Related papers: Computing with B-series
Transverse contraction methods are extremely promising tools for the efficient contraction of tensor networks associated with the time evolution of quantum many-body systems, allowing in some cases to circumvent the entanglement barrier…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are many ways to visualize these higher dimensional fractals…
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and then lift the modular results to the rationals. This method…
We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…
We present PEPSKit.jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit.jl builds on the TensorKit.jl package for tensor computations and provides…
The Yau-Yau nonlinear filter has increasingly emerged as a powerful tool to study stochastic complex systems. To leverage it to a wider spectrum of application scenarios, we pack the Yau-Yau filtering ALgorithms (YauYauAL) into a package of…
From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…
The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a…
In many population-based medical studies, the specific cause of death is unidentified, unreliable or even unavailable. Relative survival analysis addresses this scenario, outside of standard (competing risks) survival analysis, to…
The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment…
We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and Conditional Gradients variants for first-order constrained optimization. The package is designed with flexibility and high-performance in mind,…
The julia package integrates the Julia programming language into Stata. Users can transfer data between Stata and Julia, issue Julia commands to analyze and plot, and pass results back to Stata. Julia's econometric ecosystem is not as…
We present the Julia package PauliStrings ( https://github.com/nicolasloizeau/PauliStrings.jl ) for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
We present msmJAX, a Python package implementing the multilevel summation method with B-spline interpolation, a linear-scaling algorithm for efficiently evaluating electrostatic and other long-range interactions in particle-based…
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context…
Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their…
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…