Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$} ($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal $m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in $\mathbb R^{m+k}$. Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$ has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq d-m$. The converse is not true in general. We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in $\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an ordinary $\rho$-transversal. We use this result, together with the multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann category of the Grassmannian, and different versions of the colorful Helly theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

'Bunchy top symptom' of papaya in Cuba: new insights

Papaya is an important export crop in Cuba. A disease named Bunchy top symptom (BTS) was first observed in 2003 from Villa Clara province, but is now widespread throughout the country. A nested PCR assay with 16S rDNA phytoplasma primers P1/P7 and R16F2n/R2 was used to index more than 2200 papaya plants, weeds and insect samples collected between November 2005 and June 2006. RFLP patterns for all amplicons were identical with HaeIII, RsaI and AluI enzymes. No rickettsia-like bacteria were found in any of the samples. Phytoplasma rDNA was amplified from 1449 (89.7%) papaya plants with BTS symptoms. Phytoplasma rDNA was also detected in 331 apparently healthy papayas, and other plant species: Anoda acerifolia (57), Euphorbia heterophylla (73), Malvastrum coromandelianum (41) and Rynchosia minima (37) and 60/75 batches of Empoasca papayae. Sequences from the phytoplasma in papaya (DQ868531), A. acerifolia (DQ286950); E. heterophylla (DQ286951); M. coromandelianum (DQ286952); R. minima (DQ868533) and the leafhopper E. papayae (DQ868532) all showed 99% similarity to the phytoplasma associated with polygala phyllody, PPhy, (AY787140) belonging to the 16SrII group, ‘Candidatus Phytoplasma aurantifolia’. The discovery of the BTS phytoplasma in weed species and a putative vector Empoasca papayae suggests, that these plants and the leafhopper may have role in the spread of this disease

Notes about the Caratheodory number

In this paper we give sufficient conditions for a compactum in $\mathbb R^n$ to have Carath\'{e}odory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory theorem and give a Tverberg type theorem for families of convex compacta

ALBACORE (Thunnus alalunga) REPRODUCTIVE BIOLOGY STUDY FOR THE NORTH ATLANTIC STOCK:YEARS 2020 AND 2021

The ICCAT North Atlantic Albacore (Thunnus alalunga) Research Program was established to enhance knowledge on albacore to provide more accurate scientific advice to the Commission. Funds are provided to the Albacore WG to develop research activities to accomplish several objectives. One of the research objectives is to increase knowledge on reproductive biology for the northern Atlantic stock, maturity schedules (L50) and egg production (size/age related fecundity. In March 2021, Terms of Reference were published by ICCAT. A Consortium integrated by Canada, Venezuela, Chinese-Taipei and Spain presented an offer to collect gonad samples and spines throughout the year and carry out the study of reproductive biology for North Atlantic albacore stock. Results of histological analysis: maturity stages, batch fecundity and seasonal area of spawners are presented as well as the age determined of partially collection of albacore spines. Analysis were done with the total albacore gonads samples collected in 2020 and 2021 for the reproductive biology study of northern albacore.

The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovasz local lemma in probabilistic combinatorics. We show that the conclusion of the Lovasz local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovasz local lemma -- which provides a sufficient condition for this to occur -- corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer and explicitly by Dobrushin. We also present some refinements and extensions of both arguments, including a generalization of the Lovasz local lemma that allows for "soft" dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity. To be published in J. Stat. Phy

Construction of an interactive online phytoplasma classification tool, iPhyClassifier, and its application in analysis of the peach X-disease phytoplasma group (16SrIII)

Phytoplasmas, the causal agents of numerous plant diseases, are insect-vector-transmitted, cell-wall-less bacteria descended from ancestral low-G+C-content Gram-positive bacteria in the Bacillus–Clostridium group. Despite their monophyletic origin, widely divergent phytoplasma lineages have evolved in adaptation to specific ecological niches. Classification and taxonomic assignment of phytoplasmas have been based primarily on molecular analysis of 16S rRNA gene sequences because of the inaccessibility of measurable phenotypic characters suitable for conventional microbial characterization. In the present study, an interactive online tool, iPhyClassifier, was developed to expand the efficacy and capacity of the current 16S rRNA gene sequence-based phytoplasma classification system. iPhyClassifier performs sequence similarity analysis, simulates laboratory restriction enzyme digestions and subsequent gel electrophoresis and generates virtual restriction fragment length polymorphism (RFLP) profiles. Based on calculated RFLP pattern similarity coefficients and overall sequence similarity scores, iPhyClassifier makes instant suggestions on tentative phytoplasma 16Sr group/subgroup classification status and ‘Candidatus Phytoplasma’ species assignment. Using iPhyClassifier, we revised and updated the classification of strains affiliated with the peach X-disease phytoplasma group. The online tool can be accessed at http://www.ba.ars.usda.gov/data/mppl/iPhyClassifier.html

Dispersal of Adult Black Marlin (Istiompax indica) from a Great Barrier Reef Spawning Aggregation

The black marlin (Istiompax indica) is one of the largest bony fishes in the world with females capable of reaching a mass of over 700 kg. This highly migratory predator occurs in the tropical regions of the Pacific and Indian Oceans, and is the target of regional recreational and commercial fisheries. Through the sampling of ichthyoplankton and ovaries we provide evidence that the relatively high seasonal abundance of black marlin off the Great Barrier Reef is, in fact, a spawning aggregation. Furthermore, through the tracking of individual black marlin via satellite popup tags, we document the dispersal of adult black marlin away from the spawning aggregation, thereby identifying the catchment area for this spawning stock. Although tag shedding is an issue when studying billfish, we tentatively identify the catchment area for this stock of black marlin to extend throughout the Coral Sea, including the waters of Papua New Guinea, the Solomon Islands, Micronesia, New Caledonia, Kiribati, Vanuatu, Fiji, Tuvalu and Nauru

Distribution and Habitat Associations of Billfish and Swordfish Larvae across Mesoscale Features in the Gulf of Mexico

Ichthyoplankton surveys were conducted in surface waters of the northern Gulf of Mexico (NGoM) over a three-year period (2006–2008) to determine the relative value of this region as early life habitat of sailfish (Istiophorus platypterus), blue marlin (Makaira nigricans), white marlin (Kajikia albida), and swordfish (Xiphias gladius). Sailfish were the dominant billfish collected in summer surveys, and larvae were present at 37.5% of the stations sampled. Blue marlin and white marlin larvae were present at 25.0% and 4.6% of the stations sampled, respectively, while swordfish occurred at 17.2% of the stations. Areas of peak production were detected and maximum density estimates for sailfish (22.09 larvae 1000 m−2) were significantly higher than the three other species: blue marlin (9.62 larvae 1000 m−2), white marlin (5.44 larvae 1000 m−2), and swordfish (4.67 larvae 1000 m−2). The distribution and abundance of billfish and swordfish larvae varied spatially and temporally, and several environmental variables (sea surface temperature, salinity, sea surface height, distance to the Loop Current, current velocity, water depth, and Sargassum biomass) were deemed to be influential variables in generalized additive models (GAMs). Mesoscale features in the NGoM affected the distribution and abundance of billfish and swordfish larvae, with densities typically higher in frontal zones or areas proximal to the Loop Current. Habitat suitability of all four species was strongly linked to physicochemical attributes of the water masses they inhabited, and observed abundance was higher in slope waters with lower sea surface temperature and higher salinity. Our results highlight the value of the NGoM as early life habitat of billfishes and swordfish, and represent valuable baseline data for evaluating anthropogenic effects (i.e., Deepwater Horizon oil spill) on the Atlantic billfish and swordfish populations