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While the theory of labelled well-quasi-order has received significant attention in the graph setting, it has not yet been considered in the context of permutation patterns. We initiate this study here, and show how labelled well quasi…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We present a labelled and non-wellfounded calculus for the bimodal provability logic CS. The system is obtained by modelling the Kripke-like semantics of this logic. As in arXiv:2309.00532, we enforce the second-order property of converse…
A skeleton representation of the human body has been proven to be effective for this task. The skeletons are presented in graphs form-like. However, the topology of a graph is not structured like Euclidean-based data. Therefore, a new set…
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…
In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for…
Given a finite ribbon category, which is a particular case of a cyclic algebra over the operad of genus zero surfaces, there are two possibilities for an extension defined on all three-dimensional handlebodies: On the one hand, one can use…
We obtain explicit formulas for the enumeration of labelled parallelogram polyominoes. These are the polyominoes that are bounded, above and below, by north-east lattice paths going from the origin to a point (k,n). The numbers from 1 and n…
Subcortical segmentation in neuroimages plays an important role in understanding brain anatomy and facilitating computer-aided diagnosis of traumatic brain injuries and neurodegenerative disorders. However, training accurate automatic…
In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such…
Image clustering, which involves grouping images into different clusters without labels, is a key task in unsupervised learning. Although previous deep clustering methods have achieved remarkable results, they only explore the intrinsic…
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…
Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with…
Behavior Trees (BTs) have become a popular framework for designing controllers of autonomous agents in the computer game and in the robotics industry. One of the key advantages of BTs lies in their modularity, where independent modules can…
We give parallel algorithms for string diagrams represented as structured cospans of ACSets. Specifically, we give linear (sequential) and logarithmic (parallel) time algorithms for composition, tensor product, construction of diagrams from…
The point of this paper is to question typical assumptions in deep learning and suggest alternatives. A particular contribution is to prove that even if a Stacked Convolutional Auto-Encoder is good at reconstructing pictures, it is not…
The point of this paper is to question typical assumptions in deep learning and suggest alternatives. A particular contribution is to prove that even if a Stacked Convolutional Auto-Encoder is good at reconstructing pictures, it is not…
For humans, both the proprioception and touch sensing are highly utilized when performing haptic perception. However, most approaches in robotics use only either proprioceptive data or touch data in haptic object recognition. In this paper,…
Shared registers are basic objects used as communication mediums in asynchronous concurrent computation. A concurrent timestamp system is a higher typed communication object, and has been shown to be a powerful tool to solve many…
Let $(\mathcal C,\otimes,\mathbb 1)$ be an abelian symmetric monoidal category satisfying certain exactness conditions. In this paper we define a presheaf $\mathbb P^{n}_{\mathcal C}$ on the category of commutative algebras in $\mathcal C$…