More Like this

1. Root Radii and Subdivision for Polynomial Root-Finding

   https://doi.org/10.1007/978-3-030-85165-1_9  

   Imbach, R; Pan, Victor Y. (September 2021, International Workshop on Computer Algebra in Scientific Computing)

   null (Ed.)
2. Stability of Stretched Root Systems, Root Posets and Shards

   https://doi.org/10.37236/10029  

   Dana, Will (July 2021, The Electronic Journal of Combinatorics)

   Inspired by the infinite families of finite and affine root systems, we define a "stretching" operation on general crystallographic root systems which, on the level of Coxeter diagrams, replaces a vertex with a path of unlabeled edges. We embed a root system into its stretched versions using a similar operation on individual roots. For a fixed root, we describe the long-term behavior of two associated structures as we lengthen the stretched path: the downset in the root poset and Reading's arrangement of shards. We show that both eventually admit a uniform description, and deduce enumerative consequences: the size of the downset is eventually a polynomial, and the number of shards grows exponentially. 

   more » « less
3. UNTANGLING ROOT TOPOLOGY IN PLANT PHENOTYPING DATA: FROM 2D ROOT HAIR ANALYSIS TO 3D ROOT ARCHITECTURE RECONSTRUCTION

   PIETRZYK, PETER JACEK (April 2025, University of Georgia)
4. Image‐based root phenotyping links root architecture to micronutrient concentration in cassava

   https://doi.org/10.1002/ppp3.10130  

   Busener, Natalie; Kengkanna, Jitrana; Saengwilai, Patompong Johns; Bucksch, Alexander (July 2020, PLANTS, PEOPLE, PLANET)

   Societal Impact Statement Micronutrient deficiency or “hidden hunger” is estimated to affect two billion people worldwide and increasing the micronutrient concentration of food could play an important role in tackling this global challenge. Using a combination of imaging techniques and atomic absorption spectroscopy, we describe a link between root phenotype and micronutrient concentration in cassava, which could enable new phenotypic selection strategies for breeding. This approach could be used with existing breeding infrastructure to enhance the micronutrient concentration of cassava and hence, benefit the health of people, particularly in low‐income countries where cassava is consumed as a staple crop. SummaryCassava storage roots are a staple food in low‐income countries of South‐East Asia and sub‐Saharan Africa, where growth stunting is prevalent as a consequence of micronutrient deficiencies. We aim to link phenotypes of field‐grown cassava roots to micronutrient concentration in the edible storage roots as a simple way to improve phenotypic selection for nutritional value in cassava.We used existing and newly developed imaging techniques to quantify root phenotypes of the cassava root architecture over time and used flame atomic absorption spectroscopy to measure micronutrient concentration in storage roots. Both together allow the association of root phenotypes with micronutrient concentration in mature cassava roots.We show that early and late bulking genotypes in cassava exhibit distinct foraging behaviors that are associated with micronutrient concentration in the edible storage root. Our observations suggest that late bulking cassava is a key to provide sufficient micronutrients in the edible storage root.The association between root phenotype and micronutrient concentration with imaging techniques allows phenotypic selection for enhanced micronutrient concentration. Therefore, implementing image‐based phenotyping into cassava breeding programs in sub‐Saharan Africa and South‐East Asia could be an essential element to resolve micronutrient deficiencies that puts individuals at a higher risk of growth stunting. 

   more » « less
5. Root system chip-firing

   Galashin, Pavel; Hopkins, Sam; McConville, Thomas; Postnikov, Alexander (October 2018, Séminaire lotharingien de combinatoire)

   Propp recently introduced a variant of chip-firing on the infinite path where the chips are given distinct integer labels and conjectured that this process is confluent from certain (but not all) initial configurations of chips. Hopkins, McConville, and Propp proved Propp's confluence conjecture. We recast this result in terms of root systems: the labeled chip-firing game can be seen as a process which allows replacing an integer vector λ by λ+α whenever λ is orthogonal to α, for α a positive root of a root system of Type A. We give conjectures about confluence for this process in the general setting of an arbitrary root system. We show that the process is always confluent from any initial point after modding out by the action of the Weyl group (an analog of unlabeled chip-firing in arbitrary type). We also study some remarkable deformations of this process which are confluent from any initial point. For these deformations, the set of weights with given stabilization has an interesting geometric structure related to permutohedra. This geometric structure leads us to define certain `Ehrhart-like' polynomials that conjecturally have nonnegative integer coefficients. 

   more » « less