Improvement on the bound of Hermite matrix polynomials

In this paper, we introduce an improved bound on the 2-norm of Hermite matrix polynomials. As a consequence, this estimate enables us to present and prove a matrix version of the Riemann-Lebesgue lemma for Fourier transforms. Finally, our theoretical results are used to develop a novel procedure for the computation of matrix exponentials with a priori bounds. A numerical example for a test matrix is provided. © 2010 Elsevier Inc. All rights reserved.This work has been partially supported by the Universidad Politecnica de Valencia under project PAID-06-07/3283 and the Generalitat Valenciana under project GVPRE/2008/340.Defez Candel, E.; Tung, MM.; Sastre, J. (2011). Improvement on the bound of Hermite matrix polynomials. Linear algebra and its applications. 434(8):1910-1919. https://doi.org/10.1016/j.laa.2010.12.015S19101919434

On the inverse of the Caputo matrix exponential

[EN] Matrix exponentials are widely used to efficiently tackle systems of linear differential equations. To be able to solve systems of fractional differential equations, the Caputo matrix exponential of the index a > 0 was introduced. It generalizes and adapts the conventional matrix exponential to systems of fractional differential equations with constant coefficients. This paper analyzes the most significant properties of the Caputo matrix exponential, in particular those related to its inverse. Several numerical test examples are discussed throughout this exposition in order to outline our approach. Moreover, we demonstrate that the inverse of a Caputo matrix exponential in general is not another Caputo matrix exponential.This work has been partially supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grants TIN2017-89314-P and by the Programa de Apoyo a la Investigacion y Desarrollo 2018 of the Universitat Politecnica de Valencia (PAID-06-18) grant SP20180016.Defez Candel, E.; Tung, MM.; Chen-Charpentier, BM.; Alonso Abalos, JM. (2019). On the inverse of the Caputo matrix exponential. Mathematics. 7(12):1-11. https://doi.org/10.3390/math7121137S111712Moler, C., & Van Loan, C. (2003). Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later. SIAM Review, 45(1), 3-49. doi:10.1137/s00361445024180Ortigueira, M. D., & Tenreiro Machado, J. A. (2015). What is a fractional derivative? Journal of Computational Physics, 293, 4-13. doi:10.1016/j.jcp.2014.07.019Caputo, M. (1967). Linear Models of Dissipation whose Q is almost Frequency Independent--II. Geophysical Journal International, 13(5), 529-539. doi:10.1111/j.1365-246x.1967.tb02303.xRodrigo, M. R. (2016). On fractional matrix exponentials and their explicit calculation. Journal of Differential Equations, 261(7), 4223-4243. doi:10.1016/j.jde.2016.06.023Garrappa, R., & Popolizio, M. (2018). Computing the Matrix Mittag-Leffler Function with Applications to Fractional Calculus. Journal of Scientific Computing, 77(1), 129-153. doi:10.1007/s10915-018-0699-

Numerical approximations of second-order matrix differential equations using higher-degree splines

Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for non-stiff initial problems Y 00(x) = f(x, Y (x), Y 0 (x)) using higher-degree matrix splines without any dimensional increase. An estimation of the approximation error for some illustrative examples are presented by using Mathematica. Several MatLab functions have also been developed, comparing, under equal conditions, accuracy and execution times with built-in MatLab functions. Experimental results show the advantages of solving the above initial problem by using the implemented MatLab functions.The authors wish to thank for financial support by the Universidad Politecnica de Valencia [grant number PAID-06-11-2020].Defez Candel, E.; Tung ., MM.; Solis Lozano, FJ.; Ibáñez González, JJ. (2015). Numerical approximations of second-order matrix differential equations using higher-degree splines. Linear and Multilinear Algebra. 63(3):472-489. https://doi.org/10.1080/03081087.2013.873427S472489633Loscalzo, F. R., & Talbot, T. D. (1967). Spline Function Approximations for Solutions of Ordinary Differential Equations. SIAM Journal on Numerical Analysis, 4(3), 433-445. doi:10.1137/0704038Al-Said, E. A. (2001). The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Computers & Mathematics with Applications, 42(6-7), 861-869. doi:10.1016/s0898-1221(01)00204-8Al-Said, E. A., & Noor, M. A. (2003). Cubic splines method for a system of third-order boundary value problems. Applied Mathematics and Computation, 142(2-3), 195-204. doi:10.1016/s0096-3003(02)00294-1Kadalbajoo, M. K., & Patidar, K. C. (2002). Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. Applied Mathematics and Computation, 131(2-3), 299-320. doi:10.1016/s0096-3003(01)00146-1Micula, G., & Revnic, A. (2000). An implicit numerical spline method for systems for ODEs. Applied Mathematics and Computation, 111(1), 121-132. doi:10.1016/s0096-3003(98)10111-xDefez, E., Soler, L., Hervás, A., & Santamaría, C. (2005). Numerical solution ofmatrix differential models using cubic matrix splines. Computers & Mathematics with Applications, 50(5-6), 693-699. doi:10.1016/j.camwa.2005.04.012Defez, E., Hervás, A., Soler, L., & Tung, M. M. (2007). Numerical solutions of matrix differential models using cubic matrix splines II. Mathematical and Computer Modelling, 46(5-6), 657-669. doi:10.1016/j.mcm.2006.11.027Ascher, U., Pruess, S., & Russell, R. D. (1983). On Spline Basis Selection for Solving Differential Equations. SIAM Journal on Numerical Analysis, 20(1), 121-142. doi:10.1137/0720009Brunner, H. (2004). On the Divergence of Collocation Solutions in Smooth Piecewise Polynomial Spaces for Volterra Integral Equations. BIT Numerical Mathematics, 44(4), 631-650. doi:10.1007/s10543-004-3828-5Tung, M. M., Defez, E., & Sastre, J. (2008). Numerical solutions of second-order matrix models using cubic-matrix splines. Computers & Mathematics with Applications, 56(10), 2561-2571. doi:10.1016/j.camwa.2008.05.022Defez, E., Tung, M. M., Ibáñez, J. J., & Sastre, J. (2012). Approximating and computing nonlinear matrix differential models. Mathematical and Computer Modelling, 55(7-8), 2012-2022. doi:10.1016/j.mcm.2011.11.060Claeyssen, J. R., Canahualpa, G., & Jung, C. (1999). A direct approach to second-order matrix non-classical vibrating equations. Applied Numerical Mathematics, 30(1), 65-78. doi:10.1016/s0168-9274(98)00085-3Froese, C. (1963). NUMERICAL SOLUTION OF THE HARTREE–FOCK EQUATIONS. Canadian Journal of Physics, 41(11), 1895-1910. doi:10.1139/p63-189Marzulli, P. (1991). Global error estimates for the standard parallel shooting method. Journal of Computational and Applied Mathematics, 34(2), 233-241. doi:10.1016/0377-0427(91)90045-lShore, B. W. (1973). Comparison of matrix methods applied to the radial Schrödinger eigenvalue equation: The Morse potential. The Journal of Chemical Physics, 59(12), 6450-6463. doi:10.1063/1.1680025ZHANG, J. F. (2002). OPTIMAL CONTROL FOR MECHANICAL VIBRATION SYSTEMS BASED ON SECOND-ORDER MATRIX EQUATIONS. Mechanical Systems and Signal Processing, 16(1), 61-67. doi:10.1006/mssp.2001.1441Flett, T. M. (1980). Differential Analysis. doi:10.1017/cbo978051189719

Improved Drought Stress Response in Alfalfa Plants Nodulated by an IAA Over-producing Rhizobium Strain

The drought\u2013stress response in plant involves the cross-talk between abscisic acid (ABA) and other phytohormones, such as jasmonates and ethylene. The auxin indole-3- acetic acid (IAA) plays an integral part in plant adaptation to drought stress. Investigation was made to see how the main auxin IAA interacted with other plant hormones under water stress, applied through two different growth conditions (solid and hydroponic). Medicago sativa plants nodulated by the Ensifer meliloti wild type 1021 (Ms-1021) and its IAA-overproducing RD64 derivative strains (Ms-RD64) were subjected to drought stress, comparing their response. When the expression of nifH gene and the activity of the nitrogenase enzyme were measured after stress treatments, Ms-RD64 plants recorded a significantly weaker damage. These results were correlated with a lower biomass reduction, and a higher Rubisco protein level measured for the Ms-RD64- stressed plants as compared to the Ms-1021-stressed ones. It has been verified that the stress response observed for Ms-RD64-stressed plants was related to the production of greater amount of low-molecular-weight osmolytes, such as proline and pinitol, measured in these plants. For the Ms-RD64 plants the immunoblotting analysis of thylakoid membrane proteins showed that some of the photosystem proteins increased after the stress. An increased non-photochemical quenching after the stress was also observed for these plants. The reduced wilting signs observed for these plants were also connected to the significant down-regulation of the MtAA03 gene involved in the ABA biosynthesis, and with the unchanged expression of the two genes (Mt- 2g006330 and Mt-8g095330) of ABA signaling. When the expression level of the ethylene-signaling genes was evaluated by qPCR analysis no significant alteration of the key positive regulators was recorded for Ms-RD64-stressed plants. Coherently, these plants accumulated 40% less ethylene as compared to Ms-1021-stressed ones. The results presented herein indicate that the variations in endogenous IAA levels, triggered by the overproduction of rhizobial IAA inside root nodules, positively affected drought stress response in nodulated alfalfa plants

Endophytes from African Rice (Oryza glaberrima L.) Efficiently Colonize Asian Rice (Oryza sativa L.) Stimulating the Activity of Its Antioxidant Enzymes and Increasing the Content of Nitrogen, Carbon, and Chlorophyll.

Bacterial endophytes support the adaptation of host plants to harsh environments. In this study, culturable bacterial endophytes were isolated from the African rice Oryza glaberrima L., which is well-adapted to grow with poor external inputs in the tropical region of Mali. Among these, six N-fixer strains were used to inoculate O. glaberrima RAM133 and the Asian rice O. sativa L. cv. Baldo, selected for growth in temperate climates. The colonization efficiency and the N-fixing activity were evaluated and compared for the two rice varieties. Oryza sativa-inoculated plants showed a fairly good colonization efficiency and nitrogenase activity. The inoculation of Oryza sativa with the strains Klebsiella pasteurii BDA134-6 and Phytobacter diazotrophicus BDA59-3 led to the highest nitrogenase activity. In addition, the inoculation of ‘Baldo’ plants with the strain P. diazotrophicus BDA59-3 led to a significant increase in nitrogen, carbon and chlorophyll content. Finally, ‘Baldo’ plants inoculated with Kl. pasteurii BDA134-6 showed the induction of antioxidant enzymes activity and the maintenance of nitrogen-fixation under salt stress as compared to the unstressed controls. As these endophytes efficiently colonize high-yielding crop varieties grown in cold temperate climates, they become good candidates to promote their growth under unfavorable conditions

Epidemiology, practice of ventilation and outcome for patients at increased risk of postoperative pulmonary complications

BACKGROUND Limited information exists about the epidemiology and outcome of surgical patients at increased risk of postoperative pulmonary complications (PPCs), and how intraoperative ventilation was managed in these patients. OBJECTIVES To determine the incidence of surgical patients at increased risk of PPCs, and to compare the intraoperative ventilation management and postoperative outcomes with patients at low risk of PPCs. DESIGN This was a prospective international 1-week observational study using the ‘Assess Respiratory Risk in Surgical Patients in Catalonia risk score’ (ARISCAT score) for PPC for risk stratification. PATIENTS AND SETTING Adult patients requiring intraoperative ventilation during general anaesthesia for surgery in 146 hospitals across 29 countries. MAIN OUTCOME MEASURES The primary outcome was the incidence of patients at increased risk of PPCs based on the ARISCAT score. Secondary outcomes included intraoperative ventilatory management and clinical outcomes. RESULTS A total of 9864 patients fulfilled the inclusion criteria. The incidence of patients at increased risk was 28.4%. The most frequently chosen tidal volume (VT) size was 500 ml, or 7 to 9 ml kg1 predicted body weight, slightly lower in patients at increased risk of PPCs. Levels of positive end-expiratory pressure (PEEP) were slightly higher in patients at increased risk of PPCs, with 14.3% receiving more than 5 cmH2O PEEP compared with 7.6% in patients at low risk of PPCs (P < 0.001). Patients with a predicted preoperative increased risk of PPCs developed PPCs more frequently: 19 versus 7%, relative risk (RR) 3.16 (95% confidence interval 2.76 to 3.61), P < 0.001) and had longer hospital stays. The only ventilatory factor associated with the occurrence of PPCs was the peak pressure. CONCLUSION The incidence of patients with a predicted increased risk of PPCs is high. A large proportion of patients receive high VT and low PEEP levels. PPCs occur frequently in patients at increased risk, with worse clinical outcome

Epidemiology, practice of ventilation and outcome for patients at increased risk of postoperative pulmonary complications: LAS VEGAS - An observational study in 29 countries

BACKGROUND Limited information exists about the epidemiology and outcome of surgical patients at increased risk of postoperative pulmonary complications (PPCs), and how intraoperative ventilation was managed in these patients. OBJECTIVES To determine the incidence of surgical patients at increased risk of PPCs, and to compare the intraoperative ventilation management and postoperative outcomes with patients at low risk of PPCs. DESIGN This was a prospective international 1-week observational study using the ‘Assess Respiratory Risk in Surgical Patients in Catalonia risk score’ (ARISCAT score) for PPC for risk stratification. PATIENTS AND SETTING Adult patients requiring intraoperative ventilation during general anaesthesia for surgery in 146 hospitals across 29 countries. MAIN OUTCOME MEASURES The primary outcome was the incidence of patients at increased risk of PPCs based on the ARISCAT score. Secondary outcomes included intraoperative ventilatory management and clinical outcomes. RESULTS A total of 9864 patients fulfilled the inclusion criteria. The incidence of patients at increased risk was 28.4%. The most frequently chosen tidal volume (V T) size was 500 ml, or 7 to 9 ml kg−1 predicted body weight, slightly lower in patients at increased risk of PPCs. Levels of positive end-expiratory pressure (PEEP) were slightly higher in patients at increased risk of PPCs, with 14.3% receiving more than 5 cmH2O PEEP compared with 7.6% in patients at low risk of PPCs (P ˂ 0.001). Patients with a predicted preoperative increased risk of PPCs developed PPCs more frequently: 19 versus 7%, relative risk (RR) 3.16 (95% confidence interval 2.76 to 3.61), P ˂ 0.001) and had longer hospital stays. The only ventilatory factor associated with the occurrence of PPCs was the peak pressure. CONCLUSION The incidence of patients with a predicted increased risk of PPCs is high. A large proportion of patients receive high V T and low PEEP levels. PPCs occur frequently in patients at increased risk, with worse clinical outcome.</p

Bacteria-inducing legume nodules involved in the improvement of plant growth, health and nutrition

Bacteria-inducing legume nodules are known as rhizobia and belong to the class Alphaproteobacteria and Betaproteobacteria. They promote the growth and nutrition of their respective legume hosts through atmospheric nitrogen fixation which takes place in the nodules induced in their roots or stems. In addition, rhizobia have other plant growth-promoting mechanisms, mainly solubilization of phosphate and production of indoleacetic acid, ACC deaminase and siderophores. Some of these mechanisms have been reported for strains of rhizobia which are also able to promote the growth of several nonlegumes, such as cereals, oilseeds and vegetables. Less studied are the mechanisms that have the rhizobia to promote the plant health; however, these bacteria are able to exert biocontrol of some phytopathogens and to induce the plant resistance. In this chapter, we revised the available data about the ability of the legume nodule-inducing bacteria for improving the plant growth, health and nutrition of both legumes and nonlegumes. These data showed that rhizobia meet all the requirements of sustainable agriculture to be used as bio-inoculants allowing the total or partial replacement of chemicals used for fertilization or protection of crops

Sex difference and intra-operative tidal volume: Insights from the LAS VEGAS study

BACKGROUND: One key element of lung-protective ventilation is the use of a low tidal volume (VT). A sex difference in use of low tidal volume ventilation (LTVV) has been described in critically ill ICU patients.OBJECTIVES: The aim of this study was to determine whether a sex difference in use of LTVV also exists in operating room patients, and if present what factors drive this difference.DESIGN, PATIENTS AND SETTING: This is a posthoc analysis of LAS VEGAS, a 1-week worldwide observational study in adults requiring intra-operative ventilation during general anaesthesia for surgery in 146 hospitals in 29 countries.MAIN OUTCOME MEASURES: Women and men were compared with respect to use of LTVV, defined as VT of 8 ml kg-1 or less predicted bodyweight (PBW). A VT was deemed 'default' if the set VT was a round number. A mediation analysis assessed which factors may explain the sex difference in use of LTVV during intra-operative ventilation.RESULTS: This analysis includes 9864 patients, of whom 5425 (55%) were women. A default VT was often set, both in women and men; mode VT was 500 ml. Median [IQR] VT was higher in women than in men (8.6 [7.7 to 9.6] vs. 7.6 [6.8 to 8.4] ml kg-1 PBW, P &lt; 0.001). Compared with men, women were twice as likely not to receive LTVV [68.8 vs. 36.0%; relative risk ratio 2.1 (95% CI 1.9 to 2.1), P &lt; 0.001]. In the mediation analysis, patients' height and actual body weight (ABW) explained 81 and 18% of the sex difference in use of LTVV, respectively; it was not explained by the use of a default VT.CONCLUSION: In this worldwide cohort of patients receiving intra-operative ventilation during general anaesthesia for surgery, women received a higher VT than men during intra-operative ventilation. The risk for a female not to receive LTVV during surgery was double that of males. Height and ABW were the two mediators of the sex difference in use of LTVV.TRIAL REGISTRATION: The study was registered at Clinicaltrials.gov, NCT01601223