The interspecific mass–density relationship and plant geometry

We present an a priori theoretical framework for the interspecific allometric relationship between stand mass and plant population density. Our model predicts a slope of −\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\frac{1}{3}\end{equation*}\end{document} between the logarithm of stand mass and the logarithm of stand density, thus conflicting with a previously assumed slope of −½. Our model rests on a heuristic separation of resource-limited living mass and structural mass in the plant body. We point out that because of similar resource requirements among plants of different sizes, a nonzero plant mass–density slope is primarily defined by structural mass. Specifically, the slope is a result of (i) the physical size-dependent relationship between stem width and height, (ii) foliage-dependent demands of conductance, and (iii) the cumulative nature of structural mass. The data support our model, both when the potential sampling bias of taxonomic relatedness is accounted for and when it is not. Independent contrasts analyses show that observed relationships among variables are not significantly different from the assumptions made to build the model or from its a priori predictions. We note that the dependence of the plant mass–density slope on the functions of structural mass provides a cause for the difference from the zero slope found in the animal population mass–density relationship; for the most part, animals do not have a comparable cumulative tissue type.

Cloning, expression, and characterization of a cDNA encoding a novel human growth factor for primitive hematopoietic progenitor cells

Multiple growth factors synergistically stimulate proliferation of primitive hematopoietic progenitor cells. A human myeloid cell line, KPB-M15, constitutively produces a novel hematopoietic cytokine, termed stem cell growth factor (SCGF), possessing species-specific proliferative activities. Here we report the molecular cloning, expression, and characterization of a cDNA encoding human SCGF using a newly developed λSHDM vector that is more efficient for differential and expression cloning. cDNA for SCGF encodes a 29-kDa polypeptide without N-linked glycosylation. SCGF transiently produced by COS-1 cells supports growth of hematopoietic progenitor cells through a short-term liquid culture of bone marrow cells and exhibits promoting activities on erythroid and granulocyte/macrophage progenitor cells in primary semisolid culture with erythropoietin and granulocyte/macrophage colony-stimulating factor, respectively. Expression of SCGF mRNA is restricted to myeloid cells and fibroblasts, suggesting that SCGF is a growth factor functioning within the hematopoietic microenvironment. SCGF could disclose some human-specific mechanisms as yet unidentified from studies on the murine hematopoietic system.

Twist fields, the elliptic genus, and hidden symmetry

We combine infinite dimensional analysis (in particular a priori estimates and twist positivity) with classical geometric structures, supersymmetry, and noncommutative geometry. We establish the existence of a family of examples of two-dimensional, twist quantum fields. We evaluate the elliptic genus in these examples. We demonstrate a hidden SL(2,ℤ) symmetry of the elliptic genus, as suggested by Witten.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.