We present a novel approach to fully automated reconstruction of tree structures in noisy 2D images. Unlike in earlier approaches, we explicitly handle crossovers and bifurcation points, and impose geometric constraints while optimizing a global cost function. We use manually annotated retinal scans to evaluate our method and demonstrate that it brings about a very substantial improvement.

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem. A closed-form analytic solution is presented for a nonlinear diff...

This paper reexamines orientations of shear bands (fault angles) predicted by a theory of shear localization as a bifurcation from homogeneous deformation. In contrast to the Coulomb prediction, which does not depend on deviatoric stress state, the angle between the band normal and the least (most compressive) principal stress increases as the deviatoric stress state varies from axisymmetric co...

Theorems are given which guarantee the bifurcation of non-constant, periodic solutions (of fixed period) of a scalar functional equation with two independent parameters. These results are applied to a single, isolated species growth model of general form with a general Volterra (Stieltjes) delay using the 'magnitudes' of the instantaneous and delayed growth rate responses as the independent bif...

Spatially periodic solutions to the Ginzburg-Landau equation are considered. In particular we obtain: criteria for primary and secondary bifurcation; limit cycle solutions; nonlinear dispersion relations relating spatial and temporal frequencies. Only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered. Finally we briefly treat the case...

In consideration of working memory as a means for goal-directed behavior in nonstationary environments, we argue that the dynamics of working memory should satisfy two opposing demands: long-term maintenance and quick transition. These two characteristics are contradictory within the linear domain. We propose the near-saddle-node bifurcation behavior of a sigmoidal unit with a self-connection a...

We describe a Sil'nikov-Saddle-Node interaction in the proximity of a Hopf-Saddle-Node bifurcation both from numerical and theoretical viewpoints, inspired in numerical observations of a 3D model of a laser with injected signal. We describe the interaction near the codimension-2 point using a return map controlled by the parameters of the bifurcation. The theoretical predictions compare well wi...

The need for better aircraft performance is increasingly prompting designers towards the realisation of morphing or shape-adaptable structural systems. One way to achieve this is to employ multistable composites elements. In this paper a square, curved bistable plate is studied. The finite element analysis provides the load-deflection characteristic of the bistable plate. A cubic expression is ...

We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation eq...