Mehler hemigroups and embedding of discrete skew convolution semigroups on simply connected nilpotent Lie groups

It is shown how discrete skew convolution semigroups of probability measures on a simply connected nilpotent Lie group can be embedded into Lipschitz continuous semistable hemigroups by means of their generating functionals. These hemigroups are the distributions of increments of additive semi-selfsimilar processes. Considering these on an enlarged space-time group, we obtain Mehler hemigroups corresponding to periodically stationary processes of Ornstein-Uhlenbeck type, driven by certain additive processes with periodically stationary increments. The background driving processes are further represented by generalized Lie-Trotter formulas for convolutions, corresponding to a random integral approach known for finite-dimensional vector spaces

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables, respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981).Comment: revised version, to appear in: Stoch. Process. App

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05We consider subcritical Bellman-Harris branching processes with two types of immigration - one appears whenever the process hits zero state and an other one is in accordance of an independent renewal process. The law of large numbers (LLN) for the total progeny of these processes and Anscombe's type central limit theorem (CLT) for the total number of particles in the cycles completely finished by the moment t are obtained.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001

Structural elements defining elongation factor Tu mediated suppression of codon ambiguity

In most prokaryotes Asn-tRNAAsn and Gln-tRNAGln are formed by amidation of aspartate and glutamate mischarged onto tRNAAsn and tRNAGln, respectively. Coexistence in the organism of mischarged Asp-tRNAAsn and Glu-tRNAGln and the homologous Asn-tRNAAsn and Gln-tRNAGln does not, however, lead to erroneous incorporation of Asp and Glu into proteins, since EF-Tu discriminates the misacylated tRNAs from the correctly charged ones. This property contrasts with the canonical function of EF-Tu, which is to non-specifically bind the homologous aa-tRNAs, as well as heterologous species formed in vitro by aminoacylation of non-cognate tRNAs. In Thermus thermophilus that forms the Asp-tRNAAsn intermediate by the indirect pathway of tRNA asparaginylation, EF-Tu must discriminate the mischarged aminoacyl-tRNAs (aa-tRNA). We show that two base pairs in the tRNA T-arm and a single residue in the amino acid binding pocket of EF-Tu promote discrimination of Asp-tRNAAsn from Asn-tRNAAsn and Asp-tRNAAsp by the protein. Our analysis suggests that these structural elements might also contribute to rejection of other mischarged aa-tRNAs formed in vivo that are not involved in peptide elongation. Additionally, these structural features might be involved in maintaining a delicate balance of weak and strong binding affinities between EF-Tu and the amino acid and tRNA moieties of other elongator aa-tRNAs

Space-time duality for fractional diffusion

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives. They govern scaling limits of random walk models, with power law jumps leading to fractional derivatives in space, and power law waiting times between the jumps leading to fractional derivatives in time. The limit process is a stable L\'evy motion that models the jumps, subordinated to an inverse stable process that models the waiting times. Using duality, we relate the density of a spectrally negative stable process with index $1<\alpha<2$ to the density of the hitting time of a stable subordinator with index $1/\alpha$, and thereby unify some recent results in the literature. These results also provide a concrete interpretation of Zolotarev duality in terms of the fractional diffusion model.Comment: 16 page

A single tRNA base pair mediates bacterial tRNA-dependent biosynthesis of asparagine

In many prokaryotes and in organelles asparagine and glutamine are formed by a tRNA-dependent amidotransferase (AdT) that catalyzes amidation of aspartate and glutamate, respectively, mischarged on tRNA(Asn) and tRNA(Gln). These pathways supply the deficiency of the organism in asparaginyl- and glutaminyl-tRNA synthtetases and provide the translational machinery with Asn-tRNA(Asn) and Gln-tRNA(Gln). So far, nothing is known about the structural elements that confer to tRNA the role of a specific cofactor in the formation of the cognate amino acid. We show herein, using aspartylated tRNA(Asn) and tRNA(Asp) variants, that amidation of Asp acylating tRNA(Asn) is promoted by the base pair U(1)–A(72) whereas the G(1)–C(72) pair and presence of the supernumerary nucleotide U(20A) in the D-loop of tRNA(Asp) prevent amidation. We predict, based on comparison of tRNA(Gln) and tRNA(Glu) sequence alignments from bacteria using the AdT-dependent pathway to form Gln-tRNA(Gln), that the same combination of nucleotides also rules specific tRNA-dependent formation of Gln. In contrast, we show that the tRNA-dependent conversion of Asp into Asn by archaeal AdT is mainly mediated by nucleotides G(46) and U(47) of the variable region. In the light of these results we propose that bacterial and archaeal AdTs use kingdom-specific signals to catalyze the tRNA-dependent formations of Asn and Gln

Coupled continuous time random walks in finance

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that generalize the familiar stable models. In this paper, we will review the fundamental theory and present two applications with tick-by-tick stock and futures data.Comment: 7 pages, 2 figures. Paper presented at the Econophysics Colloquium, Canberra, Australia, November 200

Optical Pulse-Phased Photopolarimetry of PSR B0656+14

We have observed the optical pulse profile of PSR B0656+14 in 10 phase bins at a high signal-to-noise ratio, and have measured the linear polarization profile over 30% of the pulsar period with some significance. The pulse profile is double-peaked, with a bridge of emission between the two peaks, similar to gamma-ray profiles observed in other pulsars. There is no detectable unpulsed flux, to a 1-sigma limit of 16% of the pulse-averaged flux. The emission in the bridge is highly (~ 100%) polarized, with a position angle sweep in excellent agreement with the prediction of the Rotating Vector Model as determined from radio polarization observations. We are able to account for the gross features of the optical light curve (i.e., the phase separation of the peaks) using both polar cap and outer gap models. Using the polar cap model, we are also able to estimate the height of the optical emission regions.Comment: 27 pages, 11 figures, accepted by ApJ (scheduled v597 n2, November 10, 2003

Deinococcus glutaminyl-tRNA synthetase is a chimer between proteins from an ancient and the modern pathways of aminoacyl-tRNA formation

Glutaminyl-tRNA synthetase from Deinococcus radiodurans possesses a C-terminal extension of 215 residues appending the anticodon-binding domain. This domain constitutes a paralog of the Yqey protein present in various organisms and part of it is present in the C-terminal end of the GatB subunit of GatCAB, a partner of the indirect pathway of Gln-tRNA(Gln) formation. To analyze the peculiarities of the structure–function relationship of this GlnRS related to the Yqey domain, a structure of the protein was solved from crystals diffracting at 2.3 Å and a docking model of the synthetase complexed to tRNA(Gln) constructed. The comparison of the modeled complex with the structure of the E. coli complex reveals that all residues of E. coli GlnRS contacting tRNA(Gln) are conserved in D. radiodurans GlnRS, leaving the functional role of the Yqey domain puzzling. Kinetic investigations and tRNA-binding experiments of full length and Yqey-truncated GlnRSs reveal that the Yqey domain is involved in tRNA(Gln) recognition. They demonstrate that Yqey plays the role of an affinity-enhancer of GlnRS for tRNA(Gln) acting only in cis. However, the presence of Yqey in free state in organisms lacking GlnRS, suggests that this domain may exert additional cellular functions

The asparagine-transamidosome from Helicobacter pylori: a dual-kinetic mode in non-discriminating aspartyl-tRNA synthetase safeguards the genetic code

Helicobacter pylori catalyzes Asn-tRNAAsn formation by use of the indirect pathway that involves charging of Asp onto tRNAAsn by a non-discriminating aspartyl-tRNA synthetase (ND-AspRS), followed by conversion of the mischarged Asp into Asn by the GatCAB amidotransferase. We show that the partners of asparaginylation assemble into a dynamic Asn-transamidosome, which uses a different strategy than the Gln-transamidosome to prevent the release of the mischarged aminoacyl-tRNA intermediate. The complex is described by gel-filtration, dynamic light scattering and kinetic measurements. Two strategies for asparaginylation are shown: (i) tRNAAsn binds GatCAB first, allowing aminoacylation and immediate transamidation once ND-AspRS joins the complex; (ii) tRNAAsn is bound by ND-AspRS which releases the Asp-tRNAAsn product much slower than the cognate Asp-tRNAAsp; this kinetic peculiarity allows GatCAB to bind and transamidate Asp-tRNAAsn before its release by the ND-AspRS. These results are discussed in the context of the interrelation between the Asn and Gln-transamidosomes which use the same GatCAB in H. pylori, and shed light on a kinetic mechanism that ensures faithful codon reassignment for Asn