VANGUARD- Postdoc in Network Tensor Completion 10784

VANGUARD- Postdoc in Network Tensor Completion 10784

Mohammed VI Polytechnic University is an institution oriented towards applied research and innovation with a focus on Africa.

About Mohammed VI Polytechnic University (UM6P):

Located at the heart of the Green City of Benguerir, Mohammed VI Polytechnic University (UM6P) was established to serve Morocco and the African continent and to advance applied research and innovation. This unique university, with state-of-the-art infrastructure, has woven an extensive academic and research network, and its recruitment process is seeking outstanding academics and professionals to promote Morocco and Africa’s innovation ecosystem.

About the department

Vanguard works on the development of innovative and interdisciplinary applied research projects. From technological innovation to the transfer of research to industry, Vanguard has also the mission of developing an ecosystem of related start-ups. For more information about our Center, please visit our webpage: Vanguard Center.

A network is a set of objects that are connected to each other in some fashion. Mathematically, a network is represented by a graph, which is a collection of nodes that are connected to each other by edges. The nodes represent the objects of the network and the edges represent relationships between objects.

However, adjacency matrices only model networks with one kind of objects or relations between the objects. Many real-world networks have a multidimensional nature such as networks that contain multiple connections. For instance, transport networks in a country when considering different means of transportation. These kinds of situations can be modeled using multilayer networks which emphasize the different kinds or levels, known as layers, of connections between the elements of the network.

In order to capture the structure and complexity of relationships between the nodes of networks with a multidimensional nature, tensors are used to represent these kinds of networks. The transport network mentioned earlier would be represented by a 4th order tensor A 2RN_L_N_L where L is the number of the layers and N is the number of nodes. Using convenient tensor products, the goal is to define measures to analyze different multidimensional networks based on their adjacency tensors.

However, collecting all the interactions in the systems and sometimes even observing all the components is a challenging task. In most cases, only a sample of a network is observed. Therefore, network completion needs to be addressed. Matrix completion methods have proved to be efficient when reconstructing non-fully observed data. These methods can be applied to complete or predict links in a network.

The problem of network completion arises also for applications where the network has a multidimensional representation such as multiplexes and multilayer networks. Since multidimensional networks can be represented by tensors, one can think of applying tensor completion methods which have proved to be efficient in many applications.

An important constraint in network completion is that the factorization must only capture the non-zero entries of the tensor. The remaining entries are treated as missing values. Therefore, the next step in this project is to address sparse optimization for tensors. We propose the integration of randomized algorithms into sparse optimization frameworks for the purpose of completing multidimensional networks.

Job responsibilities

• Research and Development: Conduct research to develop novel algorithms and methodologies for tensor completion in multidimensional networks.
• Algorithm Design: Design and implement algorithms for tensor completion, considering the unique challenges posed by sparse and multidimensional network data.
• Tensor Analysis: Analyze the structure and properties of multidimensional networks represented as tensors.
• Sparse Optimization: Address the challenge of sparse optimization for tensors by integrating randomized algorithms into optimization frameworks.
• Parallel Computing: Explore opportunities for parallelism in the tensor completion process to enhance computational efficiency.
• Collaboration: Collaborate with interdisciplinary teams including computer scientists, statisticians, and domain experts.
• Publication and Dissemination: Publish research findings in top-tier journals and present results at conferences and workshops.
• Mentorship and Training: Provide mentorship and guidance to graduate students and junior researchers involved in related projects.

Qualifications and experience essential

PhD in Applied Mathematics in the fields of Numerical Linear Algebra, or equivalent. Prior experience on the subject is highly desired.

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Job details

Title: VANGUARD- Postdoc in Network Tensor Completion 10784