Discrete variational integrators and optimal control theory

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.Comment: 17 page

Tulczyjew's triples and lagrangian submanifolds in classical field theories

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.Comment: 29 page

Geometric numerical integration of nonholonomic systems and optimal control problems

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 200

Assessment of plasma chitotriosidase activity, CCL18/PARC concentration and NP-C suspicion index in the diagnosis of Niemann-Pick disease type C: A prospective observational study

Background: Niemann-Pick disease type C (NP-C) is a rare, autosomal recessive neurodegenerative disease caused by mutations in either the NPC1 or NPC2 genes. The diagnosis of NP-C remains challenging due to the non-specific, heterogeneous nature of signs/symptoms. This study assessed the utility of plasma chitotriosidase (ChT) and Chemokine (C-C motif) ligand 18 (CCL18)/pulmonary and activation-regulated chemokine (PARC) in conjunction with the NP-C suspicion index (NP-C SI) for guiding confirmatory laboratory testing in patients with suspected NP-C. Methods: In a prospective observational cohort study, incorporating a retrospective determination of NP-C SI scores, two different diagnostic approaches were applied in two separate groups of unrelated patients from 51 Spanish medical centers (n = 118 in both groups). From Jan 2010 to Apr 2012 (Period 1), patients with =2 clinical signs/symptoms of NP-C were considered ''suspected NP-C'' cases, and NPC1/NPC2 sequencing, plasma chitotriosidase (ChT), CCL18/PARC and sphingomyelinase levels were assessed. Based on findings in Period 1, plasma ChT and CCL18/PARC, and NP-C SI prediction scores were determined in a second group of patients between May 2012 and Apr 2014 (Period 2), and NPC1 and NPC2 were sequenced only in those with elevated ChT and/or elevated CCL18/PARC and/or NP-C SI =70. Filipin staining and 7-ketocholesterol (7-KC) measurements were performed in all patients with NP-C gene mutations, where possible. Results: In total across Periods 1 and 2, 10/236 (4%) patients had a confirmed diagnosis o NP-C based on gene sequencing (5/118 4.2%] in each Period): all of these patients had two causal NPC1 mutations. Single mutant NPC1 alleles were detected in 8/236 (3%) patients, overall. Positive filipin staining results comprised three classical and five variant biochemical phenotypes. No NPC2 mutations were detected. All patients with NPC1 mutations had high ChT activity, high CCL18/PARC concentrations and/or NP-C SI scores =70. Plasma 7-KC was higher than control cut-off values in all patients with two NPC1 mutations, and in the majority of patients with single mutations. Family studies identified three further NP-C patients. Conclusion: This approach may be very useful for laboratories that do not have mass spectrometry facilities and therefore, they cannot use other NP-C biomarkers for diagnosis