On Graph Refutation for Relational Inclusions

We introduce a graphical refutation calculus for relational inclusions: it reduces establishing a relational inclusion to establishing that a graph constructed from it has empty extension. This sound and complete calculus is conceptually simpler and easier to use than the usual ones.Comment: In Proceedings LSFA 2011, arXiv:1203.542

Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras

We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph C*-algebra, an Exel-Laca algebra, and an ultragraph C*-algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph C*-algebras and Exel-Laca algebras, and that all simple AF-algebras are either graph C*-algebras or Exel-Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the C*-algebra of a row-finite graph with no sinks.Comment: 34 pages, Version 2 comments: Some minor typos corrected; Version 3 comments: Some typos corrected. This is the version to appea

Irreducible matrix resolution of the elasticity tensor for symmetry systems

In linear elasticity, a fourth order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties of a material. Due to Voigt, this tensor is conventionally represented by a $6\times 6$ symmetric matrix. This classical matrix representation does not conform with the irreducible decomposition of the elasticity tensor. In this paper, we construct two alternative matrix representations. The $3\times 7$ matrix representation is in a correspondence with the permutation transformations of indices and with the general linear transformation of the basis. An additional representation of the elasticity tensor by three $3\times 3$ matrices is suitable for description the irreducible decomposition under the rotation transformations. We present the elasticity tensor of all crystal systems in these compact matrix forms and construct the hierarchy diagrams based on this representation

FUS mutant human motoneurons display altered transcriptome and microRNA pathways with implications for ALS pathogenesis

The FUS gene has been linked to amyotrophic lateral sclerosis (ALS). FUS is a ubiquitous RNA-binding protein, and the mechanisms leading to selective motoneuron loss downstream of ALS-linked mutations are largely unknown. We report the transcriptome analysis of human purified motoneurons, obtained from FUS wild-type or mutant isogenic induced pluripotent stem cells (iPSCs). Gene ontology analysis of differentially expressed genes identified significant enrichment of pathways previously associated to sporadic ALS and other neurological diseases. Several microRNAs (miRNAs) were also deregulated in FUS mutant motoneurons, including miR-375, involved in motoneuron survival. We report that relevant targets of miR-375, including the neural RNA-binding protein ELAVL4 and apoptotic factors, are aberrantly increased in FUS mutant motoneurons. Characterization of transcriptome changes in the cell type primarily affected by the disease contributes to the definition of the pathogenic mechanisms of FUS-linked ALS

Neurodegeneration and neuroinflammation are linked, but independent of a-synuclein inclusions, in a seeding/spreading mouse model of Parkinson's disease

A key pathological process in Parkinson's disease (PD) is the transneuronal spreading of α-synuclein. Alpha-synuclein (α-syn) is a presynaptic protein that, in PD, forms pathological inclusions. Other hallmarks of PD include neurodegeneration and microgliosis in susceptible brain regions. Whether it is primarily transneuronal spreading of α-syn particles, inclusion formation, or other mechanisms, such as inflammation, that cause neurodegeneration in PD is unclear. We used a model of spreading of α-syn induced by striatal injection of α-syn preformed fibrils into the mouse striatum to address this question. We performed quantitative analysis for α-syn inclusions, neurodegeneration, and microgliosis in different brain regions, and generated gene expression profiles of the ventral midbrain, at two different timepoints after disease induction. We observed significant neurodegeneration and microgliosis in brain regions not only with, but also without α-syn inclusions. We also observed prominent microgliosis in injured brain regions that did not correlate with neurodegeneration nor with inclusion load. Using longitudinal gene expression profiling, we observed early gene expression changes, linked to neuroinflammation, that preceded neurodegeneration, indicating an active role of microglia in this process. Altered gene pathways overlapped with those typical of PD. Our observations indicate that α-syn inclusion formation is not the major driver in the early phases of PD-like neurodegeneration, but that microglia, activated by diffusible, oligomeric α-syn, may play a key role in this process. Our findings uncover new features of α-syn induced pathologies, in particular microgliosis, and point to the necessity for a broader view of the process of α-syn spreading

Comparative interactomics analysis of different ALS-associated proteins identifies converging molecular pathways

Amyotrophic lateral sclerosis (ALS) is a devastating neurological disease with no effective treatment available. An increasing number of genetic causes of ALS are being identified, but how these genetic defects lead to motor neuron degeneration and to which extent they affect common cellular pathways remains incompletely understood. To address these questions, we performed an interactomic analysis to identify binding partners of wild-type (WT) and ALS-associated mutant versions of ATXN2, C9orf72, FUS, OPTN, TDP-43 and UBQLN2 in neuronal cells. This analysis identified several known but also many novel binding partners of these proteins