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A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We present the Sum-Product Probabilistic Language (SPPL), a new probabilistic programming language that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL translates probabilistic programs into…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
Nonlinear dimension reduction methods provide a low-dimensional representation of high-dimensional data by applying a Nonlinear transformation. However, the complexity of the transformations and data structures can create wildly different…
The publicly available package for an automated dipole subtraction, AutoDipole, is extended to include the SUSY dipoles in the MSSM. All fields in the SM and the MSSM are available. The code is checked against the analytical expressions for…
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
We introduce the non-SUSY orbifolder, which is a program developed in C++ that computes the low-energy effective theory of non-supersymmetric heterotic orbifold compactifications. The program includes routines to compute the massless…
A graphical representation of supersymmetry is presented. It clearly expresses the chiral flow appearing in SUSY quantities, by representing spinors by {\it directed lines} (arrows). The chiral suffixes are expressed by the directions (up,…
We present celmech, an open-source Python package designed to facilitate a wide variety of celestial mechanics calculations. The package allows users to formulate and integrate equations of motion incorporating user-specified terms from the…
A graphical representation of supersymmetry is presented. It clearly expresses the chiral flow appearing in SUSY quantities, by representing spinors by {\it directed lines} (arrows). The chiral suffixes are expressed by the directions (up,…
A new simulation package, GSEIM, for solving a set of ordinary differential equations is presented. The organisation of the program is illustrated with the help of a block diagram. Various features of GSEIM are discussed. Two ways of…
Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
The simplest supersymmetry (SUSY) algebra in four dimensional Euclidean space ($4dE$) has been shown to closely resemble the $N = 2$ SUSY algebra in four dimensional Minkowski space ($4dM$). The structure of the former algebra is examined…
This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
Simulated high-dimensional data is useful for testing, validating, and improving algorithms used in dimension reduction, supervised and unsupervised learning. High-dimensional data is characterized by multiple variables that are dependent…
In this letter we show that supersymmetry like geometry can be approximated using finite dimensional matrix models and fuzzy manifolds. In particular we propose a non-perturbative regularization of {\cal N}=2 supersymmetric U(n) gauge…
We introduce Diddy, a collection of Python scripts for analyzing infinite discrete dynamical systems. The main focus is on generalized multidimensional shifts of finite type (SFTs). We show how Diddy can be used to easily define SFTs and…