A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

T Cell Leukemia/Lymphoma 1A is essential for mouse epidermal keratinocytes proliferation promoted by insulin-like growth factor 1

T Cell Leukemia/Lymphoma 1A is expressed during B-cell differentiation and, when overexpressed, acts as an oncogene in mouse (Tcl1a) and human (TCL1A) B-cell chronic lymphocytic leukemia (B-CLL) and T-cell prolymphocytic leukemia (T-PLL). Furthermore, in the murine system Tcl1a is expressed in the ovary, testis and in pre-implantation embryos, where it plays an important role in blastomere proliferation and in embryonic stem cell (ESC) proliferation and self-renewal. We have also observed that Tcl1-/-adult mice exhibit alopecia and deep ulcerations. This finding has led us to investigate the role of TCL1 in mouse skin and hair follicles. We have found that TCL1 is expressed in the proliferative structure (i.e.The secondary hair germ) and in the stem cell niche (i.e.The bulge) of the hair follicle during regeneration phase and it is constitutively expressed in the basal layer of epidermis where it is required for the correct proliferative-differentiation program of the keratinocytes (KCs). Taking advantage of the murine models we have generated, including the Tcl1-/-and the K14-TCL1 transgenic mouse, we have analysed the function of TCL1 in mouse KCs and the molecular pathways involved. We provide evidence that in the epidermal compartment TCL1 has a role in the regulation of KC proliferation, differentiation, and apoptosis. In particular, the colony-forming efficiency (CFE) and the insulin-like growth factor 1 (IGF1)-induced proliferation are dramatically impaired, while apoptosis is increased, in KCs from Tcl1-/-mice when compared to WT. Moreover, the expression of differentiation markers such as cytokeratin 6 (KRT6), filaggrin (FLG) and involucrin (IVL) are profoundly altered in mutant mice (Tcl1-/-). Importantly, by over-expressing TCL1A in basal KCs of the K14-TCL1 transgenic mouse model, we observed a significant rescue of cell proliferation, differentiation and apoptosis of the mutant phenotype. Finally, we found TCL1 to act, at least in part, via increasing phospho-ERK1/2 and decreasing phospho-P38 MAPK. Hence, our data demonstrate that regulated levels of Tcl1a are necessary for the correct proliferation and differentiation of the interfollicular KC

Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

An algebraic proof of Bogomolov-Tian-Todorov theorem

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.Comment: 20 pages, amspro

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Higher Structures in M-Theory

The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and $L_\infty$-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update

Antideuterons as a Signature of Supersymmetric Dark Matter

Once the energy spectrum of the secondary component is well understood, measurements of the antiproton cosmic-ray flux at the Earth will be a powerful way to indirectly probe for the existence of supersymmetric relics in the galactic halo. Unfortunately, it is still spoilt by considerable theoretical uncertainties. As shown in this work, searches for low-energy antideuterons appear in the mean time as a plausible alternative, worth being explored. Above a few GeV/n, a dozen spallation antideuterons should be collected by the future AMS experiment on board ISSA. For energies less than about 3 GeV/n, the antideuteron spallation component becomes negligible and may be supplanted by a potential supersymmetric signal. If a few low-energy antideuterons are discovered, this should be seriously taken as a clue for the existence of massive neutralinos in the Milky Way.Comment: 16 pages, 9 figure

Metabolic Signatures of Lung Cancer in Biofluids: NMR-Based Metabonomics of Blood Plasma

In this work, the variations in the metabolic profile of blood plasma from lung cancer patients and healthy controls were investigated through NMR-based metabonomics, to assess the potential of this approach for lung cancer screening and diagnosis. PLS-DA modeling of CPMG spectra from plasma, subjected to Monte Carlo Cross Validation, allowed cancer patients to be discriminated from controls with sensitivity and specificity levels of about 90%. Relatively lower HDL and higher VLDL + LDL in the patients' plasma, together with increased lactate and pyruvate and decreased levels of glucose, citrate, formate, acetate, several amino acids (alanine, glutamine, histidine, tyrosine, valine), and methanol, could be detected. These changes were found to be present at initial disease stages and could be related to known cancer biochemical hallmarks, such as enhanced glycolysis, glutaminolysis, and gluconeogenesis, together with suppressed Krebs cycle and reduced lipid catabolism, thus supporting the hypothesis of a systemic metabolic signature for lung cancer. Despite the possible confounding influence of age, smoking habits, and other uncontrolled factors, these results indicate that NMR-based metabonomics of blood plasma can be useful as a screening tool to identify suspicious cases for subsequent, more specific radiological tests, thus contributing to improved disease management.ERDF - Competitive Factors Thematic Operational ProgrammeFCT/PTDC/ QUI/68017/2006FCOMP-01-0124-FEDER-007439SFRH/BD/ 63430/2009National UNESCO Committee - L'Oréal Medals of Honor for Women in Science 200Portuguese National NMR Network - RNRM

Mutations impairing GSK3-mediated MAF phosphorylation cause cataract, deafness, intellectual disability, seizures, and a down syndrome-like facies

Transcription factors operate in developmental processes to mediate inductive events and cell competence, and perturbation of their function or regulation can dramatically affect morphogenesis, organogenesis, and growth. We report that a narrow spectrum of amino-acid substitutions within the transactivation domain of the v-maf avian musculoaponeurotic fibrosarcoma oncogene homolog (MAF), a leucine zipper-containing transcription factor of the AP1 superfamily, profoundly affect development. Seven different de novo missense mutations involving conserved residues of the four GSK3 phosphorylation motifs were identified in eight unrelated individuals. The distinctive clinical phenotype, for which we propose the eponym Aymé-Gripp syndrome, is not limited to lens and eye defects as previously reported for MAF/Maf loss of function but includes sensorineural deafness, intellectual disability, seizures, brachycephaly, distinctive flat facial appearance, skeletal anomalies, mammary gland hypoplasia, and reduced growth. Disease-causing mutations were demonstrated to impair proper MAF phosphorylation, ubiquitination and proteasomal degradation, perturbed gene expression in primary skin fibroblasts, and induced neurodevelopmental defects in an in vivo model. Our findings nosologically and clinically delineate a previously poorly understood recognizable multisystem disorder, provide evidence for MAF governing a wider range of developmental programs than previously appreciated, and describe a novel instance of protein dosage effect severely perturbing developmen