TY - GEN
AU - Friedlander, Tamar
AU - Mayo, Avraham E.
AU - Tlusty, Tsvi
AU - Alon, Uri
ID - 9773
TI - Evolutionary simulation code
ER -
TY - JOUR
AB - We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation. First, we prove that adding linearly many random edges to a dense k-uniform hypergraph ensures the (asymptotically almost sure) existence of a perfect matching or a loose Hamilton cycle. The proof involves an interesting application of Szemerédi's Regularity Lemma, which might be independently useful. We next prove that digraphs with certain strong expansion properties are pancyclic, and use this to show that adding a linear number of random edges typically makes a dense digraph pancyclic. Finally, we prove that perturbing a certain (minimum-degree-dependent) number of random edges in a tournament typically ensures the existence of multiple edge-disjoint Hamilton cycles. All our results are tight.
AU - Krivelevich, Michael
AU - Kwan, Matthew Alan
AU - Sudakov, Benny
ID - 9575
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
TI - Cycles and matchings in randomly perturbed digraphs and hypergraphs
VL - 49
ER -
TY - JOUR
AB - The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature, in out-of-equilibrium conditions at which the interfacial free energy is ill defined. Here we draw a connection between the atomistic description of a diffuse solid-liquid interface and its thermodynamic characterization. This framework resolves the ambiguities in defining the solid-liquid interfacial free energy above and below the melting temperature. In addition, we introduce a simulation protocol that allows solid-liquid interfaces to be reversibly created and destroyed at conditions relevant for experiments. We directly evaluate the value of the interfacial free energy away from the melting point for a simple but realistic atomic potential, and find a more complex temperature dependence than the constant positive slope that has been generally assumed based on phenomenological considerations and that has been used to interpret experiments. This methodology could be easily extended to the study of other phase transitions, from condensation to precipitation. Our analysis can help reconcile the textbook picture of classical nucleation theory with the growing body of atomistic studies and mesoscale models of solidification.
AU - Cheng, Bingqing
AU - Tribello, Gareth A.
AU - Ceriotti, Michele
ID - 9688
IS - 18
JF - Physical Review B - Condensed Matter and Materials Physics
SN - 1098-0121
TI - Solid-liquid interfacial free energy out of equilibrium
VL - 92
ER -
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 - GEN
AU - Symonova, Olga
AU - Topp, Christopher
AU - Edelsbrunner, Herbert
ID - 9737
TI - Root traits computed by DynamicRoots for the maize root shown in fig 2
ER -