Cohomologies and derived brackets of Leibniz algebras

In this thesis, we work on the structure of Leibniz algebras and develop cohomology theories for them. The motivation comes from: • Roytenberg, Stienon-Xu and Ginot-Grutzmann's work on standard and naive cohomology of Courant algebroids (Courant-Dorfman algebras). • Kosmann-Schwarzbach, Roytenberg and Alekseev-Xu's constructions of derived brackets for Courant algebroids. • The classical equivariant cohomology theory and the generalized geometry theory. This thesis consists of three parts: 1. We introduce standard cohomology and naive cohomology for a Leibniz algebra. We discuss their properties and show that they are isomorphic. By similar methods, we prove a generalization of Ginot-Grutzmann's theorem on transitive Courant algebroids, which was conjectured by Stienon-Xu. The relation between standard complexes of a Leibniz algebra and its corresponding crossed product is also discussed. 2. We observe a canonical 3-cochain in the standard complex of a Leibniz algebra. We construct a bracket on the subspace consisting of so-called representable cochains, and prove that the subspace becomes a graded Poisson algebra. Finally we show that for a fat Leibniz algebra, the Leibniz bracket can be represented as a derived bracket. 3. In spired by the notion of a Lie algebra action and the idea of generalized geometry, we introduce the notion of a generalized action of a Lie algebra g on a smooth manifold M, to be a homomorphism of Leibniz algebras from g to the generalized tangent bundle TM+T*M. We define the interior product and Lie derivative so that the standard complex of TM+T*M becomes a g differential algebra, then we discuss its equivariant cohomology. We also study the equivariant cohomology for a subcomplex of a Leibniz complex

The standard cohomology of regular Courant algebroids

For any regular Courant algebroid $E$ over a smooth manifold $M$ with characteristic distribution $F$ and ample Lie algebroid $A_E$, we prove that there exists a canonical homological vector field on the graded manifold $A_E[1] \oplus (TM/F)^\ast[2]$ such that the associated dg manifold $\mathcal{M}_E$, which we call the minimal model of the Courant algebroid $E$, encodes all cohomological data of $E$. Thereby, the standard cohomology $H^\bullet_{\operatorname{st}}(E)$ of $E$ can be identified with the cohomology $H^\bullet(\mathcal{M}_E)$ of the function space on $\mathcal{M}_E$. To compute it, we find a natural transgression map [d_T] \colon H^{\bullet}_{\operatorname{CE}}\big(A_E; S^{\diamond}(TM/F[-2])\big) \to H^{\bullet+3}_{\CE}\big(A_E; S^{\diamond-1}(TM/F[-2])\big) from which we construct a spectral sequence which converges to $H^\bullet_{\operatorname{st}}(E)$. Moreover, we give applications to generalized exact Courant algebroids and those arising from regular Lie algebroids .Comment: 41 pages; the main body is rewritten; typos remove

Effluent-free deep dyeing of cotton fabric with cacao husk extracts using the Taguchi optimization method

Textile dyehouses are under scrutiny because they discharge colored and hazardous effluents to waterways. There is a need to develop an alternative dyeing system that does not produce any hazardous effluent. The waterless dyeing method could be a viable eco-friendly alternative to the traditional aqueous dyeing method. In this work, cacao husk extracts were used as a natural dye in the decamethylcyclopentasiloxane (D5) medium for the dyeing of cotton fabric, and subsequently, the dyed cotton was treated by a fixation treatment with a cationic dye-fixing agent in the D5 medium. The cotton fabric dyed with cacao husk extracts exhaustion in the waterless D5 medium exhibited better exhaustion, fixation rate, color strength (K/S), and colorfastness to washing and rubbing compared to the fabric dyed with the same extracts using the conventional aqueous dyeing and dye-fixing methods. The dye exhaustion percentage and the dye fixation rate were 95.6% and 94.8% in the D5 medium respectively, which is significantly higher in comparison to a 48.2% dye exhaustion percentage and a 35.3% dye fixation rate in the conventional water medium. An orthogonal array design (L9) was adopted to optimize the dyeing conditions with respect to exhaustion percentage. The results indicated that the dyebath temperature was the most important factor for achieving the optimal dye exhaustion, and dyeing time also showed considerable effects. Linear regression was used to predict the exhaustion percentage, and the resulting p value of 0.000 demonstrated that a strong coefficient was proven among all selected factors. This study has demonstrated that dyeing of cotton fabric with cacao husk extracts in the D5 dyeing system can be a viable method for the textile industry with minimal environmental pollution

Inflammatory signaling regulates embryonic hematopoietic stem and progenitor cell production

Identifying signaling pathways that regulate hematopoietic stem and progenitor cell (HSPC) formation in the embryo will guide efforts to produce and expand HSPCs ex vivo. Here we show that sterile tonic inflammatory signaling regulates embryonic HSPC formation. Expression profiling of progenitors with lymphoid potential and hematopoietic stem cells (HSCs) from aorta/gonad/mesonephros (AGM) regions of midgestation mouse embryos revealed a robust innate immune/inflammatory signature. Mouse embryos lacking interferon γ (IFN-γ) or IFN-α signaling and zebrafish morphants lacking IFN-γ and IFN-ϕ activity had significantly fewer AGM HSPCs. Conversely, knockdown of IFN regulatory factor 2 (IRF2), a negative regulator of IFN signaling, increased expression of IFN target genes and HSPC production in zebrafish. Chromatin immunoprecipitation (ChIP) combined with sequencing (ChIP-seq) and expression analyses demonstrated that IRF2-occupied genes identified in human fetal liver CD34(+) HSPCs are actively transcribed in human and mouse HSPCs. Furthermore, we demonstrate that the primitive myeloid population contributes to the local inflammatory response to impact the scale of HSPC production in the AGM region. Thus, sterile inflammatory signaling is an evolutionarily conserved pathway regulating the production of HSPCs during embryonic development

CHD7 and Runx1 interaction provides a braking mechanism for hematopoietic differentiation.

Hematopoietic stem and progenitor cell (HSPC) formation and lineage differentiation involve gene expression programs orchestrated by transcription factors and epigenetic regulators. Genetic disruption of the chromatin remodeler chromodomain-helicase-DNA-binding protein 7 (CHD7) expanded phenotypic HSPCs, erythroid, and myeloid lineages in zebrafish and mouse embryos. CHD7 acts to suppress hematopoietic differentiation. Binding motifs for RUNX and other hematopoietic transcription factors are enriched at sites occupied by CHD7, and decreased RUNX1 occupancy correlated with loss of CHD7 localization. CHD7 physically interacts with RUNX1 and suppresses RUNX1-induced expansion of HSPCs during development through modulation of RUNX1 activity. Consequently, the RUNX1:CHD7 axis provides proper timing and function of HSPCs as they emerge during hematopoietic development or mature in adults, representing a distinct and evolutionarily conserved control mechanism to ensure accurate hematopoietic lineage differentiation.Bloodwise, CRUK, MRC, Wellcome Trust, NIH, Leukemia and Lymphoma Societ

Runx1 Loss Minimally Impacts Long-Term Hematopoietic Stem Cells

RUNX1 encodes a DNA binding subunit of the core-binding transcription factors and is frequently mutated in acute leukemia, therapy-related leukemia, myelodysplastic syndrome, and chronic myelomonocytic leukemia. Mutations in RUNX1 are thought to confer upon hematopoietic stem cells (HSCs) a pre-leukemic state, but the fundamental properties of Runx1 deficient pre-leukemic HSCs are not well defined. Here we show that Runx1 deficiency decreases both apoptosis and proliferation, but only minimally impacts the frequency of long term repopulating HSCs (LT-HSCs). It has been variously reported that Runx1 loss increases LT-HSC numbers, decreases LT-HSC numbers, or causes age-related HSC exhaustion. We attempt to resolve these discrepancies by showing that Runx1 deficiency alters the expression of several key HSC markers, and that the number of functional LT-HSCs varies depending on the criteria used to score them. Finally, we identify genes and pathways, including the cell cycle and p53 pathways that are dysregulated in Runx1 deficient HSCs