Mon, 13 May 2024

14:00 - 15:00
Lecture Room 3

Compression of Graphical Data

Mihai Badiu
(Department of Engineering Science University of Oxford)
Abstract

Data that have an intrinsic network structure can be found in various contexts, including social networks, biological systems (e.g., protein-protein interactions, neuronal networks), information networks (computer networks, wireless sensor networks),  economic networks, etc. As the amount of graphical data that is generated is increasingly large, compressing such data for storage, transmission, or efficient processing has become a topic of interest. In this talk, I will give an information theoretic perspective on graph compression. 

The focus will be on compression limits and their scaling with the size of the graph. For lossless compression, the Shannon entropy gives the fundamental lower limit on the expected length of any compressed representation. I will discuss the entropy of some common random graph models, with a particular emphasis on our results on the random geometric graph model. 

Then, I will talk about the problem of compressing a graph with side information, i.e., when an additional correlated graph is available at the decoder. Turning to lossy compression, where one accepts a certain amount of distortion between the original and reconstructed graphs, I will present theoretical limits to lossy compression that we obtained for the Erdős–Rényi and stochastic block models by using rate-distortion theory.

Mon, 19 Feb 2024

14:00 - 15:00
Lecture Room 3

This seminar has been cancelled

Mihai Badiu
(Department of Engineering Science University of Oxford)
Abstract

Data that have an intrinsic network structure can be found in various contexts, including social networks, biological systems (e.g., protein-protein interactions, neuronal networks), information networks (computer networks, wireless sensor networks),  economic networks, etc. As the amount of graphical data that is generated is increasingly large, compressing such data for storage, transmission, or efficient processing has become a topic of interest. 

In this talk, I will give an information theoretic perspective on graph compression. The focus will be on compression limits and their scaling with the size of the graph. For lossless compression, the Shannon entropy gives the fundamental lower limit on the expected length of any compressed representation. 
I will discuss the entropy of some common random graph models, with a particular emphasis on our results on the random geometric graph model. 
Then, I will talk about the problem of compressing a graph with side information, i.e., when an additional correlated graph is available at the decoder. Turning to lossy compression, where one accepts a certain amount of distortion between the original and reconstructed graphs, I will present theoretical limits to lossy compression that we obtained for the Erdős–Rényi and stochastic block models by using rate-distortion theory.

Tue, 26 Jan 2021
14:30
Virtual

The construction of stable and div-free finite elements via Stokes complexes

Duygu Sap
(Department of Engineering Science University of Oxford)
Abstract
In this talk, we describe the methodology for constructing a divergence-free and stable pair of finite element spaces for the Stokes problem on cubical meshes of arbitrary dimension. We use the Stokes complex as a guiding tool. We state and exemplify the general procedure for deriving a divergence-free and stable finite element discretization from a Stokes complex. However, we develop a new strategy to prove the necessary inf-sup stability condition due to the lack of a Fortin operator. In particular, we first derive a local inf-sup condition with imposed boundary conditions and then translate this result to the global level by exploiting the element's degrees of freedom. Furthermore, we derive reduced finite elements with less global degrees of freedom. We show that the optimal order of convergence is achieved via both the original and reduced finite elements for the velocity approximation, and the pressure approximation is of optimal order when the reduced finite elements are used.
 
Ref. Stokes elements on cubic meshes yielding divergence-free approximations, M. Neilan and D. Sap, Calcolo, 53(3):263-283, 2016. 
 
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A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact @email.

 

Fri, 15 Jun 2018

14:00 - 15:00
L2

Entering the cranial vault: imaging the fetal brain with ultrasound

Dr Ana Namburete
(Department of Engineering Science University of Oxford)
Abstract

Ultrasound (US) imaging is one of the first steps in a continuum of pregnancy care. During the fetal period, the brain undergoes dramatic structural changes, many of which are informative of healthy maturation. The resolution of modern US machines enables us to observe and measure brain structures, as well as detect cerebral abnormalities in fetuses from as early as 18 weeks. Recent breakthroughs in machine learning techniques for image analysis introduce opportunities to  develop bespoke methods to track spatial and temporal patterns of fetal brain development. My work focuses on the design of appropriate data-driven techniques to extract developmental information from standard clinical US images of the brain.

 

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