Perfect Matchings with Crossings.

For sets of n points, n even, in general position in the plane, we consider straight-line drawings of perfect matchings on them. It is well known that such sets admit at least Cn/2 different plane perfect matchings, where Cn/2 is the n/2-th Catalan number. Generalizing this result we are interested in the number of drawings of perfect matchings which have k crossings. We show the following results. (1) For every k≤164n2-3532nn+122564n, any set with n points, n sufficiently large, admits a perfect matching with exactly k crossings. (2) There exist sets of n points where every perfect matching has at most 572n2-n4 crossings. (3) The number of perfect matchings with at most k crossings is superexponential in n if k is superlinear in n. (4) Point sets in convex position minimize the number of perfect matchings with at most k crossings for k=0,1,2, and maximize the number of perfect matchings with n/22 crossings and with n/22-1 crossings.

Inserting One Edge into a Simple Drawing is Hard.

A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G + e extending D(G). As a result of Levi's Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment  σ , it can be decided in polynomial time whether there exists a pseudocircle Φ σ extending σ for which A ∪ { Φ σ } is again an arrangement of pseudocircles.

A new meta-module design for efficient reconfiguration of modular robots.

We propose a new meta-module design for two important classes of modular robots. The new meta-modules are three-dimensional, robust and compact, improving on the previously proposed ones. One of them applies to so-called edge-hinged modular robot units, such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, while the other one applies to so-called central-point-hinged modular robot units, which include Molecubes and Roombots. The new meta-modules use the rotational degrees of freedom of these two types of robot units in order to expand and contract, as to double or halve their length in each of the two directions of its three dimensions, therefore simulating the capabilities of Crystalline and Telecube robots. Furthermore, in the edge-hinged case we prove that the novel meta-module can also perform the scrunch, relax and transfer moves that are necessary in any tunneling-based reconfiguration algorithm for expanding/contracting modular robots such as Crystalline and Telecube. This implies that the use of meta-meta-modules is unnecessary, and that currently existing efficient reconfiguration algorithms can be applied to a much larger set of modular robots than initially intended. We also prove that the size of the new meta-modules is optimal and cannot be further reduced. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1007/s10514-021-09977-6.

[Impact of decentralization on health financing in Mexico]. / Efectos de la descentralización en el financiamiento de la salud en México.

OBJECTIVE: To identify trends and to describe the impact of health care decentralization on health financing policies in Mexico. METHODS: The study population comprised four states selected according with six technical criteria: socioeconomic development, implementation of decentralization process, database on economical features, data consistency and reliability, and technical support from a multidisciplinary team. In-depth interviews with key personnel as well as analysis of technical reports of state budgets for health in the period 1990-2000 were conducted. RESULTS: The analysis model applied allowed to determine the trends and the impact of health care decentralization on main financing sources: householders, and federal, state and municipal governments. There was evidence of different change effectiveness, especially regarding trends of financing per source. CONCLUSIONS: There are states where householders and state and municipal governments effectively increased financing support for health care system. But there are also states where householders and state and municipal governments do not agree on the increase of financing support for health care system.

Efectos de la descentralización en el financiamiento de la salud en México / Impact of decentralization on health financing in Mexico

OBJETIVO: Identificar las tendencias y los efectos de la descentralización en las políticas de financiamiento de la salud en México. MÉTODOS: La población de estudio incluyó cuatro estados seleccionados bajo criterios técnicos: diferente desarrollo socio-económico; implementación de la descentralización; base de datos sobre información económica; confiabilidad y validéz de las bases de datos; y apoyo de un equipo interdisciplinario de investigación. Las técnicas de recopilación de información se basaron en entrevistas a profundidad con personal clave y análisis de documentos y bases de datos sobre los presupuestos estatales en salud para el período 1990-2000. RESULTADOS: El modelo de análisis propuesto permitió identificar las tendencias y efectos de la descentralización sobre las principales fuentes de financiamiento en salud: Hogares, Gobiernos Federal, Estatal y Municipal. Hay evidencias de niveles de efectividad muy variada en cuanto a los cambios en las políticas de financiamiento, particularmente en lo que se refiere a las tendencias en los montos económicos por tipo de fuente de financiamiento. CONCLUSIONES: Hay estados donde los hogares, los municipios y el mismo gobierno estatal han hecho efectivo un incremento importante en el financiamiento de la salud, pero también hay Estados donde continúa la dependencia económica del nivel federal y donde Hogares, Municipios y Estados no están dispuestos ni capacitados para asumir responsabilidad económica en materia de salud.

Financial consequences of changes in health care demands related to tobacco consumption in Mexico: information for policy makers.

This paper presents the results from a longitudinal study in which the main purpose was to determine the health-care costs and financial consequences of changes in the health care demands related to tobacco consumption in Mexico. Eleven health interventions were selected to conduct this study and four probabilistic models were developed to forecast the expected changes in the epidemiologic profile of selected diseases. The costing method was based on the identification of case management costs using the instrumentation and consensus techniques, probabilistic models were designed using the Box-Jenkins technique and allowed us to identify the expected case trends for the 2001-2003 period. The generation of information on case management costs for the selected interventions is a central instrument in the planning of health programs, above all in that which refers to resource allocation by type of demand. On the other hand, the identification of expected cases and the financial consequences allowed us to know the growing trends of the sums required to satisfy health care demands for the period under study. The three types of information are a relevant resource for decision-makers in the production and financing of health services.

Health financing changes in the context of health care decentralization: the case of three Latin American countries

Objetivo: Säo apresentados os resultados de um estudo longitudinal com o objetivo de identificar os efeitos da descentralizaçäo nas políticas de financiamento em três países da América Latina: México, Nicarágua e Peru. Métodos: A metodologia teve duas fases principais. Na primeira, foram analisadas as fontes de dados secundários, referentes às seguintes variáveis: tipo de descentralizaçäo implementada, fontes de financiamento, provedores de serviços, mecanismos de alocaçäo de recursos e destino final de recursos. Na segunda fase, foram analisadas as fontes de dados primários obtidos por meio de entrevistas diretas com pessoal-chave do setor de saúde, tomando como guia as mesmas variáveis da primeira etapa. Resultados: Os resultados identificaram as fortalezas e as debilidades de cada país em matéria de políticas de financiamento e de descentralizaçäo. Conclusöes: As principais mudanças no financiamento, assim como as tendências quantitativas dos cinco indicadores de financiamento utilizados, säo apresentadas como instrumento metodológico para implementar correçöes e ajustes do financiamento em saúde