TY - JOUR
AB - We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth.
AU - Symonova, Olga
AU - Topp, Christopher
AU - Edelsbrunner, Herbert
ID - 1793
IS - 6
JF - PLoS One
TI - DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots
VL - 10
ER -
TY - JOUR
AB - We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.
AU - Attali, Dominique
AU - Bauer, Ulrich
AU - Devillers, Olivier
AU - Glisse, Marc
AU - Lieutier, André
ID - 1805
IS - 8
JF - Computational Geometry: Theory and Applications
TI - Homological reconstruction and simplification in R3
VL - 48
ER -
TY - JOUR
AB - We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.
AU - Akopyan, Arseniy
AU - Pirogov, Sergey
AU - Rybko, Aleksandr
ID - 1828
IS - 1
JF - Journal of Statistical Physics
TI - Invariant measures of genetic recombination process
VL - 160
ER -
TY - JOUR
AB - We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.
AU - Pausinger, Florian
AU - Steinerberger, Stefan
ID - 1938
IS - 6
JF - Physics Letters, Section A
TI - On the distribution of local extrema in quantum chaos
VL - 379
ER -
TY - JOUR
AB - Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
AU - Edelsbrunner, Herbert
AU - Jablonski, Grzegorz
AU - Mrozek, Marian
ID - 2035
IS - 5
JF - Foundations of Computational Mathematics
TI - The persistent homology of a self-map
VL - 15
ER -