The Orphan Nuclear Receptor COUP-TFII Is Required for Angiogenesis and Heart Development
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Coronary Arterial Development Is Regulated by a Dll4-Jag1-Ephrinb2 Signaling Cascade
RESEARCH ARTICLE Coronary arterial development is regulated by a Dll4-Jag1-EphrinB2 signaling cascade Stanislao Igor Travisano1,2, Vera Lucia Oliveira1,2, Bele´ n Prados1,2, Joaquim Grego-Bessa1,2, Rebeca Pin˜ eiro-Sabarı´s1,2, Vanesa Bou1,2, Manuel J Go´ mez3, Fa´ tima Sa´ nchez-Cabo3, Donal MacGrogan1,2*, Jose´ Luis de la Pompa1,2* 1Intercellular Signalling in Cardiovascular Development and Disease Laboratory, Centro Nacional de Investigaciones Cardiovasculares Carlos III (CNIC), Madrid, Spain; 2CIBER de Enfermedades Cardiovasculares, Madrid, Spain; 3Bioinformatics Unit, Centro Nacional de Investigaciones Cardiovasculares, Madrid, Spain Abstract Coronaries are essential for myocardial growth and heart function. Notch is crucial for mouse embryonic angiogenesis, but its role in coronary development remains uncertain. We show Jag1, Dll4 and activated Notch1 receptor expression in sinus venosus (SV) endocardium. Endocardial Jag1 removal blocks SV capillary sprouting, while Dll4 inactivation stimulates excessive capillary growth, suggesting that ligand antagonism regulates coronary primary plexus formation. Later endothelial ligand removal, or forced expression of Dll4 or the glycosyltransferase Mfng, blocks coronary plexus remodeling, arterial differentiation, and perivascular cell maturation. Endocardial deletion of Efnb2 phenocopies the coronary arterial defects of Notch mutants. Angiogenic rescue experiments in ventricular explants, or in primary human endothelial cells, indicate that EphrinB2 is a critical effector of antagonistic Dll4 and Jag1 functions in arterial morphogenesis. Thus, coronary arterial precursors are specified in the SV prior to primary coronary plexus formation and subsequent arterial differentiation depends on a Dll4-Jag1-EphrinB2 signaling *For correspondence: [email protected] (DMG); cascade. [email protected] (JLP) Competing interests: The authors declare that no Introduction competing interests exist. -
The Geometry of Nim Arxiv:1109.6712V1 [Math.CO] 30
The Geometry of Nim Kevin Gibbons Abstract We relate the Sierpinski triangle and the game of Nim. We begin by defining both a new high-dimensional analog of the Sierpinski triangle and a natural geometric interpretation of the losing positions in Nim, and then, in a new result, show that these are equivalent in each finite dimension. 0 Introduction The Sierpinski triangle (fig. 1) is one of the most recognizable figures in mathematics, and with good reason. It appears in everything from Pascal's Triangle to Conway's Game of Life. In fact, it has already been seen to be connected with the game of Nim, albeit in a very different manner than the one presented here [3]. A number of analogs have been discovered, such as the Menger sponge (fig. 2) and a three-dimensional version called a tetrix. We present, in the first section, a generalization in higher dimensions differing from the more typical simplex generalization. Rather, we define a discrete Sierpinski demihypercube, which in three dimensions coincides with the simplex generalization. In the second section, we briefly review Nim and the theory behind optimal play. As in all impartial games (games in which the possible moves depend only on the state of the game, and not on which of the two players is moving), all possible positions can be divided into two classes - those in which the next player to move can force a win, called N-positions, and those in which regardless of what the next player does the other player can force a win, called P -positions. -
Notes Has Not Been Formally Reviewed by the Lecturer
6.896 Topics in Algorithmic Game Theory February 22, 2010 Lecture 6 Lecturer: Constantinos Daskalakis Scribe: Jason Biddle, Debmalya Panigrahi NOTE: The content of these notes has not been formally reviewed by the lecturer. It is recommended that they are read critically. In our last lecture, we proved Nash's Theorem using Broweur's Fixed Point Theorem. We also showed Brouwer's Theorem via Sperner's Lemma in 2-d using a limiting argument to go from the discrete combinatorial problem to the topological one. In this lecture, we present a multidimensional generalization of the proof from last time. Our proof differs from those typically found in the literature. In particular, we will insist that each step of the proof be constructive. Using constructive arguments, we shall be able to pin down the complexity-theoretic nature of the proof and make the steps algorithmic in subsequent lectures. In the first part of our lecture, we present a framework for the multidimensional generalization of Sperner's Lemma. A Canonical Triangulation of the Hypercube • A Legal Coloring Rule • In the second part, we formally state Sperner's Lemma in n dimensions and prove it using the following constructive steps: Colored Envelope Construction • Definition of the Walk • Identification of the Starting Simplex • Direction of the Walk • 1 Framework Recall that in the 2-dimensional case we had a square which was divided into triangles. We had also defined a legal coloring scheme for the triangle vertices lying on the boundary of the square. Now let us extend those concepts to higher dimensions. 1.1 Canonical Triangulation of the Hypercube We begin by introducing the n-simplex as the n-dimensional analog of the triangle in 2 dimensions as shown in Figure 1. -
Interval Vector Polytopes
Interval Vector Polytopes By Gabriel Dorfsman-Hopkins SENIOR HONORS THESIS ROSA C. ORELLANA, ADVISOR DEPARTMENT OF MATHEMATICS DARTMOUTH COLLEGE JUNE, 2013 Contents Abstract iv 1 Introduction 1 2 Preliminaries 4 2.1 Convex Polytopes . 4 2.2 Lattice Polytopes . 8 2.2.1 Ehrhart Theory . 10 2.3 Faces, Face Lattices and the Dual . 12 2.3.1 Faces of a Polytope . 12 2.3.2 The Face Lattice of a Polytope . 15 2.3.3 Duality . 18 2.4 Basic Graph Theory . 22 3IntervalVectorPolytopes 23 3.1 The Complete Interval Vector Polytope . 25 3.2 TheFixedIntervalVectorPolytope . 30 3.2.1 FlowDimensionGraphs . 31 4TheIntervalPyramid 38 ii 4.1 f-vector of the Interval Pyramid . 40 4.2 Volume of the Interval Pyramid . 45 4.3 Duality of the Interval Pyramid . 50 5 Open Questions 57 5.1 Generalized Interval Pyramid . 58 Bibliography 60 iii Abstract An interval vector is a 0, 1 -vector where all the ones appear consecutively. An { } interval vector polytope is the convex hull of a set of interval vectors in Rn.Westudy several classes of interval vector polytopes which exhibit interesting combinatorial- geometric properties. In particular, we study a class whose volumes are equal to the catalan numbers, another class whose legs always form a lattice basis for their affine space, and a third whose face numbers are given by the pascal 3-triangle. iv Chapter 1 Introduction An interval vector is a 0, 1 -vector in Rn such that the ones (if any) occur consecu- { } tively. These vectors can nicely and discretely model scheduling problems where they represent the length of an uninterrupted activity, and so understanding the combi- natorics of these vectors is useful in optimizing scheduling problems of continuous activities of certain lengths. -
The Evolving Cardiac Lymphatic Vasculature in Development, Repair and Regeneration
REVIEWS The evolving cardiac lymphatic vasculature in development, repair and regeneration Konstantinos Klaourakis 1,2, Joaquim M. Vieira 1,2,3 ✉ and Paul R. Riley 1,2,3 ✉ Abstract | The lymphatic vasculature has an essential role in maintaining normal fluid balance in tissues and modulating the inflammatory response to injury or pathogens. Disruption of normal development or function of lymphatic vessels can have severe consequences. In the heart, reduced lymphatic function can lead to myocardial oedema and persistent inflammation. Macrophages, which are phagocytic cells of the innate immune system, contribute to cardiac development and to fibrotic repair and regeneration of cardiac tissue after myocardial infarction. In this Review, we discuss the cardiac lymphatic vasculature with a focus on developments over the past 5 years arising from the study of mammalian and zebrafish model organisms. In addition, we examine the interplay between the cardiac lymphatics and macrophages during fibrotic repair and regeneration after myocardial infarction. Finally, we discuss the therapeutic potential of targeting the cardiac lymphatic network to regulate immune cell content and alleviate inflammation in patients with ischaemic heart disease. The circulatory system of vertebrates is composed of two after MI. In this Review, we summarize the current complementary vasculatures, the blood and lymphatic knowledge on the development, structure and function vascular systems1. The blood vasculature is a closed sys- of the cardiac lymphatic vasculature, with an emphasis tem responsible for transporting gases, fluids, nutrients, on breakthroughs over the past 5 years in the study of metabolites and cells to the tissues2. This extravasation of cardiac lymphatic heterogeneity in mice and zebrafish. -
Cardiogenesis with a Focus on Vasculogenesis and Angiogenesis
Received: 27 August 2019 | Revised: 4 February 2020 | Accepted: 20 February 2020 DOI: 10.1111/ahe.12549 SPECIAL ISSUE Cardiogenesis with a focus on vasculogenesis and angiogenesis Katrin Borasch1 | Kenneth Richardson2 | Johanna Plendl1 1Department of Veterinary Medicine, Institute of Veterinary Anatomy, Freie Abstract University Berlin, Berlin, Germany The initial intraembryonic vasculogenesis occurs in the cardiogenic mesoderm. Here, 2 College of Veterinary Medicine, School a cell population of proendocardial cells detaches from the mesoderm that subse- of Veterinary and Life Sciences, Murdoch University, Murdoch, WA, Australia quently generates the single endocardial tube by forming vascular plexuses. In the course of embryogenesis, the endocardium retains vasculogenic, angiogenic and Correspondence Johanna Plendl, Department of Veterinary haematopoietic potential. The coronary blood vessels that sustain the rapidly ex- Medicine, Institute of Veterinary Anatomy, panding myocardium develop in the course of the formation of the cardiac loop by Freie University Berlin, Berlin, Germany. Email: [email protected] vasculogenesis and angiogenesis from progenitor cells of the proepicardial serosa at the venous pole of the heart as well as from the endocardium and endothelial cells of Funding information Freie Universität Berlin the sinus venosus. Prospective coronary endothelial cells and progenitor cells of the coronary blood vessel walls (smooth muscle cells, perivascular cells) originate from different cell populations that are in close spatial as well as regulatory connection with each other. Vasculo- and angiogenesis of the coronary blood vessels are for a large part regulated by the epicardium and epicardium-derived cells. Vasculogenic and angiogenic signalling pathways include the vascular endothelial growth factors, the angiopoietins and the fibroblast growth factors and their receptors. -
Sequential Evolutionary Operations of Trigonometric Simplex Designs For
SEQUENTIAL EVOLUTIONARY OPERATIONS OF TRIGONOMETRIC SIMPLEX DESIGNS FOR HIGH-DIMENSIONAL UNCONSTRAINED OPTIMIZATION APPLICATIONS Hassan Musafer Under the Supervision of Dr. Ausif Mahmood DISSERTATION SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOHPY IN COMPUTER SCIENCE AND ENGINEERING THE SCHOOL OF ENGINEERING UNIVERSITY OF BRIDGEPORT CONNECTICUT May, 2020 SEQUENTIAL EVOLUTIONARY OPERATIONS OF TRIGONOMETRIC SIMPLEX DESIGNS FOR HIGH-DIMENSIONAL UNCONSTRAINED OPTIMIZATION APPLICATIONS c Copyright by Hassan Musafer 2020 iii SEQUENTIAL EVOLUTIONARY OPERATIONS OF TRIGONOMETRIC SIMPLEX DESIGNS FOR HIGH-DIMENSIONAL UNCONSTRAINED OPTIMIZATION APPLICATIONS ABSTRACT This dissertation proposes a novel mathematical model for the Amoeba or the Nelder- Mead simplex optimization (NM) algorithm. The proposed Hassan NM (HNM) algorithm allows components of the reflected vertex to adapt to different operations, by breaking down the complex structure of the simplex into multiple triangular simplexes that work sequentially to optimize the individual components of mathematical functions. When the next formed simplex is characterized by different operations, it gives the simplex similar reflections to that of the NM algorithm, but with rotation through an angle determined by the collection of nonisometric features. As a consequence, the generating sequence of triangular simplexes is guaranteed that not only they have different shapes, but also they have different directions, to search the complex landscape of mathematical problems and to perform better performance than the traditional hyperplanes simplex. To test reliability, efficiency, and robustness, the proposed algorithm is examined on three areas of large- scale optimization categories: systems of nonlinear equations, nonlinear least squares, and unconstrained minimization. The experimental results confirmed that the new algorithm delivered better performance than the traditional NM algorithm, represented by a famous Matlab function, known as "fminsearch". -
Computing Invariants of Hyperbolic Coxeter Groups
LMS J. Comput. Math. 18 (1) (2015) 754{773 C 2015 Author doi:10.1112/S1461157015000273 CoxIter { Computing invariants of hyperbolic Coxeter groups R. Guglielmetti Abstract CoxIter is a computer program designed to compute invariants of hyperbolic Coxeter groups. Given such a group, the program determines whether it is cocompact or of finite covolume, whether it is arithmetic in the non-cocompact case, and whether it provides the Euler characteristic and the combinatorial structure of the associated fundamental polyhedron. The aim of this paper is to present the theoretical background for the program. The source code is available online as supplementary material with the published article and on the author's website (http://coxiter.rgug.ch). Supplementarymaterialsareavailablewiththisarticle. Introduction Let Hn be the hyperbolic n-space, and let Isom Hn be the group of isometries of Hn. For a given discrete hyperbolic Coxeter group Γ < Isom Hn and its associated fundamental polyhedron P ⊂ Hn, we are interested in geometrical and combinatorial properties of P . We want to know whether P is compact, has finite volume and, if the answer is yes, what its volume is. We also want to find the combinatorial structure of P , namely, the number of vertices, edges, 2-faces, and so on. Finally, it is interesting to find out whether Γ is arithmetic, that is, if Γ is commensurable to the reflection group of the automorphism group of a quadratic form of signature (n; 1). Most of these questions can be answered by studying finite and affine subgroups of Γ, but this involves a huge number of computations. -
The Hippo Pathway Component Wwc2 Is a Key Regulator of Embryonic Development and Angiogenesis in Mice Anke Hermann1,Guangmingwu2, Pavel I
Hermann et al. Cell Death and Disease (2021) 12:117 https://doi.org/10.1038/s41419-021-03409-0 Cell Death & Disease ARTICLE Open Access The Hippo pathway component Wwc2 is a key regulator of embryonic development and angiogenesis in mice Anke Hermann1,GuangmingWu2, Pavel I. Nedvetsky1,ViktoriaC.Brücher3, Charlotte Egbring3, Jakob Bonse1, Verena Höffken1, Dirk Oliver Wennmann1, Matthias Marks4,MichaelP.Krahn 1,HansSchöler5,PeterHeiduschka3, Hermann Pavenstädt1 and Joachim Kremerskothen1 Abstract The WW-and-C2-domain-containing (WWC) protein family is involved in the regulation of cell differentiation, cell proliferation, and organ growth control. As upstream components of the Hippo signaling pathway, WWC proteins activate the Large tumor suppressor (LATS) kinase that in turn phosphorylates Yes-associated protein (YAP) and its paralog Transcriptional coactivator-with-PDZ-binding motif (TAZ) preventing their nuclear import and transcriptional activity. Inhibition of WWC expression leads to downregulation of the Hippo pathway, increased expression of YAP/ TAZ target genes and enhanced organ growth. In mice, a ubiquitous Wwc1 knockout (KO) induces a mild neurological phenotype with no impact on embryogenesis or organ growth. In contrast, we could show here that ubiquitous deletion of Wwc2 in mice leads to early embryonic lethality. Wwc2 KO embryos display growth retardation, a disturbed placenta development, impaired vascularization, and finally embryonic death. A whole-transcriptome analysis of embryos lacking Wwc2 revealed a massive deregulation of gene expression with impact on cell fate determination, 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; cell metabolism, and angiogenesis. Consequently, a perinatal, endothelial-specific Wwc2 KO in mice led to disturbed vessel formation and vascular hypersprouting in the retina. -
Arxiv:1705.01294V1
Branes and Polytopes Luca Romano email address: [email protected] ABSTRACT We investigate the hierarchies of half-supersymmetric branes in maximal supergravity theories. By studying the action of the Weyl group of the U-duality group of maximal supergravities we discover a set of universal algebraic rules describing the number of independent 1/2-BPS p-branes, rank by rank, in any dimension. We show that these relations describe the symmetries of certain families of uniform polytopes. This induces a correspondence between half-supersymmetric branes and vertices of opportune uniform polytopes. We show that half-supersymmetric 0-, 1- and 2-branes are in correspondence with the vertices of the k21, 2k1 and 1k2 families of uniform polytopes, respectively, while 3-branes correspond to the vertices of the rectified version of the 2k1 family. For 4-branes and higher rank solutions we find a general behavior. The interpretation of half- supersymmetric solutions as vertices of uniform polytopes reveals some intriguing aspects. One of the most relevant is a triality relation between 0-, 1- and 2-branes. arXiv:1705.01294v1 [hep-th] 3 May 2017 Contents Introduction 2 1 Coxeter Group and Weyl Group 3 1.1 WeylGroup........................................ 6 2 Branes in E11 7 3 Algebraic Structures Behind Half-Supersymmetric Branes 12 4 Branes ad Polytopes 15 Conclusions 27 A Polytopes 30 B Petrie Polygons 30 1 Introduction Since their discovery branes gained a prominent role in the analysis of M-theories and du- alities [1]. One of the most important class of branes consists in Dirichlet branes, or D-branes. D-branes appear in string theory as boundary terms for open strings with mixed Dirichlet-Neumann boundary conditions and, due to their tension, scaling with a negative power of the string cou- pling constant, they are non-perturbative objects [2]. -
Physical Interpretation of the 30 8-Simplexes in the E8 240-Polytope
Physical Interpretation of the 30 8-simplexes in the E8 240-Polytope: Frank Dodd (Tony) Smith, Jr. 2017 - viXra 1702.0058 248-dim Lie Group E8 has 240 Root Vectors arranged on a 7-sphere S7 in 8-dim space. The 12 vertices of a cuboctahedron live on a 2-sphere S2 in 3-dim space. They are also the 4x3 = 12 outer vertices of 4 tetrahedra (3-simplexes) that share one inner vertex at the center of the cuboctahedron. This paper explores how the 240 vertices of the E8 Polytope in 8-dim space are related to the 30x8 = 240 outer vertices (red in figure below) of 30 8-simplexes whose 9th vertex is a shared inner vertex (yellow in figure below) at the center of the E8 Polytope. The 8-simplex has 9 vertices, 36 edges, 84 triangles, 126 tetrahedron cells, 126 4-simplex faces, 84 5-simplex faces, 36 6-simplex faces, 9 7-simplex faces, and 1 8-dim volume The real 4_21 Witting polytope of the E8 lattice in R8 has 240 vertices; 6,720 edges; 60,480 triangular faces; 241,920 tetrahedra; 483,840 4-simplexes; 483,840 5-simplexes 4_00; 138,240 + 69,120 6-simplexes 4_10 and 4_01; and 17,280 = 2,160x8 7-simplexes 4_20 and 2,160 7-cross-polytopes 4_11. The cuboctahedron corresponds by Jitterbug Transformation to the icosahedron. The 20 2-dim faces of an icosahedon in 3-dim space (image from spacesymmetrystructure.wordpress.com) are also the 20 outer faces of 20 not-exactly-regular-in-3-dim tetrahedra (3-simplexes) that share one inner vertex at the center of the icosahedron, but that correspondence does not extend to the case of 8-simplexes in an E8 polytope, whose faces are both 7-simplexes and 7-cross-polytopes, similar to the cubocahedron, but not its Jitterbug-transform icosahedron with only triangle = 2-simplex faces.