Artin groups of extra-large type are biautomatic

AbstractIn this paper we develop new techniques to work with small cancellation theory diagrams for Artin groups. Using these techniques we examine paths in the Cayley graph of the Artin group. For any Artin group G, with semigroup generators oA, we define a language L(G) ⊂oA∗. The language L(G) is a set of canonical forms for the Artin group. In the case G is an Artin group of extra-large type or a two generator Artin group, we analyze the geometry of the small cancellation theory diagrams and show that L(G) is the language of a biautomatic structure for G

Protecting Players While Protecting the Integrity of the Game in Youth Soccer

Youth sports have been under severe scrutiny lately for the neurological damage coming to light after years of repeated head impact players endure. US Soccer has created somewhat controversial concussion regulations and protocols in the last couple of years to combat this criticism- such as not allowing players under the age of eleven to head the ball. Many coaches, however, believe these regulations could impair the game of soccer and the abilities of the players themselves. As a human biological sciences major as well as having played soccer for the last seventeen years, my project is centered around coalescing current research on the dangers of heading in youth soccer with various coaches’ opinions of how certain regulations can endanger the integrity of a game 2.65 billion people take part in worldwide. I have created an editorial piece that examines the coaches\u27 perspectives on how to better maintain the beauty of the game while creating a safe playing environment. To carry out this project I interviewed coaches of all playing levels ranging from coaching players five years of age to the professional level. I then asked scholars with diverse medical backgrounds their opinions on the new Return to Play Protocol. Using these sources as well as the most current research I hope to discover how to best combat the neurological impact soccer can have on current and future players. I have created an article that is easy to understand for people of all educational backgrounds to educate parents, coaches and players while also stimulating dialogue on the issue and possible solutions. This research can be used for further insight into how to integrate science into the beautiful game of soccer and create a safe, educated, and fun playing environment for all to enjoy

The argument for diversifying the NIH grant portfolio

The United States has been a leader in biomedical science for decades, in large part because of the strategy used by the National Institutes of Health (NIH) to invest its budgetary portfolio. They identified talented young scientists from each generation and gave them the resources they needed to initiate and maintain strong research programs. However, recently this investment has become less diversified, with a larger fraction of grant dollars in the hands of a smaller fraction of researchers. This threatens the future of our field, as many productive early and midcareer scientists are facing having to close their labs. NIH and others have studied this problem, gathering data that suggest that over a certain level of funding to an individual investigator, there are diminishing returns in scientific output. Here I review these data and examine the issues that led NIH to propose and then reverse a cap on funding to individual investigators, the Grant Support Index. I consider other proposed solutions, and call on all in the field to examine whether the status quo is acceptable, and if not, urge them to propose and advocate for concrete alternatives

Protecting Players While Protecting the Integrity of the Game in Youth Soccer

Youth sports have been under severe scrutiny lately for the neurological damage coming to light after years of repeated head impact players endure. US Soccer has created somewhat controversial concussion regulations and protocols in the last couple of years to combat this criticism- such as not allowing players under the age of eleven to head the ball. Many coaches, however, believe these regulations could impair the game of soccer and the abilities of the players themselves. As a human biological sciences major as well as having played soccer for the last seventeen years, my project is centered around coalescing current research on the dangers of heading in youth soccer with various coaches’ opinions of how certain regulations can endanger the integrity of a game 2.65 billion people take part in worldwide. I have created an editorial piece that examines the coaches\u27 perspectives on how to better maintain the beauty of the game while creating a safe playing environment. To carry out this project I interviewed coaches of all playing levels ranging from coaching players five years of age to the professional level. I then asked scholars with diverse medical backgrounds their opinions on the new Return to Play Protocol. Using these sources as well as the most current research I hope to discover how to best combat the neurological impact soccer can have on current and future players. I have created an article that is easy to understand for people of all educational backgrounds to educate parents, coaches and players while also stimulating dialogue on the issue and possible solutions. This research can be used for further insight into how to integrate science into the beautiful game of soccer and create a safe, educated, and fun playing environment for all to enjoy

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation