At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves towards the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different action...

from which the global properties can be understood. Here r(u, v) and w(u, v) are certain functions whose details are not so material. The important properties come from the singularities at uv = 1. There are two branches of this singularity, as u and v may be both negative or both positive. The “physical region” is the region uv < 1 between the two singularities. The branch of the singularity w...

We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRWmodels have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly correcti...

Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and softw...

In this paper, a particular actuation singularity of a 3-RPS symmetrical rotational parallel mechanism (PM) is studied. When the movable platform of this PM is restricted to rotate about the vertical axis of the base, it is equivalent to a single loop mechanism (SLM). By analyzing the constraint properties of the SLM, the motion characteristics of this 3-RPS rotational PM under this motion are ...

Every normal complex surface singularity with Q-homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian cover of a rational or minimally elliptic singularity is a complete intersection singularity defined by a system of “splice diagram equations”. In this paper we introduce a Neumann-Wahl system, which is an analogue of the syst...

The Ricci curvature at an isolated singularity of an immersed hypersurface exhibits a local behaviour echoing a global property of the Ricci curvature on a complete hypersurface in euclidean space (i.e., the Efimov theorem [12], that sup Ric ≥ 0). This local behaviour takes the form of a near universal bound on the decay of the Ricci curvature at a simple singularity (eg. a cone singularity) in...

We explicitly analyze the trajectories of learning near singularities in hierarchical networks, such as multilayer perceptrons and radial basis function networks, which include permutation symmetry of hidden nodes, and show their general properties. Such symmetry induces singularities in their parameter space, where the Fisher information matrix degenerates and odd learning behaviors, especiall...

Finite time singularity formation in a fourth order nonlinear parabolic partial differential equation (PDE) is analyzed. The PDE is a variant of a ubiquitous model found in the field of microelectromechanical systems (MEMS) and is studied on a one-dimensional (1D) strip and the unit disc. The solution itself remains continuous at the point of singularity while its higher derivatives diverge, a ...

The kinematic and algorithmic singularities in controlling robotic manipulators have been investigated intensively because they are not predictable or difficult to avoid. The problem with handling these singularities is an unnecessary performance reduction in non-singular region and the difficulty in performance tuning. In this paper, we propose a method of avoiding kinematic and algorithmic si...