Related papers: Ripser: efficient computation of Vietoris-Rips per…
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
Reservoir computing (RC) has attracted attention as an efficient recurrent neural network architecture due to its simplified training, requiring only its last perceptron readout layer to be trained. When implemented with memristors, RC…
We introduce a new algorithm, Construction of dIfferentially Private Empirical Distributions from a low-order marginals set tHrough solving linear Equations with l2 Regularization (CIPHER), that produces differentially private empirical…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
Subdivision methods such as quadtrees, octrees, and higher-dimensional orthrees are standard practice in different domains of computer science. We can use these methods to represent given geometries, such as curves, meshes, or surfaces.…
The Rips filtration over a finite metric space and its corresponding persistent homology are prominent methods in TDA to summarise the shape of data. Crucial to their use is the bottleneck stability result. A generalisation of the Rips…
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For $n$ points in $\mathbb{R}^d$,…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
A family of simplicial complexes, connected with simplicial maps and indexed by a poset $P$, is called a poset tower. The concept of poset towers subsumes classical objects of study in the persistence literature, as, for example,…
We introduce a refinement of persistent homology that detects simple-homotopy-theoretic phenomena invisible to homology. Given a filtered simplicial complex, we define the Morse complexity profile as the minimal number of critical simplices…
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…
Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
In both observational data and randomized control trials, researchers select statistical models to articulate how the outcome of interest varies with combinations of observable covariates. Choosing a model that is too simple can obfuscate…
Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here…
We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…