Classical Groups, Probabilistic Methods, and the (2, 3)-Generation Problem

1996 ◽  
Vol 144 (1) ◽  
pp. 77 ◽  
Author(s):  
Martin W. Liebeck ◽  
Aner Shalev
Author(s):  
Timothy C. Burness ◽  
Michael Giudici
Keyword(s):  

2009 ◽  
Author(s):  
P.R.F. de M. Bastos ◽  
N. Ferreira ◽  
B.A. de Souza

2020 ◽  
Vol 12 (17) ◽  
pp. 2809
Author(s):  
Meirman Syzdykbayev ◽  
Bobak Karimi ◽  
Hassan A. Karimi

Detection of terrain features (ridges, spurs, cliffs, and peaks) is a basic research topic in digital elevation model (DEM) analysis and is essential for learning about factors that influence terrain surfaces, such as geologic structures and geomorphologic processes. Detection of terrain features based on general geomorphometry is challenging and has a high degree of uncertainty, mostly due to a variety of controlling factors on surface evolution in different regions. Currently, there are different computational techniques for obtaining detailed information about terrain features using DEM analysis. One of the most common techniques is numerically identifying or classifying terrain elements where regional topologies of the land surface are constructed by using DEMs or by combining derivatives of DEM. The main drawbacks of these techniques are that they cannot differentiate between ridges, spurs, and cliffs, or result in a high degree of false positives when detecting spur lines. In this paper, we propose a new method for automatically detecting terrain features such as ridges, spurs, cliffs, and peaks, using shaded relief by controlling altitude and azimuth of illumination sources on both smooth and rough surfaces. In our proposed method, we use edge detection filters based on azimuth angle on shaded relief to identify specific terrain features. Results show that the proposed method performs similar to or in some cases better (when detecting spurs than current terrain features detection methods, such as geomorphon, curvature, and probabilistic methods.


2021 ◽  
pp. 027836492110333
Author(s):  
Gilhyun Ryou ◽  
Ezra Tal ◽  
Sertac Karaman

We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because the optimal trajectory is located on the boundary of the set of dynamically feasible trajectories. This boundary is hard to model as it involves limitations of the entire system, including complex aerodynamic and electromechanical phenomena, in agile high-speed flight. In this work, we propose a multi-fidelity Bayesian optimization framework that models the feasibility constraints based on analytical approximation, numerical simulation, and real-world flight experiments. By combining evaluations at different fidelities, trajectory time is optimized while the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct both simulation and real-world flight experiments at speeds up to 11 m/s. Resulting trajectories were found to be significantly faster than those obtained through minimum-snap trajectory planning.


Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.


Diversity ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 155
Author(s):  
Daniel Escoriza ◽  
Félix Amat

South-western Europe has a rich diversity of lacertid lizards. In this study, we evaluated the occupancy patterns and niche segregation of five species of lacertids, focusing on large-bodied species (i.e., adults having >75 mm snout-vent length) that occur in south-western Europe (Italian to the Iberian Peninsula). We characterized the niches occupied by these species based on climate and vegetation cover properties. We expected some commonality among phylogenetically related species, but also patterns of habitat segregation mitigating competition between ecologically equivalent species. We used multivariate ordination and probabilistic methods to describe the occupancy patterns and evaluated niche evolution through phylogenetic analyses. Our results showed climate niche partitioning, but with a wide overlap in transitional zones, where segregation is maintained by species-specific responses to the vegetation cover. The analyses also showed that phylogenetically related species tend to share large parts of their habitat niches. The occurrence of independent evolutionary lineages contributed to the regional species richness favored by a long history of niche divergence.


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