A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

Characterization of a Full-Length TTP Family Member Association with RNA Sequence Elements

Post-transcriptional regulation of cytoplasmic mRNAs is an efficient mechanism of regulating the amounts of active protein within a eukaryotic cell. RNA sequence elements located in the untranslated regions of mRNAs can influence transcript degradation or translation through associations with RNA-binding proteins. Tristetraprolin (TTP) is the best known member of a family of CCCH zinc finger proteins that targets adenosine-uridine rich element (ARE) binding sites in the 3’ untranslated regions (UTRs) of mRNAs, promoting transcript deadenylation through the recruitment of deadenylases. More specifically, TTP has been shown to bind AREs located in the 3’-UTRs of transcripts with known roles in the inflammatory response. The mRNA-binding region of the protein is the highly conserved CCCH tandem zinc finger (TZF) domain. The synthetic TTP TZF domain has been shown to bind with high affinity to the 13-mer sequence of UUUUAUUUAUUUU. However, the binding affinities of full-length TTP family members to the same sequence and its variants are unknown. Furthermore, the distance needed between two overlapping or neighboring UUAUUUAUU 9-mers for tandem binding events of a full-length TTP family member to a target transcript has not been explored. To address these questions, we recombinantly expressed and purified the full-length C. albicans TTP family member Zfs1. Using full-length Zfs1, tagged at the N-terminus with maltose binding protein (MBP), we determined the binding affinities of the protein to the optimal TTP binding sequence, UUAUUUAUU. Fluorescence anisotropy experiments determined that the binding affinities of MBP-Zfs1 to non-canonical AREs were influenced by ionic buffer strength, suggesting that transcript selectivity may be affected by intracellular conditions. Furthermore, electrophoretic mobility shift assays (EMSAs) revealed that separation of two core AUUUA sequences by two uridines is sufficient for tandem binding of MBP-Zfs1. Finally, we found evidence for tandem binding of MBP-Zfs1 to a 27-base RNA oligonucleotide containing only a single ARE-binding site, and showed that this was concentration and RNA length dependent; this phenomenon had not been seen previously. These data suggest that the association of the TTP TZF domain and the TZF domains of other species, to ARE-binding sites is highly conserved. Domains outside of the TZF domain may mediate transcript selectivity in changing cellular conditions, and promote protein-RNA interactions not associated with the ARE-binding TZF domain.

In summary, the evidence presented here suggests that Zfs1-mediated decay of mRNA targets may require additional interactions, in addition to ARE-TZF domain associations, to promote transcript destabilization and degradation. These studies further our understanding of post-transcriptional steps in gene regulation.

First complete genome sequence of a capsicum chlorosis tospovirus isolate from Australia with an unusually large S RNA intergenic region

The first complete genome sequence of capsicum chlorosis virus (CaCV) from Australia was determined using a combination of Illumina HiSeq RNA and Sanger sequencing technologies. Australian CaCV had a tripartite genome structure like other CaCV isolates. The large (L) RNA was 8913 nucleotides (nt) in length and contained a single open reading frame (ORF) of 8634 nt encoding a predicted RNA-dependent RNA polymerase (RdRp) in the viral-complementary (vc) sense. The medium (M) and small (S) RNA segments were 4846 and 3944 nt in length, respectively, each containing two non-overlapping ORFs in ambisense orientation, separated by intergenic regions (IGR). The M segment contained ORFs encoding the predicted non-structural movement protein (NSm; 927 nt) and precursor of glycoproteins (GP; 3366 nt) in the viral sense (v) and vc strand, respectively, separated by a 449-nt IGR. The S segment coded for the predicted nucleocapsid (N) protein (828 nt) and non-structural suppressor of silencing protein (NSs; 1320 nt) in the vc and v strand, respectively. The S RNA contained an IGR of 1663 nt, being the largest IGR of all CaCV isolates sequenced so far. Comparison of the Australian CaCV genome with complete CaCV genome sequences from other geographic regions showed highest sequence identity with a Taiwanese isolate. Genome sequence comparisons and phylogeny of all available CaCV isolates provided evidence for at least two highly diverged groups of CaCV isolates that may warrant re-classification of AIT-Thailand and CP-China isolates as unique tospoviruses, separate from CaCV.

Analysis and control of transient spectra using time-dependent density functional theory.

215 p.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.