Related papers: Decomposing Multiparameter Persistence Modules
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Most existing studies on evolutionary multi-objective optimization focus on approximating the whole Pareto-optimal front. Nevertheless, rather than the whole front, which demands for too many points (especially in a high-dimensional space),…
We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to…
Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
Missing values are pervasive in large-scale time-series data, posing challenges for reliable analysis and decision-making. Many neural architectures have been designed to model and impute the complex and heterogeneous missingness patterns…
As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
Multiple patterning lithography has been widely adopted in advanced technology nodes of VLSI manufacturing. As a key step in the design flow, multiple patterning layout decomposition (MPLD) is critical to design closure. Due to the…
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…
This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many…
The theory of persistence modules on the commutative ladders $CL_n(\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…