Enumerative Combinatorics of Intervals in the Dyck Pattern Poset

We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank. We also provide the first results on the Möbius function of the Dyck pattern poset, giving for instance a closed expression for the Möbius function of initial intervals whose maximum is a Dyck path having exactly two peaks

Evaluating a model of global psychophysical judgments for brightness: II. Behavioral properties linking summations and productions

Steingrimsson (Attention, Perception, & Psychophysics, 71, 1916–1930, 2009) outlined Luce’s (Psychological Review, 109, 520–532 2002, 111, 446–454 2004) proposed psychophysical theory and tested, for brightness, behavioral properties that, separately, gave rise to two psychophysical functions, Ψ⊕ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Psi_{{ \circ_p}}}$$\end{document}. The function Ψ⊕ maps pairs of physical intensities onto positive real numbers and represents subjective summation, and the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Psi_{{ \circ_p}}}$$\end{document} represents a form of ratio production. This article, the second in a series expected to consist of three articles, tests the properties linking summation and production such that it forces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Psi_{{ \circ_p}}} = {\Psi_\oplus } = \Psi$$\end{document}. The properties tested are a form of distributivity and, in three experiments, were subjected to an empirical evaluation. Considerable support is provided for the existence of a single function Ψ for both summation and ratio production. The scope of this series of articles is to establish the theory as a descriptive model of binocular brightness perception

Tiered trees, weights, and q-Eulerian numbers

Maxmin trees are labeled trees with the property that each vertex is either a local maximum or a local minimum. Such trees were originally introduced by Postnikov [12], who gave a formula to count them and different combinatorial interpretations for their number. In this paper we generalize this construction and define tiered trees by allowing more than two classes of vertices. Tiered trees arise naturally when counting the absolutely indecomposable representations of certain quivers, and also when one enumerates torus orbits on certain homogeneous varieties. We define a notion of weight for tiered trees and prove bijections between various weight 0 tiered trees and other combinatorial objects; in particular order n weight 0 maxmin trees are naturally in bijection with permutations on n−1 letters. We conclude by using our weight function to define a new q-analogue of the Eulerian numbers

Subcellular localization of Mitf in monocytic cells

Microphthalmia-associated transcription factor (Mitf) is a transcription factor that plays an important role in regulating the development of several cell lineages. The subcellular localization of Mitf is dynamic and is associated with its transcription activity. In this study, we examined factors that affect its subcellular localization in cells derived from the monocytic lineage since Mitf is present abundantly in these cells. We identified a domain encoded by Mitf exon 1B1b to be important for Mitf to commute between the cytoplasm and the nucleus. Deletion of this domain disrupts the shuttling of Mitf to the cytoplasm and results in its retention in the nucleus. M-CSF and RANKL both induce nuclear translocation of Mitf. We showed that Mitf nuclear transport is greatly influenced by ratio of M-CSF/Mitf protein expression. In addition, cell attachment to a solid surface also is needed for the nuclear transport of Mitf

Changes in the Expression of Myosins During Postnatal Development of Masseter Muscle in the Microphthalmic Mouse

In the present study, to elucidate the influences of the deficiency of teeth on the masseter muscle, we analyzed changes in the expression of MyHC isoform mRNAs during postnatal development in mi/mi mice using real-time PCR. By 8 weeks of age, MyHC I had nearly disappeared in the +/+ mice, while it was still present in the mi/mi, and the level of MyHC I mRNA in the mi/mi was 5.1-fold higher than that in the +/+ (p<0.01). The levels of MyHC IIx mRNAs in the mi/mi mice were 41 ~ 55% lower than those in the +/+ at both 3 weeks and 4 weeks of age (p<0.05). No significant difference in the expression of MyHC IIa and IIb mRNAs in the masseter muscle was found between the mi/mi and +/+. From these results, we speculate that the deficiency of teeth affects the masseter muscles during the postnatal development

MAD3 AND MAD4 - NOVEL MAX-INTERACTING TRANSCRIPTIONAL REPRESSORS THAT SUPPRESS C-MYC DEPENDENT TRANSFORMATION AND ARE EXPRESSED DURING NEURAL AND EPIDERMAL DIFFERENTIATION

The basic helix-loop-helix-leucine zipper (bHLHZip) protein Max associates with members of the Myc family, as well as with the related proteins Mad (Mad1) and Mxi1, Whereas both Myc:Max and Mad:Max heterodimers bind related E-box sequences, Myc:Max activates transcription and promotes proliferation while Mad:Max represses transcription and suppresses Myc dependent transformation, Here we report the identification and characterization of two novel Mad1-and Mxi1-related proteins, Mad3 and Mad4. Mad3 and Mad4 interact with both Max and mSin3 and repress transcription from a promoter containing CACGTG binding sites, Using a rat embryo fibroblast transformation assay, we show that both Mad3 and Mad4 inhibit c-Myc dependent cell transformation, An examination of the expression patterns of all mad genes during murine embryogenesis reveals that mad1, mad3 and mad4 are expressed primarily in growth-arrested differentiating cells. mxi1 is also expressed in differentiating cells, but is co-expressed with either c-myc, N-myc, or both in proliferating cells of the developing central nervous system and the epidermis, In the developing central nervous system and epidermis, downregulation of myc genes occurs concomitant with upregulation of mad family genes, These expression patterns, together with the demonstrated ability of Mad family proteins to interfere with the proliferation promoting activities of Myc, suggest that the regulated expression of Myc and Mad family proteins function in a concerted fashion to regulate cell growth in differentiating tissues