Related papers: Fast Computation of Zigzag Persistence
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
This paper introduces an efficient design approach for a fast-convolution-based variable-bandwidth (VBW) filter. The proposed approach is based on a hybrid of frequency sampling and optimization (HFSO), that offers significant computational…
This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is…
Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is called a connection matrix.These matrices, a generalization…
A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…
The Dantzig selector is a widely used and effective method for variable selection in ultra-high-dimensional data. Feature splitting is an efficient processing technique that involves dividing these ultra-high-dimensional variable datasets…
In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely…
One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…
Neural Persistence is a prominent measure for quantifying neural network complexity, proposed in the emerging field of topological data analysis in deep learning. In this work, however, we find both theoretically and empirically that the…
Edges are a basic and fundamental feature in image processing, that are used directly or indirectly in huge amount of applications. Inspired by the expansion of image resolution and processing power dilated convolution techniques appeared.…
Zig-Zag is Piecewise Deterministic Markov Process, efficiently used for simulation in an MCMC setting. As we show in this article, it fails to be exponentially ergodic on heavy tailed target distributions. We introduce an extension of the…
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…
Particle filtering methods are widely applied in sequential state estimation within nonlinear non-Gaussian state space model. However, the traditional particle filtering methods suffer the weight degeneracy in the high-dimensional state…
Feature selection is a vital technique in machine learning, as it can reduce computational complexity, improve model performance, and mitigate the risk of overfitting. However, the increasing complexity and dimensionality of datasets pose…
In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…
Reducing a set of numbers to a single value is a fundamental operation in applications such as signal processing, data compression, scientific computing, and neural networks. Accumulation, which involves summing a dataset to obtain a single…
We present FastGPL, a C++ library for the fast evaluation of generalized polylogarithms which appear in many multi-loop Feynman integrals. We implement the iterative algorithm proposed by Vollinga and Weinzierl in a two-step approach, i.e.,…
Fuzzing consists of repeatedly testing an application with modified, or fuzzed, inputs with the goal of finding security vulnerabilities in input-parsing code. In this paper, we show how to automate the generation of an input grammar…
In Zigbee backscatter systems, tags piggyback information by adding phase shifts to the RF carriers. The instantaneous-phase shift (IPS) modulation adds phase shifts by toggling between discrete phases, which is easy to realize and is…