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The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.
Why should computers interpret language incrementally? In recent years psycholinguistic evidence for incremental interpretation has become more and more compelling, suggesting that humans perform semantic interpretation before constituent…
Despite increasing interest in the field of Interpretable Machine Learning (IML), a significant gap persists between the technical objectives targeted by researchers' methods and the high-level goals of consumers' use cases. In this work,…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of…
We compute the nth derivative of a function given parametrically, and of one given implicitly, and some history for both problems. I am posting this version of the paper at the request of Shaul Zemel, whose forthcoming paper The…
Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional…
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
This paper presents an operational semantics for UML activity diagrams. The purpose of this semantics is three-fold: to give a robust basis for verifying model correctness; to help validate model transformations; and to provide a…
A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymaki et al. (2017, Global envelope tests for spatial processes, J. R. Statist.…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
This paper discusses the lexicographical concept of lexical functions and their potential exploitation in the development of a machine translation lexicon designed to handle collocations.
We show that it is possible to define a realizability interpretation for the $\Sigma_2$-fragment of classical Analysis using G\"odel's System T only. This supplements a previous result of Schwichtenberg regarding bar recursion at types 0…
We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some…
Task-oriented dialogue systems have become overwhelmingly popular in recent researches. Dialogue understanding is widely used to comprehend users' intent, emotion and dialogue state in task-oriented dialogue systems. Most previous works on…
Large language models demonstrate the intriguing ability to perform unseen tasks via in-context learning. However, it remains unclear what mechanisms inside the model drive such task-level generalization. In this work, we approach this…
Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…