Related papers: Master's thesis: Permutations With Restricted Move…

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…

Real-world networks are composed of diverse interacting and evolving entities, while most of existing researches simply characterize them as particular static networks, without consideration of the evolution trend in dynamic networks.…

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…

In this undergraduate thesis, we expand on the study of statistics on restricted growth functions avoiding patterns initiated by Campbell, et. al. Restricted growth functions are of interest because they are in bijection with set…

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has…

First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…

The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…

Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…

This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…

We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…

Transformer-based entropy models have gained prominence in recent years due to their superior ability to capture long-range dependencies in probability distribution estimation compared to convolution-based methods. However, previous…

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream…

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…

We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning…

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…