The NFL as a Mega-Crisis: Applications of Fractal Theory

The National Football League (NFL) is facing a reputation crisis—a serious problem for a powerhouse institution that airs its Super Bowl in 180 countries. Public and media scrutiny for its handling of domestic abuse cases and denial of concussions leading to Chronic Traumatic Encephalopathy (CTE) have left the NFL with a mega-crisis. Television ratings are down, player injuries are up, and fewer youth are participating in the sport. This research, presented at the International Crisis and Risk Communication conference, addresses the CTE and domestic abuse scandals in the NFL and details the League’s responses to both high-profile cases. We provide an understanding of a mega-crisis and then introduce Fractal Crisis Theory as the foundation for an analysis of both situations. The theory provides a context for analyzing how the NFL managed these two crises and offers a unique approach to studying sport and crises. We conclude with recommendations for dealing with future mega-crises

A note on stress-driven anisotropic diffusion and its role in active deformable media

We propose a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to use diffusion tensors directly coupled to mechanical stress. A proof-of-concept experiment and the proposed generalised reaction-diffusion-mechanics model reveal that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the experiment, the model, and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-assisted diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electrical feedback in actively deforming bio-materials such as the heart

Volume 31 - Issue 14 - Friday, January 12, 1996

The Rose Thorn, Rose-Hulman\u27s independent student newspaper.https://scholar.rose-hulman.edu/rosethorn/1491/thumbnail.jp

Stratified Rule-Aware Network for Abstract Visual Reasoning

Abstract reasoning refers to the ability to analyze information, discover rules at an intangible level, and solve problems in innovative ways. Raven's Progressive Matrices (RPM) test is typically used to examine the capability of abstract reasoning. The subject is asked to identify the correct choice from the answer set to fill the missing panel at the bottom right of RPM (e.g., a 3$\times$3 matrix), following the underlying rules inside the matrix. Recent studies, taking advantage of Convolutional Neural Networks (CNNs), have achieved encouraging progress to accomplish the RPM test. However, they partly ignore necessary inductive biases of RPM solver, such as order sensitivity within each row/column and incremental rule induction. To address this problem, in this paper we propose a Stratified Rule-Aware Network (SRAN) to generate the rule embeddings for two input sequences. Our SRAN learns multiple granularity rule embeddings at different levels, and incrementally integrates the stratified embedding flows through a gated fusion module. With the help of embeddings, a rule similarity metric is applied to guarantee that SRAN can not only be trained using a tuplet loss but also infer the best answer efficiently. We further point out the severe defects existing in the popular RAVEN dataset for RPM test, which prevent from the fair evaluation of the abstract reasoning ability. To fix the defects, we propose an answer set generation algorithm called Attribute Bisection Tree (ABT), forming an improved dataset named Impartial-RAVEN (I-RAVEN for short). Extensive experiments are conducted on both PGM and I-RAVEN datasets, showing that our SRAN outperforms the state-of-the-art models by a considerable margin.Comment: AAAI 2021 paper. Code: https://github.com/husheng12345/SRA

The Fractal Geometry of Invention

Fractals are geometric objects of inexhaustible detail. Fractal structures have been found in the contours of mountain ranges, the patterns of veins on a leaf, and the fluctuations of the Dow Jones Industrial Average. The endeavor of inventing new technologies, consisting of a hierarchical network of practical inquiries, exhibits fractal properties as well. Among these are multiplicity, latency, and self-similarity. Multiplicity means that a single inventive idea may lead to an immense and diverse array of technological artifacts. Latency means that the potential of an inventive idea to yield practical embodiments only reveals itself in time, and may never be fully known. Self-similarity means that invention is not scale-dependent; in other words, breakthroughs and refinements may be difficult, in principle, to distinguish. Invention, as a whole, resembles an ever-expanding fractal island of promontory upon promontory. Patent law assigns a particular inventor legal rights to a portion of that intricate coastline. The fractal properties of multiplicity, latency, and self-similarity contribute to many of the perennial difficulties in patent law, including fixing the meaning of claim language, properly applying the enablement and written description requirements, and identifying “abstract ideas” that cannot be patented. Understanding the fractal properties of invention is an important step in addressing these issues