Related papers: On the Method of Brackets

Firstly, a sequential symmetry adaptation procedure is derived for semidirect product groups. Then, this sequential symmetry adaptation procedure is used in the development of new method named Monomer Basis Representation (MBR) for…

In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential…

Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…

The multi-armed bandit (MAB) model is one of the most classical models to study decision-making in an uncertain environment. In this model, a player chooses one of $K$ possible arms of a bandit machine to play at each time step, where the…

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this…

We present and derive a technique for the introduction of defects into a beam model based on the Cosserat theory of rods. The technique is designed for the derivation of component models of non-ideal rods for use in MEMS devices. We also…

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2eps dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop…

Representing large-scale motions and topological changes in the finite volume (FV) framework, while at the same time preserving the accuracy of the numerical solution, is difficult. In this paper, we present a robust, highly efficient…

This work introduces B-spline Movement Primitives (BMPs), a new Movement Primitive (MP) variant that leverages B-splines for motion representation. B-splines are a well-known concept in motion planning due to their ability to generate…

Representation learning on multi-omics data is challenging due to extreme dimensionality, modality heterogeneity, and cohort-specific batch effects. While pre-trained transformer backbones have shown broad generalization capabilities in…

Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…

This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF)…

Feynman integrals may be represented by the Mathematica packages AMBRE and MB as multiple Mellin-Barnes integrals. With the Mathematica package MBsums these Mellin-Barnes integrals are transformed into multiple sums.

We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…

Mixture-of-Experts (MoE) architectures enhance the efficiency of large language models by activating only a subset of experts per token. However, standard MoE employs a fixed Top-K routing strategy, leading to redundant computation and…

The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…

This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…

In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…