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

On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

Three new Brazilian species in the genus Marcetia (Melastomataceae, Melastomeae)

Three new species of Marcetia are described and illustrated. Marcetia semiriana occurs only in Serra do Cip6, Minas Gerais. Marcetia shepherdii, collected in Marau, at sea level, and M. lychnophoroides, from Chapada Diamantina, are both endemic to Bahia. The new species il Marcetia shepherdii and M. lychnophoroides, together with ill. luetzelburgii Markgraf, constitute a group of closely related species. They share in common subcoriaceous, fleshy, imbricate to subimbricate, revolute leaves. Marcetia shepherdii is distinguished by its rigid, erect branchlets, yellowish green leaves that are glabrous on the adaxial surface, unappendaged and broadly dilated connectives, linear-oblong thecae with a ventrally inclined pore, and a unique 2-locular ovary, Marcetia lychnophoroides has velutinous to sublanate branchlets, cinereous-green leaves that are densely puberulous-sericeous on the abaxial surface, unprolonged and inconspicuously bilobulate connectives, and a 3- or 4-locular ovary. Marcetia semiriana is very similar to M. taxifolia (A. Saint-Hilaire) DC., differing in the prostrate branches, long pedunculate flowers, and straight anthers.10322422

Generalized transversality conditions for the Hahn quantum variational calculus

We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory

Two New Dioecious Species of Symplocos (Symplocaceae) from Southern Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Two new dioecious species of Symplocos Jacquin from Southern Brazil are described and illustrated. Both species belong to section Barberina (Vellozo) A. DC. of subgenus Symplocos. Symplocos bidana Aranha is characterized by its cymose or racemose inflorescences (9.5-)11-34 mm long, corolla with five or six lobes 3.7-4.9 mm long, and fruits (10-)13-20 x 5-10 mm with the calyx lobes covering the fruiting disc. Symplocos incrassata Aranha is characterized by its reduced cymes, bracts caducous in fruit, and fruits 12-18 x (5-)6-8 mm. In addition, both species have thick endocarps (0.8-1.2 mm), a notable character among the Brazilian species of section Barberina.19116U.S. National Science Foundation [DEB-0126631]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)U.S. National Science Foundation [DEB-0126631

TBA for non-perturbative moduli spaces

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this relation and, in particular, we identify the contact potential of quaternionic string moduli space with the free energy of the integrable system and the Kahler potential of the gauge theory moduli space with the Yang-Yang functional. We also show that the corresponding S-matrix satisfies all usual constraints of 2d integrable models, including crossing and bootstrap, and derive the associated Y-system. Surprisingly, in the simplest case the Y-system is described by the MacMahon function relevant for crystal melting and topological strings.Comment: 25 pages, 1 figur

Twisted Bethe equations from a twisted S-matrix

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.Comment: 42 pages; v2: a new appendix on sl(2) grading, 2 additional references, and some minor changes; v3: improved Appendix D, additional references, and further minor changes, to appear in JHE

Epileptic Encephalopathies of Childhood: The New Paradigm of Genetic Diagnosis

INTRODUCTION: Epileptic encephalopathies of childhood are characterized by early seizure-onset and adverse neurological outcomes. The development of new genetic techniques has allowed an exponential identification of the genes that are involved. Over the last years, we have observed a revolution in the diagnostic paradigm. However, there are no international guidelines regarding the diagnosis of genetic epileptic encephalopathies. We aim to discuss the current knowledge about the genetic architecture of epileptic encephalopathies of childhood. MATERIAL AND METHODS: review of the literature about infantile epileptic encephalopathies and the genetic tests currently available. A systematic approach and a diagnostic algorithm to use in clinical practice were proposed. RESULTS: Initially the patient's phenotype should be determined based on the seizure type, electroencephalogram pattern and neuroimaging. Patients with unclear etiology after brain magnetic resonance imaging should undergo an appropriate metabolic investigation to promptly exclude treatable conditions. Further studies should also include other genetic causes, mainly if associated with particular phenotypic features. Chromosomal microarray analysis should be firstly considered, particularly if dysmorphic or polymalformative abnormalities are present. If this is negative and/or there are no physical features, the next step should be next-generation sequencing multigene panels or whole-exome sequencing. Single gene study should only be considered when the patient's phenotype is highly suggestive of a specific syndrome. CONCLUSION: The revolution of the genetic knowledge about epileptic encephalopathies of childhood has led to a complex diagnostic approach. This new paradigm poses significant implications in genetic counselling, treatment and prognosis.Introdução: As encefalopatias epilépticas da infância constituem um grupo de patologias de início precoce e prognóstico neurológico reservado. O desenvolvimento das novas técnicas de estudo genético foi responsável pela identificação de novos genes implicados. Nos últimos anos, assistimos a uma revolução no seu paradigma diagnóstico. Contudo, actualmente não existem recomendações internacionais consensuais sobre a abordagem à investigação das encefalopatias epilépticas genéticas. Pretendemos discutir o conhecimento actual sobre a arquitectura genética das encefalopatias epilépticas infantis. Material e Métodos: Realizou-se uma revisão da literatura das encefalopatias epilépticas infantis genéticas e estudos utilizados no seu diagnóstico. Propomos uma abordagem sistematizada através de um algoritmo diagnóstico a utilizar na prática clínica. Resultados: Inicialmente deve-se determinar o fenótipo do doente com base no tipo de crises, padrão electroencefalográfico e neuroimagem. Nos doentes sem etiologia após resultados de ressonância magnética cranioencefálica, deve-se realizar estudo metabólico apropriado para o diagnóstico prioritário de doenças metabólicas tratáveis. A investigação de outras causas genéticas deve ser considerada, sobretudo perante características fenotípicas sugestivas. Primeiro deve-se realizar a análise de microarray cromossómico, principalmente se existirem alterações dismórficas ou polimalformativas. Se esta for negativa e/ou não existirem elementos físicos distintivos, o próximo passo deve ser realizar os painéis multigénicos ou sequenciação de exoma. Os estudos dirigidos do gene devem ser reservados para quando o fenótipo é indicativo de uma síndrome específica. Conclusão: A marcha diagnóstica das encefalopatias epilépticas tornou-se complexa com a expansão de conhecimentos genéticos. Este novo paradigma apresenta implicações terapêuticas, prognósticas e de aconselhamento familiar.info:eu-repo/semantics/publishedVersio

Moduli space coordinates and excited state g-functions

We consider the space of boundary conditions of Virasoro minimal models formed from the composition of a collection of flows generated by \phi_{1,3}. These have recently been shown to fall naturally into a sequence, each term having a coordinate on it in terms of a boundary parameter, but no global parameter has been proposed. Here we investigate the idea that the overlaps of particular bulk states with the boundary states give natural coordinates on the moduli space of boundary conditions. We find formulae for these overlaps using the known thermodynamic Bethe Ansatz descriptions of the ground and first excited state on the cylinder and show that they give a global coordinate on the space of boundary conditions, showing it is smooth and compact as expected.Comment: 10 pages, 4 figure

Health trajectories of Immigrant Children (CRIAS)-a prospective cohort study in the metropolitan area of Lisbon, Portugal

Funding Information: This research was financed by the Asylum, Integration and Migration Fund (ref.PT/2018/FAMI/350) under the Multianual Financial Framework 2014/20, by the Portuguese Foundation for Science and Technology (FCT) (ref.RESEARCH4COVID-19-065) and Global Health and Tropical Medicine (GHTM), Institute of Hygiene and Tropical Medicine (IHMT), NOVA University of Lisbon, Portugal (ref.UID/04413/2020). The extension of the cohort study is financed by the Portuguese Foundation for Science and Technology (FCT) (ref.PTDC/SAU-SER/4664/2020). Publisher Copyright: © 2022 BMJ Publishing Group. All rights reserved.Purpose The CRIAS (Health trajectories of Immigrant Children in Amadora) cohort study was created to explore whether children exposed to a migratory process experience different health risks over time, including physical health, cognitive, socioemotional and behavioural challenges and different healthcare utilisation patterns. Participants The original CRIAS was set up to include 604 children born in 2015, of whom 50% were immigrants, and their parents. Recruitment of 420 children took place between June 2019 and March 2020 at age 4/5 years, with follow-up carried out at age 5/6 years, at age 6/7 years currently under way. Findings to date Baseline data at age 4/5 years (2019-2020) suggested immigrant children to be more likely to belong to families with less income, compared with non-immigrant children. Being a first-generation immigrant child increased the odds of emotional and behavioural difficulties (adjusted OR 2.2; 95% CI: 1.06 to 4.76); more immigrant children required monitoring of items in the psychomotor development test (38.5% vs 28.3%). The prevalence of primary care utilisation was slightly higher among immigrant children (78.0% vs 73.8%), yet they received less health monitoring assessments for age 4 years. Utilisation of the hospital emergency department was higher among immigrants (53.2% vs 40.6%). Age 5 years follow-up (2020-2021) confirmed more immigrant children requiring monitoring of psychomotor development, compared with non-immigrant children (33.9% vs 21.6%). Economic inequalities exacerbated by post-COVID-19 pandemic confinement with parents of immigrant children 3.2 times more likely to have their household income decreased. Future plans Further follow-up will take place at 8, 10, 12/13 and 15 years of age. Funds awarded by the National Science Foundation will allow 900 more children from four other Lisbon area municipalities to be included in the cohort (cohort-sequential design).publishersversionpublishe