Related papers: Tracking p-adic precision
The p-adic numbers have found applications in a wide range of diverse fields of research. In some applications the algebraic properties of p-adics enter as an indispensable ingredient of the theory. Another class of applications has to do…
We introduce a novel framework for upsampled Point Spread Function (PSF) modeling using pixel-level Bayesian inference. Accurate PSF characterization is critical for precision measurements in many fields including: weak lensing, astrometry,…
We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect…
We discuss a new approach to realization of the well-known Weierstrass's programme on efficient continuation of an analytic element corresponding to a~multivalued analytic function with finite number of branch points. Our approach is based…
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
Given a differential equation on a smooth $p$-adic analytic curve, one may construct a new one by pushing forward by an \'etale morphism. The main result of the paper provides an explicit formula that relates the radii of convergence of the…
Amodal segmentation is a challenging task that aims to predict the complete geometric shape of objects, including their occluded regions. Although existing methods primarily focus on amodal segmentation within the training domain, these…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
A method of constructing finite $p$-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci-Sylvester (greedy) algorithm by iterating a $p$-adic division algorithm. The method extends to…
We define a function which extends Gaussian hypergeometric series to the $p$-adic setting. This new function allows results involving Gaussian hypergeometric series to be extended to a wider class of primes. We demonstrate this by providing…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
In this paper, we propose a novel learning-based polygonal point set tracking method. Compared to existing video object segmentation~(VOS) methods that propagate pixel-wise object mask information, we propagate a polygonal point set over…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…
Traditional ultrasound simulators solve the wave equation to model pressure distribution fields, achieving high accuracy but requiring significant computational time and resources. To address this, ray tracing approaches have been…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
For certain natural families of topologies, we study continuity and stability of statistical properties of random walks on linear groups over local fields. We extend large deviation results known in the Archimedean case to non-Archimedean…
We construct a $p$-adic analog to AdS/CFT, where an unramified extension of the $p$-adic numbers replaces Euclidean space as the boundary and a version of the Bruhat-Tits tree replaces the bulk. Correlation functions are computed in the…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…