Related papers: Self-modified difference ascent sequences

In this paper we collect some results about arithmetic progressions of higher order, also called polynomial sequences. Those results are applied to $(m,q)$-isometric maps.

In this paper, several variants of the ascent-plateau statistic are introduced, including flag ascent-plateau, double ascent and descent-plateau. We first study the flag ascent-plateau statistic on Stirling permutations by using…

The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for the sign change counting function is given where classical…

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old…

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label…

The combined work of Bousquet-M\'elou, Claesson, Dukes, Jel\'inek, Kitaev, Kubitzke and Parviainen has resulted in non-trivial bijections among ascent sequences, (2+2)-free posets, upper-triangular integer matrices, and pattern-avoiding…

Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model…

We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In…

Preceptron model updating with back propagation has become the routine of deep learning. Continuous feed forward procedure is required in order for backward propagate to function properly. Doubting the underlying physical interpretation on…

We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…

Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…

The Hadamard Extension of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. This construction arises in the context of identifying a mixture of product distributions on binary random variables: full column…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…

We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is…

The change point is a moment of an abrupt alteration in the data distribution. Current methods for change point detection are based on recurrent neural methods suitable for sequential data. However, recent works show that transformers based…

Contemporary machine learning models, including large language models, exhibit remarkable capabilities in static tasks yet falter in non-stationary environments due to rigid architectures that hinder continual adaptation and lifelong…

In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…

Over the past decade, Deep Convolutional Neural Networks (DCNNs) have shown remarkable performance in most computer vision tasks. These tasks traditionally use a fixed dataset, and the model, once trained, is deployed as is. Adding new…

We introduce the problem of performing set-difference range queries, where answers to queries are set-theoretic symmetric differences between sets of items in two geometric ranges. We describe a general framework for answering such queries…

In many classification problems, we want a classifier that is robust to a range of non-semantic transformations. For example, a human can identify a dog in a picture regardless of the orientation and pose in which it appears. There is…