Linear-Space Data Structures for Range Mode Query in Arrays

A mode of a multiset $S$ is an element $a \in S$ of maximum multiplicity; that is, $a$ occurs at least as frequently as any other element in $S$. Given a list $A[1:n]$ of $n$ items, we consider the problem of constructing a data structure that efficiently answers range mode queries on $A$. Each query consists of an input pair of indices $(i, j)$ for which a mode of $A[i:j]$ must be returned. We present an $O(n^{2-2\epsilon})$-space static data structure that supports range mode queries in $O(n^\epsilon)$ time in the worst case, for any fixed $\epsilon \in [0,1/2]$. When $\epsilon = 1/2$, this corresponds to the first linear-space data structure to guarantee $O(\sqrt{n})$ query time. We then describe three additional linear-space data structures that provide $O(k)$, $O(m)$, and $O(|j-i|)$ query time, respectively, where $k$ denotes the number of distinct elements in $A$ and $m$ denotes the frequency of the mode of $A$. Finally, we examine generalizing our data structures to higher dimensions.Comment: 13 pages, 2 figure

Toward behavioural innovation economics – Heuristics and biases in choice under novelty

A framework for ‘behavioural innovation economics’ is proposed here as a synthesis of behavioural economics and innovation economics in the specific context of choice under novelty. We seek to apply the heuristics and biases framework of behavioural economics to the study of the innovation process in order to map and analyze systematic choice failures in the innovation process. We elaborate the distinction between choice under uncertainty and choice under novelty, as well as drawing out the ‘efficient innovation hypothesis’ implicit in most behavioural models of innovation. The subject domain of a research program for behavioural innovation economics is then briefly outlined in terms of a catalogue of characteristic ways in which choice under novelty renders innovation processes subject to failure.

Bounding the Number of Hyperedges in Friendship rr-Hypergraphs

For $r \ge 2$, an $r$-uniform hypergraph is called a friendship $r$-hypergraph if every set $R$ of $r$ vertices has a unique 'friend' - that is, there exists a unique vertex $x \notin R$ with the property that for each subset $A \subseteq R$ of size $r-1$, the set $A \cup \{x\}$ is a hyperedge. We show that for $r \geq 3$, the number of hyperedges in a friendship $r$-hypergraph is at least $\frac{r+1}{r} \binom{n-1}{r-1}$, and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees in the case when $r = 3$. We also obtain a new upper bound on the number of hyperedges in a friendship $r$-hypergraph, which improves on a known bound given by Li, van Rees, Seo and Singhi when $r=3$.Comment: 14 page

Heavy metal redistribution in soils using compost as a soil amendment

Organic soil amendments such as compost can reduce the availability of heavy metal contaminated soil. The objectives of this study were (1) to evaluate the efficiency of compost as an soil amendment within heavy metal contaminated soil; (2) to determine the hypoaccumulation of heavy metals in the stem, shoot, and root systems of white clover and wheat; (3) to identify movement of heavy metals within the soil; (4) to evaluate the differences of nodule formation in Trifolim repens. Three volumes of compost were added to a heavy metal contaminated soil (additions of zero, 10, and 40 percent compost, by volume). Zinc, Cd, and Pb contamination was analyzed in soil fractions and the roots and shoots of wheat ( Triticum aestivum) and white clover (Trifolim repens). The increased addition of compost was found to alleviate the toxic effects that heavy metal have on plant health; while redistributing metals to a less available form. An increase of nodule formation and nitrification resulted with the addition of compost to heavy metal contaminated soil

Identifying Themes When Using a Community-based Participatory Research (CBPR) Approach with Men Living in Abstinence-based Recovery Housing

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Learning in transformational computer games: Exploring design principles for a nanotechnology game

Transformational games are digital computer and video applications purposefully designed to create engaging and immersive learning environments for delivering specified learning goals, outcomes and experiences. The virtual world of a transformational game becomes the social environment within which learning occurs as an outcome of the complex interaction of persons and digital resources. Engaging individuals with learning in these societal situations means concepts and skills are connected to the context and remain a powerful tool for decision making and problem solving in the world. Yet, a range of barriers need to be overcome to make a game effective for its educational purpose. In this paper we discuss the learning and game design principles explored and used to develop a nanotechnology game. The game development experience is framed by a review of the educational theory informing our project and the questions that are driving our future research as we take the nanotechnology game into the classroom to investigate its impact on students’ engagement with science. We propose that transformational will be an important component of the re-crafting of teaching and learning in the digital age and that the transformational potential of computer games can extend well beyond science and even schooling

Restructuring vs. Bankruptcy

We develop a model of a firm in financial distress. Distress can be mitigated by filing for bankruptcy, which is costly, or preempted by restructuring, which is impeded by a collective action problem. We find that bankruptcy and restructuring are complements, not substitutes: Reducing bankruptcy costs facilitates restructuring, rather than crowding it out. And so does making bankruptcy more debtor-friendly, under a condition that seems likely to hold now in the United States. The model gives new perspectives on current relief policies (e.g., subsidized loans to firms in bankruptcy) and on long-standing legal debates (e.g., the efficiency of the absolute priority rule)

Tuneable separation of gold by selective precipitation using a simple and recyclable diamide

The separation of metals from electronic waste is an enduring technological and societal challenge, and new metal extraction, refining and recycling solutions are needed. Here the authors report a recyclable and tuneable chemical reagent that separates valuable metals such as gold by direct and selective precipitation from various acidic, mixed-metal solutions of relevance to extraction and recycling industries