On Universal Cycles for Multisets

A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of $\binom{n+t-1}{t}$ integers from [n] with the property that each t-multiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that n divides $\binom{n+t-1}{t}$, and it is reasonable to conjecture that this condition is sufficient for large enough n in terms of t. We prove the conjecture completely for t in {2,3} and partially for t in {4,6}. These results also support a positive answer to a question of Knuth.Comment: 14 pages, two figures, will appear in Discrete Mathematics' special issue on de Bruijn Cycles, Gray Codes and their generalizations; paper revised according to journal referees' suggestion

A Duality Exact Sequence for Legendrian Contact Homology

We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact homology CH_* which maps to singular homology. In particular, the sequence implies a duality between the kernel of the map (CH_*\to H_*) and the cokernel of the map (H_* \to CH^*). Furthermore, this duality is compatible with Poincare duality in L in the following sense: the Poincare dual of a singular class which is the image of a in CH_* maps to a class \alpha in CH^* such that \alpha(a)=1. The exact sequence generalizes the duality for Legendrian knots in Euclidean 3-space [24] and leads to a refinement of the Arnold Conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [6].Comment: 57 pages, 10 figures. Improved exposition and expanded analytic detai

Deterministic Random Walks on Regular Trees

Jim Propp's rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. Cooper and Spencer (Comb. Probab. Comput. (2006)) show a remarkable similarity of both models. If an (almost) arbitrary population of chips is placed on the vertices of a grid $\Z^d$ and does a simultaneous walk in the Propp model, then at all times and on each vertex, the number of chips on this vertex deviates from the expected number the random walk would have gotten there by at most a constant. This constant is independent of the starting configuration and the order in which each vertex serves its neighbors. This result raises the question if all graphs do have this property. With quite some effort, we are now able to answer this question negatively. For the graph being an infinite $k$-ary tree ($k \ge 3$), we show that for any deviation $D$ there is an initial configuration of chips such that after running the Propp model for a certain time there is a vertex with at least $D$ more chips than expected in the random walk model. However, to achieve a deviation of $D$ it is necessary that at least $\exp(\Omega(D^2))$ vertices contribute by being occupied by a number of chips not divisible by $k$ at a certain time.Comment: 15 pages, to appear in Random Structures and Algorithm

We are the Land : Researching Environmental Repossession with Anishinaabe Elders

Research shows that Indigenous connection to land carries important health benefits. Amongst Anishinaabe peoples, the land is the foundation for Indigenous Knowledge and central to physical, spiritual, mental and emotional health. Today, many of the most pressing health inequities experienced by Indigenous peoples are shaped by historic and on-going processes of environmental dispossession. This dissertation was framed by a community-based participatory research (CBPR) approach conducted in collaboration with two Anishinaabe communities on Lake Superior (Ontario, Canada), the greater goal being to develop strategies of environmental repossession. Developed around three manuscripts, this thesis addressed four objectives: 1) to examine the strengths and challenges of applying CBPR within the context of Indigenous health research; 2) to identify the impacts of both historical and on-going experiences of environmental dispossession upon community health; 3) to explore Elders\u27 approaches for resisting environmental dispossession and maintaining their connections with traditional lands; 4) to apply an integrated knowledge translation methodology towards developing strategies for environmental repossession. Informed by in-depth interviews with Elders (n=46), this thesis opens with a methodological chapter that reviews how CBPR approaches applied in the context of Indigenous health research can be successful when founded upon notions of respect and reciprocity. Drawing from the Elders\u27 narratives, the following two empirical chapters further reveal that Elders\u27 access to their traditional lands and Indigenous Knowledge base have been negatively impacted by various processes of environmental dispossession, including Residential Schools and environmental contamination. Elders\u27 strategies for resisting these negative impacts and maintaining strong connections with their traditional lands and resources include the development of cultural camps and the planting of community gardens. In focus groups and talking circle discussions, community Elders\u27 ideas about best strategies for practicing environmental repossession and preserving Indigenous Knowledge focused squarely on increasing opportunities for Elders and youth to connect, both in social settings and out on the land. Overall, this dissertation demonstrates an applied process through which Indigenous communities can use research to begin to lay the groundwork for process of environmental repossession. While CBPR approaches may not, in and of themselves, directly reduce health inequity, these approaches are well suited for mobilizing the sorts of local action that will lead to improved health

EMBODIED POLITICAL ECOLOGIES OF HEALTH: A CASE STUDY OF ALCOHOL AND INFECTIOUS DISEASE IN THE UPPER WEST REGION OF GHANA

This research is a case study informed by qualitative methodologies examining perceptions of the misuse of an unregistered gin {akpeteshie), and it\u27s role within the promulgation of hepatitis b in the Upper West Region of Ghana. Four research objectives are addressed: 1) to describe the nature of alcohol use among adults; 2) to explore local perceptions about hepatitis b held by adults in the region; 3) to examine the nature of health accessibility in the region; and, 4) to examine the links between alcohol use and the spread of hepatitis b, including the social­ environmental processes that underwrite these links. Thematic analysis of nine focus groups with residents (n=88) and seven key informant interviews indicate that the relationship between alcohol misuse and hepatitis is underwritten by several factors emerging from the physical environment (i.e. drought, isolation) and the social environment (i.e. changing norms surrounding consumption, desires for coping, poverty)

Volunteering + Values: A Repair the World Report on Jewish Young Adults

Presents survey findings on young Jewish adults' commitments to, attitudes toward, and concerns and motivations in volunteering, including views on the links between service and Jewish identity and values. Outlines implications for boosting volunteering

The Geography of Investment: Informed Trading and Asset Prices

This paper uses geography to shed light on the role of asymmetric information in asset pricing. Demonstrating that investors possess significant informational advantages in evaluating nearby investments, we find that active mutual fund managers overweight proximate firms in their portfolios and earn substantial abnormal returns in local holdings. These findings are more pronounced among funds which are small, have few holdings, and operate out of remote locations. Aggregating across all funds, we use the fraction of a stock's shares held by local investors as a measure of the information asymmetry in its investor base. We find that a firm's degree of local ownership is positively related to the cross-section of expected returns, even when controlling for other factors known to explain return variation. The results document new evidence of informed trading and establish a link between such trading and asset prices.

A novel scaling indicator of early warning signals helps anticipate tropical cyclones

Tipping events in dynamical systems have been studied in many contexts, often modelled by the decay of critical modes, system states which are tending towards bifurcation, characterised by increased return times to stable equilibria. Temporal scaling properties of time series data can be used to detect the presence of a critical mode by estimating the decay rate, and indicators of changes in these properties may therefore be used to provide an early warning signal (EWS) for an impending tipping event. The lag-1 autocorrelation function (ACF(1)) indicator and the detrended fluctuation analysis (DFA) indicator have previously been used in such a way; in this paper we introduce a novel scaling indicator based on the decay rate of the power spectrum (PS). We compare the ACF(1), DFA- and PS-indicators using artificial data; data from a model which includes a bifurcation point; and sea-level pressure data along the paths of 14 tropical cyclones. By using the PS-indicator with such data, we show that the new indicator may be used to provide an EWS in a context where the ACF(1)- and DFA-indicators fail