An Algebraic Multigrid Preconditioner for a class of singular M-Matrices

We apply Algebraic Multigrid (AMG) as a preconditioner for solving large singular linear systems of the type $(I-T^T)x=0$ with GMRES. Here, $T$ is assumed to be the transition matrix of a Markov process. Although AMG and GMRES are originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to problems as described above

Generalisation of the Perron–Frobenius theory to matrix pencils

AbstractWe present a new extension of the well-known Perron–Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied

A-tract clusters may facilitate DNA packaging in bacterial nucleoid

Molecular mechanisms of bacterial chromosome packaging are still unclear, as bacteria lack nucleosomes or other apparent basic elements of DNA compaction. Among the factors facilitating DNA condensation may be a propensity of the DNA molecule for folding due to its intrinsic curvature. As suggested previously, the sequence correlations in genome reflect such a propensity [Trifonov and Sussman (1980) Proc. Natl Acad. Sci. USA, 77, 3816–3820]. To further elaborate this concept, we analyzed positioning of A-tracts (the sequence motifs introducing the most pronounced DNA curvature) in the Escherichia coli genome. First, we observed that the A-tracts are over-represented and distributed ‘quasi-regularly’ throughout the genome, including both the coding and intergenic sequences. Second, there is a 10–12 bp periodicity in the A-tract positioning indicating that the A-tracts are phased with respect to the DNA helical repeat. Third, the phased A-tracts are organized in ∼100 bp long clusters. The latter feature was revealed with the help of a novel approach based on the Fourier series expansion of the A-tract distance autocorrelation function. Since the A-tracts introduce local bends of the DNA duplex and these bends accumulate when properly phased, the observed clusters would facilitate DNA looping. Also, such clusters may serve as binding sites for the nucleoid-associated proteins that have affinities for curved DNA (such as HU, H-NS, Hfq and CbpA). Therefore, we suggest that the ∼100 bp long clusters of the phased A-tracts constitute the ‘structural code’ for DNA compaction by providing the long-range intrinsic curvature and increasing stability of the DNA complexes with architectural proteins

Bounded real lemmas for positive descriptor systems

A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H?H? norm less than ? and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H?H? norm of the original systems. An advantage of such method is that systems? matrices of the reduced order systems do not involve solving of LMIs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results

Autoregulation of the Escherichia coli melR promoter: repression involves four molecules of MelR

The Escherichia coli MelR protein is a transcription activator that autoregulates its own promoter by repressing transcription initiation. Optimal repression requires MelR binding to a site that overlaps the melR transcription start point and to upstream sites. In this work, we have investigated the different determinants needed for optimal repression and their spatial requirements. We show that repression requires a complex involving four DNA-bound MelR molecules, and that the global CRP regulator plays little or no role

Recombinant rubella vectors elicit SIV Gag-specific T cell responses with cytotoxic potential in rhesus macaques

AbstractLive-attenuated rubella vaccine strain RA27/3 has been demonstrated to be safe and immunogenic in millions of children. The vaccine strain was used to insert SIV gag sequences and the resulting rubella vectors were tested in rhesus macaques alone and together with SIV gag DNA in different vaccine prime-boost combinations. We previously reported that such rubella vectors induce robust and durable SIV-specific humoral immune responses in macaques. Here, we report that recombinant rubella vectors elicit robust de novo SIV-specific cellular immune responses detectable for >10 months even after a single vaccination. The antigen-specific responses induced by the rubella vector include central and effector memory CD4+ and CD8+ T cells with cytotoxic potential. Rubella vectors can be administered repeatedly even after vaccination with the rubella vaccine strain RA27/3. Vaccine regimens including rubella vector and SIV gag DNA in different prime-boost combinations resulted in robust long-lasting cellular responses with significant increase of cellular responses upon boost. Rubella vectors provide a potent platform for inducing HIV-specific immunity that can be combined with DNA in a prime-boost regimen to elicit durable cellular immunity

A direct method to obtain a realization of a polynomial matrix and its applications

[EN] In this paper we present a Silverman-Ho algorithm-based method to obtain a realization of a polynomial matrix. This method provides the final formulation of a minimal realization directly from a full rank factorization of a specific given matrix. Also, some classical problems in control theory such as model reduction in singular systems or the positive realization problem in standard systems are solved with this method.Work supported by the Spanish DGI grant MTM2017-85669-P-AR.Cantó Colomina, R.; Moll López, SE.; Ricarte Benedito, B.; Urbano Salvador, AM. (2020). A direct method to obtain a realization of a polynomial matrix and its applications. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-15. https://doi.org/10.1007/s13398-020-00819-1S1151142Anderson, B.D.O., Bongpanitlerd, S.: Network Analysis and Synthesis, A Modern Systems Theory Approach. Prentice-Hall Inc., New Jersey (1968)Benvenuti, L., Farina, L.: A tutorial on the positive realization problem. IEEE Trans. Autom. Control 49(5), 651–664 (2004). https://doi.org/10.1109/TAC.2004.826715Bru, R., Coll, C., Sánchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl. 349, 1–10 (2002). https://doi.org/10.1016/S0024-3795(02)00277-XCantó, R., Ricarte, B., Urbano, A.M.: Positive realizations of transfer matrices with real poles. IEEE Trans. Circuits Syst. II Expr. Br. 54(6), 517–521 (2007). https://doi.org/10.1109/TCSII.2007.894408Cantó, R., Ricarte, B., Urbano, A.M.: On positivity of discrete-time singular systems and the realization problem. Lect. Notes Control Inf. Sci. 389, 251–258 (2009). https://doi.org/10.1007/978-3-642-02894-6_24Climent, J., Napp, D., Requena, V.: Block Toeplitz matrices for burst-correcting convolutional codes. RACSAM 114, 38 (2020). https://doi.org/10.1007/s13398-019-00744-yDai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, New York (1989)Golub, G.H., Van Loan, C.F.: Matrix Computations, Fourth edn. Johns Hopkins University Press, Baltimore (2013)Henrion, D., Šebek, M.: Polynomial and matrix fraction description. In: Control Systems, Robotics and Automation, vol. 7, pp. 211-231, (2009). http://www.eolss.net/Sample-Chapters/C18/E6-43-13-05.pdfHo, B.L., Kalman, R.E.: Effective construction of linear state-variable models from mput/output functions. Regelungstechnik 14(12), 545–548 (1966)Kaczorek, T.: Weakly positive continuous-time linear systems. Lect. Notes Control Inf. Sci. 243, 3–16 (1999)Kaczorek, T.: Positive 1D and 2D Systems, vol. 431. Springer, London (2002)Kaczorek, T.: Externally and internally positive singular discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 12(2), 197–202 (2002)MATLAB, The Math Works, Inc., Natick, Massachusetts, United States. Official website: http://www.mathworks.comMcCrory, C., Parusinski, A.: The weight filtration for real algebraic varieties II: classical homology. RACSAM 108, 63–94 (2014). https://doi.org/10.1007/s13398-012-0098-ySilverman, L.: Realization of linear dynamical systems. IEEE Trans. Autom. Control 16(6), 554–567 (1971)Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429(10), 2640–2659 (2008

Ketorolak-dekstran konjugati: sinteza, in vitro i in vivo vrednovanje

Ketorolac is a non-steroidal anti-inflammatory drug. Dextran conjugates of ketorolac (KD) were synthesized and characterized to improve ketorolac aqueous solubility and reduce gastrointestinal side effects. An N-acylimidazole derivative of ketorolac (KAI) was condensed with a model carrier polymer, dextran of different molecular masses (40000, 60000, 110000 and 200000). IR spectral data confirmed formation of ester bonding. Ketorolac contents were evaluated by UV-spectrophotometric analysis. The molecular mass was determined by measuring viscosity using the Mark-Howink-Sakurada equation. In vitro hydrolysis studies were performed in aqueous buffers (pH 1.2, 7.4, 9) and in 80% (V/V) human plasma (pH 7.4). At pH 9, a higher rate of ketorolac release from KD was observed as compared to aqueous buffer of pH 7.4 and 80% human plasma (pH 7.4), following first-order kinetics. In vivo biological screening in mice and rats indicated that conjugates retained analgesic and anti-inflammatory activities with significantly reduced ulcerogenicity compared to the parent drug.U radu je opisana sinteza konjugata dektrana i protuupalnog lijeka ketorolaka (KD). Konjugati su pripravljeni da bi se povećala topljivost ketorolaka u vodi i smanjila njegova nusdjelovanja u gastrointestinanom traktu. Ketorak je prvo preveden u N-acilimidazolni derivat (KAI) koji je kondenziran s polimernim nosačem, dekstranom različitih molekulskih masa (40000, 60000, 110000 i 200000). IR-spektri potvrdili su nastajanje esterske veze. Udio ketorolaka u konjugatu određen je UV-spektrofotometrijskom analizom. Molekulske mase određene su mjerenjem viskoznosti koristeći Mark-Howink-Sakurada jednadžbu. Hidroliza in vitro praćena je u puferskim otopinama (pH 1,2, 7,4 i 9) i u 80% V/V humanoj plazmi (pH 7,4). Pri pH 9 primjećeno je značajno brže oslobađanje ketorolaka iz KD nego u puferskoj otopini pH 7,4 i krvnoj plazmi. Oslobađanje je prati kinetiku prvog reda. In vivo biološka ispitivanja na miševima i štakorima ukazuju da konjugati imaju analgetsko i protuupalno djelovanje, a značajno smanjeno ulcerogeno djelovanje

The antiparallel loops in gal DNA

Interactions between proteins bound to distant sites along a DNA molecule require bending and twisting deformations in the intervening DNA. In certain systems, the sterically allowed protein–DNA and protein–protein interactions are hypothesized to produce loops with distinct geometries that may also be thermodynamically and biologically distinct. For example, theoretical models of Gal repressor/HU-mediated DNA-looping suggest that the antiparallel DNA loops, A1 and A2, are thermodynamically quite different. They are also biologically different, since in experiments using DNA molecules engineered to form only one of the two loops, the A2 loop failed to repress in vitro transcription. Surprisingly, single molecule measurements show that both loop trajectories form and that they appear to be quite similar energetically and kinetically