A digraph G $G$ is k $k$‐geodetic if for any (not necessarily distinct) vertices u,v $u,v$ there is at most one directed walk from u $u$ to v $v$ with length not exceeding k $k$. The order of a k ...$k$‐geodetic digraph with minimum out‐degree d $d$ is bounded below by the directed Moore bound M(d,k)=1+d+d2+⋯+dk $M(d,k)=1+d+{d}^{2}+\cdots +{d}^{k}$. The Moore bound can be met only in the trivial cases d=1 $d=1$ and k=1 $k=1$, so it is of interest to look for k $k$‐geodetic digraphs with out‐degree d $d$ and smallest possible order M(d,k)+ϵ $M(d,k)+{\epsilon }$, where ϵ ${\epsilon }$ is the excess of the digraph. Miller, Miret and Sillasen recently ruled out the existence of digraphs with excess one for k=3,4 $k=3,4$ and d≥2 $d\ge 2$ and for k=2 $k=2$ and d≥8 $d\ge 8$. We conjecture that there are no digraphs with excess one for d,k≥2 $d,k\ge 2$ and in this paper we investigate the structure of minimal counterexamples to this conjecture. We severely constrain the possible structures of the outlier function and prove the nonexistence of certain digraphs with degree three and excess one, as well closing the open cases k=2 $k=2$ and d=3,4,5,6,7 $d=3,4,5,6,7$ left by the analysis of Miller et al. We further show that there are no involutary digraphs with excess one, that is, the outlier function of any such digraph must contain a cycle of length ≥3 $\ge 3$.
Background: Military intelligence data published in a companion paper explain how chemical fallout from US and Coalition bombing of Iraqi chemical weapons facilities early in the air campaign ...transited long distance, triggering nerve agent alarms and exposing US troops. We report the findings of a population-based survey designed to test competing hypotheses on the impact on chronic Gulf War illness of nerve agent from early-war bombing versus post-war demolition. Methods: The US Military Health Survey performed computer-assisted telephone interviews of a stratified random sample of Gulf War-era veterans (n = 8,020). Early-war exposure was measured by having heard nerve agent alarms and post-war exposure, by the computer-generated plume from the Khamisiyah demolition. Gulf War illness was measured by two widely published case definitions. Results: The OR (95% CI) for the association of alarms with the Factor case definition was 4.13 (95% CI 2.51–6.80) compared with 1.21 (95% CI 0.86–1.69) for the Khamisiyah plume. There was a dose-related trend for the number of alarms (ptrend < 0.001) but not for the number of days in the Khamisiyah plume (ptrend = 0.17). Conclusions: Exposure to low-level sarin nerve agent in fallout from bombing early in the air campaign contributed more to chronic illness than post-war demolition.
Background: Coalition bombings on the night of 18–19 January 1991, early in the Gulf War, targeted the Iraqi chemical weapons infrastructure. On 19 January 1991, nerve agent alarms sounded within ...Coalition positions hundreds of kilometers to the south, and the trace presence of sarin vapor was identified by multiple technologies. Considering only surface dispersion of plumes from explosions, officials concluded that the absence of casualties around bombed sites precluded long-distance transit of debris to US troop positions to explain the alarms and detections. Consequently, they were discounted as false positives, and low-level nerve agent exposure early in the air war was disregarded in epidemiologic investigations of chronic illnesses. Intelligence Data: Newly assembled evidence indicates that plumes from those nighttime bombings of Iraqi chemical facilities would have traversed the stable nocturnal boundary layer and penetrated the residual layer where they would be susceptible to rapid transit by supergeostrophic winds. This explanation is supported by plume height predictions, available weather charts, weather satellite images showing transit of a hot air mass, effects of solar mixing of atmospheric layers, and observations of a stationary weather front and thermal inversion in the region. Conclusions: Current evidence supports long-distance transit. Epidemiologic studies of chronic postwar illness should be reassessed using veterans’ reports of hearing nerve agent alarms as the measure of exposure.
A k-geodetic digraph with minimum out-degree d has excess ϵ if it has order M(d,k)+ϵ, where M(d,k) represents the Moore bound for out-degree d and diameter k. For given ϵ, it is simple to show that ...any such digraph must be out-regular with degree d for sufficiently large d and k. However, proving in-regularity is in general non-trivial. It has recently been shown that any digraph with excess ϵ=1 must be diregular. In this paper we prove that digraphs with minimum out-degree d=2 and excess ϵ=2 are diregular for k≥2.
An important topic in the design of efficient networks is the construction of (d,k,+ϵ)-digraphs, i.e. k-geodetic digraphs with minimum out-degree ≥d and order M(d,k)+ϵ, where M(d,k) represents the ...Moore bound for degree d and diameter k and ϵ>0 is the (small) excess of the digraph. Previous work has shown that there are no (2,k,+1)-digraphs for k≥2. In a separate paper, the present author has shown that any (2,k,+2)-digraph must be diregular for k≥2. In the present work, this analysis is completed by proving the nonexistence of diregular (2,k,+2)-digraphs for k≥3 and classifying diregular (2,2,+2)-digraphs up to isomorphism.
On the vertex position number of graphs Thankachy, Maya; Chandran S.V., Ullas; Tuite, James ...
Discussiones Mathematicae. Graph Theory,
2024, Letnik:
44, Številka:
3
Journal Article
The search for the smallest possible $d$-regular graph of girth $g$ has a long history, and is usually known as the cage problem. This problem has a natural extension to hypergraphs, where we may ask ...for the smallest number of vertices in a $d$-regular, $r$-uniform hypergraph of given (Berge) girth $g$. We show that these two problems are in fact very closely linked. By extending the ideas of Cayley graphs to the hypergraph context, we find smallest known hypergraphs for various parameter sets. Because of the close link to the cage problem from graph theory, we are able to use these techniques to find new record smallest cubic graphs of girths 23, 24, 28, 29, 30, 31 and 32.
Moore digraphs, that is digraphs with out-degree d, diameter k and order equal to the Moore bound M(d,k)=1+d+d2+⋯+dk, arise in the study of optimal network topologies. In an attempt to find digraphs ...with a ‘Moore-like’ structure, attention has recently been devoted to the study of small digraphs with minimum out-degree d such that between any pair of vertices u,v there is at most one directed path of length ≤k from u to v; such a digraph has order M(d,k)+ϵ for some small excess ϵ. Sillasen et al. have shown that there are no digraphs with minimum out-degree two and excess one (Miller et al., 2018; Sillasen, 2015). The present author has classified all digraphs with out-degree two and excess two (Tuite, 2016, 2018). In this paper it is proven that there are no diregular digraphs with out-degree two and excess three for k≥3, thereby providing the first classification of digraphs with order three away from the Moore bound for a fixed out-degree.
Immunoassay of infectious agents Andreotti, Peter E; Ludwig, George V; Peruski, Anne Harwood ...
BioTechniques,
10/2003, Letnik:
35, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Immunoassays have evolved for a broad range of applications since the pioneering work of Yalow and Berson who developed the first competitive radioimmunoassay (RIA) for human insulin in 1959. ...Immunoassay detection of specific antigens and host-produced antibodies directed against such antigens constitutes one of the most widely used and successful methods for diagnosing infectious diseases (IDs). The number and variety of new assay systems that are continually being developed reflect the increasing demand for immunoassays possessing greater sensitivity, speed, and ease of use. This trend has been driven, in part, by the need for improved immunodiagnostic systems to perform rapid testing and counter emerging IDs and biothreat (BT) agents. Another factor driving this trend is the need to integrate immunoassays with more sensitive nucleic acid-based methods for a comprehensive approach. Here we examine the development of immunoassays, some of the key formats used for the detection and identification of BT/ID agents, and the application of these technologies under different scenarios.
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