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We establish a sequential Hopf's Lemma for higher order differential inequalities in one variable and give some applications of this result.
The concept of Central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg's Central Sets Theorem highlighted their rich combinatorial…
The languages generated by interval exchange transformations have been characterized by Ferenczi-Zamboni (2008) and Belov-Cernyatev (2010) under some extra conditions on the system. Lifting these conditions leads us to consider successively…
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary…
Large language models (LLMs) are increasingly deployed with hierarchical instruction schemes, where certain instructions (e.g., system-level directives) are expected to take precedence over others (e.g., user messages). Yet, we lack a…
In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Language technologies should be judged on their usefulness in real-world use cases. An often overlooked aspect in natural language processing (NLP) research and evaluation is language variation in the form of non-standard dialects or…
n this paper, we attempt to explain the emergence of the linguistic diversity that exists across the consonant inventories of some of the major language families of the world through a complex network based growth model. There is only a…
Stuttering is a speech impediment affecting tens of millions of people on an everyday basis. Even with its commonality, there is minimal data and research on the identification and classification of stuttered speech. This paper tackles the…
Speech disfluencies, such as filled pauses or repetitions, are disruptions in the typical flow of speech. Stuttering is a speech disorder characterized by a high rate of disfluencies, but all individuals speak with some disfluencies and the…
Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. In this…
We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension of related sets, originating in the pioneering work of…
In recent studies in hyperspectral imaging, biometrics and energy analytics, the framework of deep dictionary learning has shown promise. Deep dictionary learning outperforms other traditional deep learning tools when training data is…
This article introduces innovative classes of open sets in \(\mathbb{R}^{N}\), where \(N=2, 3\), characterized by a geometric property associated with the inward normal. The focus lies on proving compactness results for the Hausdorff…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of…
Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics,…