相关论文: On geodesics of phyllotaxis
For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ is the intersection…
I present a review of chemical evolution models of the solar neighborhood. I give special attention to the necessary ingredients to reproduce the observed [Xi/Fe] ratios in nearby metal and super metal rich stars, and to the chemical…
The impact of droplets on concave surfaces is poorly understood, although it is relevant to a mode of dispersal that has evolved independently in several species of plants and fungi. This mode relies on splash-cups, specialized organs that…
The connection between geodesics on the modular surface $\operatorname{PSL}(2,{\mathbb Z})\backslash {\mathbb H}$ and regular continued fractions, established by Series, is extended to a connection between geodesics on $\Gamma\backslash…
We develop a new method which measures the projected density distribution w_p(r_p)n of photometric galaxies surrounding a set of spectroscopically-identified galaxies, and simultaneously the projected correlation function w_p(r_p) between…
A collection of distinct sets is called a sunflower if the intersection of any pair of sets equals the common intersection of all the sets. Sunflowers are fundamental objects in extremal set theory with relations and applications to many…
A sunflower is a collection of sets $\{U_1,\ldots, U_n\}$ such that the pairwise intersection $U_i\cap U_j$ is the same for all choices of distinct $i$ and $j$. We study sunflowers of convex open sets in $\mathbb R^d$, and provide a…
Understanding the emergence of biological structures and their changes is a complex problem. On a biochemical level, it is based on gene regulatory networks (GRN) consisting on interactions between the genes responsible for cell…
Accounting for the annual climatic variability is a well-known issue for simulation-based studies of environmental models. It often requires intensive sampling (e.g., averaging the simulation outputs over many climatic series), which…
Natural numbers divisible by the same prime factor lie on defined spiral graphs which are running through the Square Root Spiral (also named as the Spiral of Theodorus or Wurzel Spirale or Einstein Spiral). Prime Numbers also clearly…
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…
We describe galaxy surface photometry based on fitting ellipses to the isophotes of the galaxies. Example galaxies with different isophotal shapes are used to illustrate the process, including how the deviations from elliptical isophotes…
We study the problem of coupling a stochastic block model with a planted bisection to a uniform random graph having the same average degree. Focusing on the regime where the average degree is a constant relative to the number of vertices…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
Let $C$ be a curve in a closed orientable surface $F$ of genus $g \geq 2$ that separates $F$ into subsurfaces $\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\Mod(F)$ of the Dehn twist $t_C$ about $C$. All…
For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the…
A distribution function approach is applied to describe the dynamics of the laser beam in the Earth atmosphere. Using a formal solution of the kinetic equation for the distribution function, we have developed an iterative scheme for…
In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of $F-$Gordon equation; A PDE which…
For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ is the intersection…