The Stieltjes--Fekete problem and degenerate orthogonal polynomials

A famous result of Stieltjes relates the zeroes of the classical orthogonal polynomials with the configurations of points on the line that minimize a suitable energy. The energy has logarithmic interactions and an external field whose exponential is related to the weight of the classical orthogonal polynomials. The optimal configuration satisfies an algebraic set of equations: we call this set of algebraic equations the Stieltjes--Fekete problem or equivalently the Stieltjes--Bethe equations. In this work we consider the Stieltjes-Fekete problem when the derivative of the external field is an arbitrary rational complex function. We show that its solutions are in one-to-one correspondence with the zeroes of certain non-hermitean orthogonal polynomials that satisfy an excess of orthogonality conditions and are thus termed "degenerate". This generalizes the original result of Stieltjes.Comment: 21 pages. V2: 24 pages; improved historical overview and added references. 5 figures. Slight generalization of the proof. V3: 26 pages; expanded scope of proof and added significant example. V4: 30 pages. Added details on primality assumption and other improvement

Exactly Solvable Anharmonic Oscillator, Degenerate Orthogonal Polynomials and Painlevé II

Using WKB analysis, the paper addresses a conjecture of Shapiro and Tater on the similarity between two sets of points in the complex plane; on one side is the set the values for which the spectrum of the quartic anharmonic oscillator in the complex planewith certain boundary conditions, has repeated eigenvalues. On the other side is the set of zeroes of the Vorob’ev–Yablonskii polynomials, i.e. the poles of rational solutions of the second Painlevé equation. Along the way, we indicate a surprising and deep connection between the anharmonic oscillator problem and certain degenerate orthogonal (monic) polynomials

Between the colonial heritage and the first globalization boom: on income inequality in the Southern Cone

Special Issue on Latin American Inequality.This paper presents a first estimate of income inequality in the Southern Cone of South America (Brazil 1872 and 1920, Chile 1870 and 1920, Uruguay 1920) and some assumptions with regard to Argentina (1870 and 1920) and Uruguay (1870). We find that income distribution was relatively high on the eve of the first globalization boom. Thus, inequality is not only the result of globalization, but also a structural feature. Inequality increased between 1870 and 1920, both within individual countries and between countries. Globalization forces do not result in obvious outcomes. Rather, the effect of globalization on inequality depends on the expansion of the frontier and institutional persistence and change in old and new areas. Inequality was clearly high in the wake of the globalization process. This was a particular kind of inequality, which was part of a set of institutions closely linked to the exports of primary goods, sluggish technological change and limited human capital formation.Este artículo presenta una primera estimación de la distribución del ingreso en el Cono Sur de Sudamérica (Brasil 1872 y 1920, Chile 1870 y 1920, Uruguay 1920) y algunos supuestos sobre la desigualdad en Argentina 1870 y 1920, así como en Uruguay en 1870. Encontramos que la distribución del ingreso era relativamente alta en los albores de la primera globalización, por lo que la desigualdad del ingreso no solamente debe ser vista como el resultado de la globalización, sino como una característica estructural. La desigualdad aumentó entre 1870 y 1920, tanto dentro de cada país como entre los países del Cono Sur. Las fuerzas de la globalización no generan resultados obvios. Por el contrario, el impacto de la globalización sobre la desigualdad depende de la expansión de la frontera y de la persistencia y el cambio institucional en las viejas áreas y en las nuevas. La desigualdad fue particularmente alta al culminar la globalización. Se trató de una forma particular de desigualdad, que formó parte de un conjunto de instituciones estrechamente vinculadas a una economía exportadora de bienes primarios, con escaso desarrollo tecnológico y bajos niveles de formación de capital humano.This paper was written as part of the project «A Global History of Inequality in the Long 20th Century», directed by Luis Bértola and financed by CSIC, Universidad de la República, Uruguay

Coocorrência de mutações nos genes PTPN11 e SOS1 na síndrome de Noonan: este achado prediz um fenótipo mais grave?

Noonan syndrome (NS) is an autosomal dominant disorder, with variable phenotypic expression, characterized by short stature, facial dysmorphisms and heart disease. Different genes of the RAS/MAPK signaling pathway are responsible for the syndrome, the most common are: PTPN11, SOS1, RAF1, and KRAS. The objective of this study was to report a patient with Noonan syndrome presenting mutations in two genes of RAS/MAPK pathway in order to establish whether these mutations lead to a more severe expression of the phenotype. We used direct sequencing of the PTPN11, SOS1, RAF1, and KRAS genes. We have identified two described mutations in heterozygosity: p.N308D and p.R552G in the genes PTPN11 and SOS1, respectively. The patient has typical clinical features similar to the ones with NS and mutation in only one gene, even those with the same mutation identified in this patient. A more severe or atypical phenotype was not observed, suggesting that these mutations do not exhibit an additive effect.A síndrome de Noonan (SN) é uma doença gênica autossômica dominante, com expressão clínica variável, caracterizada por baixa estatura, dismorfismos faciais e cardiopatia. Diferentes genes da via de sinalização RAS/MAPK são responsáveis pela síndrome, sendo as mais frequentes: PTPN11, SOS1, RAF1 e KRAS. O objetivo deste estudo foi relatar um paciente com SN que apresenta mutações em dois genes da via RAS/MAPK a fim de estabelecer se essas mutações levam a uma expressão mais grave do fenótipo. Utilizou-se sequenciamento direto dos genes PTPN11, SOS1, RAF1 e KRAS. Foram identificadas duas mutações em heterozigose previamente descritas: p.N308D e p.R552G nos genes PTPN11 e SOS1, respectivamente. A paciente apresenta quadro clínico típico semelhante ao dos pacientes com SN e mutação em um único gene, mesmo naqueles com a mesma mutação identificada na paciente. Não foi observado um fenótipo mais grave ou atípico na paciente, sugerindo que as mutações não apresentam um efeito aditivo

Diabetic Amyotrophy co-occurring with treatment induced neuropathy of diabetes (TIND): a case report

Diabetic amyotrophy is a rare condition in diabetic patients, usually associated with important weight loss. In the present case, we show a rare presentation of diabetic amyotrophy phenotype in the context of treatment induced neuropathy of diabetes neuropathy (TIND) after a strict glycemic control in a patient with long-standing poor controlled diabetes and without related weight loss. Even though it’s an uncommon presentation, because of diabetes high prevalence worldwide the knowledge of its complications is important to the adequate treatment and follow-up to improve patients’ quality of life.&nbsp

Playas sostenibles en Mar del Plata

Esta obra propone un acercamiento a las costas de Mar del Plata desde una perspectiva integral. Aborda el uso de indicadores ambientales de las playas que nos permiten conocer más sobre su sostenibilidad actual y a futuro. El lector encontrará información sobre la historia y diversidad de las playas de la ciudad, así como su morfología dada por el oleaje y las corrientes. También tendrá a su disposición material relevante sobre el uso de estos ambientes desde la gestión pública y privada, así como su reglamentación y legislación, gestión de residuos y accesibilidad universal. Por medio de encuestas, efectuadas a los visitantes de las playas, los autores realizan un reconocimiento de las preferencias y exigencias en el uso de este recurso turístico.Fil: Bertola, German Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; ArgentinaFil: Cecchi, Federico Alcides. Universidad Tecnologica Nacional. Facultad Regional Mar del Plata. Departamento de Medio Ambiente.; ArgentinaFil: Chaparro, Mauro Alejandro Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; ArgentinaFil: del Rio, Julio Luis. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Geología de Costas y del Cuaternario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Geología de Costas y del Cuaternario; ArgentinaFil: Demarchi, Nora Gabriela. Universidad Nacional de Mar del Plata; ArgentinaFil: Lucero, Marcelo. Universidad Tecnologica Nacional. Facultad Regional Mar del Plata. Departamento de Medio Ambiente.; ArgentinaFil: Mantecón, Cecilia Lucía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Geología de Costas y del Cuaternario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto de Geología de Costas y del Cuaternario; ArgentinaFil: Morrell, Patricia Alejandra. Universidad Nacional de Mar del Plata; ArgentinaFil: Pérsico, María Marta. Universidad Nacional de Mar del Plata; Argentina. Universidad Tecnologica Nacional. Facultad Regional Mar del Plata. Departamento de Medio Ambiente.; ArgentinaFil: Prario, Maria Ines. Universidad Tecnologica Nacional. Facultad Regional Mar del Plata. Departamento de Medio Ambiente.; ArgentinaFil: Rigonat, María Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata; Argentin