Minimal Surfaces with Arbitrary Topology in H^2xR

We show that any open orientable surface S can be properly embedded in H^2xR as an area minimizing surface.Comment: 26 pages, 6 figures. With the editors' request, the paper splitted into two parts. The other part posted as APP for Tall Curves (arXiv:2006.01669

Where there is life there is mind: In support of a strong life-mind continuity thesis

This paper considers questions about continuity and discontinuity between life and mind. It begins by examining such questions from the perspective of the free energy principle (FEP). The FEP is becoming increasingly influential in neuroscience and cognitive science. It says that organisms act to maintain themselves in their expected biological and cognitive states, and that they can do so only by minimizing their free energy given that the long-term average of free energy is entropy. The paper then argues that there is no singular interpretation of the FEP for thinking about the relation between life and mind. Some FEP formulations express what we call an independence view of life and mind. One independence view is a cognitivist view of the FEP. It turns on information processing with semantic content, thus restricting the range of systems capable of exhibiting mentality. Other independence views exemplify what we call an overly generous non-cognitivist view of the FEP, and these appear to go in the opposite direction. That is, they imply that mentality is nearly everywhere. The paper proceeds to argue that non-cognitivist FEP, and its implications for thinking about the relation between life and mind, can be usefully constrained by key ideas in recent enactive approaches to cognitive science. We conclude that the most compelling account of the relationship between life and mind treats them as strongly continuous, and that this continuity is based on particular concepts of life (autopoiesis and adaptivity) and mind (basic and non-semantic)

Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone

By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. After a question raised by R. Hardt in the late 1980's, it seems common opinion that an area-minimizing surface of this sort does not exist for a regular tetrahedron, although a proof of this fact is still missing. In this paper we show that there exists a surface of positive genus spanning the boundary of an elongated tetrahedron and having area strictly less than the area of the conic surface.Comment: Expanding on the previous version with additional lower bounds, new images, corrections and improvements. Comparison with Reifenberg approac

Icanlearn: A Mobile Application For Creating Flashcards And Social Stories\u3csup\u3etm\u3c/sup\u3e For Children With Autistm

The number of children being diagnosed with Autism Spectrum Disorder (ASD) is on the rise, presenting new challenges for their parents and teachers to overcome. At the same time, mobile computing has been seeping its way into every aspect of our lives in the form of smartphones and tablet computers. It seems only natural to harness the unique medium these devices provide and use it in treatment and intervention for children with autism. This thesis discusses and evaluates iCanLearn, an iOS flashcard app with enough versatility to construct Social StoriesTM. iCanLearn provides an engaging, individualized learning experience to children with autism on a single device, but the most powerful way to use iCanLearn is by connecting two or more devices together in a teacher-learner relationship. The evaluation results are presented at the end of the thesis

Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions

In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability.Comment: 24 pages, 17 figure