Given a hereditary property of graphs $\mathcal{H}$ and a $p\in [0,1]$ , the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically the maximum proportion of edge additions plus edge deletions applied to a graph of edge density p sufficient to ensure that the resulting graph satisfies $\mathcal{H}$ . The edit distance function is directly related to other well-studied quantities such as the speed function for $\mathcal{H}$ and the $\mathcal{H}$ -chromatic number of a random graph.

Let $\mathcal{H}$ be the property of forbidding an Erdős–Rényi random graph $F\sim \mathbb{G}(n_0,p_0)$ , and let $\varphi$ represent the golden ratio. In this paper, we show that if $p_0\in [1-1/\varphi,1/\varphi]$ , then a.a.s. as $n_0\to\infty$ ,

\begin{align*} {\textrm{ed}}_{\mathcal{H}}(p) = (1+o(1))\,\frac{2\log n_0}{n_0} \cdot\min\left\{ \frac{p}{-\log(1-p_0)}, \frac{1-p}{-\log p_0} \right\}. \end{align*}

$p\in [1/3,2/3]$

$p_0\in (0,1)$

A primary tool in the proof is the categorization of p-core coloured regularity graphs in the range $p\in[1-1/\varphi,1/\varphi]$ . Such coloured regularity graphs must have the property that the non-grey edges form vertex-disjoint cliques.

Radiocarbon (14C) ages cannot provide absolutely dated chronologies for archaeological or paleoenvironmental studies directly but must be converted to calendar age equivalents using a calibration curve compensating for fluctuations in atmospheric 14C concentration. Although calibration curves are constructed from independently dated archives, they invariably require revision as new data become available and our understanding of the Earth system improves. In this volume the international 14C calibration curves for both the Northern and Southern Hemispheres, as well as for the ocean surface layer, have been updated to include a wealth of new data and extended to 55,000 cal BP. Based on tree rings, IntCal20 now extends as a fully atmospheric record to ca. 13,900 cal BP. For the older part of the timescale, IntCal20 comprises statistically integrated evidence from floating tree-ring chronologies, lacustrine and marine sediments, speleothems, and corals. We utilized improved evaluation of the timescales and location variable 14C offsets from the atmosphere (reservoir age, dead carbon fraction) for each dataset. New statistical methods have refined the structure of the calibration curves while maintaining a robust treatment of uncertainties in the 14C ages, the calendar ages and other corrections. The inclusion of modeled marine reservoir ages derived from a three-dimensional ocean circulation model has allowed us to apply more appropriate reservoir corrections to the marine 14C data rather than the previous use of constant regional offsets from the atmosphere. Here we provide an overview of the new and revised datasets and the associated methods used for the construction of the IntCal20 curve and explore potential regional offsets for tree-ring data. We discuss the main differences with respect to the previous calibration curve, IntCal13, and some of the implications for archaeology and geosciences ranging from the recent past to the time of the extinction of the Neanderthals.

Greenhouse-grown kochia [Kochia scoparia (L.) Schrad. # KCHSC] seedlings from populations having either a 13-yr triazine history or no triazine history were sprayed postemergence with 0, 2, or 20 kg/ha atrazine [6-chloro-N-ethyl-N′-[1-methylethyl)-1,3,5-triazine-2,4-diamine]. Fresh weight was reduced 20% in triazine history kochia treated with 20 kg/ha atrazine. Seedlings with no triazine history were killed by 2 kg/ha atrazine. Biotypes resistant to atrazine were also resistant to five other triazine herbicides. Biotypes susceptible to atrazine were susceptible to the other triazines. Atrazine-resistant biotypes were more susceptible to 2,4-D [(2,4-dichlorophenoxy)acetic acid] than atrazine-susceptible biotypes, but atrazine history had no effect on response to diuron [N′-(3,4-dichlorophenyl)-N,N-dimethylurea].

Intensive field surveys were conducted in eastern Nebraska to determine the frequency distribution model and associated parameters of broadleaf and grass weed seedling populations. The negative binomial distribution consistently fit the data over time (1992 to 1993) and space (fields) for both the inter and intrarow broadleaf and grass weed seedling populations. The other distributions tested (Poisson with zeros, Neyman type A, logarithmic with zeros, and Poisson-binomial) did not fit the data as consistently as the negative binomial distribution. Associated with the negative binomial distribution is a k parameter. k is a nonspatial aggregation parameter related to the variance at a given mean value. The k parameter of the negative binomial distribution was consistent across weed density for individual weed species in a given field except for foxtail spp. populations. Stability of the k parameter across field sites was assessed using the likelihood ratio test There was no stable or common k value across field sites and years for all weed species populations. The lack of stability in k across field sites is of concern, because this parameter is used extensively in the development of parametric sequential sampling procedures. Because k is not stable across field sites, k must be estimated at the time of sampling. Understanding the variability in it is critical to the development of parametric sequential sampling strategies and understanding the dynamics of weed species in the field.

Herbicidal control of triazine-resistant (TR) kochia was evaluated in no-till grain sorghum. Herbicides were applied early preplant (EPP) or POST. In EPP experiments, herbicides plus nonionic surfactant at 0.25% v/v were applied 7, 2, or 0 wk before planting (WBP). Fluorochloridone at 0.8 kg ai/ha applied 7 or 2 WBP, pyridate at 1.0 kg ai/ha applied 2 WBP, and paraquat at 0.4 kg ai/ha applied 0 WBP controlled 94 to 99% of TR kochia; a prepackaged mixture of glyphosate plus 2,4-D at 0.3 plus 0.6 kg ae/ha and paraquat at 0.4 kg/ha applied 7 or 2 WBP controlled 71 to 82% of TR kochia; and 2,4-D ester at 0.6 kg ae/ha applied 2 WBP controlled 75% of TR kochia. Linuron at 0.8 kg ai/ha and atrazine at 2.2 kg ai/ha were ineffective. In the POST herbicide experiments, where paraquat plus metolachlor at 0.6 plus 1.7 kg ai/ha were applied 17 d before planting, various combinations and rates of bentazon plus atrazine, bromoxynil, and dicamba with adjuvants provided good control of TR kochia that was less than 8 cm tall.

The addition of chlorflurenol (methyl 2-chloro-9-hydroxyfluorene-9-carboxylate) at 0.6 kg ai/ha or mefluidide {N-[2,4-dimethyl-5-[[(trifluoromethyl)sulfonyl]amino]phenyl] acetamide} at 0.3 kg ai/ha to picloram (4-amino-3,5,6-tricloropicolinic acid) at 0.3 kg ae/ha increased leafy spurge (Euphorbia esula L. # EPHES) control compared to picloram alone. Application of 84 kg/ha nitrogen in the fall prior to a spring treatment of 0.3 kg/ha picloram decreased the original stand (75%) compared to no nitrogen (18%). In greenhouse experiments, chlorflurenol and mefluidide increased the amount of 14C-picloram absorbed approximately twofold when applied in combination but not when applied independently. Based on 14C-picloram absorbed, chlorflurenol and mefluidide each increased the amount of 14C translocated to the root system, whether applied independently or in combination with picloram. An increase in root bud numbers was observed following an application of 0.6 kg/ha chlorflurenol or nitrogen.

A survey to determine the frequency and weed control impact of enhanced degradation of butylate or EPTC in field soils receiving repeat applications of these herbicides was conducted in a sugarbeet and three corn growing areas of Nebraska. All seven of the sugarbeet field soils exhibited enhanced EPTC degradation. In the corn areas, none of the 13 north central and southeast field soils displayed accelerated degradation; however, 10 of the 16 south central field soils did. In south central Nebraska, 60% and 45% of the surveyed growers were dissatisfied with weed control from butylate or EPTC in 1983 and 1984, respectively, compared to 24% and none in other survey areas. Enhanced herbicide degradation and the presence of shattercane were the main reasons for the disparity among areas.

The relative competitiveness of triazine-resistant (TR) and -susceptible (TS) common waterhemp, as a component of fitness, was assessed using TR and TS biotypes collected from the same field in Fillmore County, Nebraska. Competition between biotypes was evaluated under greenhouse conditions using a set of replacement series experiments with five ratios of TR:TS (1:0, 3:1, 1:1, 1:3, and 0:4) and four plant densities (50, 100, 150, and 300 plants m−2). No difference in final individual plant weight between TR and TS plants was observed in the absence of interbiotypic competition at all plant densities examined. Interbiotypic competition was indicated by ANOVA of plant weight and modified relative crowding coefficients (RCC) for plant weight, height, and volume. Replacement series diagrams showed TS plants were more competitive than TR plants, as measured by plant weight at densities of 50, 100, and 150 plants m−2. TS and TR plants were equally competitive at 300 plants m−2. Individual TS plant weight for 50, 100, and 150 plants m−2 was greatest at the 3:1 ratio (TR:TS) and decreased as the proportion of susceptible plants increased. Individual TR plant weight for 50, 100, and 150 plants m−2 was greatest at the 1:0 ratio and decreased as the TR proportion decreased. Lack of interbiotypic competition at 300 plants m−2 and decreasing TS plant weight with increasing ratios suggest intrabiotypic competition. RCC values for volume and height were calculated weekly during the experiment and indicated the competitive advantage of TS plants was constant from transplanting through harvest.

Field studies were conducted in 1986, 1987, 1988, and 1989 to determine the stability of crop loss functions across site by year environments. Environment was a significant source of variation for the soybean crop loss function as influenced by velvetleaf, but not as influenced by tall waterhemp and common sunflower. Weed density was a highly significant source of variation for all weed species studied. Regressions between percent soybean seed yield reductions and weed populations were linear. The velvetleaf interference regression equations were divided into two groups, those with high soybean-yielding intercepts and those with low-yielding intercepts, to explain the variance observed across environments. The regression equation for the high-yielding intercept group was Ŷ = 4.24X while the low-yielding group was Ŷ = 2.14X, where Y is percent soybean yield reduction and X is weed density per 10.7 m of soybean row. Tall waterhemp and common sunflower regression equations were determined to be Ŷ = 1.37X and Ŷ = 6.52X, respectively. Confidence intervals were used to account for the variance associated with the mean regression equation for each model and to develop economic threshold models that include risk aversion principles.

Field and greenhouse experiments were conducted during 1984 through 1986 to examine the efficacy of the seed protectants CGA-92194 {α-[(1,3-dioxolan-2-yl-methyl)imino]benzacetonitrile} and flurazole [2-chloro-4-(trifluoromethyl)-5-thiazolecarboxylic acid] for protecting grain sorghum [Sorghum bicolor (L.) Moench.] from alachlor [2-chloro-N-(2,6-diethylphenyl)-N-(methoxymethyl) acetamide], metolachlor [2-chloro-N-(2-ethyl-6-methylphenyl)-N-(2-methoxy-1-methylethyl)acetamide], and propachlor [2-chloro-N-(1-methylethyl)-N-phenylacetamide] injury. In the field, CGA-92194 and flurazole protected sorghum from injury, stand reduction, and yield loss due to alachlor and metolachlor. In general, sorghum was protected with either antidote, and protected response to alachlor or metolachlor was similar to sorghum subjected to propachlor. Greenhouse experiments were conducted to examine the response of bronze and yellow pericarp color to seed protectants, six sorghum hybrids to these antidotes, and the effects of cool soil temperature on the early seedling vigor of sorghum protected with the antidotes. The response of sorghum with yellow and bronze pericarp color was similar when compared across antidotes. However, there were differences among the sorghum hybrids when compared across protectants. The potential of CGA-92194 and flurazole to protect against alachlor injury was reduced when sorghum was grown in cool soil.

An intensive survey of two farmer-managed corn and soybean fields in eastern Nebraska was conducted to investigate parametric sequential sampling of weed seedling populations using a multistage procedure to estimate k, of the negative binomial distribution. k is a nonspatial aggregation parameter related to the variance at a given mean value. Mean weed seedling density ranged from 0.18 to 3.11 plants 0.38 m−2 (linear meter of crop row) based on 806 sampling locations. The average value of k, derived from 200 multistage estimation procedures, ranged from 0.17 to 0.32. A sequential sampling plan was developed with the goal of estimating the mean with a coefficient of variation (CV) of 10, 20, 30, and 40% of the sample mean. A sampling plan was also constructed to estimate the mean within a specified distance H of the true mean (H(x̄)= 0.10, 0.50 and 1.0 plants 0.38 m−2) with 80, 85, and 90% confidence. Estimating mean weed seedling density within a specified CV of the true mean CV(x̄) using parametric sequential sampling techniques was superior to estimating the mean within a specified distance (H(x̄)) of the true mean when considering the frequency of sampling and probability of error, especially at intermediate k values. At a k: value of 0.32 and 0.25, the difference between the actual CV(x̄) obtained from sampling and the CV(x̄) specified by the sampler was minimal. However, the accuracy of weed seedling density estimates was reduced with decreasing k values below 0.25, especially as the specified CV(x̄) increased.