Generalized Erdos Numbers for network analysis

In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic

The Impact of Intercultural Healthcare on Indigenous Maternal Health and Access to Care in Ecuador

Article 32 of the 2008 Ecuadorian Constitution states that all citizens have the right to intercultural healthcare, which combines traditional and western medical practices. This thesis investigates the implementation of this policy and analyzes its impacts on Indigenous maternal health. I focus on Indigenous maternal health because there is a disproportionately high maternal mortality rate among this ethnic group. Moreover, medical racism and distrust of biomedical practices in public hospitals often deters Indigenous women from attending these facilities. This policy is highly tailored towards the needs of Indigenous mothers. In order to analyze the impacts of this policy on Indigenous maternal health I conduct quantitative analysis on the maternal mortality ratio and number of births attended by skilled birth attendants in Ecuador since the implementation of the intercultural health care policy. I accessed this information from the World Data Bank. I also conducted qualitative analysis using case studies on intercultural healthcare facilities such as Hospital San Luis de Otavalo and the Jambi Huasi clinic in order to understand how the intercultural healthcare policy functions on the ground. Through my research I found that intercultural healthcare has had little impact on overall Indigenous maternal health due to lack of standardization. On the small scale level, the policy is benefitting Indigenous women in clinics with developed intercultural healthcare programs; however, this can be difficult to recognize because the program has provided more qualitative rather than quantitative impacts. Moreover, I concluded that the extreme lack of data about intercultural healthcare is an indicator that the intercultural healthcare program is not a priority of the Ecuadorian government. I assert that in order for this program to have a national impact, better data collection and more standardization is necessary. However, I also argue that the program is a worthwhile investment at any level because it provides more respectful and dignified care for Indigenous mothers

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures

A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape-changers or topological insulators: a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations---relevant for small systems---and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials in the thermodynamic limit.Comment: Main text has 4 pages, 4 figures + Methods and Supplementary Informatio