Alweiss, Lovett, Wu, and Zhang introduced $q$-spread hypergraphs in their breakthrough work regarding the sunflower conjecture, and since then $q$-spread hypergraphs have been used to give short proofs of several outstanding problems in probabilistic combinatorics. A variant of $q$-spread hypergraphs was implicitly used by Kahn, Narayanan, and Park to determine the threshold for when a square of a Hamiltonian cycle appears in the random graph $G_{n,p}$. In this paper, we give a common generalization of the original notion of $q$-spread hypergraphs and the variant used by Kahn, Narayanan, and Park.

A group is $\frac 32$-generated if every non-trivial element is part of a generating pair. In 2019, Donoven and Harper showed that many Thompson groups are $\frac 32$-generated and posed five questions. The first of these is whether there exists a 2-generated group with every proper quotient cyclic that is not $\frac 32$-generated. This is a natural question given the significant work in proving that no finite group has this property, but we show that there is such an infinite group. The groups we consider are a family of finite index subgroups $G_1,\, G_2,\, \ldots$ of the Houghton group $\operatorname {FSym}(\mathbb {Z})\rtimes \mathbb {Z}$. We then show that $G_1$ and $G_2$ are $\frac 32$-generated and investigate the related notion of spread for these groups. We are able to show that they have finite spread at least 2. These are, therefore, the first infinite groups to be shown to have finite positive spread, and the first to be shown to have spread at least 2 (other than $\mathbb {Z}$ and the Tarski monsters, which have infinite spread). As a consequence, for each $k\in \{2,\, 3,\, \ldots \}$, we also have that $G_{2k}$ is index $k$ in $G_2$ but $G_2$ is $\frac 32$-generated whereas $G_{2k}$ is not.

Mycobacterium ulcerans is recognised as the third most common mycobacterial infection worldwide. It causes necrotising infections of skin and soft tissue and is classified as a neglected tropical disease by the World Health Organization (WHO). However, despite extensive research, the environmental reservoir of the organism and mode of transmission of the infection to humans remain unknown. This limits the ability to design and implement public health interventions to effectively and consistently prevent the spread and reduce the incidence of this disease. In recent years, the epidemiology of the disease has changed. In most endemic regions of the world, the number of cases reported to the WHO are reducing, with a 64% reduction in cases reported worldwide in the last 9 years. Conversely, in a smaller number of countries including Australia and Nigeria, reported cases are increasing at a rapid rate, new endemic areas continue to appear, and in Australia cases are becoming more severe. The reasons for this changing epidemiology are unknown. We review the epidemiology of M. ulcerans disease worldwide, and document recent changes. We also outline and discuss the current state of knowledge on the ecology of M. ulcerans, possible transmission mechanisms to humans and what may be enabling the spread of M. ulcerans into new endemic areas.

For all α > 0 and real random variables X, we establish sharp bounds for the smallest and the largest deviation of αX from the logarithmic distribution also known as Benford's law. In the case of uniform X, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.

The coffee berry borer (CBB), Hypothenemus hampei (Ferrari), is a multivoltine species closely associated with coffee crops worldwide, causing severe damage to the bean. In Mexico, as in all tropical regions, CBB survives during the inter-harvest period in residual berries on the ground or in dry berries remaining on the branches, and then disperses in search of the first suitable berries. In this study, we investigated how CBB dispersed from the first infested nodes during the fruiting period of Coffea canephora Pierre, which provides a favourable trophic level for this insect. Forty-five branches equally distributed in 15 coffee trees, with one infested node and four uninfested nodes, were selected. The branches were subjected to three treatments over nine weeks: 1) glue between nodes with full protection, 2) glue between nodes without protection, and 3) no glue and no protection. In addition, 45 CBB-free branches were selected and subjected to the same three treatments. CBB colonization can occur in three ways: 1) from an infested node to an uninfested node on the same branch, 2) from infested berries to uninfested berries within the nodes, 3) from branches to other branches. We also found that CBB dispersal between nodes of the same branches never occurred by walking but by flying. Thus, in this context of coffee berry development and ripening, and unlike the phenological situation of the inter-harvest period, CBB continuously travels very short distances, thus limiting its control.

Patterns of spread of 85 weed species alien to the northwestern U.S. were simulated using principal coordinate analysis on primarily herbaria-derived data. The primary pattern detected was a west-to-east migration of weeds. The point of introduction for most weeds following this pattern appeared to be near Portland, OR, an important shipping port in the past. An east-to-west migration represented a secondary pattern. The major cattle and wheat-cropping areas of east-central Montana were the apparent introduction points for weeds following this pattern. The grain and pulse region of eastern Washington represented the point of introduction of species following a third pattern of migration. These weeds subsequently spread southward to Utah and then laterally to the east and west. Historical weed migration patterns provide insight to probable points of origin and routes of currently spreading weeds as well as those that will spread in the future. Such insight may aid in the containment of future spreading weeds.

Invasive plant species have adversely affected rangelands throughout the world and continue to invade previously uninfested lands at an alarming rate. Previous efforts have focused on eradication and control; however, recent efforts have recognized that preventing invasive plant species from infesting new areas is more cost-effective and efficient than trying to restore the system after it is infested. One of the major components of prevention is limiting the introduction of the invasive plant to uninfested areas. Guidelines to limit the introduction of invasive plants into new areas are usually general and not developed to address differences in dispersal vectors among invasive plants. To limit the dispersal of invasive plants, land managers need a framework that assists them in identifying major spatial dispersal vectors and management strategies based on those vectors. We propose an initial conceptual framework that integrates the ecology of invasive plant dispersal with prevention management. The framework identifies major potential vectors by incorporating invasive plant seed adaptations for dispersal through space and infestation locations relative to vector pathways. The framework then proposes management strategies designed to limit dispersal by those specific vectors. The framework ALSo identifies areas where research could improve the effectiveness of dispersal-prevention strategies by providing additional management tools.

Plant invasions in tropical agricultural landscapes have been poorly studied so far. Here, we use plot data collected in 2015 in the La Gamba valley in southern Costa Rica to analyse the spread of two invasive alien species (Hydrilla verticillata, Hedychium coronarium) on the landscape level. In total, we recorded the aquatic H. verticillata, which was locally introduced into the La Gamba valley in 2005, in 26% of all plots (size: 15 m2), while H. coronarium, which occurs along water courses, was recorded in 80% of all plots (size: 25 m2). Generalized Linear Models (GLMs) showed that the habitat type invaded and shading had no significant effect on H. verticillata presence and abundance. However, proximity to the point of local introduction and habitat diversity in the adjacent landscape did positively affect its presence. For H. coronarium, GLMs showed a significant correlation with the invaded habitat type. The probability of H. coronarium presence was highest in herbaceous vegetation and cover was higher compared with other habitats. There was no effect on native plant species richness and cover by H. verticillata, while H. coronarium exerted a negative impact on herbaceous plant species number and, in particular, cover. Hydrilla verticillata is a rather recent addition to the local alien flora, and thus dispersal limitation still restricts its local range. Compared with observed rates of spread in other regions, spread velocity within the first decade of its local presence was low. In contrast, H. coronarium has been locally present for a substantially longer time period. This species encounters suitable habitat conditions in herbaceous vegetation along water courses, where it builds up dense clonal stands which negatively affect herbaceous vegetation. Our results show that while both study species are invasive in Central American lowlands, their local abundance and impacts on native vegetation may differ profoundly.

Newcastle disease (ND) is one of the most important poultry diseases worldwide and can lead to annual losses of up to 80% of backyard chickens in Africa. All bird species are considered susceptible to ND virus (NDV) infection but little is known about the role that wild birds play in the epidemiology of the virus. We present a long-term monitoring of 9000 wild birds in four African countries. Overall, 3·06% of the birds were PCR-positive for NDV infection, with prevalence ranging from 0% to 10% depending on the season, the site and the species considered. Our study shows that ND is circulating continuously and homogeneously in a large range of wild bird species. Several genotypes of NDV circulate concurrently in different species and are phylogenetically closely related to strains circulating in local domestic poultry, suggesting that wild birds may play several roles in the epidemiology of different NDV strains in Africa. We recommend that any strategic plan aiming at controlling ND in Africa should take into account the potential role of the local wild bird community in the transmission of the disease.

Aquatic plants play a substantial role in almost all freshwater habitats throughout the world. Even though submerged aquatic plants dominantly spread by the dispersal of vegetative plant fragments, most aquatic plant species show a broad distribution range. Here we studied the differences in the regeneration capacity and the regeneration type of fragments (by root and/or shoot growth) of eight submerged plant species (Ceratophyllum demersum, Egeria najas, Elodea canadensis, Elodea nuttallii, Hydrilla verticillata, Myriophyllum aquaticum, Myriophyllum heterophyllum and Myriophyllum spicatum) under different water nutrients in sediment-free conditions. Overall, M. spicatum showed the highest regeneration (82±2%) in this study, followed by C. demersum (73±2%) and M. aquaticum (47±4%), whereas M. heterophyllum showed the lowest (1±1%). The shoot fragments of E. canadensis, H. verticillata, E. najas and E. nuttallii regenerated by 40±2, 23±2, 16±2 and 7±1%. The nitrate concentration affected the regeneration capacities of E. najas (P=0.05), M. spicatum (P=0.013) and C. demersum (P=0.001), whereas phosphate had no significant effect. Additionally, the different nutrient concentrations had a significant effect on the portion of the regeneration types within E. canadensis, E. nuttallii and H. verticillata. Summarizing, submerged plants differ significantly in their regeneration capacity, and water nutrients have a potential effect on the regeneration of submerged plant fragments. This might influence the further colonization and spread of the species under field conditions.

The north-west Pacific kelp, Undaria pinnatifida, was first discovered in Europe on the Mediterranean coast of France (1971) and introduced to Brittany for aquaculture (1983). In the north-east Atlantic, it occurs in Spain, France, the British Isles, Belgium and Holland. The first UK record was in the Hamble estuary (1994) and it was found off Plymouth in 2003. The UK distribution is presently restricted to the south of England and the northern Irish Sea. We assessed the distribution of U. pinnatifida and native kelps and their allies in Plymouth Sound (at 0 to +1 m relative to Chart Datum). Undaria pinnatifida was widespread along rocky shores, on other hard substrata and grew in the same areas as Saccharina latissima and Saccorhiza polyschides. Undaria pinnatifida was significantly more abundant on vertical substrata than on upward-facing hard substrata. It was almost as common as all of the other kelp species combined on vertical substrata but was outnumbered by native species on upward-facing substrata. Undaria pinnatifida has become the visually dominant macroalga in marinas and has spread to surrounding natural habitats in Plymouth Sound. The extent to which it will outcompete native kelps requires monitoring, especially in conservation areas.

A large outbreak of cholera reported during April–July 2009 in the Kendrapada district of Odisha, India was investigated. Forty-one rectal swabs and 41 water samples, collected from diarrhoeal patients and from different villages were bacteriologically analysed for the isolation of bacterial enteriopathogens, antibiogram profile and detection of various toxic genes. The bacteriological analysis of rectal swabs and environmental water samples revealed the presence of V. cholerae O1 Ogawa biotype El Tor. The V. cholerae strains were resistant to ciprofloxacin, co-trimoxazole, chloramphenicol, streptomycin, ampicillin, furazolidone and nalidixic acid. The multiplex polymerase chain reaction (PCR) assay on V. cholerae strains revealed the presence of ctxA and tcpA genes. The mismatch amplification of mutation assay (MAMA) PCR on clinical and environmental isolates of V. cholerae revealed that the strains were El Tor biotype, which harboured the ctxB gene of the classical strain. The random amplified polymorphic DNA PCR analysis and pulsed-field gel electrophoresis results indicated that the V. cholerae isolates belonged to the same clone. This investigation gives a warning that the El Tor variant of V. cholerae has spread to the coastal district causing a large outbreak that requires close monitoring and surveillance on diarrhoeal outbreaks in Odisha.

A population of the invasive slipper limpet (Crepidula fornicata) has been spreading in the Bay of Mont-Saint-Michel (Western English Channel) for 40 years. Sidescan sonar, underwater video and quantitative sampling were conducted in 1996 and 2004 to document the widening geographic spread of the species over the bay. The limpet population grew by 50% during this period, to reach a fresh biomass of about 150 000 t. This local study analyses causes and effects of the spread and provides a typical example of the limpet spreading process. This population increase has significant effects on the environment in the most densely colonized area (modification to the sediment and biodiversity), leading to the emergence of a new benthic community. Anthropic dredging activities are among the causative factors of the spread but are also adversely affected by the invasion.

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

This presentation concerns the relation of chain conditions on a space X, with the weights of compact sets in Cp(X), generalizing up to the class of dσ-bounded spaces, or stable spaces. In the last case, stronger results are obtained for Corson compact subsets of CP(X).

It is proved that a distribution F is strongly unimodal iff any two quantiles of the convolution of F with any other distribution are further apart than the corresponding quantiles of F itself. Some related characterizations of strong unimodality are also given.