An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

Bilingualism Is Associated with a Delayed Onset of Dementia but Not with a Lower Risk of Developing it: a Systematic Review with Meta-Analyses.

Some studies have linked bilingualism with a later onset of dementia, Alzheimer's disease (AD), and mild cognitive impairment (MCI). Not all studies have observed such relationships, however. Differences in study outcomes may be due to methodological limitations and the presence of confounding factors within studies such as immigration status and level of education. We conducted the first systematic review with meta-analysis combining cross-sectional studies to explore if bilingualism might delay symptom onset and diagnosis of dementia, AD, and MCI. Primary outcomes included the age of symptom onset, the age at diagnosis of MCI or dementia, and the risk of developing MCI or dementia. A secondary outcome included the degree of disease severity at dementia diagnosis. There was no difference in the age of MCI diagnosis between monolinguals and bilinguals [mean difference: 3.2; 95% confidence intervals (CI): -3.4, 9.7]. Bilinguals vs. monolinguals reported experiencing AD symptoms 4.7 years (95% CI: 3.3, 6.1) later. Bilinguals vs. monolinguals were diagnosed with dementia 3.3 years (95% CI: 1.7, 4.9) later. Here, 95% prediction intervals showed a large dispersion of effect sizes (-1.9 to 8.5). We investigated this dispersion with a subgroup meta-analysis comparing studies that had recruited participants with dementia to studies that had recruited participants with AD on the age of dementia and AD diagnosis between mono- and bilinguals. Results showed that bilinguals vs. monolinguals were 1.9 years (95% CI: -0.9, 4.7) and 4.2 (95% CI: 2.0, 6.4) older than monolinguals at the time of dementia and AD diagnosis, respectively. The mean difference between the two subgroups was not significant. There was no significant risk reduction (odds ratio: 0.89; 95% CI: 0.68-1.16) in developing dementia among bilinguals vs. monolinguals. Also, there was no significant difference (Hedges' g = 0.05; 95% CI: -0.13, 0.24) in disease severity at dementia diagnosis between bilinguals and monolinguals, despite bilinguals being significantly older. The majority of studies had adjusted for level of education suggesting that education might not have played a role in the observed delay in dementia among bilinguals vs. monolinguals. Although findings indicated that bilingualism was on average related to a delayed onset of dementia, the magnitude of this relationship varied across different settings. This variation may be due to unexplained heterogeneity and different sources of bias in the included studies. Registration: PROSPERO CRD42015019100

Crepant resolutions and open strings II

We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of threefold type A-singularities. In this paper we enlarge the body of evidence in favor of our open CRCs, along two different strands. In one direction, we consider non-hard Lefschetz targets and verify the disk CRC for local weighted projective planes. In the other, we complete the proof of the quantized (all-genus) open CRC for hard Lefschetz toric Calabi-Yau three dimensional representations by a detailed study of the G-Hilb resolution of [C3/G] for G=Z2×Z2. Our results have implications for closed-string CRCs of Coates-Iritani-Tseng, Iritani, and Ruan for this class of examples

In-home dementia caregiving is associated with greater psychological burden and poorer mental health than out-of-home caregiving: a cross-sectional study

Introduction: Caregivers who live with a person with dementia who receives care, compared with those who live elsewhere, are often considered to experience greater levels of psychological and affective burden. The evidence for this is, however, only limited to studies employing small sample sizes and that failed to examine caregivers’ psychological wellbeing. We address these issues in a large cohort of dementia caregivers. // Methods: We conducted a cross-sectional study comparing caregivers living with a dementia care recipient (n = 240) to caregivers living elsewhere (n = 255) on caregivers’ burden, anxiety, and depression. // Results: We found that caregivers living with the care recipient relative to those living elsewhere showed significantly greater burden and depression, but we found no group difference in anxiety. // Conclusions: Our study adds to the evidence by showing that cohabiting with a care recipient with dementia is associated with greater burden and poorer psychological wellbeing. Strategies aiming to improve caregivers’ burden and psychological wellbeing should take account of caregivers’ living arrangements

Crepant resolutions and open strings

In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open theories into sections of Givental’s symplectic vector space. The correspondence can be phrased as the identification of these sections via a linear morphism of Givental spaces. We deduce from this a Bryan–Graber-type statement for disk invariants, which we extend to arbitrary topologies in the Hard Lefschetz case. Motivated by ideas of Iritani, Coates–Corti–Iritani–Tseng and Ruan, we furthermore propose (1) a general form of the morphism entering the OCRC, which arises from a geometric correspondence between equivariant K-groups, and (2) an all-genus version of the OCRC for Hard Lefschetz targets. We provide a complete proof of both statements in the case of minimal resolutions of threefold An-singularities; as a necessary step of the proof we establish the all-genus closed Crepant Resolution Conjecture with descendents in its strongest form for this class of examples. Our methods rely on a new description of the quantum D-modules underlying the equivariant Gromov–Witten theory of this family of targets

Exact Results in ABJM Theory from Topological Strings

Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and TrancanelliComment: 18 pages, two figures, small misprints corrected and references added, final version to appear in JHE

Correction to: Bilingualism is associated with a delayed onset of dementia but not with a lower risk of developing it: A systematic review with meta-analyses

The original version of this article unfortunately contained the following mistakes. 1. In the Results section under the paragraph Disease Severity, the sentence “The PIs ranged between -0.47 and 0.57 MMSE points” should read -0.49 and 0.59 MMSE points. 2. In Figs. 3, 5, and 7, the labels “favour bilinguals” and “favours monolinguals” should be inverted. Therefore, it should be “favours monolinguals” and “favours bilinguals”. Please see below for the correct figures. © 2020, The Author(s)

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

The novel RASSF6 and RASSF10 candidate tumour suppressor genes are frequently epigenetically inactivated in childhood leukaemias.

BACKGROUND: The Ras-association family (RASSF) of tumour suppressor genes (TSGs) contains 10 members that encode proteins containing Ras-association (RA) domains. Several members of the RASSF family are frequently epigenetically inactivated in cancer, however, their role in leukaemia has remained largely uninvestigated. Also, RASSF10 is a predicted gene yet to be experimentally verified. Here we cloned, characterised and demonstrated expression of RASSF10 in normal human bone marrow. We also determined the methylation status of CpG islands associated with RASSF1-10 in a series of childhood acute lymphocytic leukaemias (ALL) and normal blood and bone marrow samples. RESULTS: COBRA and bisulphite sequencing revealed RASSF6 and RASSF10 were the only RASSF members with a high frequency of leukaemia-specific methylation. RASSF6 was methylated in 94% (48/51) B-ALL and 41% (12/29) T-ALL, whilst RASSF10 was methylated in 16% (8/51) B-ALL and 88% (23/26) T-ALL. RASSF6 and RASSF10 expression inversely correlated with methylation which was restored by treatment with 5-aza-2'deoxycytidine (5azaDC). CONCLUSION: This study shows the hypermethylation profile of RASSF genes in leukaemias is distinct from that of solid tumours and represents the first report of inactivation of RASSF6 or RASSF10 in cancer. These data show epigenetic inactivation of the candidate TSGs RASSF6 and RASSF10 is an extremely frequent event in the pathogenesis of childhood leukaemia. This study also warrants further investigation of the newly identified RASSF member RASSF10 and its potential role in leukaemia.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

In-home dementia caregiving is associated with greater psychological burden and poorer mental health than out-of-home caregiving: a cross-sectional study

Introduction Caregivers who live with a person with dementia who receives care, compared with those who live elsewhere, are often considered to experience greater levels of psychological and affective burden. The evidence for this is, however, only limited to studies employing small sample sizes and that failed to examine caregivers’ psychological wellbeing. We address these issues in a large cohort of dementia caregivers. Methods We conducted a cross-sectional study comparing caregivers living with a dementia care recipient (n = 240) to caregivers living elsewhere (n = 255) on caregivers’ burden, anxiety, and depression. Results We found that caregivers living with the care recipient relative to those living elsewhere showed significantly greater burden and depression, but we found no group difference in anxiety. Conclusions Our study adds to the evidence by showing that cohabiting with a care recipient with dementia is associated with greater burden and poorer psychological wellbeing. Strategies aiming to improve caregivers’ burden and psychological wellbeing should take account of caregivers’ living arrangements