symplectic symmetric spaces. The present work presents a unified method producing every quantization of the hyperbolic plane, and provides, in the 2-dimensional context, an exact solution to Weinstein's WKB quantization program within geometric terms. The construction reveals the existence of a metric of Lorentz signature canonically attached (or `dual') to the geometry of the hyperbolic plane through the quantization process.Comment: 26 pages, 5 figure

A method for purification, identification and validation of DNMT1 mRNA binding proteins

DNA methyltransferase 1 (DNMT1) is the enzyme responsible for the maintenance of DNA methylation patterns during cell division. DNMT1 expression is tightly regulated within the cell cycle. Our previous study showed that the binding of a protein with an apparent size of ~40 kDa on DNMT1 3’-UTR triggered the destabilization of DNMT1 mRNA transcript during Go/G1 phase. Using RNA affinity capture with the 3’-UTR of DNMT1 mRNA and matrix-assisted laser desorption-time of flight tandem mass spectrometry (MALDI-TOF-MS-MS) analysis, we isolated and identified AUF 1 (AU-rich element ARE:poly-(U)-binding/degradation factor) as the binding protein. We then validated the role of this protein in the destabilization of DNMT1 mRNA. In this report, we detail the different approaches used for the isolation, the identification of a RNA binding protein and the validation of its role

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Anthropogenic Space Weather

Anthropogenic effects on the space environment started in the late 19th century and reached their peak in the 1960s when high-altitude nuclear explosions were carried out by the USA and the Soviet Union. These explosions created artificial radiation belts near Earth that resulted in major damages to several satellites. Another, unexpected impact of the high-altitude nuclear tests was the electromagnetic pulse (EMP) that can have devastating effects over a large geographic area (as large as the continental United States). Other anthropogenic impacts on the space environment include chemical release ex- periments, high-frequency wave heating of the ionosphere and the interaction of VLF waves with the radiation belts. This paper reviews the fundamental physical process behind these phenomena and discusses the observations of their impacts.Comment: 71 pages, 35 figure

Antiproliferative Effects of DNA Methyltransferase 3B Depletion Are Not Associated with DNA Demethylation

Silencing of genes by hypermethylation contributes to cancer progression and has been shown to occur with increased frequency at specific genomic loci. However, the precise mechanisms underlying the establishment and maintenance of aberrant methylation marks are still elusive. The de novo DNA methyltransferase 3B (DNMT3B) has been suggested to play an important role in the generation of cancer-specific methylation patterns. Previous studies have shown that a reduction of DNMT3B protein levels induces antiproliferative effects in cancer cells that were attributed to the demethylation and reactivation of tumor suppressor genes. However, methylation changes have not been analyzed in detail yet. Using RNA interference we reduced DNMT3B protein levels in colon cancer cell lines. Our results confirm that depletion of DNMT3B specifically reduced the proliferation rate of DNMT3B-overexpressing colon cancer cell lines. However, genome-scale DNA methylation profiling failed to reveal methylation changes at putative DNMT3B target genes, even in the complete absence of DNMT3B. These results show that DNMT3B is dispensable for the maintenance of aberrant DNA methylation patterns in human colon cancer cells and they have important implications for the development of targeted DNA methyltransferase inhibitors as epigenetic cancer drugs

The N-Terminal, Polybasic Region Is Critical for Prion Protein Neuroprotective Activity

Several lines of evidence suggest that the normal form of the prion protein, PrPC, exerts a neuroprotective activity against cellular stress or toxicity. One of the clearest examples of such activity is the ability of wild-type PrPC to suppress the spontaneous neurodegenerative phenotype of transgenic mice expressing a deleted form of PrP (Δ32–134, called F35). To define domains of PrP involved in its neuroprotective activity, we have analyzed the ability of several deletion mutants of PrP (Δ23–31, Δ23–111, and Δ23–134) to rescue the phenotype of Tg(F35) mice. Surprisingly, all of these mutants displayed greatly diminished rescue activity, although Δ23–31 PrP partially suppressed neuronal loss when expressed at very high levels. Our results pinpoint the N-terminal, polybasic domain as a critical determinant of PrPC neuroprotective activity, and suggest that identification of molecules interacting with this region will provide important clues regarding the normal function of the protein. Small molecule ligands targeting this region may also represent useful therapeutic agents for treatment of prion diseases