Simple maps, Hurwitz numbers, and Topological Recursion

We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a restriction is not imposed are called ordinary. We study in detail the combinatorics of fully simple maps with topology of a disk or a cylinder. We show that the generating series of simple disks is given by the functional inversion of the generating series of ordinary disks. We also obtain an elegant formula for cylinders. These relations reproduce the relation between moments and free cumulants established by Collins et al. math.OA/0606431, and implement the symplectic transformation $x \leftrightarrow y$ on the spectral curve in the context of topological recursion. We conjecture that the generating series of fully simple maps are computed by the topological recursion after exchange of $x$ and $y$. We propose an argument to prove this statement conditionally to a mild version of symplectic invariance for the $1$-hermitian matrix model, which is believed to be true but has not been proved yet. Our argument relies on an (unconditional) matrix model interpretation of fully simple maps, via the formal hermitian matrix model with external field. We also deduce a universal relation between generating series of fully simple maps and of ordinary maps, which involves double monotone Hurwitz numbers. In particular, (ordinary) maps without internal faces -- which are generated by the Gaussian Unitary Ensemble -- and with boundary perimeters $(\lambda_1,\ldots,\lambda_n)$ are strictly monotone double Hurwitz numbers with ramifications $\lambda$ above $\infty$ and $(2,\ldots,2)$ above $0$. Combining with a recent result of Dubrovin et al. math-ph/1612.02333, this implies an ELSV-like formula for these Hurwitz numbers.Comment: 66 pages, 7 figure

Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes

We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$, $g\geq 2$. We then prove several cases of the combinatorial identity, providing a new proof of Faber's formula for those cases

Un heroe sen tempo: 20 anos de cultura galega sen Reimundo Patiño

El propósito de este artículo es revisar la lectura histórica del proyecto estético de Reimundo Patiño en el vigésimo aniversario de su fallecimiento.This article review the aesthetic project of Reimundo Patiño when take place the 20th aniversary of his death

Relating ordinary and fully simple maps via monotone Hurwitz numbers

A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten calculus for matrix integrals. The goal of this paper is to present two independent proofs that are purely combinatorial and generalise in various directions, such as to the setting of stuffed maps and hypermaps. The main motivation to understand the relation between ordinary and fully simple maps is the fact that it could shed light on fundamental, yet still not well-understood, problems in free probability and topological recursion.Comment: 19 pages, 7 figure

Health Related Quality of Life in Coronary Patients.

The increase observed in the survival of patients with ischemic cardiopathy, together with the effect of the disease on the social, professional, and family life of those suffering from it, have led researchers to consider that the traditional ways of measuring morbidity and mortality are not adequate for assessing the potential benefits of health care interventions. For this reason, there is common agreement on the need to use an indicator of subjective assessment of health, and of health related quality of life (HRQL), as a complementary criterion for monitoring the results of medical interventions in these patients. The term "quality of life" (QoL) or health related quality of life (HRQL) came into use during the 1970s as a multidimensional concept reflecting the overall subjective condition of the physical and mental welfare of the individual, which is a consequence not only of the disease but also of the family and social conditions forming the patient’s environment. The assessment of these patients’ HRQL has been tackled by several authors using both disease-specific and generic instruments such as the Nottingham Health Profile, the Sickness Impact Profile, the SF-36 or the SF-12 health questionnaire. Both types of instrument have advantages and disadvantages, and they may provide additional information since they quantify the patient’s overall health. Using different multidimensional measures, poorer HRQL has been observed in patients with Acute Myocardial Infarction (AMI) and angina pectoris than in other populations, and these differences have been related to low social class, female sex, the presence of mental disorders and the severity of the clinical condition. Measuring changes in the HRQL of coronary patients is also important as a way of assessing interventions and predicting needs for social care, because it has been shown that the focus of attention in the immediate period following a cardiac attack is generally the physical functioning, but following discharge from hospital and in the longer term, general health, vitality, social and emotional functions could be at least as important. In this chapter, we aim to provide an overview of the concept of HRQL and the usefulness of this measure from the perspective of a coronary patient. Likewise, we intend to review the main instruments used to assess HRQL and we analyse the factors that have been seen to affect the quality of life of these patients

Medicine 5th course student’s attitudes towards mental health

Introducción. El estigma social que persiste hacia la enfermedad mental puede estar presente en los estudiantes de medicina e impactar en la forma de considerar ésta y la psiquiatría como especialidad. Objetivo. Investigar la actitud hacia la enfermedad mental y la psiquiatría en una muestra de estudiantes. Sujetos y métodos. Se realizó una encuesta estructurada, voluntaria y anónima a los 27 estudiantes de quinto curso del grado de medicina de la Universidad San Pablo-CEU de Madrid. La encuesta incluía un cuestionario sobre el nivel de familiaridad hacia la enfermedad mental, el cuestionario de actitud hacia la enfermedad mental (AMI) y el cuestionario adaptado de Balon sobre la actitud hacia la psiquiatría. Resultados. Un total de 22 alumnos respondió la encuesta (72,7% mujeres). Estos alumnos presentaron una alta familiaridad con la enfermedad mental (puntuación media: 7,27; máximo: 11). El 81,8% refirieron una actitud positiva hacia la enfermedad mental (escala AMI). Las puntuaciones de la escala de Balon también mostraron un nivel alto de acuerdo en los méritos globales de la psiquiatría y en la eficacia de ésta. Tampoco las respuestas respecto al rol y función del psiquiatra y a la carrera profesional revelaron una postura negativa. No hubo relación entre la familiaridad y la actitud hacia la enfermedad mental o hacia la psiquiatría. Conclusiones. En esta muestra no se evidencia la existencia de estigma hacia la enfermedad mental o hacia la psiquiatría. Posteriores estudios en muestras más amplias y evaluaciones de la enseñanza de la psiquiatría son necesarios para profundizar en este tema

El Deterioro Cognitivo: un Factor a Tener en Cuenta en la Evaluación e Intervención de Pacientes con Dolor Crónico.

El dolor crónico constituye un grave problema de salud pública, dada su elevada prevalencia y las consecuencias personales y sociales que produce. La presencia de dolor crónico se ha asociado con un deterioro cognitivo leve, sobre todo en los pacientes afectados por fibromialgia o dolor neuropático, habiéndose relacionado esto con la concurrencia en estos pacientes, de otros procesos, como la ansiedad, la depresión, los trastornos del sueño y el consumo de ciertos fármacos, todos ellos habituales en los pacientes con dolor crónico. En esta revisión, hacemos un repaso del complejo proceso de la cognición así como de los distintos elementos que lo integran. Asimismo, revisamos los mecanismos mediante los que el dolor crónico puede afectar el proceso de la cognición y el modo en el que este puede verse afectado por la concurrencia de otras patologías, o por los fármacos habitualmente utilizados para su tratamiento. Finalmente se plantea la necesidad de evaluar el deterioro cognitivo en los pacientes con dolor crónico, con el objetivo de evitar la progresión de la enfermedad cognitiva hacia un cuadro de deterioro más grave, así como de contribuir a mejorar la respuesta terapéutica al dolor y el aumento de la calidad de vida de los pacientes.Chronic pain constitutes a serious public health problem due to its high prevalence and the social and personal consequences. The presence of chronic pain has been associated with mild cognitive impairment, especially in patients with fibromyalgia and neuropathic pain, and it has been also related with other disease like anxiety, depression, sleep disorders and the use of certain drugs, usually taken on these patients. This document revises the complex issue of the cognitive process and the several elements that comprise it. Likewise, we review the different mechanisms by which pain affect cognitive process and the way it could be affected by other disease, or by drugs commonly used on treatment. It is necessary to assess mild cognitive impairment on chronic pain patients, in order to prevent the develop and the evolution of cognitive disease to a more severe impairment, as well as help to improve therapeutic response to pain and increase health related quality of life of patients

Undiagnosed mood disorders and sleep disturbances in primary care patients with chronic musculoskeletal pain.

Objective. The study aims to determine the prevalence of undiagnosed comorbid mood disorders in patients suffering chronic musculoskeletal pain in a primary care setting and to identify sleep disturbances and other associated factors in these patients, and to compare the use of health services by chronic musculoskeletal pain patients with and without comorbid mood disorders. Design. Cross-sectional study. Subjects. A total of 1,006 patients with chronic musculoskeletal pain from a representative sample of primary care centers were evaluated. Outcome Measures. Pain was measured using a visual analog scale and the Primary Care Evaluation of Mental Disorders questionnaire was used to measure mood disorders. Results. We observed a high prevalence of undiagnosed mood disorders in chronic musculoskeletal pain patients (74.7%, 95% confidence interval [CI] 71.9–77.4%), with greater comorbidity in women (adjusted odds ratio [OR] = 1.91, 95% CI 1.37–2.66%) and widow(er)s (adjusted OR = 1.87, 95% CI 1.19–2.91%). Both sleep disturbances (adjusted OR = 1.60, 95% CI 1.17–2.19%) and pain intensity (adjusted OR = 1.02, 95% CI 1.01–1.02%) displayed a direct relationship with mood disorders. Moreover, we found that chronic musculoskeletal pain patients with comorbid mood disorders availed of health care services more frequently than those without (P < 0.001). Conclusions. The prevalence of undiagnosed mood disorders in patients with chronic musculoskeletal pain is very high in primary care settings. Our findings suggest that greater attention should be paid to this condition in general practice and that sleep disorders should be evaluated in greater detail to achieve accurate diagnoses and select the most appropriate treatment