Tight bounds and conjectures for the isolation lemma

Given a hypergraph $H$ and a weight function $w: V \rightarrow \{1, \dots, M\}$ on its vertices, we say that $w$ is isolating if there is exactly one edge of minimum weight $w(e) = \sum_{i \in e} w(i)$. The Isolation Lemma is a combinatorial principle introduced in Mulmuley et. al (1987) which gives a lower bound on the number of isolating weight functions. Mulmuley used this as the basis of a parallel algorithm for finding perfect graph matchings. It has a number of other applications to parallel algorithms and to reductions of general search problems to unique search problems (in which there are one or zero solutions). The original bound given by Mulmuley et al. was recently improved by Ta-Shma (2015). In this paper, we show improved lower bounds on the number of isolating weight functions, and we conjecture that the extremal case is when $H$ consists of $n$ singleton edges. When $M \gg n$ our improved bound matches this extremal case asymptotically. We are able to show that this conjecture holds in a number of special cases: when $H$ is a linear hypergraph or is 1-degenerate, or when $M = 2$. We also show that it holds asymptotically when $M \gg n \gg 1$

Edge-coloring linear hypergraphs with medium-sized edges

Motivated by the Erd\H{o}s-Faber-Lov\'{a}sz (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded between $i$ and $C_{i,\epsilon} \sqrt{n}$ inclusive, then there is a list edge coloring using $(1 + \epsilon) \frac{n}{i - 1}$ colors. The dependence on $n$ in the upper bound is optimal (up to the value of $C_{i,\epsilon}$)

Denitrification pathways and rates in the sandy sediments of the Georgia continental shelf, USA

Denitrification in continental shelf sediments has been estimated to be a significant sink of oceanic fixed nitrogen (N). The significance and mechanisms of denitrification in organic-poor sands, which comprise 70% of continental shelf sediments, are not well known. Core incubations and isotope tracer techniques were employed to determine processes and rates of denitrification in the coarse-grained, sandy sediments of the Georgia continental shelf. In these sediments, heterotrophic denitrification was the dominant process for fixed N removal. Processes such as coupled nitrification-denitrification, anammox (anaerobic ammonium oxidation), and oxygen-limited autotrophic nitrification-denitrification were not evident over the 24 and 48 h time scale of the incubation experiments. Heterotrophic denitrification processes produce 22.8–34.1 μmole N m(-2 )d(-1 )of N(2 )in these coarse-grained sediments. These denitrification rates are approximately two orders of magnitude lower than rates determined in fine-grained shelf sediments. These lower rates may help reconcile unbalanced marine N budgets which calculate global N losses exceeding N inputs

Bounds and algorithms for graph trusses

The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of real-world graphs. Despite its simplicity and its utility, the combinatorial and algorithmic aspects of trusses have not been thoroughly explored. We provide nearly-tight bounds on the edge counts of $k$-trusses. We also give two improved algorithms for finding trusses in large-scale graphs. First, we present a simplified and faster algorithm, based on approach discussed in Wang & Cheng (2012). Second, we present a theoretical algorithm based on fast matrix multiplication; this converts a triangle-generation algorithm of Bjorklund et al. (2014) into a dynamic data structure

The cyanoetylation of 5 amino tetrazole.

http://www.archive.org/details/cyanoetylationof00harrU.S. Navy (U.S.N.) author

DNA Evidence of a Croatian and Sephardic Jewish Settlement on the North Carolina Coast Dating from the Mid to Late 1500s

While the British origins of North American colonization currently are widely accepted, there is new evidence that other countries and non-Christians may have been earlier in establishing permanent settlements on the North Atlantic coast. Using the new research tool of human genomics, this paper provides DNA evidence that Croatians and Sephardic Jews were absorbed into the ancestral population of the Lumbee Native American tribe of North Carolina during the mid- to late-1500s. We further propose that these Sephardic Jews originated, in part, from a subgroup of the Roanoke colonists of 1586. Given this, a new historical narrative of early European colonization in North America during the 1500s is proposed

Do #BlackLivesMatter? Implicit Bias, Institutional Racism and Fear of the Black Body

The paper implores a brief cultural analysis to examine racial tensions and injustices in the U.S. that have led to the Black Lives Matter movement. Specifically, implicit bias is of primary focus as the authors examine how bias of the Black male frames the “Black-as-criminal” mentality, as well as connotes fear of the Black male body. The authors further discuss how fear of the Black face and Black male body has led to discriminatory actions such as institutional racism and, in the most vehement yet consistent cases, the killing of unarmed Black men and women. Cases such as Freddie Gray, Sandra Bland, Trayvon Martin, and Michael Brown are presented as exemplars of instances in which implicit bias and institutional racism result in malicious and racially framed discriminatory actions. The paper concludes with a presentation of how the Black Lives Matter movement is a modern-day representation of movements born from historical racial unrest for Black Americans around matters of social injustice, and how the movement can serve to project U.S. society toward an All Lives Matter position. The paper also presents implications that can be used for research and policy-level chang

Small-Area Estimation for the USDA Forest Service, National Woodland Owner Survey: Creating a Fine-Scale Land Cover and Ownership Layer to Support County-Level Population Estimates

Small area estimation is a powerful modeling technique in which ancillary data can be utilized to “borrow” additional information, effectively increasing sample sizes in small spatial, temporal, or categorical domains. Though more commonly applied to biophysical variables within the study of forest inventory analyses, small area estimation can also be implemented in the context of understanding social values, behaviors, and trends among types of forest landowners within small domains. Here, we demonstrate a method for deriving a continuous fine-scale land cover and ownership layer for the state of Delaware, United States, and an application of that ancillary layer to facilitate small-area estimation of several variables from the USDA Forest Service’s National Woodland Owner Survey. Utilizing a proprietary parcel layer alongside the National Land Cover Database, we constructed a continuous layer with 10-meter resolution depicting land cover and land ownership classes. We found that the National Woodland Owner Survey state-level estimations of total acreage and total ownerships by ownership class were generally within one standard error of the population values calculated from the raster layer, which supported the direct calculation of several population-level summary variables at the county levels. Subsequently, we compare design-based and model-based methods of predicting commercial harvesting by family forest ownerships in Delaware in which forest ownership acreage, taken from the parcel map, was utilized to inform the model-based approach. Results show general agreement between the two modes, indicating that a small area estimation approach can be utilized successfully in this context and shows promise for other variables, especially if additional variables, e.g., United States Census Bureau data, are also incorporated