Spatiotemporal mechanisms of root branching

The fundamental tasks of the root system are, besides anchoring, mediating interactions between plant and soil and providing the plant with water and nutrients. The architecture of the root system is controlled by endogenous mechanisms that constantly integrate environmental signals, such as availability of nutrients and water. Extremely important for efficient soil exploitation and survival under less favorable conditions is the developmental flexibility of the root system that is largely determined by its postembryonic branching capacity. Modulation of initiation and outgrowth of lateral roots provides roots with an exceptional plasticity, allows optimal adjustment to underground heterogeneity, and enables effective soil exploitation and use of resources. Here we discuss recent advances in understanding the molecular mechanisms that shape the plant root system and integrate external cues to adapt to the changing environment

Direct computation of elliptic singularities across anisotropic, multi-material edges

We characterise the singularities of elliptic div-grad operators at points or edges where several materials meet on a Dirichlet or Neumann part of the boundary of a two- or three-dimensional domain. Special emphasis is put on anisotropic coefficient matrices. The singularities can be computed as roots of a characteristic transcendental equation. We establish uniform bounds for the singular values for several classes of three- and four-material edges. These bounds can be used to prove optimal regularity results for elliptic div-grad operators on three-dimensional, heterogeneous, polyhedral domains with mixed boundary conditions. We demonstrate this for the benchmark L--shape problem

Stable Complete Intersections

A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which all the complete intersection ideals share the same number of isolated real zeros. In the second part we show how to modify the complete intersection and get a new one which generates the same ideal but whose real zeros are more stable with respect to perturbations of the coefficients.Comment: 1 figur

Parameters for Carrot Quality: and the development of the Inner Quality concept

The life processes of the carrot plant were demonstrated by various parameters in this study. Growth processes, including photosynthesis, absorption of nitrogen and other nutrients and formation of cells, tissues and organs, are measured by the parameters weight of leaves and roots and emission 30-50 white of delayed luminescence. The nitrate content may indicate growth but has to be investigated further. Differentiation processes, including refining, ordering, ripening and secondary metabolisms, are measured by the parameters root stumpiness, saccharose, sweetness, dry matter and emission 30-50 ratio of delayed luminescence. Some other parameters may indicate differentiation processes but have to be further investigated: leaves/root weight ratio, monosaccharides/saccharose ratio, carotenes, initial and total emission white, hyperbolicity ratio and slope white of delayed luminescence. Integration of growth and differentiation is measured by resistance to pests and disease, total appreciation and storage test. Some other parameters may indicate integration but need further investigation: carrot taste, slope white of delayed luminescence. Copper chloride crystallisation did not produce clear pictures due to failure of the method applied and should be further investigated since, in the Apple-1 and -2 studies (Bloksma et al., 2001, 2004 b), it was one of the indicators of the life processes. Electro-chemical parameters, except possibly pH, did not indicate growth processes in his study or in the Apple-1 and -2 studies

An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2

Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration. We use Macaulay 2 to investigate some problems from enumerative geometry, illustrating some applications of symbolic computation to this important problem of solving systems of polynomial equations. Besides enumerating solutions to the resulting polynomial systems, which include overdetermined, deficient, and improper systems, we address the important question of real solutions to these geometric problems. The text contains evaluated Macaulay 2 code to illuminate the discussion. This is a chapter in the forthcoming book "Computations in Algebraic Geometry with Macaulay 2", edited by D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels. While this chapter is largely expository, the results in the last section concerning lines tangent to quadrics are new.Comment: LaTeX 2e, 22 pages, 1 .eps figure. Source file (.tar.gz) includes Macaulay 2 code in article, as well as Macaulay 2 package realroots.m2 Macaulay 2 available at http://www.math.uiuc.edu/Macaulay2 Revised with improved exposition, references updated, Macaulay 2 code rewritten and commente

Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution

The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and Derrida using a linear stability analysis of the hydrodynamical limit of the process and further arguments have been given by Mallick and Prolhac. However it has been impossible so far to study what happens after the transition. The present paper presents an analysis of the large deviation function of the current on both sides of the transition from a Bethe ansatz approach of the weak asymmetry regime of the exclusion process.Comment: accepted to J.Stat.Phys, 1 figure, 1 reference, 2 paragraphs adde