Related papers: Computing the Skyscraper Invariant
The Harder-Narasimhan type of a quiver representation is a discrete invariant parameterised by a real-valued function (called a central charge) defined on the vertices of the quiver. In this paper, we investigate the strength and…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
We present our novel evolutionary algorithm for generating Special Quasirandom Structures (SQS) designed to optimize the computational efficiency of Density Functional Theory (DFT) computations. Operating on the premise that symmetry…
Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can…
With their high energy efficiency, processing-in-memory (PIM) arrays are increasingly used for convolutional neural network (CNN) inference. In PIM-based CNN inference, the computational latency and energy are dependent on how the CNN…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
We present a versatile open-source framework designed to facilitate efficient, numerically-tailored Matrix-Matrix Multiplications (MMMs). The framework offers two primary contributions: first, a fine-tuned, automated pipeline for arithmetic…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…
It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new…
Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable…
Let $M$ be a representation of an acyclic quiver $Q$ over an infinite field $k$. We establish a deterministic algorithm for computing the Harder-Narasimhan filtration of $M$. The algorithm is polynomial in the dimensions of $M$, the weights…
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham…
It is well-known that the cohomology ring has a richer structure than homology groups. However, until recently, the use of cohomology in persistence setting has been limited to speeding up of barcode computations. Some of the recently…
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a…
Precise reconstruction of top quark properties is a challenging task at the Large Hadron Collider due to combinatorial backgrounds and missing information. We introduce a physics-informed neural network architecture called the Covariant…
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…