Latinas\u27 Persistence in High Education STEM

Graduate Theoretica

Map Matching with Simplicity Constraints

We study a map matching problem, the task of finding in an embedded graph a path that has low distance to a given curve in R^2. The Fr\'echet distance is a common measure for this problem. Efficient methods exist to compute the best path according to this measure. However, these methods cannot guarantee that the result is simple (i.e. it does not intersect itself) even if the given curve is simple. In this paper, we prove that it is in fact NP-complete to determine the existence a simple cycle in a planar straight-line embedding of a graph that has at most a given Fr\'echet distance to a given simple closed curve. We also consider the implications of our proof on some variants of the problem

The Amphioxus SoxB Family: Implications for the Evolution of Vertebrate Placodes

Cranial placodes are regions of thickened ectoderm that give rise to sense organs and ganglia in the vertebrate head. Homologous structures are proposed to exist in urochordates, but have not been found in cephalochordates, suggesting the first chordates lacked placodes. SoxB genes are expressed in discrete subsets of vertebrate placodes. To investigate how placodes arose and diversified in the vertebrate lineage we isolated the complete set of SoxB genes from amphioxus and analyzed their expression in embryos and larvae. We find that while amphioxus possesses a single SoxB2 gene, it has three SoxB1 paralogs. Like vertebrate SoxB1 genes, one of these paralogs is expressed in non-neural ectoderm destined to give rise to sensory cells. When considered in the context of other amphioxus placode marker orthologs, amphioxus SoxB1 expression suggests a diversity of sensory cell types utilizing distinct placode-type gene programs was present in the first chordates. Our data supports a model for placode evolution and diversification whereby the full complement of vertebrate placodes evolved by serial recruitment of distinct sensory cell specification programs to anterior pre-placodal ectoderm

Experimental analysis of the accessibility of drawings with few segments

The visual complexity of a graph drawing is defined as the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges, e.g., one needs only one line segment to draw two collinear incident edges. We study the question if drawings with few segments have a better aesthetic appeal and help the user to asses the underlying graph. We design an experiment that investigates two different graph types (trees and sparse graphs), three different layout algorithms for trees, and two different layout algorithms for sparse graphs. We asked the users to give an aesthetic ranking on the layouts and to perform a furthest-pair or shortest-path task on the drawings.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Dissecting early regulatory relationships in the lamprey neural crest gene network

The neural crest, a multipotent embryonic cell type, originates at the border between neural and nonneural ectoderm. After neural tube closure, these cells undergo an epithelial–mesenchymal transition, migrate to precise, often distant locations, and differentiate into diverse derivatives. Analyses of expression and function of signaling and transcription factors in higher vertebrates has led to the proposal that a neural crest gene regulatory network (NC-GRN) orchestrates neural crest formation. Here, we interrogate the NC-GRN in the lamprey, taking advantage of its slow development and basal phylogenetic position to resolve early inductive events, 1 regulatory step at the time. To establish regulatory relationships at the neural plate border, we assess relative expression of 6 neural crest network genes and effects of individually perturbing each on the remaining 5. The results refine an upstream portion of the NC-GRN and reveal unexpected order and linkages therein; e.g., lamprey AP-2 appears to function early as a neural plate border rather than a neural crest specifier and in a pathway linked to MsxA but independent of ZicA. These findings provide an ancestral framework for performing comparative tests in higher vertebrates in which network linkages may be more difficult to resolve because of their rapid development

'If I have only two children and they die. who will take care of me?' : a qualitative study exploring knowledge, attitudes and practices about family planning among Mozambican female and male adults

Background: By focusing upon family planning counselling services, the Mozambican government has significantly enhanced the general health of female and male clients. However, little is known about the experiences of family planning by female and male adults. This article focuses on knowledge, attitudes and practices regarding contraceptive methods and fertility intentions. Methods: An in-depth qualitative study of female and male clients was conducted in two settings in Maputo province - Ndlavela and Boane. A total of sixteen in-depth interviews, four informal conversations, and observations were equally divided between both study sites. The analysis followed a constructionist approach. Three steps were considered in the analysis: examining commonalities, differences and relationships. Results: Although there was a high level of family planning knowledge, there were discrepancies in clients' everyday practices. Male and female clients are confronted with a variety of expectations concerning fertility intentions and family size, and are under pressure in numerous ways. Social pressures include traditional expectations and meanings connected to having children, as well as religious factors. Short interaction time between clients and health workers is a problem. Additionally, imposed contraceptive methods, and typically brief conversations about birth control between couples only adds to the burden. Because family planning is largely viewed as a woman's concern, most clients have never attended counselling sessions with their partners. Attitudes towards responsibility for contraceptive use and risk-taking are strongly gendered. Conclusions: Female and male clients have differing expectations about contraceptive use and fertility intentions. They participate differently in family planning programs leading to their inconsistent and ambivalent practices as well as vague perceptions of risk-taking. Therefore, policymakers must address the reasons behind ambivalence and inconsistency regarding contraceptives and family planning

Locally Correct Frechet Matchings

The Frechet distance is a metric to compare two curves, which is based on monotonous matchings between these curves. We call a matching that results in the Frechet distance a Frechet matching. There are often many different Frechet matchings and not all of these capture the similarity between the curves well. We propose to restrict the set of Frechet matchings to "natural" matchings and to this end introduce locally correct Frechet matchings. We prove that at least one such matching exists for two polygonal curves and give an O(N^3 log N) algorithm to compute it, where N is the total number of edges in both curves. We also present an O(N^2) algorithm to compute a locally correct discrete Frechet matching

A Framework for Algorithm Stability

We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays an important role in a wide variety of areas, such as numerical analysis, machine learning, and topology, but is poorly understood in the context of (combinatorial) algorithms. In this paper we present a framework for analyzing the stability of algorithms. We focus in particular on the tradeoff between the stability of an algorithm and the quality of the solution it computes. Our framework allows for three types of stability analysis with increasing degrees of complexity: event stability, topological stability, and Lipschitz stability. We demonstrate the use of our stability framework by applying it to kinetic Euclidean minimum spanning trees

Four Soviets Walk the Dog-Improved Bounds for Computing the Fr\'echet Distance

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One popular measure is the Fr\'echet distance. Since it was proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original $O(n^2 \log n)$ algorithm by Alt and Godau for computing the Fr\'echet distance remains the state of the art (here, $n$ denotes the number of edges on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUM-hard. In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Fr\'echet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fr\'echet distance between two polygonal curves in time $O(n^2 \sqrt{\log n}(\log\log n)^{3/2})$ on a pointer machine and in time $O(n^2(\log\log n)^2)$ on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth $O(n^{2-\varepsilon})$, for some $\varepsilon > 0$. We believe that this reveals an intriguing new aspect of this well-studied problem. Finally, we show how to obtain the first subquadratic algorithm for computing the weak Fr\'echet distance on a word RAM.Comment: 34 pages, 15 figures. A preliminary version appeared in SODA 201