arXiv research

A novel method compresses point cloud attributes by folding them onto a 2D grid.

The paper studies how grid cell patterns emerge in neural networks.

This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.

The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…

Study freezing sets for digital images in a 2D grid.

The uninformative ordering of artificial neurons in Deep Neural Networks complicates visualizing activations in deeper layers. This is one reason why the internal structure of such models is very unintuitive. In neuroscience, activity of real brains can be visualized by highlighting active regions. Inspired by those te…

Computes elastic grids that approximate 3D surfaces without physical simulations.

2D path planning in static environment is a well-known problem and one of the common ways to solve it is to 1) represent the environment as a grid and 2) perform a heuristic search for a path on it. At the same time 2D grid resembles much a digital image, thus an appealing idea comes to being -- to treat the problem as…

3D RadViz improves 3D data visualization of multidimensional datasets.

Deep learning speeds spectral density estimation for large 2D/3D grids.

Extends knot invariant to filtered grid complexes.

Designs a Cellular Automata rule for forming touching loop patterns.

This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector. Each component of the vector is a unit or a cell. The mode…

Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.

Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid cells which encode space using tessellating patterns. However, the mechanisms and fu…

Study of harmonic maps on 2D simplicial complexes, proving existence and regularity.

We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.

Proves continuity and singular set dimension for 2D maps with Q values.

It will be shown that according to theorems of K. Menger, every neuron grid if identified with a curve is able to preserve the adopted qualitative structure of a data space. Furthermore, if this identification is made, the neuron grid structure can always be mapped to a subset of a universal neuron grid which is constr…

Deep learning predicts curvature of 2D interfaces in level-set method.

Develops equivariant grid homology for strongly invertible knots.

The paper establishes T-duality for 2D σ-models with H-flux.

Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance…

Paper connects 3D gravity averages to 2D CFT correlators.

Study on p-biharmonic maps from gradient Ricci solitons, focusing on 2D cigar soliton.

Insights in power grid pixel maps (PGPMs) refer to important facility operating states and unexpected changes in the power grid. Identifying insights helps analysts understand the collaboration of various parts of the grid so that preventive and correct operations can be taken to avoid potential accidents. Existing sol…

pLSTM tackles long-range language modeling and computer vision tasks with parallelizable linear source transition mark networks.

When using Convolutional Neural Networks (CNNs) for segmentation of organs and lesions in medical images, the conventional approach is to work with inputs and outputs either as single slice (2D) or whole volumes (3D). One common alternative, in this study denoted as pseudo-3D, is to use a stack of adjacent slices as in…

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher acc…

Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D d…

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…

For a closed topological manifold M with dim (M) >= 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure group of M as defined by Ranicki. If dim (M) = 2d-1, M is oriented and M is equipped with a map to the classifying space of a finite group G, th…

Strict type-II blowup in harmonic map flow is proven to have Hölder continuous body map.

WindDragon forecasts wind power with deep learning.

In the monitoring of a complex electric grid, it is of paramount importance to provide operators with early warnings of anomalies detected on the network, along with a precise classification and diagnosis of the specific fault type. In this paper, we propose a novel multi-stage early warning system prototype for electr…

Node2Grids uncouples GCN training for large graphs, saving memory and computation.

Efficiently prices American options with multiple assets using sparse grids.

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this s…

We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the spac…

Bayesian deep learning improves geostatistical mapping with auxiliary data.

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. …

The paper finds a family of 2D surfaces where Laplacian and Dirichlet-to-Neumann commute.

The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architec…

We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization of the uniform norm of polynomials and rational functions. The decomposition of …

Assisted by neural networks, reinforcement learning agents have been able to solve increasingly complex tasks over the last years. The simulation environment in which the agents interact is an essential component in any reinforcement learning problem. The environment simulates the dynamics of the agents' world and henc…

The complexity of a finite connected graph is its number of spanning trees; for a non-connected graph it is the product of complexities of its connected components. If $G$ is an infinite graph with cofinite free ${\mathbb Z}^d$-symmetry, then the logarithmic Mahler measure $m(Δ)$ of its Laplacian polynomial $Δ$ is the …

New method characterizes surface quadrilateral layouts as special immersions.