Mathematics: Fully Funded EPSRC and Swansea University PhD Scholarship: Reconstruction of Mixed-Up Messages (RS458)

Funding providers: EPSRC and Swansea University's Faculty of Science and Engineering

Subject areas: Mathematics, Probability, Information theory, Efficient Algorithms

Project start date: 

• 1 October 2024 (Enrolment open from mid-September)
• 1 January 2025 (Enrolment open from mid-December)

Supervisors:

• Dr Angelica Pachon (Primary Supervisor - a.y.pachon@swansea.ac.uk)
• Dr Dmtri Finkelshtein (Secondary Supervisor)
• Professor Gibin Powathil (Additional Supervisor)

Aligned programme of study: PhD in Mathematics

Mode of study: Full-time 

Project description: 

A famous problem in probability, information theory and theoretical computer science is the following: A long message over a finite alphabet is sent via an information channel. Now suppose that the message that arrives at the receiver is not the original one, but a randomly corrupted version. Suppose further that the receiver knows the random mechanism corrupting the message. Now the question is: Can the receiver recover the original message?

To formulate this mathematically, suppose that to each integer number a letter from the finite alphabet is assigned and a simple random walk runs on the integers. At each time t it registers the letter it observes at its current position. This produces a new random sequence of letters. Now the question is: Can the original message be reconstructed with probability one from this newly created random sequence? In general, it cannot, but under appropriate restrictions, it can. Lindenstrauss (1999) showed that there are messages which cannot be reconstructed. However, it is known that almost surely a “typical” message, drawn at random according to a given distribution, can be reconstructed (possibly up to shift and/or reflection).

A natural extension of this problem is to consider it in higher dimensions. In the proposed project we want focus dimension two, which is a critical case, and understand under which conditions a finite piece of the message can be reconstructed in polynomial time (polynomial in relation to the size of the piece reconstructed). In addition, we aim to provide a concrete algorithm that achieves this reconstruction without using supercomputers and quantum computers.

Candidates must hold an Upper Second Class (2.1) honours degree or an appropriate master’s degree with a minimum overall grade at ‘Merit’ in a closely related discipline. If you are eligible to apply for the scholarship (i.e. a student who is eligible to pay the UK rate of tuition fees) but do not hold a UK degree, you can check our comparison entry requirements (see country specific qualifications). Please note that you may need to provide evidence of your English Language proficiency. 

English Language: IELTS 6.0 Overall (with no individual component below 5.5) or Swansea University recognised equivalent. Full details of our English Language policy, including certificate time validity, can be found here.

The candidate is expected to have a strong mathematical background. Computational and programming skills in one or more programming languages such as Python or Matlab are preferred. Strong interpersonal skills and the capacity to work and learn independently will be required.

This scholarship is open to candidates of any nationality.

EPSRC funded studentships are available to home and international students. Up to 30% of our cohort can comprise international students, once the limit has been reached, we are unable to make offers to international students.  

We are still accepting applications from international applicants.   

International students will not be charged the fee difference between the UK and international rate. Applicants should satisfy the UKRI eligibility requirements. 

ATAS

Please note that the programme requires some applicants to hold ATAS clearance, further details on ATAS scheme eligibility are available on the UK Government website. 

ATAS clearance IS NOT required to be held as part of the scholarship application process, successful award winners (as appropriate) are provided with details as to how to apply for ATAS clearance in tandem with scholarship course offer. 

If you have any questions regarding your academic or fee eligibility based on the above, please email pgrscholarships@swansea.ac.uk with the web-link to the scholarship(s) you are interested in. 

This scholarship covers the full cost of tuition fees and an annual stipend at UKRI rate (currently £18,622 for 2023/24).

Additional research expenses will also be available.

To apply, please complete your application online with the following information:

1. Course choice – please select Mathematics / PhD / Full-time / 3 Year / October

   In the event you have already applied for the above programme previously, the application system may issue a warning notice and prevent application, in this event, please email pgrscholarships@swansea.ac.uk where staff will be happy to assist you in submitting your application.

2. Start year – please select 2024
3. Funding (page 8) –

• ‘Are you funding your studies yourself?’ – please select No
• ‘Name of Individual or organisation providing funds for study’ – please enter ‘RS458 - Mixed Up Messages’

*It is the responsibility of the applicant to list the above information accurately when applying, please note that applications received without the above information listed will not be considered for the scholarship award.

One application is required per individual Swansea University led research scholarship award; applications cannot be considered listing multiple Swansea University led research scholarship awards.

We encourage you to complete the following to support our commitment to providing an environment free of discrimination and celebrating diversity at Swansea University: 

• Equality, Diversity and Inclusion (EDI) Monitoring Form (online form) 

As part of your online application, you MUST upload the following documents (please do not send these via email):

• CV
• Degree certificates and transcripts (if you are currently studying for a degree, screenshots of your grades to date are sufficient)
• A cover letter including a ‘Supplementary Personal Statement’ to explain why the position particularly matches your skills and experience and how you choose to develop the project.
• Two references (academic or previous employer) on headed paper or using the Swansea University reference form. Please note that we are not able to accept references received citing private email accounts, e.g. Hotmail. Referees should cite their employment email address for verification of reference.
• Evidence of meeting English Language requirement (if applicable).
• Copy of UK resident visa (if applicable)
• Confirmation of EDI form submission (optional) 

Informal enquiries are welcome, please contact Dr Angelica Pachon (a.y.pachon@swansea.ac.uk).

*External Partner Application Data Sharing – Please note that as part of the scholarship application selection process, application data sharing may occur with external partners outside of the University, when joint/co- funding of a scholarship project is applicable.