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

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

A split-GFP tool reveals differences in the sub-mitochondrial distribution of wt and mutant alpha-synuclein

Parkinson's disease (PD), the second most common neurodegenerative disorder, is characterized by dopaminergic neuronal loss that initiates in the substantia nigra pars compacta and by the formation of intracellular inclusions mainly constituted by aberrant \u3b1-synuclein (\u3b1-syn) deposits known as Lewy bodies. Most cases of PD are sporadic, but about 10% are familial, among them those caused by mutations in SNCA gene have an autosomal dominant transmission. SNCA encodes \u3b1-syn, a small 140-amino acids protein that, under physiological conditions, is mainly localized at the presynaptic terminals. It is prevalently cytosolic, but its presence has been reported in the nucleus, in the mitochondria and, more recently, in the mitochondria-associated ER membranes (MAMs). Whether different cellular localizations may reflect specific \u3b1-syn activities is presently unclear and its action at mitochondrial level is still a matter of debate. Mounting evidence supports a role for \u3b1-syn in several mitochondria-derived activities, among which maintenance of mitochondrial morphology and modulation of complex I and ATP synthase activity. \u3b1-syn has been proposed to localize at the outer membrane (OMM), in the intermembrane space (IMS), at the inner membrane (IMM) and in the mitochondrial matrix, but a clear and comparative analysis of the sub-mitochondrial localization of WT and mutant \u3b1-syn is missing. Furthermore, the reasons for this spread sub-mitochondrial localization under physiological and pathological circumstances remain elusive. In this context, we decided to selectively monitor the sub-mitochondrial distribution of the WT and PD-related \u3b1-syn mutants A53T and A30P by taking advantage from a bimolecular fluorescence complementation (BiFC) approach. We also investigated whether cell stress could trigger \u3b1-syn translocation within the different mitochondrial sub-compartments and whether PD-related mutations could impinge on it. Interestingly, the artificial targeting of \u3b1-syn WT (but not of the mutants) to the mitochondrial matrix impacts on ATP production, suggesting a potential role within this compartment

Isolation, characterization and osteogenic differentiation of adipose-derived stem cells : from small to large size animal models

One of the most important issues in orthopaedic surgery is the loss of bone resulting from trauma, infections, tumours or congenital deficiency. In view of the hypothetical future application of mesenchymal stem cells isolated from human adipose tissue in regenerative medicine, we have analysed and characterized adipose-derived stem cells (ASCs) isolated from adipose tissue of rat, rabbit and pig. We have compared their in vitro osteogenic differentiation abilities for exploitation in the repair of critical osteochondral defects in autologous pre-clinical models. The number of pluripotent cells per millilitre of adipose tissue is variable and the yield of rabbit ASCs is lower than that in rat and pig. However, all ASCs populations show both a stable doubling time during culture and a marked clonogenic ability. After exposure to osteogenic stimuli, ASCs from rat, rabbit and pig exhibit a significant increase in the expression of osteogenic markers such as alkaline phosphatase, extracellular calcium deposition, osteocalcin and osteonectin. However, differences have been observed depending on the animal species and/or differentiation period. Rabbit and porcine ASCs have been differentiated on granules of clinical grade hydroxyapatite (HA) towards osteoblast-like cells. These cells grow and adhere to the scaffold, with no inhibitory effect of HA during osteo-differentiation. Such in vitro studies are necessary in order to select suitable pre-clinical models to validate the use of autologous ASCs, alone or in association with proper biomaterials, for the repair of critical bone defects

Hypoxia promotes the inflammatory response and stemness features in visceral fat stem cells from obese subjects

Low-grade chronic inflammation is a salient feature of obesity and many associated disorders. This condition frequently occurs in central obesity and is connected to alterations of the visceral adipose tissue (AT) microenvironment. Understanding how obesity is related to inflammation may allow the development of therapeutics aimed at improving metabolic parameters in obese patients. To achieve this aim, we compared the features of 2 subpopulations of adipose-derived stem cells (ASC) isolated from both subcutaneous and visceral AT of obese patients with the features of 2 subpopulations of ASC from the same isolation sites of non-obese individuals. In particular, the behavior of ASC of obese vs non-obese subjects during hypoxia, which occurs in obese AT and is an inducer of the inflammatory response, was evaluated. Obesity deeply influenced ASC from visceral AT (obV-ASC); these cells appeared to exhibit clearly distinguishable morphology and ultrastructure as well as reduced proliferation, clonogenicity and expression of stemness, differentiation and inflammation-related genes. These cells also exhibited a deregulated response to hypoxia, which induced strong tissue-specific NF-kB activation and an NF-kB-mediated increase in inflammatory and fibrogenic responses. Moreover, obV-ASC, which showed a less stem-like phenotype, recovered stemness features after hypoxia. Our findings demonstrated the peculiar behavior of obV-ASC, their influence on the obese visceral AT microenvironment and the therapeutic potential of NF-kB inhibitors. These novel findings suggest that the deregulated hyper-responsiveness to hypoxic stimulus of ASC from visceral AT of obese subjects may contribute via paracrine mechanisms to low-grade chronic inflammation, which has been implicated in obesity-related morbidity

Cascading Quivers from Decaying D-branes

We use an argument analogous to that of Kachru, Pearson and Verlinde to argue that cascades in L^{a,b,c} quiver gauge theories always preserve the form of the quiver, and that all gauge groups drop at each step by the number M of fractional branes. In particular, we demonstrate that an NS5-brane that sweeps out the S^3 of the base of L^{a,b,c} destroys M D3-branes.Comment: 11 pages, 1 figure; v2: references adde

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

Global Properties of Topological String Amplitudes and Orbifold Invariants

We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.Comment: 34 pages, 3 figure

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