Related papers: Modular links: Bunch algorithm and upper volume bo…
A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…
The smallest known example of a family of modular categories that is not determined by its modular data are the rank 49 categories $\mathcal{Z}(\text{Vec}_G^{\omega})$ for $G=\mathbb{Z}_{11} \rtimes \mathbb{Z}_{5}$. However, these…
In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly,…
This paper introduces a new algebra, the crossing algebra, that is applied to count the number of components for arborescent knots, links, tangles or states (of a state polynomial expansion such as the Kauffman bracket). This algebra is…
We show that the volume of any Montesinos link can be bounded above and below in terms of the combinatorics of its diagram. This was known for Montesinos links with at most two tangles, and those with at least five tangles. We complete the…
We present a novel algorithm, called Links, designed to perform online clustering on unit vectors in a high-dimensional Euclidean space. The algorithm is appropriate when it is necessary to cluster data efficiently as it streams in, and is…
Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…
This paper proposes a deep convolutional neural network model for ordinal regression by considering a family of probabilistic ordinal link functions in the output layer. The link functions are those used for cumulative link models, which…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
Recommendation algorithms that incorporate techniques from deep learning are becoming increasingly popular. Due to the structure of the data coming from recommendation domains (i.e., one-hot-encoded vectors of item preferences), these…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
While Branch and Bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective Branch and Bound methods are only rarely applied compared to the predominant objective space…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
Over the past decade, community detection in overlapping un-weighted networks, where nodes can belong to multiple communities, has been one of the most popular topics in modern network science. However, community detection in overlapping…
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and…
Ontology alignment, a critical process in the Semantic Web for detecting relationships between different ontologies, has traditionally focused on identifying so-called "simple" 1-to-1 relationships through class labels and properties…
The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner)…
The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with…
In Guts, Volume and Skein Modules of 3-Manifolds (arXiv:2010.06559), we showed that the twist number of certain hyperbolic weakly generalized alternating links can be recovered from a Jones-like polynomial, and offers a lower bound for the…