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A key motivation in the development of Distributed Model Predictive Control (DMPC) is to accelerate centralized Model Predictive Control (MPC) for large-scale systems. DMPC has the prospect of scaling well by parallelizing computations…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
The goal of this introductory survey is to present the major developments of algorithmic randomness with an eye toward its historical development. While two highly comprehensive books and one thorough survey article have been written on the…
In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
Machine learning techniques are now routinely encountered in research laboratories across the globe. Impressive progress has been made through ML and AI techniques with regards to large data set processing. This progress has increased the…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Today's distributed and pervasive computing addresses large-scale cyber-physical ecosystems, characterised by dense and large networks of devices capable of computation, communication and interaction with the environment and people. While…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
A system that could reliably identify and sum up the most important points of a conversation would be valuable in a wide variety of real-world contexts, from business meetings to medical consultations to customer service calls. Recent…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Collaborative filtering is amongst the most preferred techniques when implementing recommender systems. Recently, great interest has turned towards parallel and distributed implementations of collaborative filtering algorithms. This work is…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
In distributed optimization and machine learning, multiple nodes coordinate to solve large problems. To do this, the nodes need to compress important algorithm information to bits so that it can be communicated over a digital channel. The…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…