The study of gyration stability in projective planes.
problem Whether gyrations of projective planes share the same homotopy type.
method Exploration of gyration stability for complex, quaternionic, and octonionic projective planes.
result Complete description of gyration stability for projective planes up to homotopy.
Abstract: Study gyrations of sphere products and connected sums, generalizing Fico's Lemmata.
problem Understanding the homotopy type of gyrations of sphere products and connected sums.
method Recasting Fico's Lemmata into modern homotopy theoretic setting.
result Generalization of Fico's Lemmata to sphere products and connected sums.
The paper extends stabilization methods to Poincaré Duality complexes.
problem Stabilization of Poincaré Duality complexes and homotopy gyrations.
method Develops new methods for stabilization of Poincaré Duality complexes, including a homotopy theoretic generalization of a gyration.
result Shows there are only finitely many possible homotopy types of gyrations for a fixed Poincaré Duality complex.
The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a method for turning any knot into the regular planar polygon using on…
Paper constructs and proves existence of chiral triply-periodic minimal surfaces.
problem Existence of chiral triply-periodic minimal surfaces of genus 4.
method Construction based on dual qtz--qzd nets, existence proof using Weierstrass method on branched torus.
result Family of chiral triply-periodic minimal surfaces of genus 4 constructed and proved to exist.
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the complex Stiefel manifold of 2-frames in n-space to the space of closed n-gons in 3-space of total length 2. Our probability measure on polygon s…
Study forecasts stock returns on JSE using SGDLMs capturing cross-series dependencies.
problem Accurate forecasting of multivariate time series data.
method Simultaneous Graphical Dynamic Linear Models (SGDLMs) with customised DLMs and importance sampling/mean-field variational Bayes.
result SGDLMs accurately forecast stock data on JSE and respond to market changes.
Modeling financial market dynamics with 2D Levy flights.
problem Capturing the complex, scaling laws in financial market dynamics.
method 2D Lévy flight model applied to S\&P 500 index prices.
result Empirical spectral properties match model predictions.
DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.
problem Designing molecules with ensemble properties rather than single conformations.
method DECAF uses Boltzmann-expected design with decoupled annealing flows to optimize molecular graphs.
result DECAF optimizes molecular graphs to shift ensemble properties towards targets, improving accuracy over single-conformer methods.