The Hedgehog signaling pathway regulates embryo patterning and progenitor cell homeostasis in adult tissues, including epidermal appendages. A role for the Hh pathway in mammary biology and breast ...cancer has also been suggested. The aim of this study was to analyze Hh signaling in the mouse mammary gland through the generation of transgenic mice that express Sonic Hedgehog (Shh) under the control of the mammary-specific WAP promoter (WAP-Shh mice). To identify mammary cells capable of activating the Hh pathway we bred WAP-Shh mice to Ptch1-lacZ knock-in mice, in which the expression of a nuclear-targeted β-galactosidase reporter protein (β-gal) is driven by the endogenous Patched 1 gene regulatory region. After two cycles of induction of transgenic Shh expression, we detected areas of X-gal reactivity. Immunohistochemical analysis showed nuclear β-gal staining in clusters of mammary cells in WAP-Shh/Ptch1-lacZ bitransgenic mice. These were epithelial cells present in a basal location of displastic ducts and alveoli, adjacent to Shh-expressing luminal cells, and overexpressed epithelial basal markers keratin 5, 14 and 17 and transcription factor p63. Absence of smooth muscle actin expression and a cuboidal morphology differentiated Hh-responding cells from flat-shaped mature myoepithelial cells. Groups of cells expressing stem cell markers integrin β3 and keratins 6 and 15 were also detected within Hh-responding areas. In addition, we found that Hh-responding cells in the mammary glands of WAP-Shh/Ptch1-lacZ mice were ciliated and exhibited a low proliferation rate. Our data show the paracrine nature of hedgehog signaling in the epithelial compartment of the mouse mammary gland, where a subset of basal cells that express mammary progenitor cell markers and exhibit primary cilia is expanded in response to secretory epithelium-derived Shh.
► Mammary secretory epithelium-derived Shh activates the Hh pathway in a paracrine intraepithelial fashion. ► Hedgehog signaling induces the expansion of Hh-responsive cells in the basal epithelium. ► Hedgehog-responsive cells are ciliated, cubical and express progenitor cell markers.
A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. The best known of these allocations is the Shapley value. A communication structure ...defines the feasible bilateral communication relationships among the agents in a cooperative situation. Some solutions incorporating this information have been defined from the Shapley value: the Myerson value, the position value, etc. Later fuzzy communication structures were introduced. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Several ways of defining the Myerson value for games on fuzzy communication structure were proposed, one of them is the Choquet by graphs (cg) version. Now we study in this work the cg-position value and its calculation. The cg-position value is defined as a solution for games with fuzzy communication structure which considers the bilateral communications as players. So, the Shapley value is applied for a new game (the link game) over the fuzzy sets of links in the fuzzy communication structure and the profit obtained for each link is allocated between both players in the link. As we see in our examples and results the cg-position value is more concerned with the graphical position of the players and their communications than the other cg-values. In this paper we also introduce a procedure to compute exactly the position value, avoiding to calculate the characteristic function of the link game for all coalitions. This procedure is used to determine the cg-position value. Finally we compare the new value with other cg-values in an applied example about the power of the groups in the European Parliament.
The Banzhaf index is a function determining the power or influence in the decision of a set of agents. The extension of this index to the family of the cooperative games is named Banzhaf value. The ...relationships of closeness among the agents should modify their power. Games with a priori unions study situations where the closeness relations among the agents are taken into account. In this model the agents are organized in an a priori partition where each element of the partition represents a group of agents with close interests or ideas. The power is determined in two steps, first as a problem among the unions and later, inside each one, the power of each agent is determined. Proximity relations extend this model considering leveled closeness among the agents. In this paper we analyze a version of the Banzhaf value for games with a proximity relation and we show the interest of this value by applying it to the allocation of the power of the political groups in the European Parliament.
•We use proximity relations to level the closeness of interests among the agents in a game.•We define a Banzhaf value to measure the power of the agents in a game with a proximity relation.•We propose an axiomatization of the new value.•We apply the new value as a index to determine the power of the groups in the European Parliament.
In 2013, Jiménez-Losada et al. introduced several extensions of the Myerson value for games with fuzzy communication structure. In a fuzzy communication structure the membership of the players and ...the relations among them are leveled. Now we study a Banzhaf value for these situations. The Myerson model is followed to define the fuzzy graph Banzhaf value taking as base point the Choquet integral. We propose an axiomatization for this value introducing leveled amalgamation of players. An algorithm to calculate this value is provided and its complexity is studied. Finally we show an applied example computing by this fuzzy value the power of the groups in the European Parliament.
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