Combinatorial Hopf algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.Comment: 7 page

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Analysis of single nucleotide polymorphisms in the FAS and CTLA-4 genes of peripheral T-cell lymphomas

Angioimmunoblastic T-cell lymphoma (AILT) represents a subset of T-cell lymphomas but resembles an autoimmune disease in many of its clinical aspects. Despite the phenotype of effector T-cells and high expression of FAS and CTLA-4 receptor molecules, tumor cells fail to undergo apoptosis. We investigated single nucleotide polymorphisms (SNPs) of the FAS and CTLA-4 genes in 94 peripheral T-cell lymphomas. Although allelic frequencies of some FAS SNPs were enriched in AILT cases, none of these occurred at a different frequency compared to healthy individuals. Therefore, SNPs in these genes are not associated with the apoptotic defect and autoimmune phenomena in AILT

Linear extension sums as valuations on cones

33 pagesInternational audienceThe geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset

Case report: a unique pediatric case of a primary CD8 expressing ALK-1 positive anaplastic large cell lymphoma of skeletal muscle

Primary involvement of skeletal muscle is a very rare event in ALK-1 positive anaplastic large cell lymphoma (ALCL). We describe a case of a 10-year old boy presenting with a three week history of pain and a palpable firm swelling at the dorsal aspect of the left thigh. Histological examination of the lesion revealed a tumoral and diffuse polymorphic infiltration of the muscle by large lymphoid cells. Tumor cells displayed eccentric, lobulated "horse shoe" or "kidney-shape" nuclei. The cells showed immunohistochemical positivity for CD30, ALK-1, CD2, CD3, CD7, CD8, and Perforin. Fluorescence in situ hybridization analysis revealed a characteristic rearrangement of the ALK-1 gene in 2p23 leading to the diagnosis of ALK-1 positive ALCL. Chemotherapy according to the ALCL-99-NHL-BFM protocol was initiated and resulted in a complete remission after two cycles. This case illustrates the unusual presentation of a pediatric ALCL in soft tissue with a good response to chemotherapy

Gene expression analysis after receptor tyrosine kinase activation reveals new potential melanoma proteins

<p>Abstract</p> <p>Background</p> <p>Melanoma is an aggressive tumor with increasing incidence. To develop accurate prognostic markers and targeted therapies, changes leading to malignant transformation of melanocytes need to be understood. In the <it>Xiphophorus </it>melanoma model system, a mutated version of the EGF receptor Xmrk (<it>Xiphophorus </it>melanoma receptor kinase) triggers melanomagenesis. Cellular events downstream of Xmrk, such as the activation of Akt, Ras, B-Raf or Stat5, were also shown to play a role in human melanomagenesis. This makes the elucidation of Xmrk downstream targets a useful method for identifying processes involved in melanoma formation.</p> <p>Methods</p> <p>Here, we analyzed Xmrk-induced gene expression using a microarray approach. Several highly expressed genes were confirmed by realtime PCR, and pathways responsible for their induction were revealed using small molecule inhibitors. The expression of these genes was also monitored in human melanoma cell lines, and the target gene <it>FOSL1 </it>was knocked down by siRNA. Proliferation and migration of siRNA-treated melanoma cell lines were then investigated.</p> <p>Results</p> <p>Genes with the strongest upregulation after receptor activation were FOS-like antigen 1 (<it>Fosl1</it>), early growth response 1 (<it>Egr1</it>), osteopontin (<it>Opn</it>), insulin-like growth factor binding protein 3 (<it>Igfbp3</it>), dual-specificity phosphatase 4 (<it>Dusp4</it>), and tumor-associated antigen L6 (<it>Taal6</it>). Interestingly, most genes were blocked in presence of a SRC kinase inhibitor. Importantly, we found that <it>FOSL1</it>, <it>OPN</it>, <it>IGFBP3</it>, <it>DUSP4</it>, and <it>TAAL6 </it>also exhibited increased expression levels in human melanoma cell lines compared to human melanocytes. Knockdown of <it>FOSL1 </it>in human melanoma cell lines reduced their proliferation and migration.</p> <p>Conclusion</p> <p>Altogether, the data show that the receptor tyrosine kinase Xmrk is a useful tool in the identification of target genes that are commonly expressed in Xmrk-transgenic melanocytes and melanoma cell lines. The identified molecules constitute new possible molecular players in melanoma development. Specifically, a role of FOSL1 in melanomagenic processes is demonstrated. These data are the basis for future detailed analyses of the investigated target genes.</p

A Typology of Digital Sharing Business Models: A Design Science Research Approach

The digitally enabled sharing economy, also called the “digital sharing economy” (DSE), has changed patterns of consumption by introducing new choices and channels for provision and receipt of services. The DSE encompasses sharing systems whose business models may vary distinctly from platform to platform. Although business models in the context of the sharing economy have been studied so far, we have observed that the current literature does not provide an approach that covers all the possible business models (in the broadest sense of the term) that (potentially) exist within the scope of the DSE. The present paper, therefore, aims to propose a typology of business models in the DSE that covers a wide space of models – even those which may not involve “business” in the commercial sense. This is achieved through an iterative inductive process based on a design science research approach. The typology can assist in positioning the current and future sharing systems in the DSE by systematically classifying their business models. It is intended to serve as a guiding tool for the sustainability assessment of platforms from both resource and socio-economic perspectives. The present study can also enable researchers and practitioners to capture and systematically analyse digital sharing business models based on a structured, actionable approach

Conserved Molecular Underpinnings and Characterization of a Role for Caveolin-1 in the Tumor Microenvironment of Mature T-Cell Lymphomas

Neoplasms of extra-thymic T-cell origin represent a rare and difficult population characterized by poor clinical outcome, aggressive presentation, and poorly defined molecular characteristics. Much work has been done to gain greater insights into distinguishing features among malignant subtypes, but there also exists a need to identify unifying characteristics to assist in rapid diagnosis and subsequent potential treatment. Herein, we investigated gene expression data of five different mature T-cell lymphoma subtypes (n = 187) and found 21 genes to be up- and down-regulated across all malignancies in comparison to healthy CD4+ and CD8+ T-cell controls (n = 52). From these results, we sought to characterize a role for caveolin-1 (CAV1), a gene with previous description in the progression of both solid and hematological tumors. Caveolin-1 was upregulated, albeit with a heterogeneous nature, across all mature T-cell lymphoma subtypes, a finding confirmed using immunohistochemical staining on an independent sampling of mature T-cell lymphoma biopsies (n = 65 cases). Further, stratifying malignant samples in accordance with high and low CAV1 expression revealed that higher expression of CAV1 in mature T-cell lymphomas is analogous with an enhanced inflammatory and invasive gene expression profile. Taken together, these results demonstrate a role for CAV1 in the tumor microenvironment of mature T-cell malignancies and point toward potential prognostic implications

Comparative analyses imply that the enigmatic sigma factor 54 is a central controller of the bacterial exterior

Contains fulltext : 95738.pdf (publisher's version ) (Open Access)BACKGROUND: Sigma-54 is a central regulator in many pathogenic bacteria and has been linked to a multitude of cellular processes like nitrogen assimilation and important functional traits such as motility, virulence, and biofilm formation. Until now it has remained obscure whether these phenomena and the control by Sigma-54 share an underlying theme. RESULTS: We have uncovered the commonality by performing a range of comparative genome analyses. A) The presence of Sigma-54 and its associated activators was determined for all sequenced prokaryotes. We observed a phylum-dependent distribution that is suggestive of an evolutionary relationship between Sigma-54 and lipopolysaccharide and flagellar biosynthesis. B) All Sigma-54 activators were identified and annotated. The relation with phosphotransfer-mediated signaling (TCS and PTS) and the transport and assimilation of carboxylates and nitrogen containing metabolites was substantiated. C) The function annotations, that were represented within the genomic context of all genes encoding Sigma-54, its activators and its promoters, were analyzed for intra-phylum representation and inter-phylum conservation. Promoters were localized using a straightforward scoring strategy that was formulated to identify similar motifs. We found clear highly-represented and conserved genetic associations with genes that concern the transport and biosynthesis of the metabolic intermediates of exopolysaccharides, flagella, lipids, lipopolysaccharides, lipoproteins and peptidoglycan. CONCLUSION: Our analyses directly implicate Sigma-54 as a central player in the control over the processes that involve the physical interaction of an organism with its environment like in the colonization of a host (virulence) or the formation of biofilm