maths cambridge thesis

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How do I find a Cambridge thesis?

Ph.D., M.Litt., M.Sc., and Divinity M.Phil. theses approved after 1970 are catalogued in iDiscover, as are M.D. and M.Chir. theses approved after May 2006. Earlier theses are listed in a card catalogue in the Manuscripts Reading Room and are gradually being added to iDiscover.

Since 1 October 2017, all PhD theses are being deposited in electronic form to the University repository Apollo . Many earlier theses are also in the repository, but if they are not yet in digital form it is possible to request access to these theses. There is more information on how to request a copy of a printed thesis further down this page.

Gaining access to electronic copies of a thesis

The author of a given thesis in Apollo can choose whether their thesis is available to be downloaded, available on request or unavailable. While many of the theses in Apollo are openly available for download, some theses in the repository are not open access because they have either been embargoed by the author or because they are unable to be made openly available for copyright or other reasons.

Requesting a copy of a printed thesis

Researchers can order a copy of an unpublished thesis which was deposited in print form through the Library’s Digital Content Unit via the image request form . Copies of theses may be provided to researchers in accordance with the law and in a manner that is common across UK libraries.The law allows us to provide whole copies of unpublished theses to individuals as long as they sign a declaration saying that it is for non-commercial research or private study. The agreement used for access to theses at Cambridge has been drafted using the guidance by the Chartered Institute of Library and Information Professionals (CILIP).

Theses are not available for borrowing or inter library loan. The copyright of theses remains with the author. The law does not allow us to provide a copy for inclusion in a general library collection or for wider distribution beyond the individual receiving the copy, without the explicit permission of the author or copyright holder. Where someone approaches us asking for a copy for their library or wider distribution, they must obtain the explicit permission of the author or copyright owner.

Please note any periods of access restriction requested by the author apply to both electronic and print copies.

This project is a joint initiative of Cambridge University Library and the Research Strategy Office .

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Cambridge Libraries

Physical & Digital Collections

Theses & dissertations: home, access to theses and dissertations from other institutions and from the university of cambridge.

This guide provides information on searching for theses of Cambridge PhDs and for theses of UK universities and universities abroad.

For information and guidance on depositing your thesis as a cambridge phd, visit the cambridge office of scholarly communication pages on theses here ., this guide gives essential information on how to obtain theses using the british library's ethos service. .

On the last weekend of October, the British Library became the victim of a major cyber-attack. Essential digital services including the BL catalogue, website and online learning resources went dark, with research services like the EThOS collection of more than 600,000 doctoral theses suddenly unavailable. The BL state that they anticipate restoring more services in the next few weeks, but disruption to certain services is now expected to persist for several months. For the latest news on the attack and information on the restoration of services, please follow the BL blog here: Knowledge Matters blog and access the LibGuide page here: British Library Outage Update - Electronic Legal Deposit - LibGuides at University of Cambridge Subject Libraries

A full list of resources for searching theses online is provided by the Cambridge A-Z, available here .

University of Cambridge theses

Finding a cambridge phd thesis online via the institutional repository.

The University's institutional repository, Apollo , holds full-text digital versions of over 11,000 Cambridge PhD theses and is a rapidly growing collection deposited by Cambridge Ph.D. graduates. Theses in Apollo can be browsed via this link . More information on how to access theses by University of Cambridge students can be found on the access to Cambridge theses webpage. The requirement for impending PhD graduates to deposit a digital version in order to graduate means the repository will be increasing at a rate of approximately 1,000 per year from this source. About 200 theses are added annually through requests to make theses Open Access or via requests to digitize a thesis in printed format.

Locating and obtaining a copy of a Cambridge PhD thesis (not yet available via the repository)

Theses can be searched in iDiscover . Guidance on searching for theses in iDiscover can be found here . Requests for consultation of printed theses, not available online, should be made at the Manuscripts Reading Room (Email: [email protected] Telephone: +44 (0)1223 333143). Further information on the University Library's theses, dissertations and prize essays collections can be consulted at this link .

Researchers can order a copy of an unpublished thesis which was deposited in print form either through the Library’s Digital Content Unit via the image request form , or, if the thesis has been digitised, it may be available in the Apollo repository. Copies of theses may be provided to researchers in accordance with the law and in a manner that is common across UK libraries. The law allows us to provide whole copies of unpublished theses to individuals as long as they sign a declaration saying that it is for non-commercial research or private study.

How to make your thesis available online through Cambridge's institutional repository

Are you a Cambridge alumni and wish to make your Ph.D. thesis available online? You can do this by depositing it in Apollo the University's institutional repository. Click here for further information on how to proceed. Current Ph.D students at the University of Cambridge can find further information about the requirements to deposit theses on the Office of Scholarly Communication theses webpages.

UK Theses and Dissertations

Electronic copies of Ph.D. theses submitted at over 100 UK universities are obtainable from EThOS , a service set up to provide access to all theses from participating institutions. It achieves this by harvesting e-theses from Institutional Repositories and by digitising print theses as they are ordered by researchers using the system. Over 250,000 theses are already available in this way. Please note that it does not supply theses submitted at the universities of Cambridge or Oxford although they are listed on EThOS.

Registration with EThOS is not required to search for a thesis but is necessary to download or order one unless it is stored in the university repository rather than the British Library (in which case a link to the repository will be displayed). Many theses are available without charge on an Open Access basis but in all other cases, if you are requesting a thesis that has not yet been digitised you will be asked to meet the cost. Once a thesis has been digitised it is available for free download thereafter.

When you order a thesis it will either be immediately available for download or writing to hard copy or it will need to be digitised. If you order a thesis for digitisation, the system will manage the process and you will be informed when the thesis is available for download/preparation to hard copy.

See the Search results section of the help page for full information on interpreting search results in EThOS.

EThOS is managed by the British Library and can be found at http://ethos.bl.uk . For more information see About EThOS .

World-wide (incl. UK) theses and dissertations

Electronic versions of non-UK theses may be available from the institution at which they were submitted, sometimes on an open access basis from the institutional repository. A good starting point for discovering freely available electronic theses and dissertations beyond the UK is the Networked Digital Library of Theses and Dissertations (NDLTD) , which facilitates searching across institutions. Information can also usually be found on the library web pages of the relevant institution.

The DART Europe etheses portal lists several thousand full-text theses from a group of European universities.

The University Library subscribes to the ProQuest Dissertations and Theses (PQDT) database which from August 31 2023 is accessed on the Web of Science platform. To search this index select it from the Web of Science "Search in" drop-down list of databases (available on the Documents tab on WoS home page)

PQDT includes 2.4 million dissertation and theses citations, representing 700 leading academic institutions worldwide from 1861 to the present day. The database offers full text for most of the dissertations added since 1997 and strong retrospective full text coverage for older graduate works. Each dissertation published since July 1980 includes a 350-word abstract written by the author. Master's theses published since 1988 include 150-word abstracts.

IMPORTANT NOTE: The University Library only subscribes to the abstracting & indexing version of the ProQuest Dissertations and Theses database and NOT the full text version. A fee is payable for ordering a dissertation from this source. To obtain the full text of a dissertation as a downloadable PDF you can submit your request via the University Library Inter-Library Loans department (see contact details below). NB this service is only available to full and current members of the University of Cambridge.

Alternatively you can pay yourself for the dissertation PDF on the PQDT platform. Link from Web of Science record display of any thesis to PQDT by clicking on "View Details on ProQuest". On the "Preview" page you will see an option "Order a copy" top right. This will allow you to order your own copy from ProQuest directly.

Dissertations and theses submitted at non-UK universities may also be requested on Inter-Library Loan through the Inter-Library Loans department (01223 333039 or 333080, [email protected] )

Last Updated: Dec 20, 2023 9:47 AM
URL: https://libguides.cam.ac.uk/theses

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Mathematics in Cambridge

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Postgraduate Study

The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.

Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.

Research Areas and Potential Supervisors

Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.

We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.

Before making an application to study with us we recommend you:

Investigate our areas of research and consider how they fit with your interests and ambitions.

A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.

Identify 2 or 3 appropriate supervisor(s) with whom you might work.

The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.

If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.

Give some thought to your intended research and why you want to study with us.

On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.

Research areas

Click on a research area to find out more about available supervisors and their research:

Please note that a large majority of the successful applicants for PhD studentships with the High Energy Physics, and General Relativity & Cosmology (GR) groups will have taken Part III of the Mathematical Tripos.

Funding Opportunities

Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.

All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:

Note for PhD applicants:

We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.

Note for MPhil applicants:

We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).

Most interviews are expected to take place in the second half of January.

The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.

Not all applicants will be selected for interview.

If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:

the location of the interview (it may be in-person or on-line dependent upon interviewer availability, your distance from Cambridge, as well as individual preferences),
the interview format and whether you should prepare anything specific in advance,
the approximate duration of the interview,
who you will be meeting.

Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.

Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.

Decision timeline

Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.

To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.

Communication of outcomes

You will be notified of the formal outcome of your application via the Applicant Portal.

Following an interview, you can normally expect to receive notification of the outcome within a week or two.

If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.

We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.

Take a look at our frequently asked questions for PhD applicants.

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PhD in Pure Mathematics and Mathematical Statistics

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Course closed:

Pure Mathematics and Mathematical Statistics is no longer accepting new applications.

This course is a three to four year programme culminating in the submission and examination of a single research thesis. Students joining the course will often have completed prior study at a level comparable to our Part III (MMath/MASt) course and many have postgraduate experience. Our students, therefore, begin their PhD research with a good understanding of advanced material, which they build on in various ways throughout the course of their PhD studies.

Structure of the PhD

Students are required to undertake a minimum of nine full-time terms of research (ie three years). Students are not registered for the PhD in the first instance but are instead admitted on a probationary basis. All students are assessed for registration towards the end of their first year of full-time study (usually June). This assessment is based on a short written report which is reviewed by two assessors. In the fifth term, there may also be a further assessment of progress, for which students submit a longer piece of written work and receive an oral assessment.

Research areas

Research in DPMMS can be divided into the following broad areas: Algebra, Algebraic Geometry, Analysis and Partial Differential Equations, Combinatorics, Differential Geometry and Topology, Number Theory, Information and Finance, Probability, and Statistics. The boundaries between such areas are not rigid, however, and staff may contribute to more than one area.

Additional training and opportunities

Whilst there are no mandatory taught components to the PhD degree, students may wish to undertake specific courses or further training to expand their knowledge, either for personal interest or to directly assist with their PhD research. All students are encouraged to participate in and attend the wide range of lectures, seminars and events on offer within DPMMS and the Centre for Mathematical Sciences.

Many students submit a prize essay at the beginning of their fifth term. The best essays each year are of a scale and quality already adequate for a PhD thesis, incorporating work already, or about to be, published. We intend that our students publish their work in leading journals. Our PhD students might have written several papers before they submit their thesis, and can go on to win academic positions at leading institutions around the world.

DPMMS also promotes and encourages researcher development and transferable skills training. This can take the form of assisting with Part III preparatory workshops, attendance at skills-based training sessions, or presenting work at seminars and conferences. The University also offers training via the Researcher Development Programme .

There is no requirement for PhD students to teach but there are plenty of opportunities to do so, such as offering supervisions for third-year undergraduates (this involves the supervisor sitting with a pair of students for an hour, discussing their work). PhD students might help with running examples classes for Part III students, too.

The Postgraduate Virtual Open Day usually takes place at the end of October. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the Postgraduate Open Day page for more details.

See further the Postgraduate Admissions Events pages for other events relating to Postgraduate study, including study fairs, visits and international events.

Departments

This course is advertised in the following departments:

Faculty of Mathematics
Department of Pure Mathematics and Mathematical Statistics

Key Information

3-4 years full-time, 4-7 years part-time, study mode : research, doctor of philosophy, department of pure mathematics and mathematical statistics this course is advertised in multiple departments. please see the overview tab for more details., course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, michaelmas 2024 (closed).

Some courses can close early. See the Deadlines page for guidance on when to apply.

Funding Deadlines

These deadlines apply to applications for courses starting in Michaelmas 2024, Lent 2025 and Easter 2025.

Similar Courses

Mathematics MPhil
Mathematics (Applied Mathematics) MASt
Mathematics (Mathematical Statistics) MASt
Mathematics (Pure Mathematics) MASt
Mathematics (Theoretical Physics) MASt

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Apollo - University of Cambridge Repository

Apollo is the institutional repository of the University of Cambridge, managed by the Open Research Systems team based in Cambridge University Library. The Repository is committed to store and preserve the University’s research outputs. Research outputs can include, but are not limited to, publications, conference proceedings, book chapters, monographs, theses, various forms of research data (video recordings, spreadsheets, computational scripts, code, images etc.), presentations and others.

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Detailed information about deposit processes into Apollo, including eligibility for inclusion in Apollo.

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University policies & guidance

The University does not require electronic copies of Masters Theses to be deposited in Apollo, which means that the Thesis team does not deposit individual Masters Theses via Symplectic Elements.

However, there is a batch upload arrangement in place for faculties/departments who wish to deposit their Masters Theses in Apollo. Interested faculties/departments should contact the Thesis team for further information ( [email protected]).

Key features of the batch upload arrangement

All Theses deposited via the batch upload will be made immediately open access in Apollo;
Faculties/departments will be provided with a shared drive, which they will use to provide electronic copies of Theses, Deposit Licence Agreements and metadata;
Faculties/departments create their own local policies to determine the number and frequency of their uploads to their shared drive;
Batch uploads are run once per term, at the end of each term by Repository staff.

Guidelines for faculties/departments

As all Theses that are deposited into Apollo via the batch upload arrangement will be immediately available (open access) in Apollo, it is only suitable for Theses that do not contain:

uncleared copyrighted material and/or
unauthorised confidential/sensitive information.

However, Faculties/departments may instead opt provide a redacted version of any Theses that do contain such content. If this option is chosen, Faculties/departments should deposit the original, unredacted Thesis and a redacted version. We have further information on our website about redacting material from theses.

It is important that these issues are resolved in advance of uploading the thesis to their shared drive, because depositing these items into Apollo may breach copyright or GDPR laws. If in doubt about a thesis, faculties/departments are advised not to include it in the batch upload request.

Should a Thesis have supplementary data files, the data should be uploaded separately via Symplectic Elements by the faculty/departmental administrator.

Third party copyright

Copyright held by someone other than the author is known as third party copyright. If an author has used third party copyright material, they should ascertain whether or not they need permission to use it in their thesis.

We recommend that authors obtain permission to include material as they are researching. Clearing permission can take a long time, so unless a redacted version is supplied, it is not appropriate to include Theses for batch upload where permissions have been sought but are still outstanding. It is also not appropriate to include theses where permission has not been sought, or where permission has been denied.

Please be aware that different copyright rules apply to the hardbound copy that is deposited in the library for reference and the electronic version that is deposited in the repository. This is because the hardbound copy is considered unpublished and the electronic version, if made available as open access, is considered published. The thesis must credit the copyright holder(s) and source(s) of all third party copyright material.

There is more information on third party copyright on our website .

Sensitive information

Sensitive information is data that must be protected for the privacy or security of an individual, group, or organisation. The kinds of sensitive information most likely to be included in theses are:

Commercial (trade secrets or information which could damage commercial interests)
Health and safety (information which could damage the health and/or safety of an individual)
Information provided in confidence Personal (as defined by the Data Protection Act 2018 - GDPR)
Culturally sensitive material (information or arguments which some cultural groups might find offensive or upsetting)
Content referring to legal cases

The Freedom of Information Act 2000 sets out the types of sensitive information to which legally enforceable restrictions may be applied. The University of Cambridge is bound by this Act. It may decide to apply restrictions to other types of information, including theses deposited in the University Library or Departmental and Faculty libraries, but they are not legally binding if not falling under the Act.

Unless a redacted version is supplied, it is also not appropriate to include theses for batch upload that contain sensitive/confidential information without authorisation from whom the information relates.

There is more information about sensitive material on our website

This project is a joint initiative of Cambridge University Library and the Research Strategy Office .

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The Manuscripts Reading Room administers the University's collection of doctoral and higher degree theses. Before 1920, degrees were awarded on the basis of examinations or certificates of research, and little written work composed specifically for such purposes survives, other than a small collection of Advanced Student Dissertations. Revised regulations were approved, instituting the new degree of PhD, which required a written work to be deposited in the University Library. Our collection of doctoral theses thus dates from 1921, when just four arrived in the Library. Statistics illustrate a great increase in output: for the academic year 2015-2016 just over one thousand new dissertations were approved and added to our collection. There are now over 39,000 volumes.

Contact: Manuscripts Reading Room (01223 333143, [email protected] )

Cambridge theses held by CUL

A small but growing proportion of Cambridge theses are available to consult in digital form in the university repository Apollo .

See the Office of Scholarly Communication's webpages on theses .

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You can access undergraduate and graduate student dissertations in Anthropology and Archaeology via the Haddon Library. You must be a current member of the University to access student dissertations. When you find a dissertation that you'd like to read, please request it by emailing us or asking at the front desk.

List of Archaeology/BioAnth (undergraduate) dissertations available to view online, 2020-Present (Google Sheet)
List of Social Anthropology (undergraduate) dissertations available to view online, 2020-Present (Google Sheet)

Please note that as of April 2024 , all requests for online access to dissertations will be granted for seven calendar days , so use your reading time wisely. If you require access past this time, you will need to submit a new request.

Print dissertations are for use in the library only and cannot be borrowed.

List of Social Anthropology/Archaeology/BioAnth (undergraduate/graduate) dissertations in print , up to 2019 (Excel)

Recently completed Cambridge PhD theses are available via Apollo , the University Repository (unless under embargo).

You can also search for the full text of PhD theses across the UK using the British Library's EThOS service or browse the Proquest Dissertations and Theses database for research across 700 academic institutions worldwide.

You can request theses from other institutions via the University Library's Inter-Library Loan service .

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TOM ROCKS MATHS

Maths, but not as you know it…, my phd thesis.

My PhD thesis on modelling the spread of river water in the ocean in its entirety – not for the faint hearted! Unless you are a researcher in fluid mechanics, I strongly recommend reading the summary articles here before tackling the beast below. If you have any questions/comments please do get in touch via the contact form .

CrawfordTJ-Thesis

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DSpace@MIT Home
MIT Libraries

This collection of MIT Theses in DSpace contains selected theses and dissertations from all MIT departments. Please note that this is NOT a complete collection of MIT theses. To search all MIT theses, use MIT Libraries' catalog .

MIT's DSpace contains more than 58,000 theses completed at MIT dating as far back as the mid 1800's. Theses in this collection have been scanned by the MIT Libraries or submitted in electronic format by thesis authors. Since 2004 all new Masters and Ph.D. theses are scanned and added to this collection after degrees are awarded.

MIT Theses are openly available to all readers. Please share how this access affects or benefits you. Your story matters.

If you have questions about MIT theses in DSpace, [email protected] . See also Access & Availability Questions or About MIT Theses in DSpace .

If you are a recent MIT graduate, your thesis will be added to DSpace within 3-6 months after your graduation date. Please email [email protected] with any questions.

Permissions

MIT Theses may be protected by copyright. Please refer to the MIT Libraries Permissions Policy for permission information. Note that the copyright holder for most MIT theses is identified on the title page of the thesis.

Theses by Department

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Doctoral theses, graduate theses, undergraduate theses, recent submissions.

Locomotive superheaters and feed water heaters

A cost accounting system for the F. L. & J. C. Codman Company buffing wheels

The electrical strength of insulators in high vacua

Dissertations

Most Harvard PhD dissertations from 2012 forward are available online in DASH , Harvard’s central open-access repository and are linked below. Many older dissertations can be found on ProQuest Dissertation and Theses Search which many university libraries subscribe to.

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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 . What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

Articles in press
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Symmetric function generalizations of the $q$-Baker–Forrester ex-conjecture and Selberg-type integrals HTML articles powered by AMS MathViewer

Vasyl A. Alba , Vladimir A. Fateev , Alexey V. Litvinov , and Grigory M. Tarnopolskiy , On combinatorial expansion of the conformal blocks arising from AGT conjecture , Lett. Math. Phys. 98 (2011), no. 1, 33–64. MR 2836428 , DOI 10.1007/s11005-011-0503-z
Seamus P. Albion , Eric M. Rains , and S. Ole Warnaar , AFLT-type Selberg integrals , Comm. Math. Phys. 388 (2021), no. 2, 735–791. MR 4334246 , DOI 10.1007/s00220-021-04157-0
Richard Askey , Some basic hypergeometric extensions of integrals of Selberg and Andrews , SIAM J. Math. Anal. 11 (1980), no. 6, 938–951. MR 595822 , DOI 10.1137/0511084
T. H. Baker and P. J. Forrester , Generalizations of the $q$-Morris constant term identity , J. Combin. Theory Ser. A 81 (1998), no. 1, 69–87. MR 1492869 , DOI 10.1006/jcta.1997.2819
Tommy Wuxing Cai , Macdonald symmetric functions of rectangular shapes , J. Combin. Theory Ser. A 128 (2014), 162–179. MR 3265922 , DOI 10.1016/j.jcta.2014.08.005
Peter J. Forrester and S. Ole Warnaar , The importance of the Selberg integral , Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 4 , 489–534. MR 2434345 , DOI 10.1090/S0273-0979-08-01221-4
George Gasper and Mizan Rahman , Basic hypergeometric series , 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 96, Cambridge University Press, Cambridge, 2004. With a foreword by Richard Askey. MR 2128719 , DOI 10.1017/CBO9780511526251
Ira M. Gessel , Lun Lv , Guoce Xin , and Yue Zhou , A unified elementary approach to the Dyson, Morris, Aomoto, and Forrester constant term identities , J. Combin. Theory Ser. A 115 (2008), no. 8, 1417–1435. MR 2455586 , DOI 10.1016/j.jcta.2008.02.006
Ira M. Gessel and Guoce Xin , A short proof of the Zeilberger-Bressoud $q$-Dyson theorem , Proc. Amer. Math. Soc. 134 (2006), no. 8 , 2179–2187. MR 2213689 , DOI 10.1090/S0002-9939-06-08224-4
Laurent Habsieger , Une $q$-intégrale de Selberg et Askey , SIAM J. Math. Anal. 19 (1988), no. 6, 1475–1489 (French, with English summary). MR 965268 , DOI 10.1137/0519111
James Haglund , The $q$,$t$-Catalan numbers and the space of diagonal harmonics , University Lecture Series, vol. 41, American Mathematical Society, Providence, RI, 2008. With an appendix on the combinatorics of Macdonald polynomials. MR 2371044 , DOI 10.1007/s10711-008-9270-0
Kevin W. J. Kadell , A proof of Askey’s conjectured $q$-analogue of Selberg’s integral and a conjecture of Morris , SIAM J. Math. Anal. 19 (1988), no. 4, 969–986. MR 946655 , DOI 10.1137/0519067
Kevin W. J. Kadell , The Selberg-Jack symmetric functions , Adv. Math. 130 (1997), no. 1, 33–102. MR 1467311 , DOI 10.1006/aima.1997.1642
Gyula Károlyi , Zoltán Lóránt Nagy , Fedor V. Petrov , and Vladislav Volkov , A new approach to constant term identities and Selberg-type integrals , Adv. Math. 277 (2015), 252–282. MR 3336087 , DOI 10.1016/j.aim.2014.09.028
Alain Lascoux , Symmetric functions and combinatorial operators on polynomials , CBMS Regional Conference Series in Mathematics, vol. 99, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2003. MR 2017492 , DOI 10.1090/cbms/099
Michel Lassalle , A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials , Jack, Hall-Littlewood and Macdonald polynomials, Contemp. Math., vol. 417, Amer. Math. Soc., Providence, RI, 2006, pp. 271–280. MR 2284133 , DOI 10.1090/conm/417/07927
Lun Lv , Guoce Xin , and Yue Zhou , A family of $q$-Dyson style constant term identities , J. Combin. Theory Ser. A 116 (2009), no. 1, 12–29. MR 2469245 , DOI 10.1016/j.jcta.2008.04.002
I. G. Macdonald , Symmetric functions and Hall polynomials , 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144 , DOI 10.1093/oso/9780198534891.001.0001
Walter Garfield Morris II , CONSTANT TERM IDENTITIES FOR FINITE AND AFFINE ROOT SYSTEMS: CONJECTURES AND THEOREMS , ProQuest LLC, Ann Arbor, MI, 1982. Thesis (Ph.D.)–The University of Wisconsin - Madison. MR 2631899
Eric Rains and S. Ole Warnaar , Bounded Littlewood identities , Mem. Amer. Math. Soc. 270 (2021), no. 1317, vii+115. MR 4259867 , DOI 10.1090/memo/1317
John R. Stembridge , First layer formulas for characters of $\textrm {SL}(n,\textbf {C})$ , Trans. Amer. Math. Soc. 299 (1987), no. 1 , 319–350. MR 869415 , DOI 10.1090/S0002-9947-1987-0869415-X
S. Ole Warnaar , $q$-Selberg integrals and Macdonald polynomials , Ramanujan J. 10 (2005), no. 2, 237–268. MR 2195565 , DOI 10.1007/s11139-005-4849-7
Guoce Xin , The ring of Malcev-Neumann series and the residue theorem , ProQuest LLC, Ann Arbor, MI, 2004. Thesis (Ph.D.)–Brandeis University. MR 2705745
Guoce Xin , A fast algorithm for MacMahon’s partition analysis , Electron. J. Combin. 11 (2004), no. 1, Research Paper 58, 20. MR 2097324 , DOI 10.37236/1811
Guoce Xin and Yue Zhou , A Laurent series proof of the Habsieger-Kadell $q$-Morris identity , Electron. J. Combin. 21 (2014), no. 3, Paper 3.38, 16. MR 3262275 , DOI 10.37236/4221
Doron Zeilberger and David M. Bressoud , A proof of Andrews’ $q$-Dyson conjecture , Discrete Math. 54 (1985), no. 2, 201–224. MR 791661 , DOI 10.1016/0012-365X(85)90081-0
Yue Zhou , On the $q$-Dyson orthogonality problem , Adv. in Appl. Math. 130 (2021), Paper No. 102224, 33. MR 4266754 , DOI 10.1016/j.aam.2021.102224
Yue Zhou , The AFLT $q$-Morris constant term identity , Adv. in Appl. Math. 147 (2023), Paper No. 102506, 45. MR 4560439 , DOI 10.1016/j.aam.2023.102506
Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 05A30 , 33D70 , 05E05
Affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China
MR Author ID: 735352
ORCID: 0000-0002-2505-5759
Email: [email protected]
Affiliation: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410075, People’s Republic of China
Email: [email protected]
Received by editor(s): July 3, 2022
Received by editor(s) in revised form: January 29, 2024
Published electronically: April 9, 2024
Additional Notes: Yue Zhou is the corresponding author. This work was supported by the National Natural Science Foundation of China (No. 12071311, 12171487).
© Copyright 2024 American Mathematical Society
Journal: Trans. Amer. Math. Soc. 377 (2024), 4303-4363
DOI: https://doi.org/10.1090/tran/9142

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Birth by C-section more than doubles odds of measles vaccine failure

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Very sick 5 year old little boy fighting measles infection, boy is laying in bed under the blanket with an agonizing expression, boy is covered with rash caused by virus.

Researchers say it is vital that children born by caesarean section receive two doses of the measles vaccine for robust protection against the disease.

A study by the University of Cambridge, UK, and Fudan University, China, has found that a single dose of the measles jab is up to 2.6 times more likely to be completely ineffective in children born by C-section, compared to those born naturally.

Failure of the vaccine means that the child’s immune system does not produce antibodies to fight against measles infection, so they remain susceptible to the disease.

A second measles jab was found to induce a robust immunity against measles in C-section children.

Measles is a highly infectious disease, and even low vaccine failure rates can significantly increase the risk of an outbreak.

A potential reason for this effect is linked to the development of the infant’s gut microbiome – the vast collection of microbes that naturally live inside the gut. Other studies have shown that vaginal birth transfers a greater variety of microbes from mother to baby, which can boost the immune system.

“We’ve discovered that the way we’re born - either by C-section or natural birth - has long-term consequences on our immunity to diseases as we grow up,” said Professor Henrik Salje in the University of Cambridge’s Department of Genetics, joint senior author of the report.

He added: “We know that a lot of children don't end up having their second measles jab, which is dangerous for them as individuals and for the wider population.

“Infants born by C-section are the ones we really want to be following up to make sure they get their second measles jab, because their first jab is much more likely to fail.”

The results are published today in the journal Nature Microbiology .

At least 95% of the population needs to be fully vaccinated to keep measles under control but the UK is well below this, despite the Measles, Mumps and Rubella (MMR) vaccine being available through the NHS Routine Childhood Immunisation Programme.

An increasing number of women around the world are choosing to give birth by caesarean section: in the UK a third of all births are by C-section, in Brazil and Turkey over half of all children are born this way.

“With a C-section birth, children aren’t exposed to the mother’s microbiome in the same way as with a vaginal birth. We think this means they take longer to catch up in developing their gut microbiome, and with it, the ability of the immune system to be primed by vaccines against diseases including measles,” said Salje.

To get their results, the researchers used data from previous studies of over 1,500 children in Hunan, China, which included blood samples taken every few weeks from birth to the age of 12. This allowed them to see how levels of measles antibodies in the blood change over the first few years of life, including following vaccination.

They found that 12% of children born via caesarean section had no immune response to their first measles vaccination, as compared to 5% of children born by vaginal delivery. This means that many of the children born by C-section did still mount an immune response following their first vaccination.

Two doses of the measles jab are needed for the body to mount a long-lasting immune response and protect against measles. According to the World Health Organisation, in 2022 only 83% of the world's children had received one dose of measles vaccine by their first birthday – the lowest since 2008.

Salje said: “Vaccine hesitancy is really problematic, and measles is top of the list of diseases we’re worried about because it’s so infectious.”

Measles is one of the world’s most contagious diseases, spread by coughs and sneezes. It starts with cold-like symptoms and a rash, and can lead to serious complications including blindness, seizures, and death.

Before the measles vaccine was introduced in 1963, there were major measles epidemics every few years causing an estimated 2.6 million deaths each year.

The research was funded by the National Natural Science Foundation of China.

Wang, W et al: ‘Dynamics of measles immunity from birth and following vaccination.’ Nature Microbiology, 13 May 2024. DOI: 10.1038/s41564-024-01694-x

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Janabel Xia: Algorithms, dance rhythms, and the drive to succeed

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Janabel Xia dancing in front of a blackboard. Her back is arched, head thrown back, hair flying, and arms in the air as she looks at the camera and smiles.

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Senior math major Janabel Xia is a study of a person in constant motion.

When she isn’t sorting algorithms and improving traffic control systems for driverless vehicles, she’s dancing as a member of at least four dance clubs. She’s joined several social justice organizations, worked on cryptography and web authentication technology, and created a polling app that allows users to vote anonymously.

In her final semester, she’s putting the pedal to the metal, with a green light to lessen the carbon footprint of urban transportation by using sensors at traffic light intersections.

First steps

Growing up in Lexington, Massachusetts, Janabel has been competing on math teams since elementary school. On her math team, which met early mornings before the start of school, she discovered a love of problem-solving that challenged her more than her classroom “plug-and-chug exercises.”

At Lexington High School, she was math team captain, a two-time Math Olympiad attendee, and a silver medalist for Team USA at the European Girls' Mathematical Olympiad.

As a math major, she studies combinatorics and theoretical computer science, including theoretical and applied cryptography. In her sophomore year, she was a researcher in the Cryptography and Information Security Group at the MIT Computer Science and Artificial Intelligence Laboratory, where she conducted cryptanalysis research under Professor Vinod Vaikuntanathan .

Part of her interests in cryptography stem from the beauty of the underlying mathematics itself — the field feels like clever engineering with mathematical tools. But another part of her interest in cryptography stems from its political dimensions, including its potential to fundamentally change existing power structures and governance. Xia and students at the University of California at Berkeley and Stanford University created zkPoll , a private polling app written with the Circom programming language, that allows users to create polls for specific sets of people, while generating a zero-knowledge proof that keeps personal information hidden to decrease negative voting influences from public perception.

Her participation in the PKG Center’s Active Community Engagement Freshman Pre-Orientation Program introduced her to local community organizations focusing on food security, housing for formerly incarcerated individuals, and access to health care. She is also part of Reading for Revolution , a student book club that discusses race, class, and working-class movements within MIT and the Greater Boston area.

Xia’s educational journey led to her ongoing pursuit of combining mathematical and computational methods in areas adjacent to urban planning. “When I realized how much planning was concerned with social justice as it was concerned with design, I became more attracted to the field.”

Going on autopilot

She took classes with the Department of Urban Studies and Planning and is currently working on an Undergraduate Research Opportunities Program (UROP) project with Professor Cathy Wu in the Institute for Data, Systems, and Society.

Recent work on eco-driving by Wu and doctoral student Vindula Jayawardana investigated semi-autonomous vehicles that communicate with sensors localized at traffic intersections, which in theory could reduce carbon emissions by up to 21 percent.

Xia aims to optimize the implementation scheme for these sensors at traffic intersections, considering a graded scheme where perhaps only 20 percent of all sensors are initially installed, and more sensors get added in waves. She wants to maximize the emission reduction rates at each step of the process, as well as ensure there is no unnecessary installation and de-installation of such sensors.

Dance numbers

Meanwhile, Xia has been a member of MIT’s Fixation , Ridonkulous , and MissBehavior groups, and as a traditional Chinese dance choreographer for the MIT Asian Dance Team .

A dancer since she was 3, Xia started with Chinese traditional dance, and later added ballet and jazz. Because she is as much of a dancer as a researcher, she has figured out how to make her schedule work.

“Production weeks are always madness, with dancers running straight from class to dress rehearsals and shows all evening and coming back early next morning to take down lights and roll up marley [material that covers the stage floor],” she says. “As busy as it keeps me, I couldn’t have survived MIT without dance. I love the discipline, creativity, and most importantly the teamwork that dance demands of us. I really love the dance community here with my whole heart. These friends have inspired me and given me the love to power me through MIT.”

Xia lives with her fellow Dance Team members at the off-campus Women's Independent Living Group (WILG). “I really value WILG's culture of independence, both in lifestyle — cooking, cleaning up after yourself, managing house facilities, etc. — and thought — questioning norms, staying away from status games, finding new passions.”

In addition to her UROP, she’s wrapping up some graduation requirements, finishing up a research paper on sorting algorithms from her summer at the University of Minnesota Duluth Research Experience for Undergraduates in combinatorics, and deciding between PhD programs in math and computer science.

“My biggest goal right now is to figure out how to combine my interests in mathematics and urban studies, and more broadly connect technical perspectives with human-centered work in a way that feels right to me,” she says.

“Overall, MIT has given me so many avenues to explore that I would have never thought about before coming here, for which I’m infinitely grateful. Every time I find something new, it’s hard for me not to find it cool. There’s just so much out there to learn about. While it can feel overwhelming at times, I hope to continue that learning and exploration for the rest of my life.”

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Five MIT faculty elected to the National Academy of Sciences for 2024

Guoping feng, piotr indyk, daniel kleitman, daniela rus, senthil todadri, and nine alumni are recognized by their peers for their outstanding contributions to research..

The National Academy of Sciences has elected 120 members and 24 international members, including five faculty members from MIT. Guoping Feng, Piotr Indyk, Daniel J. Kleitman, Daniela Rus, and Senthil Todadri were elected in recognition of their “distinguished and continuing achievements in original research.” Membership to the National Academy of Sciences is one of the highest honors a scientist can receive in their career.

Among the new members added this year are also nine MIT alumni, including Zvi Bern ’82; Harold Hwang ’93, SM ’93; Leonard Kleinrock SM ’59, PhD ’63; Jeffrey C. Lagarias ’71, SM ’72, PhD ’74; Ann Pearson PhD ’00; Robin Pemantle PhD ’88; Jonas C. Peters PhD ’98; Lynn Talley PhD ’82; and Peter T. Wolczanski ’76. Those elected this year bring the total number of active members to 2,617, with 537 international members.

The National Academy of Sciences is a private, nonprofit institution that was established under a congressional charter signed by President Abraham Lincoln in 1863. It recognizes achievement in science by election to membership, and — with the National Academy of Engineering and the National Academy of Medicine — provides science, engineering, and health policy advice to the federal government and other organizations.

Guoping Feng

Guoping Feng is the James W. (1963) and Patricia T. Poitras Professor in the Department of Brain and Cognitive Sciences. He is also associate director and investigator in the McGovern Institute for Brain Research, a member of the Broad Institute of MIT and Harvard, and director of the Hock E. Tan and K. Lisa Yang Center for Autism Research.

His research focuses on understanding the molecular mechanisms that regulate the development and function of synapses, the places in the brain where neurons connect and communicate. He’s interested in how defects in the synapses can contribute to psychiatric and neurodevelopmental disorders. By understanding the fundamental mechanisms behind these disorders, he’s producing foundational knowledge that may guide the development of new treatments for conditions like obsessive-compulsive disorder and schizophrenia.

Feng received his medical training at Zhejiang University Medical School in Hangzhou, China, and his PhD in molecular genetics from the State University of New York at Buffalo. He did his postdoctoral training at Washington University at St. Louis and was on the faculty at Duke University School of Medicine before coming to MIT in 2010. He is a member of the American Academy of Arts and Sciences, a fellow of the American Association for the Advancement of Science, and was elected to the National Academy of Medicine in 2023.

Piotr Indyk

Piotr Indyk is the Thomas D. and Virginia W. Cabot Professor of Electrical Engineering and Computer Science. He received his magister degree from the University of Warsaw and his PhD from Stanford University before coming to MIT in 2000.

Indyk’s research focuses on building efficient, sublinear, and streaming algorithms. He’s developed, for example, algorithms that can use limited time and space to navigate massive data streams, that can separate signals into individual frequencies faster than other methods, and can address the “nearest neighbor” problem by finding highly similar data points without needing to scan an entire database. His work has applications on everything from machine learning to data mining.

He has been named a Simons Investigator and a fellow of the Association for Computer Machinery. In 2023, he was elected to the American Academy of Arts and Sciences.

Daniel J. Kleitman

Daniel Kleitman, a professor emeritus of applied mathematics, has been at MIT since 1966. He received his undergraduate degree from Cornell University and his master’s and PhD in physics from Harvard University before doing postdoctoral work at Harvard and the Niels Bohr Institute in Copenhagen, Denmark.

Kleitman’s research interests include operations research, genomics, graph theory, and combinatorics, the area of math concerned with counting. He was actually a professor of physics at Brandeis University before changing his field to math, encouraged by the prolific mathematician Paul Erdős. In fact, Kleitman has the rare distinction of having an Erdős number of just one. The number is a measure of the “collaborative distance” between a mathematician and Erdős in terms of authorship of papers, and studies have shown that leading mathematicians have particularly low numbers.

He’s a member of the American Academy of Arts and Sciences and has made important contributions to the MIT community throughout his career. He was head of the Department of Mathematics and served on a number of committees, including the Applied Mathematics Committee. He also helped create web-based technology and an online textbook for several of the department’s core undergraduate courses. He was even a math advisor for the MIT-based film “Good Will Hunting.”

Daniela Rus

Daniela Rus, the Andrew (1956) and Erna Viterbi Professor of Electrical Engineering and Computer Science, is the director of the Computer Science and Artificial Intelligence Laboratory (CSAIL). She also serves as director of the Toyota-CSAIL Joint Research Center.

Her research on robotics, artificial intelligence, and data science is geared toward understanding the science and engineering of autonomy. Her ultimate goal is to create a future where machines are seamlessly integrated into daily life to support people with cognitive and physical tasks, and deployed in way that ensures they benefit humanity. She’s working to increase the ability of machines to reason, learn, and adapt to complex tasks in human-centered environments with applications for agriculture, manufacturing, medicine, construction, and other industries. She’s also interested in creating new tools for designing and fabricating robots and in improving the interfaces between robots and people, and she’s done collaborative projects at the intersection of technology and artistic performance.

Rus received her undergraduate degree from the University of Iowa and her PhD in computer science from Cornell University. She was a professor of computer science at Dartmouth College before coming to MIT in 2004. She is part of the Class of 2002 MacArthur Fellows; was elected to the National Academy of Engineering and the American Academy of Arts and Sciences; and is a fellow of the Association for Computer Machinery, the Institute of Electrical and Electronics Engineers, and the Association for the Advancement of Artificial Intelligence.

Senthil Todadri

Senthil Todadri , a professor of physics, came to MIT in 2001. He received his undergraduate degree from the Indian Institute of Technology in Kanpur and his PhD from Yale University before working as a postdoc at the Kavli Institute for Theoretical Physics in Santa Barbara, California.

Todadri’s research focuses on condensed matter theory. He’s interested in novel phases and phase transitions of quantum matter that expand beyond existing paradigms. Combining modeling experiments and abstract methods, he’s working to develop a theoretical framework for describing the physics of these systems. Much of that work involves understanding the phenomena that arise because of impurities or strong interactions between electrons in solids that don’t conform with conventional physical theories. He also pioneered the theory of deconfined quantum criticality, which describes a class of phase transitions, and he discovered the dualities of quantum field theories in two dimensional superconducting states, which has important applications to many problems in the field.

Todadri has been named a Simons Investigator, a Sloan Research Fellow, and a fellow of the American Physical Society. In 2023, he was elected to the American Academy of Arts and Sciences

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Math discovery provides new method to study cell activity, aging

by Meg Henderson, Mississippi State University

New mathematical tools revealing how quickly cell proteins break down are poised to uncover deeper insights into how we age, according to a recently published paper co-authored by a Mississippi State researcher and his colleagues from Harvard Medical School and the University of Cambridge.

Galen Collins, assistant professor in MSU's Department of Biochemistry, Molecular Biology, Entomology and Plant Pathology, co-authored the paper published in the Proceedings of the National Academy of Sciences in April.

"We already understand how quickly proteins are made, which can happen in a matter of minutes," said Collins, who is also a scientist in the Mississippi Agricultural and Forestry Experiment Station. "Until now, we've had a very poor understanding of how much time it takes them to break down."

The paper in applied mathematics, " Maximum entropy determination of mammalian proteome dynamics ," presents the new tools that quantify the degradation rates of cell proteins—how quickly they break down—helping us understand how cells grow and die and how we age. Proteins— complex molecules made from various combinations of amino acids—carry the bulk of the workload within a cell, providing its structure, responding to messages from outside the cell and removing waste.

The results proved that not all proteins degrade at the same pace but instead fall into one of three categories, breaking down over the course of minutes, hours or days. While previous research has examined cell protein breakdown, this study was the first to quantify mathematically the degradation rates of all cell protein molecules, using a technique called maximum entropy.

"For certain kinds of scientific questions, experiments can often reveal infinitely many possible answers; however, they are not all equally plausible," said lead author Alexander Dear, research fellow in applied mathematics at Harvard University.

"The principle of maximum entropy is a mathematical law that shows us how to precisely calculate the plausibility of each answer—its 'entropy'—so that we can choose the one that is the most likely."

"This kind of math is sort of like a camera that zooms in on your license plate from far away and figures out what the numbers should be," Collins said. "Maximum entropy gives us a clear and precise picture of how protein degradation occurs in cells."

In addition, the team used these tools to study some specific implications of protein degradation for humans and animals. For one, they examined how those rates change as muscles develop and adapt to starvation.

"We found that starvation had the greatest impact on the intermediate group of proteins in muscular cells, which have a half-life of a few hours, causing the breakdown to shift and accelerate," Collins said. "This discovery could have implications for cancer patients who experience cachexia, or muscle wasting due to the disease and its treatments."

They also explored how a shift in the breakdown of certain cell proteins contributes to neurodegenerative disease.

"These diseases occur when waste proteins, which usually break down quickly, live longer than they should," Collins said. "The brain becomes like a teenager's bedroom, accumulating trash, and when you don't clean it up, it becomes uninhabitable."

Dear affirmed the study's value lies not only in what it revealed about cell protein degeneration, but also in giving scientists a new method to investigate cell activity with precision.

"Our work provides a powerful new experimental method for quantifying protein metabolism in cells," he said. "Its simplicity and rapidity make it particularly well-suited for studying metabolic changes."

Journal information: Proceedings of the National Academy of Sciences

Provided by Mississippi State University

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There are now over 39,000 volumes. Contact: Manuscripts Reading Room (01223 333143, [email protected]) Cambridge theses held by CUL. Finding and ordering Cambridge theses. A small but growing proportion of Cambridge theses are available to consult in digital form in the university repository Apollo. See the Office of Scholarly Communication's ...
Department of Pure Mathematics and Mathematical Statistics
Welcome to DPMMS The Department of Pure Mathematics and Mathematical Statistics (DPMMS) (including the Statistical Laboratory as a sub-department) conducts teaching and research across a wide range of pure mathematics, probability and statistics. DPMMS currently hosts over 100 Academic and Research Staff and around 80 PhD students over three Pavilions as part of the Centre for Mathematical ...
Dissertations and theses
Recently completed Cambridge PhD theses are available via Apollo, the University Repository (unless under embargo). You can also search for the full text of PhD theses across the UK using the British Library's EThOS service or browse the Proquest Dissertations and Theses database for research across 700 academic institutions worldwide.
Srinivasa Ramanujan
Srinivasa Ramanujan [a] (22 December 1887 - 26 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.
Online Senior Thesis
Cambridge, MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132 Department Main Office Contact Web Site Contact Digital Accessibility
My PhD Thesis
My PhD Thesis. My PhD thesis on modelling the spread of river water in the ocean in its entirety - not for the faint hearted! Unless you are a researcher in fluid mechanics, I strongly recommend reading the summary articles here before tackling the beast below. If you have any questions/comments please do get in touch via the contact form.
PhD Theses
First-order gradient regularisation methods for image restoration: reconstruction of tomographic images with thin structures and denoising piecewise affine images. Read more.
MIT Theses
MIT's DSpace contains more than 58,000 theses completed at MIT dating as far back as the mid 1800's. Theses in this collection have been scanned by the MIT Libraries or submitted in electronic format by thesis authors. Since 2004 all new Masters and Ph.D. theses are scanned and added to this collection after degrees are awarded.
Harvard Mathematics Department Harvard Department of Mathematics PhD
Harvard Math Thesis Party 2001; Harvard Math Thesis Party 2005; Photos of Graduation Party 2008; Photos of Graduation Party 2009; ... Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact Web Site Contact Digital Accessibility. Legacy Department of Mathematics Website ...
AMS :: Transactions of the American Mathematical Society
Transactions of the American Mathematical Society. Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics. ISSN 1088-6850 (online) ISSN 0002-9947 (print)
Birth by C-section more than doubles odds of measles vaccine failure
A study by the University of Cambridge, UK, and Fudan University, China, has found that a single dose of the measles jab is up to 2.6 times more likely to be completely ineffective in children born by C-section, compared to those born naturally. Failure of the vaccine means that the child's immune system does not produce antibodies to fight ...
Department of Pure Mathematics and Mathematical Statistics
Publications. Stochastic wave equation with Hölder noise coefficient: Well-posedness and small mass limit. Y Han. - Journal of Functional Analysis. (2024) 286, 110224. (doi: 10.1016/j.jfa.2023.110224) A support theorem for parabolic stochastic PDEs with nondegenerate Hölder diffusion coefficients.
Jack Smith
Jack Smith. Photo credit: Layton Thompson I am a College Lecturer, and the Director of Studies in Pure Mathematics, at St John's College, Cambridge. I am also an Affiliated Lecturer in the Department of Pure Mathematics and Mathematical Statistics. Previously I was a visiting researcher at the Fields Institute, Toronto, a postdoc at University College London, and a PhD student of Ivan Smith.
Janabel Xia: Algorithms, dance rhythms, and the drive to succeed
MIT math major Janabel Xia sorts algorithms and improving traffic control systems for driverless vehicles, is a member of several dance clubs, is active in several social justice organizations, worked on cryptography and web authentication technology, and created a polling app that allows users to vote anonymously.
Five MIT faculty elected to the National Academy of Sciences for 2024
The National Academy of Sciences has elected 120 members and 24 international members, including five faculty members from MIT. Guoping Feng, Piotr Indyk, Daniel J. Kleitman, Daniela Rus, and Senthil Todadri were elected in recognition of their "distinguished and continuing achievements in original research.". Membership to the National ...
Math discovery provides new method to study cell activity, aging
Math discovery provides new method to study cell activity, aging. by Meg Henderson, Mississippi State University. Credit: Unsplash/CC0 Public Domain. New mathematical tools revealing how quickly ...

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Locomotive superheaters and feed water heaters

A cost accounting system for the F. L. & J. C. Codman Company buffing wheels

The electrical strength of insulators in high vacua