Consequences of an incorrect model specification on population growth

We consider stochastic differential equations to model the growth of a population ina randomly varying environment. These growth models are usually based on classical deterministic models, such as the logistic or the Gompertz models, taken as approximate models of the "true" (usually unknown) growth rate. We study the effect of the gap between the approximate and the "true" model on model predictions, particularly on asymptotiv behavior and mean and variance of the time to extinction of the population

Random differential operational calculus: Theory and applications

A product rule and a chain rule for mean square derivatives are obtained using fourth order properties. Applications to the mean square solution of random differential equations are shown

Random differential operational calculus: theory and applications

In this article, we obtain a product rule and a chain rule for mean square derivatives. An application of the chain rule to the mean square solution of random differential equations is shown. However, to achieve such mean square differentiation rules, fourth order properties were needed and, therefore, we first studied a mean fourth order differential and integral calculus. Results are applied to solve random linear variable coefficient differential problems

Solving Riccati time-dependent models with random quadratic coefficient

This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition is a random variable. Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity. Next, an approximate solution of the nonlinear problem is constructed in terms of a random power series solution of the associate linear problem. Approximations of the average and variance of the solution are provided. The proposed technique is illustrated through an example where comparisons with respect to Monte Carlo simulations are shown. © 2011 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universitat Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Company Rossi, R.; Villafuerte Altuzar, L. (2011). Solving Riccati time-dependent models with random quadratic coefficient. Applied Mathematics Letters. 24(12):2193-2196. https://doi.org/10.1016/j.aml.2011.06.024S21932196241

Solving linear and quadratic random matrix differential equations: A mean square approach

[EN] In this paper linear and Riccati random matrix differential equations are solved taking advantage of the so called L-p-random calculus. Uncertainty is assumed in coefficients and initial conditions. Existence of the solution in the L-p-random sense as well as its construction are addressed. Numerical examples illustrate the computation of the expectation and variance functions of the solution stochastic process. (C) 2016 Elsevier Inc. All rights reserved.This work has been partially supported by the Spanish Ministerio de Economia y Competitividad grant MTM2013-41765-P and by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement no. 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance).Casabán Bartual, MC.; Cortés López, JC.; Jódar Sánchez, LA. (2016). Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling. 40(21-22):9362-9377. https://doi.org/10.1016/j.apm.2016.06.017S936293774021-2

Gene expression analysis of cell death induction by Taurolidine in different malignant cell lines

<p>Abstract</p> <p>Background</p> <p>The anti-infective agent Taurolidine (TRD) has been shown to have cell death inducing properties, but the mechanism of its action is largely unknown. The aim of this study was to identify potential common target genes modulated at the transcriptional level following TRD treatment in tumour cell lines originating from different cancer types.</p> <p>Methods</p> <p>Five different malignant cell lines (HT29, Chang Liver, HT1080, AsPC-1 and BxPC-3) were incubated with TRD (100 μM, 250 μM and 1000 μM). Proliferation after 8 h and cell viability after 24 h were analyzed by BrdU assay and FACS analysis, respectively. Gene expression analyses were carried out using the <it>Agilent </it>-microarray platform to indentify genes which displayed conjoint regulation following the addition of TRD in all cell lines. Candidate genes were subjected to <it>Ingenuity Pathways Analysis </it>and selected genes were validated by qRT-PCR and Western Blot.</p> <p>Results</p> <p>TRD 250 μM caused a significant inhibition of proliferation as well as apoptotic cell death in all cell lines. Among cell death associated genes with the strongest regulation in gene expression, we identified pro-apoptotic transcription factors (EGR1, ATF3) as well as genes involved in the ER stress response (PPP1R15A), in ubiquitination (TRAF6) and mitochondrial apoptotic pathways (PMAIP1).</p> <p>Conclusions</p> <p>This is the first conjoint analysis of potential target genes of TRD which was performed simultaneously in different malignant cell lines. The results indicate that TRD might be involved in different signal transduction pathways leading to apoptosis.</p

Solving the random diffusion model in an infinite medium: A mean square approach

[EN] This paper deals with the construction of an analytic-numerical mean square solution of the random diffusion model in an infinite medium. The well-known Fourier transform method, which is used to solve this problem in the deterministic case, is extended to the random framework. Mean square operational rules to the Fourier transform of a stochastic process are developed and stated. The main statistical moments of the stochastic process solution are also computed. Finally, some illustrative numerical examples are included.This work has been partially supported by the Ministerio de Economia y Competitividad grant: DPI2010-20891-c0-01, and Universitat Politecnica de Valencia grant: PAID06-11-2070.Casabán, M.; Company Rossi, R.; Cortés, J.; Jódar Sánchez, LA. (2014). Solving the random diffusion model in an infinite medium: A mean square approach. Applied Mathematical Modelling. 38(24):5922-5933. https://doi.org/10.1016/j.apm.2014.04.063S59225933382

Some recommendations for applying gPC (generalized polynomial chaos) to modeling: An analysis through the Airy random differential equation

In this paper we study the use of the generalized polynomial chaos method to differential equations describing a model that depends on more than one random input. This random input can be in the form of parameters or of initial or boundary conditions. We investigate the effect of the choice of the probability density functions for the inputs on the output stochastic processes. The study is performed on the Airy¿s differential equation. This equation is a good test case since its solutions are highly oscillatory and errors can develop both in the amplitude and the phase. Several different situations are considered and, finally, conclusions are presented.This work has been partially supported by the Spanish M.C.Y.T. and FEDER Grants MTM2009-08587, DPI2010-20891-C02-01 as well as the Universitat Politecnica de Valencia Grants PAID-00-11 (Ref. 2751) and PAID-06-11 (Ref. 2070).Chen Charpentier, BM.; Cortés López, JC.; Romero Bauset, JV.; Roselló Ferragud, MD. (2013). Some recommendations for applying gPC (generalized polynomial chaos) to modeling: An analysis through the Airy random differential equation. Applied Mathematics and Computation. 219(9):4208-4218. https://doi.org/10.1016/j.amc.2012.11.007S42084218219

Clinical significance of pneumatosis intestinalis - correlation of MDCT-findings with treatment and outcome.

To evaluate the clinical significance of pneumatosis intestinalis (PI) including the influence on treatment and outcome. Two radiologists jointly reviewed MDCT-examinations of 149 consecutive emergency patients (53 women, mean age 64, range 21-95) with PI of the stomach (n = 4), small (n = 68) and/or large bowel (n = 96). PI extension, distribution and possibly associated porto-mesenteric venous gas (PMVG) were correlated with other MDCT-findings, risk factors, clinical management, laboratory, histopathology, final diagnosis and outcome. The most frequent cause of PI was intestinal ischemia (n = 80,53.7 %), followed by infection (n = 18,12.1 %), obstructive (n = 12,8.1 %) and non-obstructive (n = 10,6.7 %) bowel dilatation, unknown aetiologies (n = 8,5.4 %), drugs (n = 8,5.4 %), inflammation (n = 7,4.7 %), and others (n = 6,4 %). Neither PI distribution nor extension significantly correlated with underlying ischemia. Overall mortality was 41.6 % (n = 62), mostly related to intestinal ischemia (p = 0.003). Associated PMVG significantly correlated with underlying ischemia (p = 0.009), as did the anatomical distribution of PMVG (p = 0.015). Decreased mural contrast-enhancement was the only other MDCT-feature significantly associated with ischemia (p p &lt; 0.001). Elevated white blood count significantly correlated with ischemia (p = 0.03). In emergency patients, ischemia remains the most common aetiology of PI, showing the highest mortality. PI with associated PMVG is an alerting sign. PI together with decreased mural contrast-enhancement indicates underlying ischemia. • In emergency patients, PI may be caused by various disorders. • Intestinal ischemia remains the most common cause of PI in acute situations. • PI associated with decreased mural contrast-enhancement indicates acute intestinal ischemia. • PI associated with PMVG should alert the radiologist to possible underlying ischemia