532 research outputs found
How sufficient conditions are related for topology-preserving reductions
A crucial issue in digital topology is to ensure topology preservation for reductions acting on binary pictures (i.e., operators that never change a white point to black one). Some sufficient conditions for topology-preserving reductions have been proposed for pictures on the three possible regular partitionings of the plane (i.e., the triangular, the square, and the hexagonal grids). In this paper, the relationships among these conditions are stated
An analysis of surface area estimates of binary volumes under three tilings
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 77-79).by Erik G. Miller.M.S
Place cells dynamically refine grid cell activities to reduce error accumulation during path integration in a continuous attractor model
Navigation is one of the most fundamental skills of animals. During spatial navigation, grid cells in the medial entorhinal cortex process speed and direction of the animal to map the environment. Hippocampal place cells, in turn, encode place using sensory signals and reduce the accumulated error of grid cells for path integration. Although both cell types are part of the path integration system, the dynamic relationship between place and grid cells and the error reduction mechanism is yet to be understood. We implemented a realistic model of grid cells based on a continuous attractor model. The grid cell model was coupled to a place cell model to address their dynamic relationship during a simulated animal’s exploration of a square arena. The grid cell model processed the animal’s velocity and place field information from place cells. Place cells incorporated salient visual features and proximity information with input from grid cells to define their place fields. Grid cells had similar spatial phases but a diversity of spacings and orientations. To determine the role of place cells in error reduction for path integration, the animal’s position estimates were decoded from grid cell activities with and without the place field input. We found that the accumulated error was reduced as place fields emerged during the exploration. Place fields closer to the animal’s current location contributed more to the error reduction than remote place fields. Place cells’ fields encoding space could function as spatial anchoring signals for precise path integration by grid cells.Fil: Fernandez Leon, Jose Alberto. Universidad Nacional del Centro de la Provincia de Buenos Aires. Centro de Investigaciones en FÃsica e IngenierÃa del Centro de la Provincia de Buenos Aires. - Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Tandil. Centro de Investigaciones en FÃsica e IngenierÃa del Centro de la Provincia de Buenos Aires. - Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones CientÃficas. Centro de Investigaciones en FÃsica e IngenierÃa del Centro de la Provincia de Buenos Aires; ArgentinaFil: Uysal, Ahmet Kerim. Baylor College of Medicine; Estados UnidosFil: Ji, Daoyun. Baylor College of Medicine; Estados Unido
Eco-ISEA3H, a machine learning ready spatial database for ecometric and species distribution modeling
We present the Eco-ISEA3H database, a compilation of global spatial data characterizing climate, geology, land cover, physical and human geography, and the geographic ranges of nearly 900 large mammalian species. The data are tailored for machine learning (ML)-based ecological modeling, and are intended primarily for continental- to global-scale ecometric and species distribution modeling. Such models are trained on present-day data and applied to the geologic past, or to future scenarios of climatic and environmental change. Model training requires integrated global datasets, describing species' occurrence and environment via consistent observational units. The Eco-ISEA3H database incorporates data from 17 sources, and includes 3,033 variables. The database is built on the Icosahedral Snyder Equal Area (ISEA) aperture 3 hexagonal (3H) discrete global grid system (DGGS), which partitions the Earth's surface into equal-area hexagonal cells. Source data were incorporated at six nested ISEA3H resolutions, using scripts developed and made available here. We demonstrate the utility of the database in a case study analyzing the bioclimatic envelopes of ten large, widely distributed mammalian species.Peer reviewe
A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids
A new algorithm is presented for the solution of the shallow water
equations on quasi-uniform spherical grids. It combines a mimetic
finite volume spatial discretization with a Crank–Nicolson time
discretization of fast waves and an accurate and conservative
forward-in-time advection scheme for mass and potential vorticity
(PV). The algorithm is implemented and tested on two families of
grids: hexagonal–icosahedral Voronoi grids, and modified equiangular
cubed-sphere grids.
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Results of a variety of tests are presented, including convergence
of the discrete scalar Laplacian and Coriolis operators, advection,
solid body rotation, flow over an isolated mountain, and
a barotropically unstable jet. The results confirm a number of
desirable properties for which the scheme was designed: exact mass
conservation, very good available energy and potential enstrophy
conservation, consistent mass, PV and tracer transport, and good
preservation of balance including vanishing ∇ × ∇,
steady geostrophic modes, and accurate PV advection. The scheme is
stable for large wave Courant numbers and advective Courant numbers
up to about 1.
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In the most idealized tests the overall accuracy of the scheme
appears to be limited by the accuracy of the Coriolis and other
mimetic spatial operators, particularly on the cubed-sphere grid.
On the hexagonal grid there is no evidence for damaging effects of
computational Rossby modes, despite attempts to force them
explicitly
Inference and experimental design for percolation and random graph models.
The problem of optimal arrangement of nodes of a random weighted graph is
studied in this thesis. The nodes of graphs under study are fixed, but their edges
are random and established according to the so called edge-probability function.
This function is assumed to depend on the weights attributed to the pairs of graph
nodes (or distances between them) and a statistical parameter. It is the purpose
of experimentation to make inference on the statistical parameter and thus to
extract as much information about it as possible. We also distinguish between two
different experimentation scenarios: progressive and instructive designs.
We adopt a utility-based Bayesian framework to tackle the optimal design
problem for random graphs of this kind. Simulation based optimisation methods,
mainly Monte Carlo and Markov Chain Monte Carlo, are used to obtain
the solution. We study optimal design problem for the inference based on partial
observations of random graphs by employing data augmentation technique.
We prove that the infinitely growing or diminishing node configurations asymptotically
represent the worst node arrangements. We also obtain the exact solution
to the optimal design problem for proximity graphs (geometric graphs) and numerical
solution for graphs with threshold edge-probability functions.
We consider inference and optimal design problems for finite clusters from bond
percolation on the integer lattice Zd and derive a range of both numerical and
analytical results for these graphs. We introduce inner-outer plots by deleting
some of the lattice nodes and show that the ‘mostly populated’ designs are not
necessarily optimal in the case of incomplete observations under both progressive
and instructive design scenarios.
Finally, we formulate a problem of approximating finite point sets with lattice
nodes and describe a solution to this problem
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