Higher Order Variational Integrators: a polynomial approach

We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the structural properties of these systems, like the symplectic form, the evolution of the momentum maps or the energy behaviour. Also they are easily applicable to optimal control problems based on mechanical systems as proposed in Ober-Bl\"obaum et al. [2011]. Following the same approach, we develop a family of variational integrators to which we refer as symplectic Galerkin schemes in contrast to symplectic partitioned Runge-Kutta. These two families of integrators are, in principle and by construction, different one from the other. Furthermore, the symplectic Galerkin family can as easily be applied in optimal control problems, for which Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and Applications, CEDYA 201

Discrete Variational Optimal Control

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.Comment: 30 pages, 6 figure

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Is tagging with visual implant elastomer a reliable technique for marking earthworms?

Visual implant elastomer (VIE) has recently been employed to investigate different aspects of earthworm ecology. However, a number of fundamental questions relating to the detection and positioning of the tag, its persistence and potential effects on earthworms remain unknown. Seven earthworm species belonging to three ecological groupings, with different pigmentation and burrowing behaviour, were tagged using different coloured VIE. External inspection after two days, one week and 1, 10 and 27 months were followed by preservation, dissection and internal inspection. Tags could be seen in living specimens to 27 months, and dissection revealed that in most cases they were lodged in the coelomic cavity, held in place by septa. However, over longer time periods (more than two years), the chlorogogenous tissue tended to bind to the tags and made external observation increasingly difficult. Migration of the VIE material towards the posterior of the earthworm and potential loss of the tag were only observed on rare occasions, and a recovery rate in excess of 98% was recorded. By introducing a reasonable amount of VIE into segments, just after the clitellum, this technique can become a valuable tool in earthworm ecology and life history studies, particularly in short-medium term laboratory and field experiments

High-resolution magnetic resonance imaging reveals nuclei of the human amygdala: manual segmentation to automatic atlas

Available online 4 May 2017The amygdala is composed of multiple nuclei with unique functions and connections in the limbic system and to the rest of the brain. However, standard in vivo neuroimaging tools to automatically delineate the amygdala into its multiple nuclei are still rare. By scanning postmortem specimens at high resolution (100–150 µm) at 7 T field strength (n = 10), we were able to visualize and label nine amygdala nuclei (anterior amygdaloid, cortico-amygdaloid transition area; basal, lateral, accessory basal, central, cortical medial, paralaminar nuclei). We created an atlas from these labels using a recently developed atlas building algorithm based on Bayesian inference. This atlas, which will be released as part of FreeSurfer, can be used to automatically segment nine amygdala nuclei from a standard resolution structural MR image. We applied this atlas to two publicly available datasets (ADNI and ABIDE) with standard resolution T1 data, used individual volumetric data of the amygdala nuclei as the measure and found that our atlas i) discriminates between Alzheimer's disease participants and age-matched control participants with 84% accuracy (AUC=0.915), and ii) discriminates between individuals with autism and age-, sex- and IQ-matched neurotypically developed control participants with 59.5% accuracy (AUC=0.59). For both datasets, the new ex vivo atlas significantly outperformed (all p < .05) estimations of the whole amygdala derived from the segmentation in FreeSurfer 5.1 (ADNI: 75%, ABIDE: 54% accuracy), as well as classification based on whole amygdala volume (using the sum of all amygdala nuclei volumes; ADNI: 81%, ABIDE: 55% accuracy). This new atlas and the segmentation tools that utilize it will provide neuroimaging researchers with the ability to explore the function and connectivity of the human amygdala nuclei with unprecedented detail in healthy adults as well as those with neurodevelopmental and neurodegenerative disorders.This work was supported by the PHS grant DA023427 and NICHD/ NIH grant F32HD079169 (Z.M.S); Feodor Lynen Postdoctoral Fellowship of the Alexander von Humboldt Foundation (D.K.); R21(MH106796), R21 (AG046657) and K01AG28521 (J.C.A.), the National Cancer Institute (1K25CA181632-01) as well as the Genentech Foundation (M.R.); the European Union's Horizon 2020 Marie Sklodowska-Curie grant agreement No 654911 (project ”THALAMODEL”) and ERC Starting Grant agreement No 677697 (project “BUNGEE-TOOLS”); and the Spanish Ministry of Economy and Competitiveness (MINECO) reference TEC2014-51882-P (J.E.I.); and the NVIDIA hardware award (M.R. and J.E.I.). Further support for this research was provided in part by the National Institute for Biomedical Imaging and Bioengineering (P41EB015896, R01EB006758, R21EB018907, R01EB019956, R01- EB013565), the National Institute on Aging (5R01AG008122, R01AG016495), the National Institute of Diabetes and Digestive and Kidney Diseases (1-R21-DK-108277-01), the National Institute for Neurological Disorders and Stroke (R01NS0525851, R21NS072652, R01NS070963, R01NS083534, 5U01NS086625), the Massachusetts ADRC (P50AG005134) and was made possible by the resources provided by Shared Instrumentation Grants 1S10RR023401, 1S10RR019307, and 1S10RR023043. Additional support was provided by the NIH Blueprint for Neuroscience Research (5U01-MH093765), part of the multi-institutional Human Connectome Project. In addition, BF has a financial interest in CorticoMetrics, a company whose medical pursuits focus on brain imaging and measurement technologies. BF's interests were reviewed and are managed by Massachusetts General Hospital and Partners HealthCare in accordance with their conflict of interest policies. The collection and sharing of the ADNI MRI data used in the evaluation was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2- 0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: Alzheimer's Association; Alzheimer's Drug Discovery Foundation; BioClinica, Inc.; Biogen Idec Inc.; Bristol-Myers Squibb Company; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; GE Healthcare; Innogenetics, N.V.; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Medpace, Inc.; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Synarc Inc.; and Takeda Pharmaceutical Company. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www. fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer's Disease Cooperative Study at the University of California, San Diego. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California

Comparison of the h-index for different fields of research using bootstrap methodology

An important disadvantage of the h-index is that typically it cannot take into account the specific field of research of a researcher. Usually sample point estimates of the average and median h-index values for the various fields are reported that are highly variable and dependent of the specific samples and it would be useful to provide confidence intervals of prediction accuracy. In this paper we apply the non-parametric bootstrap technique for constructing confidence intervals for the h-index for different fields of research. In this way no specific assumptions about the distribution of the empirical h-index are required as well as no large samples since that the methodology is based on resampling from the initial sample. The results of the analysis showed important differences between the various fields. The performance of the bootstrap intervals for the mean and median h-index for most fields seems to be rather satisfactory as revealed by the performed simulation

Unusual magnetic relaxation behavior in La0.5Ca0.5MnO3 and Nd0.5Sr0.5MnO3

We have carried out a systematic magnetic relaxation study, measured after applying and switching off a 5 T magnetic field to polycrystalline samples of La0.5Ca0.5MnO3 and Nd0.5Sr0.5MnO3. The long time logarithmic relaxation rate (LTLRR), decreased from 10 K to 150 K and increased from 150 K to 195 K in La0.5Ca0.5MnO3. This change in behavior was found to be related to the complete suppression of the antiferromagnetic phase above 150 K and in the presence of a 5 T magnetic field. At 195 K, the magnetization first decreased, and after a few minutes increased slowly as a function of time. Moreover, between 200 K and 245 K, the magnetization increased throughout the measured time span. The change in the slope of the curves, from negative to positive at about 200 K was found to be related to the suppression of antiferromagnetic fluctuations in small magnetic fields. A similar temperature dependence of the LTLRR was found for the Nd0.5Sr0.5MnO3 sample. However, the temperature where the LTLRR reached the minimum in Nd0.5Sr0.5MnO3 was lower than that of La0.5Ca0.5MnO3. This result agrees with the stronger ferromagnetic interactions that exist in Nd0.5Sr0.5MnO3 in comparison to La0.5Ca0.5MnO3. The above measurements suggested that the general temperature dependence of the LTLRR and the underlying physics were mainly independent of the particular charge ordering system considered. All relaxation curves could be fitted using a logarithmic law at long times. This slow relaxation was attributed to the coexistence of ferromagnetic and antiferromagnetic interactions between Mn ions, which produced a distribution of energy barriers.Comment: Accepted to PRB as a regular article, 10 figures, Scheduled Issue: 01 June 200

A Generalization of Chaplygin's Reducibility Theorem

In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincare-Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.Comment: 27 pages, 3 figures, submitted to Reg. and Chaotic Dy