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First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
This study introduces a novel training paradigm, audio difference learning, for improving audio captioning. The fundamental concept of the proposed learning method is to create a feature representation space that preserves the relationship…
Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been…
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…
This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…
Constraint Handling Rules (CHR) is a high-level programming language based on multi-headed multiset rewrite rules. Originally designed for writing user-defined constraint solvers, it is now recognized as an elegant general purpose language.…
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows…
Differential categories were introduced by Blute, Cockett, and Seely as categorical models of differential linear logic and have since lead to abstract formulations of many notions involving differentiation such as the directional…
In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from…
We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b)…
Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…
Hierarchical clustering is a common algorithm in data analysis. It is unique among many clustering algorithms in that it draws dendrograms based on the distance of data under a certain metric, and group them. It is widely used in all areas…
The Hausdorff $\delta$-dimension game was introduced by Das, Fishman, Simmons and {Urba{\'n}ski} and shown to characterize sets in $\mathbb{R}^d$ having Hausdorff dimension $\leq \delta$. We introduce a variation of this game which also…
We define hierarchies of differential--q-difference equations, which are q-deformations of the equations of the generalized KdV hierarchies. We show that these hierarchies are bihamiltonian, one of the hamiltonian structures being that of…
We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
This paper proves a version for stochastic differential equations of the Lie-Scheffers Theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution…