Abstract Given r⩾3$r \geqslant 3$, we prove that there exists λ>0$\lambda >0$ depending only on r$r$ so that if G$G$ is a metric graph of rank r$r$ with metric entropy 1, then there exists a proper subgraph H$H$ of G$G$ with metric entropy at least λ$\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a
Tawfiq Hamed, Tarik Aougab, Matt Clay
wiley +1 more source
STRESS, an automated geometrical characterization of deformable particles for in vivo measurements of cell and tissue mechanical stresses. [PDF]
Gross BJ +4 more
europepmc +1 more source
Some structure theorems for Weingarten surfaces
Abstract Let M⊂R3$M\subset \mathbb {R}^3$ be a properly embedded, connected, complete surface with boundary a convex planar curve C$C$, satisfying an elliptic equation H=f(H2−K)$H=f(H^2-K)$, where H$H$ and K$K$ are the mean and the Gauss curvature, respectively—which we will refer to as Weingarten equation.
Angelo Benedetti
wiley +1 more source
Morphological changes in smectic liquid crystal microstructures.
Sato D +4 more
europepmc +1 more source
Thermodynamically Consistent Linear Electroelastic Formulation and FEM Study of Patch-Actuated Smart Structures: Validation and Interface Stress Evaluation. [PDF]
Usal MMA, Özer H.
europepmc +1 more source
Towards the boundary of the fine curve graph
Abstract The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper, we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We then give several applications including finding dynamically explicit elements with positive stable ...
Jonathan Bowden +2 more
wiley +1 more source
Construction of virtual whole eye model based on ultra-widefield optical coherence tomography in myopia. [PDF]
Tang X +14 more
europepmc +1 more source
Combinatorial zeta functions counting triangles
Abstract In this paper, we compute special values of certain combinatorial zeta functions counting geodesic paths in the (n−1)$(n-1)$‐skeleton of a triangulation of an n$n$‐dimensional manifold. We show that they carry a topological meaning. As such, we recover the first Betti and L2$L^2$‐Betti numbers of compact manifolds, and the linking number of ...
Leo Benard +3 more
wiley +1 more source
Minimum Spacetime Length and the Thermodynamics of Spacetime. [PDF]
Rossi V, Cacciatori SL, Pesci A.
europepmc +1 more source
A projection-based inverse kinematic model for extensible continuum robots and hyper-redundant robots with an elbow joint. [PDF]
Fritsch S, Oberschmidt D.
europepmc +1 more source

