On the stability and spectral radius of a finite set of matrices

This paper studies some problems related to the stability and the spectral radius of a finite set of matrices. A seasonal epidemic model is given to illustrate the use of the obtained results. In this example, the relationship between the obtained results and the stability of a discrete time periodic linear system is obtained.This work has been partially supported by Spanish [grant number MTM2013-43678-P].Cantó Colomina, B.; Coll, C.; Sánchez, E. (2016). On the stability and spectral radius of a finite set of matrices. Linear and Multilinear Algebra. 64(3):353-361. https://doi.org/10.1080/03081087.2015.1040404S35336164

Dynamic optimization of a gas-liquid reactor

The final publication is available at Springer via http://dx.doi.org/10.1007/s10910-011-9941-1A dynamic gas-liquid transfer model without chemical reaction based on unsteady film theory is considered. In this case, the mathematical model presented for gas-liquid mass-transfer processes is based on mass balances of the transferred substance in both phases. The identificability property of this model is studied in order to confirm the possible identifiable parameters of the model from a given set of experimental data. For that, a different modeled of the system is given. A procedure for the identification is proposed. On the other hand, the aim of this work is to solve the quadratic optimal control problem, using an explicit representation of the model. The problem includes some results on controllability, observability and stability criteria and the relation between these properties and the parameters of the model. Using the optimal control problem we study the stability of the system and show how the choice of the weighting matrices can improve the behavior of the system but with an increase of the energy control cost. © 2011 Springer Science+Business Media, LLC.This work has been partially supported by PAID-05-10-003-295 and by MTM2010-18228.Cantó Colomina, B.; Cardona Navarrete, SC.; Coll, C.; Navarro-Laboulais, J.; Sánchez, E. (2012). Dynamic optimization of a gas-liquid reactor. Journal of Mathematical Chemistry. 50(2):381-393. https://doi.org/10.1007/s10910-011-9941-1S381393502Bayón L., Grau J.M., Ruiz M.M., Suárez P.M.: Initial guess of the solution of dynamic optimization of chemical processes. J. Math. Chem. Model. 48, 28–37 (2010)Ben-Zvi A., McLellan P.J., McAuley K.B.: Ind. Eng. Chem. Res. 42, 6607–6618 (2003)Cantó B., Coll C., Sánchez E.: Structural identifiability of a model of dialysis. Math. Comp. Model. 50, 733–737 (2009)Cantó B., Coll C., Sánchez E.: Identifiability of a class of discretized linear partial differential algebraic equations. Math. Probl. Eng. 2011, 1–12 (2011)Craciun G., Pantea C.: Identifiability of chemical reaction networks. J. Math. Chem. 44, 244–259 (2008)Dai L.: Descriptor Control Systems. Springer, New York (1989)Deckwer W.D.: Bubble Column Reactors. Wiley, Chichester (1992)Kantarci N., Borak F., Ulgen K.O.: Bubble column reactors. Proc. Biochem. 40(7), 2263–2283 (2005)Kawakernaak H., Sivan R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972)Kuo B.C.: Automatic Control Systems, 6th edn. Prentice-Hall, Englewood Cliffs (1991)Navarro-Laboulais J., Cardona S.C., Torregrosa J.I., Abad A., López F.: Practical identifiability analysis in dynamic gas-liquid reactors. Optimal experimental design for mass-transfer parameters determination. Comp. Chem. Eng. 32, 2382–2394 (2008)Navarro-Laboulais J., López F., Torregrosa J.I., Cardona S.C., Abad A.: Transient response, model structure and systematic errors in hybrid respirometers: structural identifiabilit analysis based on OUR and DO measurements. J. Math. Chem. 44(4), 969–990 (2007)Patel R., Munro N.: Multivariable Systen. Theory and Design. Pergamon Press, New York (1982)Sondergeld K.: A generalization of the Routh–Hurwitz stability criteria and a application to a problem in robust controller design. IEEE Trans. Automat. Contr. AC-28(10), 965–970 (1983

On identifiability for chemical systems from measurable variables

The final publication is available at Springer via http://dx.doi.org/10.1007/s10910-013-0149-4The dynamics of the composition of chemical species in reacting systems can be characterized by a set of autonomous differential equations derived from mass conservation principles and some elementary hypothesis related to chemical reactivity. These sets of ordinary differential equations are basically non-linear, their complexity grows as much increases the number of substances present in the reacting media an can be characterized by a set of phenomenological constants which contains all the relevant information about the physical system. The determination of these kinetic constants is critical for the design or control of chemical systems from a technological point of view but the non-linear nature of the equations implies that there are hidden correlations between the parameters which maybe can be revealed with a identifiability analysis.This work has been partially supported by MTM2010-18228.Cantó Colomina, B.; Coll, C.; Sánchez, E.; Cardona Navarrete, SC.; Navarro-Laboulais, J. (2014). On identifiability for chemical systems from measurable variables. Journal of Mathematical Chemistry. 52(4):1023-1035. https://doi.org/10.1007/s10910-013-0149-4S10231035524M.J. Almendral, A. Alonso, M.S. Fuentes, Development of new methodologies for on-line determination of the bromate. J. Environ. Monit. 11, 1381–1388 (2009)A. Ben-Zvi, P.J. McLellan, K.B. McAuley, Identifiability of linear time-invariant differential-algebraic systems. I. The generalized Markov parameter approach. Ind. Eng. Chem. Res. 42, 6607–6618 (2003)T.P. Bonacquisti, A drinking water utility’s perspective on bromide, bromate, and ozonation. Toxicology 221, 145–148 (2006)R. Butler, A. Godley, L. Lytton, E. Cartmell, Bromate environmental contamination: review of impact and possible treatment. Crit. Rev. Environ. Sci. Tech. 35, 193–217 (2005)R. Butler, L. Lytton, A.R. Godley, I.E. Tothill, E. Cartmell, Bromate analysis in groundwater and wastewater samples. J. Environ. Monit. 7, 999–1006 (2005)B. Cantó, S.C. Cardona, C. Coll, J. Navarro-Laboulais, E. Sánchez, Dynamic optimization of a gas-liquid reactor. J. Math. Chem. 50, 381–393 (2012)B. Cantó, C. Coll and E. Sánchez, Identifiability of a class of discretized linear partial differential algebraic equations, Math. Problems Eng. 2011, 1–12 (2011)A. Constantinides, N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications, Alkis Constantinides and Navid Mostoufi, Upper Saddle River (Prentice Hall, New Jersey, 1999)P. Englezos, N. Kalogerakis, Applied Parameter Estimation for Chemical Engineers (Marcel Dekker, New York, 2001)U. von Gunten, Ozonation of drinking water. Part II. Disinfection and by-product formation in presence of bromide, iodide or chlorine. Water Res. 37, 1469–1487 (2003)B. Legube, B. Parinet, K. Gelinet, F. Berne, J-Ph Croue, Modeling of bromate formation by ozonation of surface waters in drinking water treatment. Water Res. 38, 2185–2195 (2004)Q. Liu, L.M. Schurter, C.E. Muller, S. Aloisio, J.S. Francisco, D.W. Margerum, Kinetics and mechanisms of aqueous ozone reactions with bromide, sulfite, hydrogen sulfite, iodide, and nitrite ions. Inorg. Chem. 40, 4436–4442 (2001)J.B. Rawling, J.G. Ekerdt, Chemical Reactor Analysis and Design Fundamentals (Nob Hill Pub, Madison, 2002)W.E. Stewart, M. Caracotsios, Computer Aided Modelling of Reactive Systems (John Wiley and Sons, New York, 2008)P. Westerhoff, R. Song, G. Amy, R. Minear, Numerical kinetic models for bromide oxidation to bromine and bromate. Water Res. 32, 1687–1699 (1998)World Health Organization, Bromate in Drinking-water, Document WHO/SDE/WSH/05.08/78, http://www.who.int/water_sanitation_health/dwq/chemicals/en/ (accesed 26/07/12

Estimation of parameters in a structured SIR model

[EN] In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model. We propose an iterative algorithm to study the identifiability of the system and a method to estimate the parameters which are identifiable. A least squares approach based on a finite set of observations helps us to estimate the initial values of the parameters. Finally, we test the proposed algorithms.The authors would like to thank the referees and the editor for their comments and useful suggestions for improvement of the manuscript. This work has been partially supported by Spanish Grant MTM2013-43678-P.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2017). Estimation of parameters in a structured SIR model. Advances in Difference Equations. 33:1-13. https://doi.org/10.1186/s13662-017-1078-5S11333Strogatz, S, Friedman, M, Mallinck-Rodt, AJ, McKay, S: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books, Washington (1994)De La Sen, M, Quesada, A: Some equilibrium, stability, instability and oscillatory results for an extended discrete epidemic model with evolution memory. Adv. Differ. Equ. 2013, 234 (2013)Han, Q, Wang, Z: On extinction of infectious diseases for multi-group SIRS models with satured incidence rate. Adv. Differ. Equ. 2015, 333 (2015)Cantó, B, Coll, C, Sánchez, E: Structural identifiability of a model of dialysis. Math. Comput. Model. 50, 733-737 (2009)Cantó, B, Coll, C, Sánchez, E: Identifiability of a class of discretized linear partial differential algebraic equations. Math. Probl. Eng., 1-12 (2011)Craciun, G, Pantea, C: Identifiability of chemical reaction networks. J. Math. Chem. 44, 244-259 (2008)Malik, MB, Salman, M: State-space least mean square. Digit. Signal Process. 18, 334-345 (2008)Ding, F, Liu, PX, Liu, G: Multiinnovatiovation least-squares identification for system modeling. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 18(3), 767-778 (2010)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, I. The generalized Markov parameter approach. Ind. Eng. Chem. Res. 42, 6607-6618 (2003)Boyadjiev, C, Dimitrova, E: An iterative method for model parameter identification. Comput. Chem. Eng. 29, 941-948 (2005)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, 2. The differential-algebraic approach. Ind. Eng. Chem. Res. 43, 1251-1259 (2004)Dion, JM, Commault, C, van der Woude, J: Generic properties and control of linear structured systems: a survey. Automatica 39, 1125-1144 (2003)Chou, IC, Voit, EO: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math. Biosci. 219, 57-83 (2009)Schmitz, OJ: Ecology and Ecosystems Conservation. Island Press, Washington (2013

The lower mass function of the young open cluster Blanco 1: from 30 Mjup to 3 Mo

We performed a deep wide field optical survey of the young (~100-150 Myr) open cluster Blanco1 to study its low mass population well down into the brown dwarf regime and estimate its mass function over the whole cluster mass range.The survey covers 2.3 square degrees in the I and z-bands down to I ~ z ~ 24 with the CFH12K camera. Considering two different cluster ages (100 and 150 Myr), we selected cluster member candidates on the basis of their location in the (I,I-z) CMD relative to the isochrones, and estimated the contamination by foreground late-type field dwarfs using statistical arguments, infrared photometry and low-resolution optical spectroscopy. We find that our survey should contain about 57% of the cluster members in the 0.03-0.6 Mo mass range, including 30-40 brown dwarfs. The candidate's radial distribution presents evidence that mass segregation has already occured in the cluster. We took it into account to estimate the cluster mass function across the stellar/substellar boundary. We find that, between 0.03Mo and 0.6Mo, the cluster mass distribution does not depend much on its exact age, and is well represented by a single power-law, with an index alpha=0.69 +/- 0.15. Over the whole mass domain, from 0.03Mo to 3Mo, the mass function is better fitted by a log-normal function with m0=0.36 +/- 0.07Mo and sigma=0.58 +/- 0.06. Comparison between the Blanco1 mass function, other young open clusters' MF, and the galactic disc MF suggests that the IMF, from the substellar domain to the higher mass part, does not depend much on initial conditions. We discuss the implications of this result on theories developed to date to explain the origin of the mass distribution.Comment: 18 pages, 15 figures and 5 tables accepted in A&

Modelling of big game populations when hunting is age and sex selective

The main objective of this work is to model the dynamics of cynegetic populations by means of a linear control system. We want to estimate the annual corrective measures, which may be improvements or hunting, that must be implemented to achieve and maintain a study population around the carrying capacity of a certain area. Moreover, the model must be able to distinguish between different age-sex classes and lead the population to a desired distribution of individuals among these stage groups.Supported by the Spanish DGI grant MTM2010-18228 and by the UPV under its research program PAID-06-10.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2011). Modelling of big game populations when hunting is age and sex selective. Mathematical and Computer Modelling. 57(7-8):1744-1750. https://doi.org/10.1016/j.mcm.2011.11.027S17441750577-

A study on vaccination models for a seasonal epidemic process

In this paper seasonal epidemiological processes are considered and a strategy of periodic vaccination is proposed. The invariant formulations associated with an N-periodic system and the reproduction numbers associated with them are considered. A collection of measures to study the stability of the system is introduced. Moreover, the collection of s-basic reproduction number at time j help us to establish conditions on the periodic vaccination rates in the vaccination program. Finally, an SIR model is showed and a comparison between the results obtained using constant or periodic vaccination program is analyzed. (C) 2014 Elsevier Inc. All rights reserved.The authors wish to express their thanks to the reviewers for helpful comments and suggestions. This paper is supported by Grant MTM2010-18228.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2014). A study on vaccination models for a seasonal epidemic process. Applied Mathematics and Computation. 243:152-160. https://doi.org/10.1016/j.amc.2014.05.104S15216024

Distinctive waves of innate immune response in the retina in experimental autoimmune encephalomyelitis

Neurodegeneration mediates neurological disability in inflammatory demyelinating diseases of the CNS. The role of innate immune cells in mediating this damage has remained controversial with evidence for destructive and protective effects. This has complicated efforts to develop treatment. The time sequence and dynamic evolution of the opposing functions are especially unclear. Given limits of in vivo monitoring in human diseases such as multiple sclerosis (MS), animal models are warranted to investigate the association and timing of innate immune activation with neurodegeneration. Using noninvasive in vivo retinal imaging of experimental autoimmune encephalitis (EAE) in CX3CR1GFP/+–knock-in mice followed by transcriptional profiling, we are able to show 2 distinct waves separated by a marked reduction in the number of innate immune cells and change in cell morphology. The first wave is characterized by an inflammatory phagocytic phenotype preceding the onset of EAE, whereas the second wave is characterized by a regulatory, antiinflammatory phenotype during the chronic stage. Additionally, the magnitude of the first wave is associated with neuronal loss. Two transcripts identified — growth arrest–specific protein 6 (GAS6) and suppressor of cytokine signaling 3 (SOCS3) — might be promising targets for enhancing protective effects of microglia in the chronic phase after initial injury

Somatostatin subtype-2 receptor-targeted metal-based anticancer complexes

Conjugates of a dicarba analogue of octreotide, a potent somatostatin agonist whose receptors are overexpressed on tumor cells, with [PtCl 2(dap)] (dap = 1-(carboxylic acid)-1,2-diaminoethane) (3), [(η 6-bip)Os(4-CO 2-pico)Cl] (bip = biphenyl, pico = picolinate) (4), [(η 6-p-cym)RuCl(dap)] + (p-cym = p-cymene) (5), and [(η 6-p-cym)RuCl(imidazole-CO 2H)(PPh 3)] + (6), were synthesized by using a solid-phase approach. Conjugates 3-5 readily underwent hydrolysis and DNA binding, whereas conjugate 6 was inert to ligand substitution. NMR spectroscopy and molecular dynamics calculations showed that conjugate formation does not perturb the overall peptide structure. Only 6 exhibited antiproliferative activity in human tumor cells (IC 50 = 63 ± 2 μ in MCF-7 cells and IC 50 = 26 ± 3 μ in DU-145 cells) with active participation of somatostatin receptors in cellular uptake. Similar cytotoxic activity was found in a normal cell line (IC 50 = 45 ± 2.6 μ in CHO cells), which can be attributed to a similar level of expression of somatostatin subtype-2 receptor. These studies provide new insights into the effect of receptor-binding peptide conjugation on the activity of metal-based anticancer drugs, and demonstrate the potential of such hybrid compounds to target tumor cells specifically. © 2012 American Chemical Society

Exendin-4 Improves Steatohepatitis by Increasing Sirt1 Expression in High-Fat Diet-Induced Obese C57BL/6J Mice

The effects of exendin-4 on Sirt1 expression as a mechanism of reducing fatty liver have not been previously reported. Therefore, we investigated whether the beneficial effects of exendin-4 treatment on fatty liver are mediated via Sirt1 in high-fat (HF) diet-induced obese C57BL/6J mice and related cell culture models. Exendin-4 treatment decreased body weight, serum free fatty acid (FA), and triglyceride levels in HF-induced obese C57BL/6J mice. Histological analysis showed that exendin-4 reversed HF-induced hepatic accumulation of lipids and inflammation. Exendin-4 treatment increased mRNA and protein expression of Sirt1 and its downstream factor, AMPK, in vivo and also induced genes associated with FA oxidation and glucose metabolism. In addition, a significant increase in the hepatic expression of Lkb1 and Nampt mRNA was observed in exendin-4-treated groups. We also observed increased expression of phospho-Foxo1 and GLUT2, which are involved in hepatic glucose metabolism. In HepG2 and Huh7 cells, mRNA and protein expressions of GLP-1R were increased by exendin-4 treatment in a dose-dependent manner. Exendin-4 enhanced protein expression of Sirt1 and phospho-AMPKα in HepG2 cells treated with 0.4 mM palmitic acid. We also found that Sirt1 was an upstream regulator of AMPK in hepatocytes. A novel finding of this study was the observation that expression of GLP-1R is proportional to exendin-4 concentration and exendin-4 could attenuate fatty liver through activation of Sirt1