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Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
We present the Streaming Gaussian Dirichlet Random Field (S-GDRF) model, a novel approach for modeling a stream of spatiotemporally distributed, sparse, high-dimensional categorical observations. The proposed approach efficiently learns…
We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…
We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the…
Non-Gaussianity in the cosmic microwave background and the large-scale structure of galaxies provides an increasingly powerful probe of the universe. I implement an algorithm to generate realisations of fields that possess an arbitrary…
Constructing a 3D scene capable of accommodating open-ended language queries, is a pivotal pursuit, particularly within the domain of robotics. Such technology facilitates robots in executing object manipulations based on human language…
Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…
Neural Radiance Fields (NeRFs) have demonstrated the remarkable potential of neural networks to capture the intricacies of 3D objects. By encoding the shape and color information within neural network weights, NeRFs excel at producing…
We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…
The 3D Gaussian Splatting technique has significantly advanced the construction of radiance fields from multi-view images, enabling real-time rendering. While point-based rasterization effectively reduces computational demands for…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…
Occupancy mapping has been a key enabler of mobile robotics. Originally based on a discrete grid representation, occupancy mapping has evolved towards continuous representations that can predict the occupancy status at any location and…
We construct a concise gauge invariant formulation for massless, partially massless, and massive bosonic AdS fields of arbitrary symmetry type at the level of equations of motion. Our formulation admits two equivalent descriptions: in terms…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
By considering gauge transformations on the macroscopic Maxwell's equations, a two dimensional gauge field, with its pseudo magnetic field in the real space, is identified as tilted anisotropy in the constitutive parameters. We show that…
Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using the field theoretic…
3D Semantic Occupancy Prediction is fundamental for spatial understanding, yet existing approaches face challenges in scalability and generalization due to their reliance on extensive labeled data and computationally intensive voxel-wise…
We construct generating functions for operators dual to systems of giant gravitons with open strings attached. These operators have a bare dimension of order $N$ so that the usual methods used to solve the planar limit are not applicable.…