Delta-Nabla Optimal Control Problems

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Contro

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

Optimal impulse control of dynamical systems

Using the tools of the Markov decision processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for the study of piecewise deterministic Markov processes

Reproductive output, foraging destinations, and isotopic niche of olive ridley and loggerhead sea turtles, and their hybrids, in Brazil

Hybridization is a fundamental evolutionary and ecological process with significant conservation ramifications. Sea turtle hybridization occurs at unusually high frequencies along the northeastern coast of Brazil. To better understand the process, we studied the reproductive output, migration patterns (through satellite telemetry), and isotopic niches of loggerhead turtles Caretta caretta and olive ridley turtles Lepidochelys olivacea and their hybrids. We classified 154 nesting females as loggerhead (n = 91), olive ridley (n = 38), or hybrid (n = 25) based on mitochondrial and nuclear DNA. Further, we compared nesting female morphological data and reproductive parameters (clutch size, emergence success, hatchling production, incubation period) of 405 nests among hybrids and parental species. We found no significant differences among the 3 groups when hatchling production was corrected for female body size, indicating that hybrids and parental species produce similar numbers of hatchlings per clutch. Satellite tracking of 8 post-nesting hybrid females revealed shared foraging grounds with both parental species, as well as neritic migrations between foraging and nesting areas similar to those previously reported for loggerheads and olive ridleys. Analyses of 13C and 15N isotope values (n = 69) further confirmed this pattern, as hybrid isotopic niches overlapped extensively with both parental species. Thus, given the similarities presented between hybrids and their parental species in reproductive, ecological, and behavioral characteristics, we conclude that these hybrids may persist along with other sea turtle nesting populations in the area, with research and conservation implications. © The authors 2021. Open Access under Creative Commons by Attribution Licence. Use, distribution and reproduction are unrestricted. Authors and original publication must be credited

InterMiG: international differences in the therapeutic approach to migraine patients in specialized headache centers

Antidepressiu; Migranya; Tractament preventiuAntidepresivo; Migraña; Tratamiento preventivoAntidepressant; Migraine; Preventive treatmentBackground There is currently a wide therapeutic arsenal for migraine patients, without a single first-line preventive drug and we choose the different available alternatives taking into account comorbidities, national guidelines, previous treatments and personal experiences. Our objective was to evaluate the differences in the use of migraine treatments between neurologists from different countries. Methods This is a multi-centre observational study carried out by neurologists from specialized headache units in seven countries, retrospective with consecutive inclusion of all patients presenting with a migraine diagnosis, over a period of three months. Results A total of 734 patients were recruited but only 600 were considered in the analysis in order to homogenize the patient cohorts from countries: 200 Spain (ES), 100 Italy (IT), 85 Russia (RUS), 80 Germany (DE), 60 Portugal (PT), 45 Poland (PL) and 30 Australia (AU). 85.4 % of patients were women with a mean age of 42.6 ± 11.8 years. Considering previous and current preventive treatment, the order of use was: antidepressants (69.3 %), antiepileptic drugs (54.7 %), beta-blockers and antihypertensive drugs (49.7 %), OnabotulinumtoxinA (44.0 %) and others (36.2 %). Statistically significant differences were found between all pharmacological classes: antidepressants were commonly used in all countries, with the exception of Poland (AU: 76.7 %, IT: 71.0 %, DE: 60.0 %, PL: 31.1 %, PT: 71.7 %, RUS: 70.6 %, ES: 78.5 %; p < 0.0001); antiepileptic drugs were more frequently prescribed in Portugal, Australia and Spain (AU: 73.3 %, IT: 40.0 %, DE: 37.5 %, PL: 48.9 %, PT: 85.0 %, RUS: 29.4 % and ES: 69.0 %; p < 0.0001); beta-blockers and antihypertensive drugs were frequently used in all countries except Italy (AU: 60.0 %, IT: 14.0 %, DE: 53.8 %, PL: 48.9 %, PT: 68.3 %, RUS: 49.4 % and ES: 59.0 %; p < 0.0001); BTX-A were predominately used in Spain, Italy and Australia (AU:56.7 %, IT:58.0 %, DE:20.0 %, PL: 42.2 %, PT: 26.7 %, RUS: 24.7 % and ES: 58.5 %; p < 0.0001) and others were most frequently used in Poland (AU: 0.0 %, IT: 19.0 %, DE: 42.5 %, PL: 95.6 %, PT: 31.7 %, RUS: 3.5 % and ES: 49.5 %; p < 0.0001). If only patients without comorbidities are considered (200/600), statistically differences between countries persist in all preventive treatments. Conclusions There is heterogeneity in the choice of preventive treatment between different countries. Prospective comparative studies of the different oral and subcutaneous alternatives would help to create a global therapeutic algorithm that would guarantee the best option for our patients.This work did not receive any funds

Land Use Sector Involvement in Mitigation Policies Across Carbon Markets

Different local and international experiences show that the agroforestry sector can be fully included in the global warming mitigation strategies and in the market mechanisms that may have environmental and socioeconomic benefits. At present, however, the primary sector plays only a minor role in mitigation policies within the UNFCCC and under Kyoto’s Protocol, due to problems and difficulties related to emission/absorption accounting models andmonitoring and standardisation systems. If, on one hand, the progress in science has enabled to overcome accountingrelated problems, on the other, there are no adequate mechanisms to encourage and remunerate the primary sector’s efforts. More specifically, if the primary sector is considered as a source of emissions, it should also be recognised that it has beneficial impacts, notably in economic terms, as carbon sink. Therefore, the definition of clear and internationally shared rules might increase the carbon friendly initiatives and help reduce greenhouse gas emissions. This article is focused on the international experiences that have concerned the primary sector and is intended to supply researchers and policymakers with suggestions and recommendations for implementing local market practices related to carbon credits