A Recipe for State Dependent Distributed Delay Differential Equations

We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that the resulting delay differential equation preserves non-negativity of initial conditions and we characterise local stability of equilibria. By specifying the distribution of maturation age, we recover state dependent discrete, uniform and gamma distributed delay differential equations. We show how to reduce the uniform case to a system of state dependent discrete delay equations and the gamma distributed case to a system of ordinary differential equations. To illustrate the benefits of these reductions, we convert previously published transit compartment models into equivalent distributed delay differential equations.Comment: 28 page

Home Appreciation Participation Notes: A Solution to Housing Affordability and the Current Mortgage Crisis

This paper introduces Home Appreciation Participation Notes (HAPNs), an innovative new housing finance tool. Housing is a commodity providing two distinct utilities: shelter and investment. Traditionally, buyers have had to purchase both elements in tandom. HAPNs allow buyers to purchase these elements individually. Thus, buyers can focus on purchasing housing units that best fit their shelter needs, investing in housing appreciation to whatever extent is appropriate for the needs of their investment portfolio. HAPNs are different from previous financing tools in three key ways: there is no payment burden until ownership of the home is transferred, the risk of housing price declines is shifted to investors, and the final payoff is indexed to the appreciation rates of local housing prices. With these three features, HAPNs considerably improve the affordability of homeownership while reducing the risk of default and avoiding the moral hazard associated with shared appreciation instruments.

S18RS SGB No. 6 (Amend Governing Documents)

A Bill To amend the Student Government Governing Document

The particle detector in your pocket: The Distributed Electronic Cosmic-ray Observatory

The total area of silicon in cell phone camera sensors worldwide surpasses that in any experiment to date. Based on semiconductor technology similar to that found in modern astronomical telescopes and particle detectors, these sensors can detect ionizing radiation in addition to photons. The Distributed Electronic Cosmic-ray Observatory (DECO) uses the global network of active cell phones in order to detect cosmic rays and other energetic particles such as those produced by radioactive decays. DECO consists of an Android application, database, and public data browser available to citizen scientists around the world (https://wipac.wisc.edu/deco). Candidate cosmic-ray events have been detected on all seven continents and can be categorized by the morphology of their corresponding images. We present the DECO project, a novel particle detector with wide applications in public outreach and education.Comment: Presented at ICRC 2017, Busan, Korea. See https://wipac.wisc.edu/deco for more informatio