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Wireless networks are very popular nowadays. Wireless Local Area Network (WLAN) that uses the IEEE 802.11 standard and WiMAX (Worldwide Interoperability for Microwave Access) that uses the IEEE 802.16 standard are networks that we want to…
The design of convolutional neural architectures that are exactly equivariant to continuous translations is an active field of research. It promises to benefit scientific computing, notably by making existing imaging systems more physically…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make…
This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…
Human language can be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and neighboring words in sentences are connected by edges. It was recently found (Ferrer and…
There have been several attempts to mathematically understand neural networks and many more from biological and computational perspectives. The field has exploded in the last decade, yet neural networks are still treated much like a black…
Over the years, with the advancement of technology, Web technology has many improvements. In the early days, the web was one-way communication, and only the customer was able to see the content of the site and could not enter information.…
Research on the robustness of the Internet has gained critical importance in the last decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business…
Real-world networks typically exhibit several aspects, or layers, of interactions among their nodes. By permuting the role of the nodes and the layers, we establish a new criterion to construct the dual of a network. This approach allows to…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
Network embeddings, which learn low-dimensional representations for each vertex in a large-scale network, have received considerable attention in recent years. For a wide range of applications, vertices in a network are typically…
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that…
Recent research, such as BitNet, is paving the way for a new era of 1-bit Large Language Models (LLMs). In this work, we introduce a 1-bit LLM variant, namely BitNet b1.58, in which every single parameter (or weight) of the LLM is ternary…
In this paper we examine how concurrency has been embodied in mainstream programming languages. In particular, we rely on the evolutionary talking borrowed from biology to discuss major historical landmarks and crucial concepts that shaped…
The ubiquity of networking infrastructure in modern life necessitates scrutiny into networking fundamentals to ensure the safety and security of that infrastructure. The formalization of concurrent algorithms, a cornerstone of networking,…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…