Specimens of Euproops sp. (Xiphosura, Chelicerata) from the Carboniferous Piesberg quarry near Osnabrück, Germany, represent a relatively complete growth series of 10 stages. Based on this growth sequence, morphological changes throughout the ontogeny can be identified. The major change affects the shape of the epimera of the opisthosoma. In earlier stages, they appear very spine-like, whereas in later stages the bases of these spine-like structures become broader; the broadened bases are then successively drawn out distally. In the most mature stage known, the epimera are of trapezoidal shape and approach each other closely to form a complete flange around the thoracetron (=fused tergites of the opisthosoma). These ontogenetic changes question the taxonomic status of different species of Euproops, as the latter appear to correspond to different stages of the ontogenetic series reconstructed from the Piesberg specimens. This means that supposed separate species could, in fact, represent different growth stages of a single species. It could alternatively indicate that heterochrony (=evolutionary change of developmental timing) plays an important role in the evolution of Xiphosura. We propose a holomorph approach, i.e., reconstructing ontogenetic sequences for fossil and extant species as a sound basis for a taxonomic, phylogenetic, and evolutionary discussion of Xiphosura.
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Commun Math Phys
October 2024
CNRS, LJAD, Université Côte d'Azur, Nice, France.
Given a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coefficients in a triangulated DG-category. These spectral networks are analogs of special Lagrangian submanifolds, combining a graph with additional algebraic data, and conjecturally correspond to semistable objects of a suitable stability condition on the Fukaya category with coefficients. They are closely related to the spectral networks of Gaiotto-Moore-Neitzke.
View Article and Find Full Text PDFPLoS One
June 2023
Department of Electrical and Computer Engineering, United States Naval Academy, Annapolis, Maryland, United States of America.
Objective: This research pioneers a novel approach to obtain a closed-form analytic solution to the nonlinear second order differential swing equation that models power system dynamics. The distinctive element of this study is the integration of a generalized load model known as a ZIP load model (constant impedance Z, constant current I, and constant power P loads).
Methods: Building on previous work where an analytic solution for the swing equation was derived in a linear system with limited load types, this study introduces two fundamental novelties: 1) the innovative examination and modeling of the ZIP load model, successfully integrating constant current loads to augment constant impedance and constant power loads; 2) the unique derivation of voltage variables in relation to rotor angles employing the holomorphic embedding (HE) method and the Padé approximation.
Entropy (Basel)
February 2021
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA.
Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor's question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators.
View Article and Find Full Text PDFJ Chem Theory Comput
December 2020
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham density-functional theory (KS-DFT) have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parameterized functional that scales between the two representations.
View Article and Find Full Text PDFIEEE Trans Vis Comput Graph
March 2022
We propose an algorithm to compute global conformal parameterizations of high-genus meshes, which is based on an implementation of holomorphic quadratic differentials. First, we design a novel diffusion method which is capable of computing a pole-free discrete harmonic measured foliation. Second, we propose a definition for discrete holomorphic quadratic differential which consists of a horizontal and a vertical harmonic measured foliation.
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