On the speed of once-reinforced biased random walk on trees

We study the asymptotic behaviour of once-reinforced biased random walk (ORbRW) on Galton-Watson trees. Here the underlying (unreinforced) random walk has a bias towards or away from the root. We prove that in the setting of multiplicative once-reinforcement the ORbRW can be recurrent even when the underlying biased random walk is ballistic. We also prove that, on Galton-Watson trees without leaves, the speed is positive in the transient regime. Finally, we prove that, on regular trees, the speed of the ORbRW is monotone decreasing in the reinforcement parameter when the underlying random walk has high speed, and the reinforcement parameter is small

Semi-hidden markov models for visible light communication channels

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering, Johannesburg 2018Visible Light Communication (VLC) is an emerging field in optical wireless communication that uses light emitting diodes (LEDs) for data transmission. LEDs are being widely adopted both indoors and outdoors due to their low cost, long lifespan and high efficiency. Furthermore, LEDs can be modulated to provide both illumination and wireless communication. There is also potential for VLC to be incorporated into future smart lighting systems. One of the current challenges in VLC is being able to deal with noise and interference; including interference from other dimmed, Pulse-Width Modulated (PWM) LEDs. Other noise includes natural light from the sun and artificial light from other non-modulating light sources. Modelling these types of channels is one of the first steps in understanding the channel and eventually designing techniques for mitigating the effects of noise and interference. This dissertation presents a semi-hidden Markov model, known as the Fritchman model, that discretely models the effects of as well as errors introduced from noise and interference in on-off keying modulated VLC channels. Models have been developed for both the indoor and outdoor environments and can be used for VLC simulations and designing error mitigation techniques. Results show that certain channels are able to be better modelled than others. Experimental error distributions shows insights into the impact that PWM interference has on VLC channels. This can be used for assisting in the development of error control codes and interference avoidance techniques in standalone VLC systems, as well as systems where VLC and smart lighting coexist. The models developed can also be used for simulations of VLC channels under different channel conditionsXL201

Mobile Music Development Tools for Creative Coders

This project is a body of work that facilitates the creation of musical mobile artworks. The project includes a code toolkit that enhances and simplifies the development of mobile music iOS applications, a flexible notation system designed for mobile musical interactions, and example apps and scored compositions to demonstrate the toolkit and notation system. The code library is designed to simplify the technical aspect of user-centered design and development with a more direct connection between concept and deliverable. This sim- plification addresses learning problems (such as motivation, self-efficacy, and self-perceived understanding) by bridging the gap between idea and functional prototype and improving the ability to contextualize the development process for musicians and other creatives. The toolkit helps to circumvent the need to learn complex iOS development patterns and affords more readable code. CSPD (color, shape, pattern, density) notation is a pseudo-tablature that describes performance interactions. The system leverages visual density and patterns of both color and shape to describe types of gestures (physical or musical) and their relationships rather than focusing on strict rhythmic or pitch/frequency content. The primary design goal is to visualize macro musical concepts that create middleground structure

Brockport Normal Quarter Centennial Address

Brockport Normal School, history of

Taxpayer Standing: Maintaining Separation of Powers While Ensuring Democratic Administrative Action

In a landmark 2007 decision, the U.S. Supreme Court broadly expanded its standing doctrine. Traditionally, the U.S. standing doctrine has been narrow, relying largely on the “cases and controversies” language of Art. III of the U.S. Constitution. This doctrine has precluded third-party or tax-payer suits concerning administrative action. This Note compares the U.S. standing doctrine to that of South Africa, which has a much broader notion of who may bring suit. South Africa’s history with apartheid and distrust of government has led to a liberal standing doctrine in which any individual aggrieved by administrative action may bring suit to receive a written explanation from the offending agency. By exploring the doctrines, this Note argues that a similar type of standing in the United States would serve to democratize administrative action while still ensuring a constitutional separation of powers

Coexistence of lazy frogs on Z

We study the so-called frog model on with two types of lazy frogs, with parameters respectively, and a finite expected number of dormant frogs per site. We show that for any such and there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.</p