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

Gaze Behavior, Believability, Likability and the iCat

The iCat is a user-interface robot with the ability to express a range of emotions through its facial features. This paper summarizes our research whether we can increase the believability and likability of the iCat for its human partners through the application of gaze behaviour. Gaze behaviour serves several functions during social interaction such as mediating conversation flow, communicating emotional information and avoiding distraction by restricting visual input. There are several types of eye and head movements that are necessary for realizing these functions. We designed and evaluated a gaze behaviour system for the iCat robot that implements realistic models of the major types of eye and head movements found in living beings: vergence, vestibulo ocular reflexive, smooth pursuit movements and gaze shifts. We discuss how these models are integrated into the software environment of the iCat and can be used to create complex interaction scenarios. We report about some user tests and draw conclusions for future evaluation scenarios

Four Soviets walk the dog, with an application to Alt's conjecture

Given two polygonal curves in the plane, there are several ways to define a measure of similarity between them. One measure that has been extremely popular in the past is the Frechet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been described. However, even 20 years later, the original O(n^2 log n) algorithm by Alt and Godau for computing the Frechet distance remains the state of the art (here n denotes the number of vertices 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 Frechet distance, where we consider sequences of points instead of polygonal curves. Building on their work, we give an algorithm to compute the Frechet distance between two polygonal curves in time O(n^2 (log n)^(1/2) (\log\log n)^(3/2)) on a pointer machine and in time O(n^2 (loglog n)^2) on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the Frechet problem of depth O(n^(2-epsilon)), for some epsilon > 0. This provides evidence that computing the Frechet distance may not be 3SUM-hard after all and reveals an intriguing new aspect of this well-studied problem

Four Soviets walk the dog, with an application to Alt's conjecture

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Fréchet distance. Since it has been 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 Fréchet distance remains the state of the art (here n denotes the number of vertices 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 Fréchet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fréchet 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¿}), for some ¿ > 0. This provides evidence that the decision problem may not be 3SUM-hard after all and reveals an intriguing new aspect of this well-studied problem

Insights from Amphioxus into the Evolution of Vertebrate Cartilage

Central to the story of vertebrate evolution is the origin of the vertebrate head, a problem difficult to approach using paleontology and comparative morphology due to a lack of unambiguous intermediate forms. Embryologically, much of the vertebrate head is derived from two ectodermal tissues, the neural crest and cranial placodes. Recent work in protochordates suggests the first chordates possessed migratory neural tube cells with some features of neural crest cells. However, it is unclear how and when these cells acquired the ability to form cellular cartilage, a cell type unique to vertebrates. It has been variously proposed that the neural crest acquired chondrogenic ability by recruiting proto-chondrogenic gene programs deployed in the neural tube, pharynx, and notochord. To test these hypotheses we examined the expression of 11 amphioxus orthologs of genes involved in neural crest chondrogenesis. Consistent with cellular cartilage as a vertebrate novelty, we find that no single amphioxus tissue co-expresses all or most of these genes. However, most are variously co-expressed in mesodermal derivatives. Our results suggest that neural crest-derived cartilage evolved by serial cooption of genes which functioned primitively in mesoderm

Mapping polygons to the grid with small Hausdorff and Fréchet distance

We show how to represent a simple polygon P by a (pixel-based) grid polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P, a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the boundaries. We present algorithms accompanying these constructions, heuristics to improve their output while keeping the distance bounds, and experiments to assess the output