Related papers: Mathematics of the MML functional quantizer module…
There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present \texttt{VolCE}, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume…
In this article, we present musicaiz, an object-oriented library for analyzing, generating and evaluating symbolic music. The submodules of the package allow the user to create symbolic music data from scratch, build algorithms to analyze…
In this paper, we explore the application of Large Language Models (LLMs) to the pre-training of music. While the prevalent use of MIDI in music modeling is well-established, our findings suggest that LLMs are inherently more compatible…
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions…
Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
Synthesizing a reactive system from specifications given in linear temporal logic (LTL) is a classical problem, finding its applications in safety-critical systems design. These systems are typically represented using either Mealy machines…
Knowledge of quantum mechanical systems is becoming more important for many science and engineering students who are looking to join the emerging quantum workforce. To better prepare a wide range of students for these careers, we must seek…
Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first…
This paper introduces Modular Linear Tokenization (MLT), a reversible and deterministic technique for encoding high-cardinality categorical identifiers into compact numerical vectors. Unlike traditional hashing or one-hot encodings, MLT…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…
Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment…
$\mathtt{qnm}$ is an open-source Python package for computing the Kerr quasinormal mode frequencies, angular separation constants, and spherical-spheroidal mixing coefficients. The $\mathtt{qnm}$ package includes a Leaver solver with the…
Despite their ability to understand chemical knowledge, large language models (LLMs) remain limited in their capacity to propose novel molecules with desired functions (e.g., drug-like properties). In addition, the molecules that LLMs…
This paper presents a new hybrid Quantum Machine Learning (QML) model composed of three elements: a classical computer in charge of the data preparation and interpretation; a Gate-based Quantum Computer running the Variational Quantum…
SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials…
Modeling complex semiconductor fabrication processes such as Ohmic contact formation remains challenging due to high-dimensional parameter spaces and limited experimental data. While classical machine learning (CML) approaches have been…
We study Fourier multipliers with logarithmic oscillation at high frequency. The guiding example is the radial symbol \[ m_{\gamma,\beta}(\xi) = \bigl(\log(e+|\xi|)\bigr)^{-\beta} e^{i(\log(e+|\xi|))^\gamma}, \qquad \gamma>1, \] whose…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…