Waiwhakareke Restoration Plantings: Establishment of Monitoring Plots 2005-06

Waiwhakareke Natural Heritage Park is being developed to reconstruct native lowland and wetland ecosystems as were once widespread in the Waikato Region. The 60ha Natural Heritage Park is located on the north-west outskirts of Hamilton City and includes a peat lake (Horseshoe Lake) which is surrounded by introduced willow trees. There is some native marginal vegetation around the lake, including rushes and sedges, and an extensive area of gently sloping pasture completes the catchment. The restoration and recreation of the native plant and animal communities is being lead by the Hamilton City Council in partnership with The University of Waikato, Wintec, Nga Mana Toopu o Kirikiriroa Limited Resource Management and Cultural Consultants and Tui 2000 (McQueen 2005; McQueen & Clarkson 2003)

Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Mahonian Pairs

We introduce the notion of a Mahonian pair. Consider the set, P^*, of all words having the positive integers as alphabet. Given finite subsets S,T of P^*, we say that (S,T) is a Mahonian pair if the distribution of the major index, maj, over S is the same as the distribution of the inversion number, inv, over T. So the well-known fact that maj and inv are equidistributed over the symmetric group, S_n, can be expressed by saying that (S_n,S_n) is a Mahonian pair. We investigate various Mahonian pairs (S,T) with S different from T. Our principal tool is Foata's fundamental bijection f: P^* -> P^* since it has the property that maj w = inv f(w) for any word w. We consider various families of words associated with Catalan and Fibonacci numbers. We show that, when restricted to words in {1,2}^*, f transforms familiar statistics on words into natural statistics on integer partitions such as the size of the Durfee square. The Rogers-Ramanujan identities, the Catalan triangle, and various q-analogues also make an appearance. We generalize the definition of Mahonian pairs to infinite sets and use this as a tool to connect a partition bijection of Corteel-Savage-Venkatraman with the Greene-Kleitman decomposition of a Boolean algebra into symmetric chains. We close with comments about future work and open problems.Comment: Minor changes suggested by the referees and updated status of the problem of finding new Mahonian pairs; [email protected] and [email protected]

Massively-Parallelized, Deterministic Mechanoporation for Intracellular Delivery

Microfluidic intracellular delivery approaches based on plasma membrane poration have shown promise for addressing the limitations of conventional cellular engineering techniques in a wide range of applications in biology and medicine. However, the inherent stochasticity of the poration process in many of these approaches often results in a trade-off between delivery efficiency and cellular viability, thus potentially limiting their utility. Herein, we present a novel microfluidic device concept that mitigates this trade-off by providing opportunity for deterministic mechanoporation (DMP) of cells en masse. This is achieved by the impingement of each cell upon a single needle-like penetrator during aspiration-based capture, followed by diffusive influx of exogenous cargo through the resulting membrane pore, once the cells are released by reversal of flow. Massive parallelization enables high throughput operation, while single-site poration allows for delivery of small and large-molecule cargos in difficult-to-transfect cells with efficiencies and viabilities that exceed both conventional and emerging transfection techniques. As such, DMP shows promise for advancing cellular engineering practice in general and engineered cell product manufacturing in particular

Procès des accusés d'avril devant la Cour des pairs.

Bound with: Procès Fieschi devant la Cour des Pairs. [Tome première], Faits préliminaires.Mode of access: Internet

Procès des accusés d'avril devant la Cour des pairs.

Bound with: Procès des accusés d'avril devant la Cour des pairs. Tome troisième.Mode of access: Internet