Women at work in Mali: the case of the Markala Cooperative

African Studies Center Working Paper No. 5

The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that any irreducible $T$-module $W$ is both thin and dual thin in the sense of Terwilliger. We produce two bases for $W$ and describe the action of $T$ on these bases. We prove that the isomorphism class of $W$ as a $T$-module is determined by two parameters, the dual endpoint and diameter of $W$. We find a recurrence which gives the multiplicities with which the irreducible $T$-modules occur in the standard module. We compute this multiplicity for those irreducible $T$-modules which have diameter at least $D-3$.Comment: 22 page

Notch3 Signaling Promotes Adhesion and Tumor Progression in a Murine Epithelial Ovarian Cancer Model

Ovarian cancer is the 5th leading cause of cancer death in women in the United States and is the most fatal gynecological malignancy. High grade serous ovarian cancer (HGSC) is the most common and deadly type of ovarian cancer largely due to the rapid metastasis throughout the peritoneum (abdominal cavity wall and organ lining). Metastatic spread of ovarian cancer usually occurs before diagnosis and can lead to bowel obstruction, organ failure, ascites, cachexia, infection and sepsis, and pulmonary embolism all causing death. Current methods to detect early stage ovarian cancer do not increase overall survival. A better understanding of the metastatic ability of ovarian cancers and the mechanism of cancer cell dissemination are critical to the development of new treatments for this devastating disease. In particular, investigation of pathways that affect early metastasis may indicate treatments that will lower disease burden and may suggest biomarkers of recurrent and/or chemotherapy resistant disease. Notch3 expression correlates with worse prognosis, chemotherapy resistance, and increased tumorigenic cell behaviors in HGSC. Here, we demonstrate that Notch3 acts to promote early stages of metastasis in a model of HGSC using the murine ID8 IP2 ovarian surface epithelial cell line. ID8 IP2 cells have little to no endogenous Notch3 expression and model metastatic disease when introduced intraperitoneally. We investigated the role of Notch3 by ectopically expressing the intracellular domain of murine Notch3 to induce constitutive Notch3 signaling in ID8 IP2 cells and verified Notch signal activation by target gene assessment. Induction of Notch3 signaling in ID8 IP2 reduced survival and accelerated disease burden, as measured by ascites accumulation, after intraperitoneal introduction of cells into nude mice. We interrogated downstream targets in Notch3 activated cells by RNA-Seq and found that Notch3 induced a significant enrichment of adhesion and extracellular matrix pathways. Notch3 active cells showed increased ITGA1 expression and increased adhesion on collagens I and IV in vitro, suggesting that increased adhesion to collagen-rich peritoneal surfaces drives the observed increase in tumor burden. Notch3 active cells showed reduced migration on surfaces coated with multiple types of extracellular matrix and no detectable increase in invasion through extracellular matrix, indicating that Notch3 effects may be specific to the initial adhesion of tumor cells and not the later stages of metastasis. These results demonstrate that Notch3 upregulates the expression of specific adhesion genes in ovarian cancer cells and this promotes increased attachment to the collagen-rich extracellular matrix. The implications of this study are that oncogenic Notch signal activation, as documented in human disease, may promote dissemination and metastasis of primary and/or recurrent HGSC by increasing attachment to the peritoneal lining

Higher Dimensional Lattice Chains and Delannoy Numbers

Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new proof of a recent result of Duichi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.Comment: 15 page

Proof of the Kresch-Tamvakis Conjecture

In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following. Theorem: For any positive integer $D$ and any integers $i,j$ $(0\leq i,j \leq D)$, the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left[ \begin{array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem

The Multiplicities of a Dual-thin Q-polynomial Association Scheme

Let Y=(X,{Ri}1≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E0,...,ED of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0≤i≤D) of Yis unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi≤mi+1 and mi≤mD−i for i\u3cD/2. We prove that if Y is dual-thin in the sense of Terwilliger, then the Stanton conjecture is true

Electron Bernstein waves emission in the TJ-II Stellarator

Taking advantage of the electron Bernstein waves heating (EBWH) system of the TJ-II stellarator, an electron Bernstein emission (EBE) diagnostic was installed. Its purpose is to investigate the B-X-O radiation properties in the zone where optimum theoretical EBW coupling is predicted. An internal movable mirror shared by both systems allows us to collect the EBE radiation along the same line of sight that is used for EBW heating. The theoretical EBE has been calculated for different orientations of the internal mirror using the TRUBA code as ray tracer. A comparison with experimental data obtained in NBI discharges is carried out. The results provide a valuable information regarding the experimental O-X mode conversion window expected in the EBW heating experiments. Furthermore, the characterization of the radiation polarization shows evidence of the underlying B-X-O conversion process.Comment: 21 pages, 14 figure

Kernels of Directed Graph Laplacians

Let G denote a directed graph with adjacency matrix Q and in- degree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of G. This fact has a meaningful generalization to directed graphs, as was observed by Chebotarev and Agaev in 2005. Since this result has many important applications in the sciences, we offer an independent and self-contained proof of their theorem, showing in this paper that the algebraic and geometric multiplicities of 0 are equal, and that a graph-theoretic property determines the dimension of this eigenspace--namely, the number of reaches of the directed graph. We also extend their results by deriving a natural basis for the corresponding eigenspace. The results are proved in the general context of stochastic matrices, and apply equally well to directed graphs with non-negative edge weights