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Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that $\mathrm{PSL}(2,q)\times \mathrm{PSL}(2,q)$ acting in its diagonal action on $\mathrm{PSL}(2,q)$ is separating, and hence synchronising, for $q=13$ and $q=17$. Furthermore, we show that such groups are non-spreading for all prime powers $q$.

H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger’s axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala’s formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.

PREMISE Plant domestication can be detected when transport, use, and manipulation of propagules impact reproductive functionality, especially in species with self-incompatible breeding systems. METHODS Evidence for human-caused founder effect in the Four Corners potato (Solanum jamesii Torr.) was examined by conducting 526 controlled matings between archaeological and non-archaeological populations from field-collected tubers grown in a greenhouse. Specimens from 24 major herbaria and collection records from >160 populations were examined to determine which produced fruits. RESULTS Archaeological populations did not produce any fruits when self-crossed or outcrossed between individuals from the same source. A weak ability to self- or outcross within populations was observed in non-archaeological populations. Outcrossing between archaeological and non-archaeological populations, however, produced fully formed, seed-containing fruits, especially with a non-archaeological pollen source. Fruit formation was observed in 51 of 162 occurrences, with minimal evidence of constraint by monsoonal drought, lack of pollinators, or spatial separation of suitable partners. Some archaeological populations (especially those along ancient trade routes) had records of fruit production (Chaco Canyon), while others (those in northern Arizona, western Colorado, and southern Utah) did not. CONCLUSIONS The present study suggests that archaeological populations could have different origins at different times-some descending directly from large gene pools to the south and others derived from gardens already established around occupations. The latter experienced a chain of founder events, which presumably would further reduce genetic diversity and mating capability. Consequently, some archaeological populations lack the genetic ability to sexually reproduce, likely as the result of human-caused founder effect.

Potato has about 100 related wild Solanum species growing naturally in the Americas. The US Potato Genebank aims to keep samples useful for research and breeding to improve the crop, often in the form of botanical seed families. A key component of genebank efficiency is assessing diversity within and among populations, and DNA marker sequence diversity is a powerful proxy for trait diversity. We previously reported on three factors which can cause under-estimation of heterozygosity: ascertainment, allele frequency, and ploidy bias. We here report, using GBS data for four diploid potato species, that average percent of apparent heterozygosity increases as data is more complete—the maximum difference was 2% heterozygotes when only a few individuals are called, to 36% when nearly all individuals were called. However, there was evidence that estimates of average heterozygosity based only on loci for which every individual has data can also be biased upward. Implausibly high levels of heterozygosity suggest non-segregating non-homologous SNPs, which occurred as 5–9% of all loci with complete data. We propose that best estimates of average heterozygosity in unselected seedlings should be based on loci with data for all samples after eliminating those loci that appear to be artificially fixed as heterozygous, which reduces observed heterozygote frequency by 16–26%. On that basis, the wild species examined have similar heterozygosity to the cultivated phureja.

A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ is a non-empty set of points and $\mathcal{L}$ is a collection of subsets of $\mathcal{P}$ called lines such that any two distinct points are contained in at most one line, and every line contains at least two points. A partial linear space is proper when it is not a linear space or a graph. A group of automorphisms $G$ of a proper partial linear space acts transitively on ordered pairs of distinct collinear points and ordered pairs of distinct non-collinear points precisely when $G$ is transitive of rank 3 on points. In this paper, we classify the finite proper partial linear spaces that admit rank 3 affine primitive automorphism groups, except for certain families of small groups, including subgroups of $A\Gamma L_1(q)$. Up to these exceptions, this completes the classification of the finite proper partial linear spaces admitting rank 3 primitive automorphism groups. We also provide a more detailed version of the classification of the rank 3 affine primitive permutation groups, which may be of independent interest., Comment: In this version, we have removed the assumption $V\leq H$ from 18.1 (old 13.2) and we have a new elementary proof of 10.10 (old 13.1). We have also reorganised some of the sections and made minor revisions throughout. 69 pages, 1 figure

Potato has about 100 related wild Solanum species growing naturally in the Americas. Solanum jamesii (jam), native to the southwest USA and Mexico, has many valuable traits for breeding, but making hybrids is extremely difficult. We investigated the approach of using the bridge species Solanum verrucosum (ver). A survey of all ver populations in the US Potato Genebank identified the best females. The standard bridge crossing technique using emasculation of ver and “mentor” double pollination after first pollinating with jam was very inefficient for most ver because: 1) emasculation depressed seedset in ver females, 2) despite very careful emasculation many accidental ver selfs resulted, and 3) mentor pollination produced many unwanted hybrids with the mentor pollen parent. We therefore produced populations of ver by backcrossing five generations into tuberosum cytoplasm. The BC5 lines are very vigorous in growth and flowering, but having very low male fertility and complete self-incompatibility they can be mass crossed with jam pollen without emasculation. Even with no mentor pollen, most pistils of verBC5 pollinated with jam produce a small fruit with an average of less than one normal seed. Resulting seedlings were confirmed ver-jam hybrids by DNA markers.

Ostrom and Wagner (1959) proved that if the automorphism group $G$ of a finite projective plane $\pi$ acts $2$-transitively on the points of $\pi$, then $\pi$ is isomorphic to the Desarguesian projective plane and $G$ is isomorphic to $\mathrm{P\Gamma L}(3,q)$ (for some prime-power $q$). In the more general case of a finite rank $2$ irreducible spherical building, also known as a \emph{generalized polygon}, the theorem of Fong and Seitz (1973) gave a classification of the \emph{Moufang} examples. A conjecture of Kantor, made in print in 1991, says that there are only two non-classical examples of flag-transitive generalized quadrangles up to duality. Recently, the authors made progress toward this conjecture by classifying those finite generalized quadrangles which have an automorphism group $G$ acting transitively on antiflags. In this paper, we take this classification much further by weakening the hypothesis to $G$ being transitive on ordered pairs of collinear points and ordered pairs of concurrent lines., Comment: Sections 3-6 rewritten and restructured to fill in gaps in, streamline, and avoid repetition of arguments. To appear in Transactions of the American Mathematical Society

Potato cultivars are propagated by tubers which are sensitive to damage by freezing. Potato has about 100 related wild Solanum species growing naturally in the Americas. When tubers of a spectrum of these species were slowly cooled, most were killed at a few degrees below 0 C. Only tubers of Solanum jamesii, native to the southwest USA, remained firm, sprouted and grew after one week exposure to freezing temperatures as cold as -15C. Differential Thermal Analysis was performed to detect low temperature exotherms (LTEs) in jamesii and similar-sized tubers of cultivars Russet Burbank and Snowden. LTEs, indicating supercooling, were detected only in the jamesii tubers. Survival of potato tubers at freezing temperatures could be useful in several ways. Even non-lethal cold exposure of potato tubers at harvest reduces quality for eating and for seed, but storage at freezing temperatures without damage could help preserve tuber dormancy and limit diseases.

Useful genetic diversity found in wild potato germplasm is important for progress in potato breeding and science. An effective way to maximize its utilization is through characterization of ex situ collections. For example, marker-based core subsets from large collections are an effective strategy to accelerate evaluation, utilize germplasm, and enhance cost-effectiveness. This project used AFLP markers to create a core subset for the US Potato Genebank’s collection of S. demissum. This species from Mexico and Guatemala is known for excellent levels of late blight resistance and frost tolerance. A total of 149 accessions with diverse geographic origin were characterized with 1403 AFLP markers; these markers were effective on determining genetic associations among the accessions. For the core subset, the AFLP loci were considered as traits, with the presence of the marker as the required state to include in a core. The results of the analyses identified that 10 of the accessions of S. demissum captured 83% of all the markers detected in the whole collection. The inclusion of 28 additional accessions, which had between 1 to 5 unique markers, resulted in a core set of 38 accessions that captured 96% of all the marker diversity. We expect this can benefit the genebank and the potato community by opening opportunities for research, trait screenings, and marker association studies.

Solanum jamesii is a wild potato found in the US southwest. There is ample evidence that this potato was used by ancestral Puebloans as a food source, where some researchers think it was used as a starvation food while others consider it to be regular food source. Currently this potato is being grown by Native Americans, notably the Navajo, as a specialty food as well as a food crop. There are several attributes to this potato that make it especially suitable for development as our climate changes and food needs become more demanding, including its drought tolerance and ability to be crossed with other wild potato species and cultivars.

Crop genebanks keep a sample of the diversity in wild and cultivated germplasm. Knowing the structure of diversity within and among populations informs best decisions on efficient collecting, preservation and use. The US Potato Genebank has over 90 Solanum species, ranging in representation from only a few populations to several hundred. In a previous study we showed that populations of three species captured nearly all AFLP bands in polymorphic loci when represented by 100 populations that had been added over time to the genebank. In the current study we add analysis of two additional species and propose a simple metric, L100, to compare the expected marker diversity capture of 100 populations among different species. L100 detects when there is less population overlap and more rare markers, indicating that more populations are needed to capture the available diversity in a species.

AFLP markers were used to build a core subset in 144 accessions of the United States Potato Genebank (USPG) ex situ collection of the species formerly known as Solanum phureja (now reclassified as Solanum tuberosum L. subsp. andigenum). A core subset aims to sample the minimum number possible of non-redundant germplasm units capturing the maximum diversity of the entire collection. Characterization and trait evaluation of a core subset is expected to be easier and more effective when compared to the entire germplasm collection. In this study 1534 polymorphic AFLP markers were generated and demonstrated to be useful to determine genetic relationships in the materials used. All the accessions were clearly discriminated from each other with genetic similarity levels ranging from 62 to 89%, and no duplicate germplasm samples were detected. To create the core subset, the presence of the AFLP marker was considered as the genetic trait to retain and the selection of accessions was determined by their rankings on the number of most markers added to the core. The results of this selection process revealed that the 9 top-ranked accessions of phureja, when combined, achieved the benchmark of capturing 85% of the markers detected in the complete collection. Further selection to increase the percentage of marker capture added 17 accessions with unique marker contributions which resulted in a final core subset of 26 accessions capturing 96% of the marker diversity. A Principal Component analysis determined that spatial distribution of diversity in the core was a proportional sampling of the entire diversity of the collection validating the selecting approach used. A review of the public database for valuable traits for the USPG phureja germplasm revealed that the core subset also included accessions with desirable pest/disease resistances and stress tolerances (in 25 out of the 30 traits reported in the database). The USPG expects this core subset would create opportunities for facilitating evaluation and research by using a reduced set of germplasm units with nearly all the diversity of the entire set.

Genebanks aim to maximize the preservation, classification, evaluation and distribution of germplasm in their collections to researchers and breeders. The wild is the source of most of the diversity available to genebanks, so diversity in the wild and how to best capture it also deserves study. The ultimate in valuable information from the wild would be the discovery of a large robust population at a single location on public land that is very easy to visit and contains a large proportion of the total genetic diversity detected in the species, which we have termed a “MegaPopulation”. We here report such a population of the wild potato species Solanum fendleri in the USA (also known as S. stoloniferum) on Mount Lemmon at the top of the Santa Catalina mountains near Tucson, Arizona.

Let $p$ be an odd prime. We construct a $p$-group $P$ of nilpotency class two, rank seven and exponent $p$, such that $\text{Aut}(P)$ induces $N_{\text{GL}(7,p)}(G_{2}(p))=Z(\text{GL}(7,p))G_{2}(p)$ on the Frattini quotient $P/\unicode[STIX]{x1D6F7}(P)$. The constructed group $P$ is the smallest $p$-group with these properties, having order $p^{14}$, and when $p=3$ our construction gives two nonisomorphic $p$-groups. To show that $P$ satisfies the specified properties, we study the action of $G_{2}(q)$ on the octonion algebra over $\mathbb{F}_{q}$, for each power $q$ of $p$, and explore the reducibility of the exterior square of each irreducible seven-dimensional $\mathbb{F}_{q}[G_{2}(q)]$-module.

A better understanding on how genetic diversity is structured at natural habitats can be helpful for exploration and acquisition of plant germplasm. Historically, studies have relied on DNA markers to elucidate potato genetic diversity. Current advances in genomics are broadening applications allowing the identification of markers linked to genomic regions under selection. Those markers, known as adaptive markers, unlock additional ways to value and organize germplasm diversity. For example, conservation priorities could be given to germplasm units containing markers associated to unique geographic identity, and/or linked to traits of tolerance to abiotic stresses. This study investigated if adaptive marker loci were possible to be identified in a large AFLP marker dataset of ninety-four populations of the wild potato species S. fendleri. These populations originated from six different mountain ranges in southern Arizona, USA. A total of 2094 polymorphic AFLP markers were used to conduct genetic diversity analyses of populations and mountain ranges. Adaptive markers were detected using Bayesian methods which distinguished marker loci departing significantly from frequencies expected under neutral models of genetic differentiation. This identified 16 AFLP loci that were considered to be adaptive. To contrast diversity parameters generated with each set of markers, analyses that included all the 2094 AFLP markers, and only the 16 adaptive markers were conducted. The results showed that both were efficient for establishing genetic associations among populations and mountain ranges. However, adaptive markers were better on revealing geographic patterns and identity which would suggest these markers were linked to selection at the natural sites. An additional test to determine if adaptive markers associated to climate variables found two loci associated to specific climate variables in populations from different regions but sharing similar environmental structure. The distribution of adaptive markers among populations revealed that only two were needed to build a core subset able to keep all the markers. This preliminary assessment shows that adaptive genetic diversity could offer an additional way to measure diversity in potato germplasm and to set up options for conservation and research.

The Potato Introduction Station in Sturgeon Bay Wisconsin has maintained herbarium specimens as part of its operations. These specimens mostly were grown from seeds in the field plots or greenhouses, but also include original specimens made during germplasm collecting expeditions. The herbarium of the Station (herbarium acronym PTIS) has been transferred from the potato genebank in Sturgeon Bay Wisconsin to the Wisconsin State Herbarium (acronym WIS) in Birge Hall, University of Wisconsin-Madison where it is now fully integrated and curated and funded by WIS; PTIS is discontinued and is no longer maintained as a separate herbarium. Separately, maps and taxonomic literature that were used by the potato taxonomist in Madison were transferred to the Potato Station in Sturgeon Bay.

Ploidy manipulation and the resulting need for rapid ploidy screening can be important in potato research and breeding programs. We tested three predictors of ploidy, particularly seeking the quickest, simplest, and most reliable: Chloroplast number per guard cell (C#), guard cell length (GC), and pollen diameter (P), with a total of seven variations in methods of preparation. Time required for each preparation was assessed, and a panel of inexperienced volunteers compared these methods for accuracy using a standard set of coded samples of known ploidy. The common method of counting C# with iodine stain took longer and was no more accurate than observing C# or GC in tap water. GC from tape impressions of the underside of leaves was reliable and has the advantage of permanent slides for later reference. We recommend GC, whether in water, stained, or as tape impressions. GC is significantly different in diploids and tetraploids, but the distributions do overlap, so experience and care in selecting a representative sample of cells contributes to accuracy. The standard measurement of P after staining with aceto-carmine was faster to prep and just as reliable as epidermal methods for some technicians, even with no previous experience. Pursuit of ultra-simplified methods led us to measure P in tap water. Diameters of pollen in plain water are significantly larger, but only for living pollen, suggesting this method might also be developed into a rapid and reliable way to estimate pollen viability.

A $pseudo$-$oval$ of a finite projective space over a finite field of odd order $q$ is a configuration of equidimensional subspaces that is essentially equivalent to a translation generalised quadrangle of order $(q^n,q^n)$ and a Laguerre plane of order $q^n$ (for some $n$). In setting out a programme to construct new generalised quadrangles, Shult and Thas asked whether there are pseudo-ovals consisting only of lines of an elliptic quadric ${Q}^-(5,q)$, non-equivalent to the $classical$ $example$, a so-called $pseudo$-$conic$. To date, every known pseudo-oval of lines of ${Q}^-(5,q)$ is projectively equivalent to a pseudo-conic. Thas characterised pseudo-conics as pseudo-ovals satisfying the $perspective$ property, and this paper is on characterisations of pseudo-conics from an algebraic combinatorial point of view. In particular, we show that pseudo-ovals in $Q^-(5,q)$ and pseudo-conics can be characterised as certain Delsarte designs of an interesting five-class association scheme. These association schemes are introduced and explored, and we provide a complete theory of how pseudo-ovals of lines of $Q^-(5,q)$ can be analysed from this viewpoint., Comment: 33 pages

Potato has a great impact on the economic and nutritional status of people worldwide. To capitalize on its potential, continued improvements in the current crop through breeding, production, and management technology are needed. We also need to expand potato use in diverse market outlets. In this review, we provide background on the challenge, examples of innovation in adapting other foods in response to changes in society, and explore several new possibilities for expansion of potato use.

We prove that an abstract oval is an abstract conic if and only if all of its involutions are regular and all of its secant lines are Pascalian. In doing so, we provide a new characterisation of the rank 1 projective general linear groups over arbitrary fields.

Meloidogyne chitwoodi (Columbia root-knot nematode, CRKN) can cause serious damage in potato production systems, decreasing tuber value in the fresh market and processing industries. Genetic resistance to CRKN was first identified from the wild diploid potato species Solanum bulbocastanum accession SB22 and was successfully introgressed into tetraploid potato breeding material. To expand the base of genetic resistance, 40 plant accessions representing nine wild potato species were screened for their resistance to M. chitwoodi. Greenhouse screening identified fifteen clones from S. hougasii, one clone from S. bulbocastanum, and one clone from S. stenophyllidium with moderate to high levels of resistance against three isolates of M. chitwoodi. Geographical mapping showed that the resistance sources identified in this and previous studies primarily originated in the states of Jalisco and Michoacan in west-central Mexico. These new sources of resistance will be introgressed into elite potato populations to facilitate the development of potato cultivars with durable resistance to M. chitwoodi.

The potato crop has much exotic related germplasm, so optimizing the techniques for obtaining hybrid seeds from interspecific crosses is of interest to potato researchers and breeders, especially when the cross of interest is very difficult and few hybrid seeds are expected per pollination. A model plant of Solanum verrucosum (a particularly useful wild bridge species) was selected to have very uniform and robust flower and seed production in natural crosses as a backdrop for detecting effects of different emasculation techniques. For three uniform buds in single inflorescences, one was pollinated naturally (N) after no emasculation, one was emasculated by gently opening the corolla and plucking out only the immature anthers (A) with a tweezer, and one had total (T) removal of the sepals, corolla and anthers with a tweezers. Pollen of a highly fertile diploid tuberosum male was applied uniformly to all three buds within an inflorescence one day later. No pistil abortion occurred, excluding that as a limiting factor for getting hybrid seed. But both average fruit weight and average seeds per fruit were highly significantly reduced by emasculation in the pattern T

Potato has about 100 wild species relatives that are multiplied in the form of botanical seed populations by genebanks and distributed for use in research and breeding, so understanding factors that affect seed germination is valuable. This is especially true for problematic seedlots that have slow and low (“trickle”) germination even when subjected to germination techniques that give optimal results in most other seedlots in the genebank. Twelve seedlots with trickle germination even after at least 2 years of storage and 2 robustly-germinating positive control seedlots encompassing 9 species were germinated in petri plates, and subjected to day/night = 10 h/14 h = 20C/6C alternating temperature (AT) trials along with constant room temperature (RT) controls, in the spring of 2015 and 2016. When Relative Area Under the Germination Progress Curve (RAUGPC) was calculated, normal germinating seedlots’ germination in AT was not significantly different from RT control. Some species’ seedlots’ RAUGPC germination in AT was nearly zero, some were about 50% of RT control, and some in AT germination had RAUGPC double or even triple that of RT control. In a separate trial in 2017, four seedlots most responsive to AT were shown to germinate significantly better in constant cold than their RT controls, but not as well as seeds germinated under AT. Also in 2017, two seedlots known to be very dependent on gibberellin pretreatment were tested. RT germination without gibberellin had RAUGPC of only 13% of RT control, but AT without gibberellin pretreatment increased this to 65%, showing AT substantially substitutes for gibberellin pretreatment in these seedlots. AT could be a useful application to all seed germination assays in the genebank if it facilitated a better assessment of the potential viability of trickle-germinating seedlots. But one would need to identify and exclude those seedlots for which alternating temperature greatly depresses germination.

Recently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that $S(t,k,n)$ exists whenever the necessary divisibility conditions on the parameters are satisfied and $n$ is sufficiently large in terms of $k$ and $t$. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called \emph{synchronizing} and \emph{separating}) lying between primitive and $2$-homogeneous are defined. A big open question is how the permutation group induced by $S_n$ on $k$-subsets of $\{1,\ldots,n\}$ fits in this hierarchy; our conjecture would give a solution to this problem for $n$ large in terms of $k$. We prove the conjecture in the case $k=4$: our result asserts that $S_n$ acting on $4$-sets is separating for $n\ge10$ (it fails to be synchronizing for $n=9$)., Comment: Error in previous version corrected

Bajos niveles productivos de papa en el Perú y otros países de la región son atribuidos al poco uso de semilla de calidad y reciclaje de tubérculos contaminados. Por ello hay consenso en la necesidad de incorporar tecnologías de producción de semilla de calidad que sean efectivas y eficientes pero que sean consecuentes con la realidad de la papa en Latinoamérica. Este estudio examinó un sistema tecnológico de producción de semillas desarrollado por la compañía americana CETS de Wisconsin. Este sistema usa cámaras de crecimiento llamadas fitotrones donde los parámetros de crecimiento son todos controlados automáticamente. Las plantas pueden producir mini-tubérculos entre 60 y 70 días, permitiendo hasta seis cosechas por año. Para validar el uso de esta tecnología diez variedades nativas de ocho especies cultivadas de papa fueron usadas. Los resultados demostraron que las plantas completaron sus ciclos fenológicos y fisiológicos dentro de los rangos de tiempos establecidos. La producción de tubérculos fue variable, en algunos casos fue muy alta (Solanum x ajanhuiri) pero en otros fue solo moderada (S. phureja). En resumen, el sistema de CETS ofrece una posibilidad para la producción de semilla de calidad en variedades de papas nativas de la región. Este sistema podría también tener impacto en otras áreas como conservación de biodiversidad, mejoramiento genético e investigación básica.

The classification of flag-transitive generalized quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalized quadrangles are also point-primitive (up to point–line duality), it is likewise natural to seek a classification of the point-primitive examples. Working toward this aim, we are led to investigate generalized quadrangles that admit a collineation group$G$preserving a Cartesian product decomposition of the set of points. It is shown that, under a generic assumption on$G$, the number of factors of such a Cartesian product can be at most four. This result is then used to treat various types of primitive and quasiprimitive point actions. In particular, it is shown that$G$cannot haveholomorph compoundO’Nan–Scott type. Our arguments also pose purely group-theoretic questions about conjugacy classes in nonabelian finite simple groups and fixities of primitive permutation groups.

Potato has about 100 wild species relatives that are multiplied in the form of botanical seed populations by genebanks, and distributed for use in research and breeding, so factors that affect long term seed germination are of interest. In 1987 the US Potato Genebank conducted routine seed multiplication on 127 populations of 31 species as greenhouse-grown potted plants. Half of the parent plants in each population were given two doses of liquid fertilizer in addition to the standard slow-release granular fertilizer which had been mixed into the medium for all plants. Plants with this extra liquid fertilizer application grew larger, and produced significantly more fruit and seeds. However, seeds from parents fertilized extra did not have improved seed weight or germination after 26 years of storage. We conclude that optimizing the fertilizer regime used on parent plants, while doubling the average seed yield, does not result in higher quality seeds.

The only known examples of finite generalised hexagons and octagons arise from the finite almost simple groups of Lie type G 2 , D 4 3 , and F 4 2 . These groups act transitively on flags, primitively on points, and primitively on lines. The best converse result prior to the writing of this paper was that of Schneider and Van Maldeghem (2008): if a group G acts flag-transitively, point-primitively, and line-primitively on a finite generalised hexagon or octagon, then G is an almost simple group of Lie type. We strengthen this result by showing that the same conclusion holds under the sole assumption of point-primitivity.

A generalised quadrangle is a point–line incidence geometry G such that: (i) any two points lie on at most one line, and (ii) given a line L and a point p not incident with L , there is a unique point on L collinear with p . They are a specific case of the generalised polygons introduced by Tits (1959), and these structures and their automorphism groups are of some importance in finite geometry. An integral part of understanding the automorphism groups of finite generalised quadrangles is knowing which groups can act primitively on their points, and in particular, which almost simple groups arise as automorphism groups. We show that no sporadic almost simple group can act primitively on the points of a finite (thick) generalised quadrangle. We also present two new ideas contributing towards analysing point-primitive groups acting on generalised quadrangles. The first is the outline and implementation of an algorithm for determining whether a given group can act primitively on the points of some generalised quadrangle. The second is the discussion of a conjecture resulting from observations made in the course of this work: any group acting primitively on the points of a generalised quadrangle must either act transitively on lines or have exactly two line-orbits, each containing half of the lines.

We provide new proofs for the non-existence of ovoids in hyperbolic spaces of rank at least four in even characteristic, and for the Hermitian polar space H(5,4). We also improve the results of A. Klein on the non-existence of ovoids of Hermitian spaces and hyperbolic quadrics.

In this paper, we construct an infinite family of hemisystems of the Hermitian surface $\mathsf{H}(3,q^2)$. In particular, we show that for every odd prime power $q$ congruent to $3$ modulo $4$, there exists a hemisystem of $\mathsf{H}(3,q^2)$ admitting $C_{(q^3+1)/4} : C_3$., Fixed typos, added open problems section

Potato has two wild relatives native to the USA, Solanum jamesii (jam) and S. fendleri (fen). Core collections are a useful tool for genebanks, identifying a ranked minimum number of samples that together encompass most of the total genetic diversity. With diversity measured as presence of AFLP bands, we made core collections for each species such that >90 % of diversity was captured in a minimum of populations. For fen, bulks containing about 25 % of populations accomplished that standard. For jam, a single “mega-population” at Mesa Verde, CO, consisting of many thousands of plants, was found to encompass 82 % of the AFLP bands detected in all samples across the entire USA range, and adding three more populations captured a total of >90 %. Core members for both jam and fen with the most diversity originated from the northern part of the range. That suggests that these areas merit more collecting. If resources for germplasm preservation and evaluation are limited, samples in the core collections should take priority.

Let G be a group of collineations of a finite thick generalised quadrangle Γ. Suppose that G acts primitively on the point set 𝒫 ${\mathcal{P}}$ of Γ, and transitively on the lines of Γ. We show that the primitive action of G on 𝒫 ${\mathcal{P}}$ cannot be of holomorph simple or holomorph compound type. In joint work with Glasby, we have previously classified the examples Γ for which the action of G on 𝒫 ${\mathcal{P}}$ is of affine type. The problem of classifying generalised quadrangles with a point-primitive, line-transitive collineation group is therefore reduced to the case where there is a unique minimal normal subgroup M and M is non-Abelian.

The third most important food crop worldwide, potato (Solanum tuberosum L.) is a tetraploid outcrossing species propagated from tubers. Breeders have long been challenged by polyploidy, heterozygosity, and asexual reproduction. It has been assumed that tetraploidy is essential for high yield, that the creation of inbred potato is not feasible, and that propagation by seed tubers is ideal. In this paper, we question those assumptions and propose to convert potato into a diploid inbred line–based crop propagated by true seed. Although a conversion of this magnitude is unprecedented, the possible genetic gains from a breeding system based on inbred lines and the seed production benefits from a sexual propagation system are too large to ignore. We call on leaders of public and private organizations to come together to explore the feasibility of this radical and exciting new strategy in potato breeding. S.H. Jansky, USDA–ARS Vegetable Crops Research Unit, Dep. of Horticulture, Univ. of Wisconsin, 1575 Linden Dr., Madison, WI; A.O. Charkowski, Dep. of Plant Pathology, Univ. of Wisconsin, Madison, WI; D.S. Douches, Dep. of Plant, Soil, and Microbial Sciences, Mich. State Univ., East Lansing, MI; G. Gusmini, Pepsico, St. Paul, MN; C. Richael, Simplot Plant Sciences, Boise, ID; P.C. Bethke and D.M. Spooner, USDA–ARS Vegetable Crops Research Unit, Dep. of Horticulture, Univ. of Wisconsin, Madison, WI; R.G. Novy, USDA– ARS Small Grains and Potato Germplasm Research Unit, Aberdeen, ID; H. De Jong, Agriculture and Agri-Food Canada, Fredericton, New Brunswick, Canada (retired); W.S. De Jong, School of Integrative Plant Sciences, Cornell Univ., Ithaca, NY; J.B. Bamberg USDA–ARS, Dep. of Horticulture, Univ. of Wisconsin, Madison, WI, and US Potato Genebank, Sturgeon Bay, WI; A.L. Thompson, Dep. of Plant Sciences, North Dakota State Univ.; B. Bizimungu, Agriculture and Agri-Food Canada, Fredericton, New Brunswick, Canada; D.G. Holm, Dep. of Horticulture and Landscape Architecture, Colorado State Univ., San Luis Valley Research Center, Center, CO; C.R. Brown, USDA– ARS, Prosser, WA; K.G. Haynes, USDA–ARS, Beltsville, MD; V.R. Sathuvalli, Dep. of Crop and Soil Science, Oregon State Univ., Hermiston Agricultural Research and Extension Center, Hermiston, OR; R.E. Veilleux, Dep. of Horticulture, Virginia Tech, Blacksburg, VA; J.C. Miller, Jr., Dep. of Horticultural Sciences, Texas AM J.M. Bradeen, Dep. of Plant Pathology, Univ. of Minnesota, St. Paul, MN; J. Jiang, Dep. of Horticulture, Univ. of Wisconsin, Madison, WI. G. Gusmini is an employee of PepsiCo, Inc.; the views expressed in this presentation are those of the author and do not necessarily reflect the position or policy of PepsiCo Inc. C. Richael is an employee of Simplot Plant Sciences; the views expressed in this presentation are those of the author and do not necessarily reflect the position or policy of Simplot Plant Sciences. Received 3 Dec. 2015. Accepted 25 Jan. 2016. *Corresponding author (shelley.jansky@ars. usda.gov; shjansky@wisc.edu). Abbreviations: CIP, International Potato Center; ILs, introgression lines; RILs, recombinant inbred lines; TPS, true potato seed. Published in Crop Sci. 56:1412–1422 (2016). doi: 10.2135/cropsci2015.12.0740 © Crop Science Society of America | 5585 Guilford Rd., Madison, WI 53711 USA This is an open access article distributed under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Published July 7, 2016

Aims and objectives The purpose of our paper was to explore primary caregivers' experience of the way public mental health nurses and other mental health clinicians responded to them as primary carers of older adults with mental illness. Background As populations age, the prevalence of mental illness in older adults will increase and the burden of care placed on family carers will intensify. While family carers are essential to the well-being and quality of life of older adults with mental illness, they frequently experience marginalisation from clinicians. Design An interpretative phenomenological analysis approach was used to inform data collection and analysis. Method Individual, semistructured, audio-recorded qualitative interviews were conducted with a purposive sample of 30 primary carers. Results Two themes were abstracted from the data highlighting carers' contrasting satisfaction with, and delivery of culturally competent care by, clinicians. A third theme, strategies for enhancing carers' experience of care, incorporated carers' suggestions about ways to strengthen their experience of caring. Conclusion Although some primary carers had favourable experiences with clinicians, most were dissatisfied and this, in turn, clouded their overall experience of caring. Relevance to clinical practice Our findings have implications for the provision of education, ongoing support for, and building the cultural competence of, clinicians about working with carers. They also highlight the need for a change in organisational and practice culture to encompass mutual respect and partnership with carers within the context of the providing person-centred care for carers and older adults with mental illness.

Potato psyllid, Bactericera cockerelli (Sulc) (Hemiptera: Triozidae), is a key pest of potato and the vector of “Candidatus Liberibacter solanacearum,” the pathogen associated with zebra chip disease. Development of potato cultivars with genetic resistance to potato psyllid would enable cost-effective control of this pest with reduced use of insecticides. To facilitate the development of resistant cultivars, the objective of our study was to screen germplasm accessions of Solanum verrucosum for resistance to potato psyllid. The susceptibility of S. verrucosum germplasm accessions to potato psyllid was highly variable in choice prescreening assays and no-choice performance assays. Compared with the susceptible potato cultivar, ‘Russet Burbank,’ several S. verrucosum populations exhibited strong resistance to potato psyllid. The S. verrucosum accession, PI 195170 was highly resistant to potato psyllid, and is a potential source of genetic resistance for the development of resistant potato cultivars.

The US Potato Genebank in Sturgeon Bay, Wisconsin, is the national germplasm collection for the world’s most important vegetable crop. It contains about 6,000 accessions of 100 species of tuber-bearing relatives of Solanum tuberosum. The potato of commerce is a clonal crop susceptible to many systemic pathogens, so the genebank routinely uses in vitro clonal maintenance and distribution for named cultivars. In vitro management is also the tool of choice for various breeding and genetic stocks of interest to breeders and researchers. Long-term backup cryopreservation of clones is done at the base collection in Fort Collins, Colorado. In vitro techniques also play an important role in virus elimination from clones. Recently, in vitro propagation has expanded to the temporary safekeeping of meristem propagules in antimicrobial medium during plant collecting expeditions in the southwest USA. The genebank’s mission includes promoting technology that supports expanded use of the germplasm, in particular, finding ways to overcome interspecific hybridization barriers. Thus, in vitro techniques such as pollen viability testing, ploidy manipulation, protoplast fusion, and embryo rescue have contributed technology for major advances in interspecific hybridization, utilization of noncommercial species, and introgression of genes from wild near-relatives. Finally, advancing in vitro technology holds promise as a tool for mass bioassay and selection of seeds, pollen, or somaclones for useful traits.

We investigate intriguing sets of an association scheme introduced by Penttila and Williford (2011) that was the basis for their construction of primitive cometric association schemes that are not P-polynomial nor the dual of a P-polynomial scheme. In particular, we give examples and characterisation results for the four types of intriguing sets that arise in this scheme.

In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space $${\mathrm {H}}(3,q^2)$$H(3,q2), unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente's, and develop techniques that are likely to be useful in finding relative hemisystems in future.

While the burden of caring for older people with chronic medical illness and dementia has been well documented, considerably less is known about how carers develop the strength and resilience to sustain this important role with older family members with mental illness. The aim of the study was to understand the lived experience of primary caregivers of older people with severe and persistent mental illness, and to explore what, if anything, helps to sustain them in their caring role. An interpretative phenomenological analysis approach was adopted, and qualitative interviews were used with 30 primary caregivers. Two overarching themes, and related subthemes, were abstracted from the data. First, caring is a difficult and demanding responsibility. It affects carers adversely, emotionally, physically, socially, and financially, and their lifestyle in general. This is reflected in three subthemes: (i) physically and emotionally draining; (ii) grieving about the loss; (iii) and adverse effects on lifestyle and social relationships. Second, carers develop resilience in caring, which helps sustain them in their role, as illustrated in three subthemes: (i) caring as purposeful and satisfying; (ii) harnessing social support from others; and (iii) purposefully maintaining their own well-being. Community mental health nurses have a key role in assessing carers’ needs and supporting them in their caring role.