5 citations · 6 across the 9 of their papers we have counts for
9 papers
Analytic integration of metric-valued functions in Lipschitz free spaces
Roger Arnau, Álvaro González Cortés, Enrique A. Sánchez Pérez
We develop an integration theory for functions taking values in a metric space. Following a Bochner-type construction, we define the concept of free integral as an element of the L…
Diagonalization of nonlinear functions in finite-dimensional spaces and the case of
Roger Arnau, Juan Carlos Cortés López, Álvaro González Cortés +1
This paper introduces a new theoretical framework for the diagonalization of nonlinear functions defined in finite-dimensional real Euclidean spaces. Extending classical results fr…
Lattice Lipschitz operators on space
Roger Arnau, Jose M. Calabuig, Enrique A. Sánchez-Pérez
Given a Banach lattice the space of lattice Lipschitz operators on has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and…
A Bellman-Ford algorithm for the path-length-weighted distance in graphs
R. Arnau, J. M. Calabuig, L. M. García Raffi +2
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distanc…
Eccentric summing Lipschitz operators and integral inequalities on metric spaces and graphs
R. Arnau, E. A. Sánchez Pérez, S. Sanjuan
The extension of the concept of summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This resea…
Lattice Lipschitz superposition operators on Banach function spaces
Roger Arnau, Jose M. Calabuig, Ezgi Erdoğan +1
We analyse and characterise the notion of lattice Lipschitz operator (a class of superposition operators, diagonal Lipschitz maps) when defined between Banach function spaces. Afte…
Moduli of Continuity in Metric Models and Extension of Liveability Indices
R. Arnau, J. M. Calabuig, Álvaro González +1
Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real…
Easy attention: A simple attention mechanism for temporal predictions with transformers
Marcial Sanchis-Agudo, Yuning Wang, Roger Arnau +4
To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention whic…
Approximation of almost diagonal non-linear maps by lattice Lipschitz operators
Roger Arnau, Jose M. Calabuig, Ezgi Erdoğan +1
Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the dimensi…