Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem

Aravind and Lee-Elkin (1997) gave a proof of the Bell-Kochen-Specker theorem by showing that it is impossible to color the 60 directions from the center of a 600-cell to its vertices in a certain way. This paper refines that result by showing that the 60 directions contain many subsets of 36 and 30 directions that cannot be similarly colored, and so provide more economical demonstrations of the theorem. Further, these subsets are shown to be critical in the sense that deleting even a single direction from any of them causes the proof to fail. The critical sets of size 36 and 30 are shown to belong to orbits of 200 and 240 members, respectively, under the symmetries of the polytope. A comparison is made between these critical sets and other such sets in four dimensions, and the significance of these results is discussed.Comment: 2 new references added, caption to Table 9 correcte

Identification and validation of a QTL influencing bitter pit symptoms in apple (Malus x domestica)

Bitter pit is one of the most economically important physiological disorders affecting apple fruit production, causing soft discrete pitting of the cortical flesh of the apple fruits which renders them unmarketable. The disorder is heritable; however, the environment and cultural practices play a major role in expression of symptoms. Bitter pit has been shown to be controllable to a certain extent using calcium sprays and dips; however, their use does not entirely prevent the incidence of the disorder. Previously, bitter pit has been shown to be controlled by two dominant genes, and markers on linkage group 16 of the apple genome were identified that were significantly associated with the expression of bitter pit symptoms in a genome-wide association study. In this investigation, we identified a major QTL for bitter pit defined by two microsatellite (SSR) markers. The association of the SSRs with the bitter pit locus, and their ability to predict severe symptom expression, was confirmed through screening of individuals with stable phenotypic expression from an additional mapping progeny. The data generated in this current study suggest a two gene model could account for the control of bitter pit symptom expression; however, only one of the loci was detectable, most likely due to dominance of alleles carried by both parents of the mapping progeny used. The SSR markers identified are cost-effective, robust and multi-allelic and thus should prove useful for the identification of seedlings with resistance to bitter pit using marker-assisted selection in apple breeding programs

Attosecond imaging of molecular electronic wavepackets

International audienceA strong laser field may tunnel ionize a molecule from several orbitals simultaneously, forming an attosecond electron–hole wavepacket. Both temporal and spatial information on this wavepacket can be obtained through the coherent soft X-ray emission resulting from the laser-driven recollision of the liberated electron with the core. By characterizing the emission from aligned N 2 molecules, we demonstrate the attosecond contributions of the two highest occupied molecular orbitals. We determine conditions where they are disentangled in the real and imaginary parts of the emission dipole moment. This allows us to carry out a tomographic reconstruction of both orbitals with angstrom spatial resolution. Their coherent superposition provides experimental images of the attosecond wavepacket created in the ionization process. Our results open the prospect of imaging ultrafast intramolecular dynamics combining attosecond and angstrom resolutions

Mortality by age, gene and gender in carriers of pathogenic mismatch repair gene variants receiving surveillance for early cancer diagnosis and treatment: a report from the prospective Lynch syndrome database

BACKGROUND: The Prospective Lynch Syndrome Database (PLSD) collates information on carriers of pathogenic or likely pathogenic MMR variants (path_MMR) who are receiving medical follow-up, including colonoscopy surveillance, which aims to the achieve early diagnosis and treatment of cancers. Here we use the most recent PLSD cohort that is larger and has wider geographical representation than previous versions, allowing us to present mortality as an outcome, and median ages at cancer diagnoses for the first time. METHODS: The PLSD is a prospective observational study without a control group that was designed in 2012 and updated up to October 2022. Data for 8500 carriers of path_MMR variants from 25 countries were included, providing 71,713 years of follow up. Cumulative cancer incidences at 65 years of age were combined with 10-year crude survival following cancer, to derive estimates of mortality up to 75 years of age by organ, gene, and gender. FINDINGS: Gynaecological cancers were more frequent than colorectal cancers in path_MSH2, path_MSH6 and path_PMS2 carriers [cumulative incidence: 53.3%, 49.6% and 23.3% at 75 years, respectively]. Endometrial, colon and ovarian cancer had low mortality [8%, 13% and 15%, respectively] and prostate cancers were frequent in male path_MSH2 carriers [cumulative incidence: 39.7% at 75 years]. Pancreatic, brain, biliary tract and ureter and kidney and urinary bladder cancers were associated with high mortality [83%, 66%, 58%, 27%, and 29%, respectively]. Among path_MMR carriers undergoing colonoscopy surveillance, particularly path_MSH2 carriers, more deaths followed non-colorectal Lynch syndrome cancers than colorectal cancers. INTERPRETATION: In path_MMR carriers undergoing colonoscopy surveillance, non-colorectal Lynch syndrome cancers were associated with more deaths than were colorectal cancers. Reducing deaths from non-colorectal cancers presents a key challenge in contemporary medical care in Lynch syndrome. FUNDING: We acknowledge funding from the Norwegian Cancer Society, contract 194751-2017

No Difference in Penetrance between Truncating and Missense/Aberrant Splicing Pathogenic Variants in MLH1 and MSH2: A Prospective Lynch Syndrome Database Study

Background. Lynch syndrome is the most common genetic predisposition for hereditary cancer. Carriers of pathogenic changes in mismatch repair (MMR) genes have an increased risk of developing colorectal (CRC), endometrial, ovarian, urinary tract, prostate, and other cancers, depending on which gene is malfunctioning. In Lynch syndrome, differences in cancer incidence (penetrance) according to the gene involved have led to the stratification of cancer surveillance. By contrast, any differences in penetrance determined by the type of pathogenic variant remain unknown. Objective. To determine cumulative incidences of cancer in carriers of truncating and missense or aberrant splicing pathogenic variants of the MLH1 and MSH2 genes. Methods. Carriers of pathogenic variants of MLH1 (path_MLH1) and MSH2 (path_MSH2) genes filed in the Prospective Lynch Syndrome Database (PLSD) were categorized as truncating or missense/aberrant splicing according to the InSiGHT criteria for pathogenicity. Results. Among 5199 carriers, 1045 had missense or aberrant splicing variants, and 3930 had truncating variants. Prospective observation years for the two groups were 8205 and 34,141 years, respectively, after which there were no significant differences in incidences for cancer overall or for colorectal cancer or endometrial cancers separately. Conclusion. Truncating and missense or aberrant splicing pathogenic variants were associated with similar average cumulative incidences of cancer in carriers of path MLH1 and path_MSH2

No Difference in Penetrance between Truncating and Missense/Aberrant Splicing Pathogenic Variants in MLH1 and MSH2: A Prospective Lynch Syndrome Database Study

Background. Lynch syndrome is the most common genetic predisposition for hereditary cancer. Carriers of pathogenic changes in mismatch repair (MMR) genes have an increased risk of developing colorectal (CRC), endometrial, ovarian, urinary tract, prostate, and other cancers, depending on which gene is malfunctioning. In Lynch syndrome, differences in cancer incidence (penetrance) according to the gene involved have led to the stratification of cancer surveillance. By contrast, any differences in penetrance determined by the type of pathogenic variant remain unknown. Objective. To determine cumulative incidences of cancer in carriers of truncating and missense or aberrant splicing pathogenic variants of the MLH1 and MSH2 genes. Methods. Carriers of pathogenic variants of MLH1 (path_MLH1) and MSH2 (path_MSH2) genes filed in the Prospective Lynch Syndrome Database (PLSD) were categorized as truncating or missense/aberrant splicing according to the InSiGHT criteria for pathogenicity. Results. Among 5199 carriers, 1045 had missense or aberrant splicing variants, and 3930 had truncating variants. Prospective observation years for the two groups were 8205 and 34,141 years, respectively, after which there were no significant differences in incidences for cancer overall or for colorectal cancer or endometrial cancers separately. Conclusion. Truncating and missense or aberrant splicing pathogenic variants were associated with similar average cumulative incidences of cancer in carriers of path MLH1 and path_MSH2