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The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm…

This paper presents a SysML-based approach to enhance functional and software development process within an industrial context. The recent changes in technology such as electromobility and increased automation in heavy construction…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

Necessary and/or sufficient conditions are studied for the existence, uniqueness and holonomicity of bases in which on sufficiently general subsets of a differentiable manifold the components of derivations of the tensor algebra over it…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will…

Task and motion planning problems in robotics combine symbolic planning over discrete task variables with motion optimization over continuous state and action variables. Recent works such as PDDLStream have focused on optimistic planning…

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional approaches to tensor eigenvalue analysis often extend…

Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…

The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…

Executing multiple tasks concurrently is important in many robotic applications. Moreover, the prioritization of tasks is essential in applications where safety-critical tasks need to precede application-related objectives, in order to…

The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…