Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give...

The aim of this work is to study N−dual structures of representable implications generated from a set M of aggregation functions and pairs of mutual dual functions, founded on the isomorphism between the unit interval and special instances of the Goguen’s L-fuzzy sets. We discuss under which conditions representable functions preserve the main properties of their N−dual interval approach.

Background: Parkinson Disease (PD) is characterized by motor and non-motor symptoms that affect patients’ functions, especially while performing dual tasks--a critical factor in everyday living. However, many controversies exist about the benefits of dual-task training in patients with PD. Objectives: This study assessed the efficacy of motor and cognitive dual-task training in improving balanc...

Dual-feasible functions have been used in the broad area of combinatorial optimization to compute bounds and cutting planes for integer programming problems. These functions have been rediscovered recently, and studied in depth in different articles published in the literature. In this paper, we propose a new strategy for building families of staircase maximal dual-feasible functions using the ...