On the multiple Borsuk numbers of sets

The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.Comment: 16 pages, 3 figure

Enhancement of glucosinolate and isothiocyanate profiles in brassicaceae crops: addressing challenges in breeding for cultivation, storage, and consumer-related traits

Glucosinolates (GSLs) and isothiocyanates (ITCs) produced by Brassicaceae plants are popular targets for analysis due to the health benefits associated with them. Breeders aim to increase the concentrations in commercial varieties; however, there are few examples of this. The most well-known is Beneforté broccoli, which has increased glucoraphanin/ sulforaphane concentrations compared to those of conventional varieties. It was developed through traditional breeding methods with considerations for processing, consumption, and health made throughout this process. Many studies presented in the literature do not take a holistic approach, and key points about breeding, cultivation methods, postharvest storage, sensory attributes, and consumer preferences are not properly taken into account. In this review, we draw together data for multiple species and address how such factors can influence GSL profiles. We encourage researchers and institutions to engage with industry and consumers to produce research that can be utilized in the improvement of Brassicaceae crops

Minor Abnormalities of Testis Development in Mice Lacking the Gene Encoding the MAPK Signalling Component, MAP3K1

In mammals, the Y chromosome is a dominant male determinant, causing the bipotential gonad to develop as a testis. Recently, cases of familial and spontaneous 46,XY disorders of sex development (DSD) have been attributed to mutations in the human gene encoding mitogen-activated protein kinase kinase kinase 1, MAP3K1, a component of the mitogen-activated protein kinase (MAPK) signal transduction pathway. In individuals harbouring heterozygous mutations in MAP3K1, dysregulation of MAPK signalling was observed in lymphoblastoid cell lines, suggesting a causal role for these mutations in disrupting XY sexual development. Mice lacking the cognate gene, Map3k1, are viable and exhibit the eyes open at birth (EOB) phenotype on a mixed genetic background, but on the C57BL/6J genetic background most mice die at around 14.5 dpc due to a failure of erythropoiesis in the fetal liver. However, no systematic examination of sexual development in Map3k1-deficient mice has been described, an omission that is especially relevant in the case of C57BL/6J, a genetic background that is sensitized to disruptions to testis determination. Here, we report that on a mixed genetic background mice lacking Map3k1 are fertile and exhibit no overt abnormalities of testis development. On C57BL/6J, significant non-viability is observed with very few animals surviving to adulthood. However, an examination of development in Map3k1-deficient XY embryos on this genetic background revealed no significant defects in testis determination, although minor abnormalities were observed, including an increase in gonadal length. Based on these observations, we conclude that MAP3K1 is not required for mouse testis determination. We discuss the significance of these data for the functional interpretation of sex-reversing MAP3K1 mutations in humans

Glucosinolates, myrosinase hydrolysis products, and flavonols found in rocket (Eruca sativa and Diplotaxis tenuifolia)

Rocket species have been shown to have very high concentrations of glucosinolates and flavonols, which have numerous positive health benefits with regular consumption. In this review we highlight how breeders and processors of rocket species can utilize genomic and phytochemical research to improve varieties and enhance the nutritive benefits to consumers. Plant breeders are increasingly looking to new technologies such as HPLC, UPLC, LC-MS and GC-MS to screen populations for their phytochemical content to inform plant selections. Here we collate the research that has been conducted to-date in rocket, and summarise all glucosinolate and flavonol compounds identified in the species. We emphasize the importance of the broad screening of populations for phytochemicals and myrosinase degradation products, as well as unique traits that may be found in underutilized gene bank resources. We also stress that collaboration with industrial partners is becoming essential for long-term plant breeding goals through research

Alkaline-Side Extraction of Cesium from Savannah River Tank Waste Using a Calixarene-Crown Ether Extractant

Results are presented supporting the viability of the alkaline-side CSEX process as a potential replacement for the In-Tank Precipitation process for removal of cesium from aqueous high-level waste (HLW) at the Savannah River Site (SRS). Under funding from the USDOE Efficient Separations and Crosscutting program, a flowsheet was suggested in early June of 1998, and in the following four months, this flowsheet underwent extensive testing, both in batch tests at ORNL and ANL and in two centrifugal-contactor tests at ANL. To carry out these tests, the initial ESP funding was augmented by direct funds from Westinghouse Savannah River Corporation. The flowsheet employed a solvent containing a calixarene-crown hybrid compound called BoBCalixC6 that was invented at ORNL and can now be obtained commercially for government use from IBC Advanced Technologies. This special extractant is so powerful and selective that it can be used at only 0.01 M, compensating for its expense, but a modifier is required for use in an aliphatic diluent, primarily to increase the cesium distribution ratio D{sub Cs} in extraction. The modifier selected is a relatively economical fluorinated alcohol called Cs3, invented at ORNL and so far available. only from ORNL. For the flowsheet, the modifier is used at 0.2 M in the branched aliphatic kerosene Isopar{reg_sign} L. Testing at ORNL and ANL involved simulants of the SRS HLW. After extraction of the Cs from the waste simulant, the solvent is scrubbed with 0.05 M HNO{sub 3} and stripped with a solution comprised of 0.0005 M HNO{sub 3} and 0.0001 M CsNO{sub 3}. The selection of these conditions is justified in this report, both on the basis of experimental data and underlying theory

Solvent Extraction of Radionuclides From Aqueous Tank Waste

This task aims toward the development of efficient solvent-extraction processes for the removal of the fission products {sup 99}Tc, {sup 90}Sr, and {sup 137}Cs from alkaline tank wastes. Processes already developed or proposed entail direct treatment of the waste solution with the solvent and subsequent stripping of the extracted contaminants from the solvent into a dilute aqueous solution. Working processes to remove Tc(and SR) separately and Cs separately have been developed; the feasibility of a combined process is under investigation. Since Tc, Sr, and Cs will be vitrified together in the high-level fraction, however, a process that could separate Tc, Sr, and Cs simultaneously, as opposed to sequentially, potentially offers the greatest impact. A figure presents a simplified diagram of a proposed solvent-extraction cycle followed by three possible treatments for the stripping solution. Some degree of recycle of the stripping solution (option a) is expected. Simple evaporation (option c) is possible prior to vitrification; this offers the greatest possible volume reduction with simple operation and no consumption of chemicals, but it is energy intensive. However, if the contaminants are concentrated (option b) by fixed-bed technology, the energy penalty of evaporation can be avoided and vitrification facilitated without any additional secondary waste being produced

The Etiology of Multiple Sclerosis: Genetic Evidence for the Involvement of the Human Endogenous Retrovirus HERV-Fc1

We have investigated the role of human endogenous retroviruses in multiple sclerosis by analyzing the DNA of patients and controls in 4 cohorts for associations between multiple sclerosis and polymorphisms near viral restriction genes or near endogenous retroviral loci with one or more intact or almost-intact genes. We found that SNPs in the gene TRIM5 were inversely correlated with disease. Conversely, SNPs around one retroviral locus, HERV-Fc1, showed a highly significant association with disease. The latter association was limited to a narrow region that contains no other known genes. We conclude that HERV-Fc1 and TRIM5 play a role in the etiology of multiple sclerosis. If these results are confirmed, they point to new modes of treatment for multiple sclerosis

Synchronization in G0/G1 enhances the mitogenic response of cells overexpressing the human insulin receptor A isoform to insulin

Evaluating mitogenic signaling specifically through the human insulin receptor (IR) is relevant for the preclinical safety assessment of developmental insulin analogs. It is known that overexpression of IR sensitizes cells to the mitogenic effects of insulin, but it is essentially unknown how mitogenic responses can be optimized to allow practical use of such recombinant cell lines for preclinical safety testing. We constitutively overexpressed the short isoform of the human insulin receptor (hIR-A, exon 11-negative) in L6 rat skeletal myoblasts. Because the mitogenic effect of growth factors such as insulin is expected to act in G0/G1, promoting S-phase entry, we developed a combined topoinhibition + serum deprivation strategy to explore the effect of G0/G1 synchronization as an independent parameter in the context of serum deprivation, the latter being routinely used to reduce background in mitogenicity assays. G0/G1 synchronization significantly improved the mitogenic responses of L6-hIR cells to insulin, measured by 3H-thymidine incorporation. Comparison with the parental L6 cells using phospho-mitogen-activated protein kinase, phospho-AKT, as well as 3H-thymidine incorporation end points supported that the majority of the mitogenic effect of insulin in L6-hIR cells was mediated by the overexpressed hIR-A. Using the optimized L6-hIR assay, we found that the X-10 insulin analog was more mitogenic than native human insulin, supporting that X-10 exhibits increased mitogenic signaling through the hIR-A. In summary, this study provides the first demonstration that serum deprivation may not be sufficient, and G0/G1 synchronization may be required to obtain optimal responsiveness of hIR-overexpressing cell lines for preclinical safety testing