Counting Hamilton cycles in sparse random directed graphs

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically $n!(p(1+o(1)))^{n}$. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically $n!(\log n/n(1+o(1)))^{n}$ directed Hamilton cycles

Partnering with Public Schools to End Family Homelessness in San Francisco

Hamilton Family Center (HFC) is a nonprofit organization with the mission of ending family homelessness in the San Francisco Bay Area. As part of their initiative to end family homelessness in San Francisco by 2019, HFC partnered with the San Francisco Unified School District (SFUSD) to more effectively assist families of public school students who are experiencing homelessness or housing instability. Google.org provided a $1 million grant to help launch this partnership and serve 100 homeless or at-risk SFUSD families from November 1, 2014 – October 31, 2016.During the first year of the pilot program (Nov. 2014 – Oct. 2015), 51 families received direct services through this partnership. Twenty-two homeless families were placed into permanent housing and 29 at-risk families were able to avoid eviction and probable homelessness. An additional 14 families were seeking housing as of October 31, 2015 and 86 were referred to other services (HFC data). The most significant finding to date is that the 22 families placed into permanent housing were homeless for an average of 8.2 months less than families served outside of this pilot project. Although this is a small sample size, the results from the first year of this pilot project indicate it has great potential to reduce the length of time a family is homeless.The partnership between HFC and the SFUSD is part of a larger effort to end family homelessness in San Francisco that began in late 2014. The result of this initiative has been a reduction in the average waitlist for family shelter by nearly 40% since the spring of 2013 (Connecting Point data). In addition, the number of homeless students decreased by 255 within one school year (SFUSD data). As a result of these successes, the City and County of San Francisco is providing additional public funding to expand the partnership between service providers and the school district.The purpose of this report is to provide information to other communities on the benefit of building similar partnerships to address family homelessness. It provides information based on experiences in San Francisco and highlights the need for further research and improvements to service delivery systems

Pedalling for safety: Schoolchildren and safe active transport

This research will add to the international body of knowledge around safe active transport and its benefits for individuals and their communities. In order to achieve this, the report begins with a brief description of the risks associated with active transport, 3 and considers why active transport to school should be encouraged, despite the risks. Our dependence on cars is discussed in relation to the prevailing chauffeuring culture, before the objectives of the research are outlined. Chapter one concludes with an account of the methodology used to undertake this research, which combined a literature review and a search for educational resources with some participant observation field research. In chapter 2 we present a summary of the resources available to parents in Hamilton and provide a profile of the city, which is in many ways ideally suited to active transport, though participation rates are low. Chapter 3 discusses the benefits of active transport and the barriers to participation in it. Following a discussion that draws all the various strands together, we evaluate existing strategies with a view to endorsing those most likely to enhance safety, while also offering some further ideas on how to minimise the risks of active transport for children

Packing Hamilton Cycles Online

It is known that w.h.p. the hitting time $\tau_{2\sigma}$ for the random graph process to have minimum degree $2\sigma$ coincides with the hitting time for $\sigma$ edge disjoint Hamilton cycles. In this paper we prove an online version of this property. We show that, for a fixed integer $\sigma\geq 2$, if random edges of $K_n$ are presented one by one then w.h.p. it is possible to color the edges online with $\sigma$ colors so that at time $\tau_{2\sigma}$, each color class is Hamiltonian.Comment: Minor change

Protecting the Watchdog: Using the Freedom of Information Act to Preference the Press

The fourth estate is undergoing dramatic changes. Many newspaper reporters, already surrounded by a growing number of empty desks, are shifting their focus away from costly investigative reporting and towards amassing Twitter followers and writing the perfect “share line.” Newspapers’ budgets can no longer robustly support accountability journalism and pitching fights against the government. And so, while this busier and noisier media environment may have a desirable democratizing effect—more of us are able to participate in analyzing, debating, and perhaps even making the news—it has not succeeded in filling a role that print journalists have traditionally played well—keeping watch on the government. In order to perpetuate its historical role as watchdog, the fourth estate needs fortification. This fortification should come in the form of legal preferences for the press. Providing such preferences is not new, but it arguably has not been done in a significant way since postal subsidies were granted to newspapers in the colonial era. Today, with few exceptions, the law generally treats journalists just like any other citizens and news organizations like any other business. This article proposes a new way to preference the press—one that would not involve direct subsidies or discriminating between old media and new. Instead, it would give journalists a commodity that is fundamental to their work: information. To preference the press, this article looks to the Freedom of Information Act, the law governing when and how the executive branch discloses information to the public. While in theory the law facilitates the press’s access to vast amounts of information in the hands of the executive branch, implementation of FOIA has, since it was passed in 1966, been fraught with problems. Agencies routinely take months and even years to respond to journalists’ requests, making the process incompatible with a news cycle that is spinning ever faster. This article proposes focusing on FOIA’s expedited processing provisions to prioritize journalists’ requests over those of other requesters, expedite agency fulfillment of them, and ease the press’s ability to challenge late, incomplete, or otherwise unsatisfactory disclosures. It argues that any journalist filing a FOIA request seeking expedited processing should presumptively go to the front of the queue. At that point, there would be firm deadlines (where none exist now) for providing the journalist with the information requested. These small but significant changes to an already established provision of FOIA could help the media better serve as a watchdog at a time when that role needs protecting

Science in the New Zealand Curriculum e-in-science

This milestone report explores some innovative possibilities for e-in-science practice to enhance teacher capability and increase student engagement and achievement. In particular, this report gives insights into how e-learning might be harnessed to help create a future-oriented science education programme. “Innovative” practices are considered to be those that integrate (or could integrate) digital technologies in science education in ways that are not yet commonplace. “Future-oriented education” refers to the type of education that students in the “knowledge age” are going to need. While it is not yet clear exactly what this type of education might look like, it is clear that it will be different from the current system. One framework used to differentiate between these kinds of education is the evolution of education from Education 1.0 to Education 2.0 and 3.0 (Keats & Schmidt, 2007). Education 1.0, like Web 1.0, is considered to be largely a one-way process. Students “get” knowledge from their teachers or other information sources. Education 2.0, as defined by Keats and Schmidt, happens when Web 2.0 technologies are used to enhance traditional approaches to education. New interactive media, such as blogs, social bookmarking, etc. are used, but the process of education itself does not differ significantly from Education 1.0. Education 3.0, by contrast, is characterised by rich, cross-institutional, cross-cultural educational opportunities. The learners themselves play a key role as creators of knowledge artefacts, and distinctions between artefacts, people and processes become blurred, as do distinctions of space and time. Across these three “generations”, the teacher’s role changes from one of knowledge source (Education 1.0) to guide and knowledge source (Education 2.0) to orchestrator of collaborative knowledge creation (Education 3.0). The nature of the learner’s participation in the learning also changes from being largely passive to becoming increasingly active: the learner co-creates resources and opportunities and has a strong sense of ownership of his or her own education. In addition, the participation by communities outside the traditional education system increases. Building from this framework, we offer our own “framework for future-oriented science education” (see Figure 1). In this framework, we present two continua: one reflects the nature of student participation (from minimal to transformative) and the other reflects the nature of community participation (also from minimal to transformative). Both continua stretch from minimal to transformative participation. Minimal participation reflects little or no input by the student/community into the direction of the learning—what is learned, how it is learned and how what is learned will be assessed. Transformative participation, in contrast, represents education where the student or community drives the direction of the learning, including making decisions about content, learning approaches and assessment