Related papers: Spot-Based Generations for Meta-Fibonacci Sequence…
In this paper we extend a notion of Cassini determinant to recently introduced hyperfibonacci sequences. We find $Q$-matrix for the $r$-th generation hyperfibonacci numbers and prove an explicit expression of the Cassini determinant for…
Object detection and instance segmentation are dominated by region-based methods such as Mask RCNN. However, there is a growing interest in reducing these problems to pixel labeling tasks, as the latter could be more efficient, could be…
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…
We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…
Partial-label learning (PLL) is a multi-class classification problem, where each training example is associated with a set of candidate labels. Even though many practical PLL methods have been proposed in the last two decades, there lacks a…
The sequence $F_{dn+h}$ and its convolutions have (for $h=0$) been studied in a recent paper at the arxiv [arXiv:2603.08636]. The instance with general $h$ is more involved and uses Chebyshev polynomials.
We develop an algorithm which can learn from partially labeled and unsegmented sequential data. Most sequential loss functions, such as Connectionist Temporal Classification (CTC), break down when many labels are missing. We address this…
The present paper introduces the $\eta$ and {\eta} connections in order to add regional information on $\lambda$-flat zones, which only take into account a local information. A top-down approach is considered. First $\lambda$-flat zones are…
We introduce a class of sequences, defined by means of partial Bell polynomials, that contains a basis for the space of linear recurrence sequences with constant coefficients as well as other well-known sequences like Catalan and Motzkin.…
Sequence classification has a wide range of real-world applications in different domains, such as genome classification in health and anomaly detection in business. However, the lack of explicit features in sequence data makes it difficult…
Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level…
We define integer multimodal sequences, which are generalizations of unimodal sequences having multiple local peaks of equal size. The generating functions for multimodal sequences represent novel types of $q$-series that combine generating…
Semantic part localization can facilitate fine-grained categorization by explicitly isolating subtle appearance differences associated with specific object parts. Methods for pose-normalized representations have been proposed, but generally…
Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By…
We propose a simple yet effective method for detecting anomalous instances on an attribute graph with label information of a small number of instances. Although with standard anomaly detection methods it is usually assumed that instances…
Sequential sensor data is generated in a wide variety of practical applications. A fundamental challenge involves learning effective classifiers for such sequential data. While deep learning has led to impressive performance gains in recent…
We propose a simple yet effective instance segmentation framework, termed CondInst (conditional convolutions for instance segmentation). Top-performing instance segmentation methods such as Mask R-CNN rely on ROI operations (typically…
In this paper, some properties and applications of MV-algebras are provided. We define a Fibonacci sequence in an MV-algebra and we prove that such a stationary sequence gives us an idempotent element. Taking into account of the…
We give an $n$-space generalized $q$-binomial theorem, and some new $q$ series identities that resemble the traditional $q$ series partition generating functions. These identities enumerate stepping stone weighted vector partitions.
Multiple sequence alignment is a key process in today's biology, and finding a relevant alignment of several sequences is much more challenging than just optimizing some improbable evaluation functions. Our approach for addressing multiple…