Draft — African Institute for Mathematical Sciences (AIMS) Bursaries

MOTIVATION LETTER

The CCT model, a Bayesian-calibrated dynamical systems framework for addiction neuropharmacology, is the work I would bring to the AIMS AI for Science Master's programme. This model integrates machine learning calibration with mathematical modeling to address a health challenge that disproportionately affects African populations, and it demonstrates exactly the kind of AI-for-science research AIMS prioritizes. I am a Nigerian pharmacist and computational researcher, currently enrolled in the M.Sc. Digital Health programme at the Hasso Plattner Institute, University of Potsdam, and I seek the AIMS bursary to deepen the mathematical foundations that underpin this work.

The CCT model encodes a tripartite hypothesis: reward-memory consolidation in addiction can be prevented by simultaneously modulating dopaminergic reward prediction error, NMDAR-dependent long-term potentiation, and affective contrast. I implemented this as a coupled three-axis ODE system solved with RK45, then calibrated all 14 free parameters using Bayesian MCMC with PyMC's DEMetropolisZ sampler. Prior distributions were elicited from a systematic screen of 1,847 records from the addiction neuroscience literature. All five pre-registered hypotheses, H1 through H5, were confirmed, with posterior super-additivity of 13 to 22 percentage points across model versions. Three sole-authored preprints are under review at peer-reviewed journals, and a co-authored paper is under review at Alcohol (Elsevier).

This work is AI for science in the precise sense AIMS defines it. The model uses Bayesian inference to constrain a mechanistic mathematical model of a biological system, producing predictions that are interpretable and testable. The pre-registration of hypotheses and the transparent reporting of calibration procedures reflect a commitment to scientific rigor that I understand AIMS expects from its scholars.

The AIMS AI for Science Master's programme is the right next step for this research trajectory. My current training at HPI focuses on digital health applications, but the CCT model's mathematical core, dynamical systems theory, Bayesian statistics, and stochastic simulation, demands deeper formal training. AIMS's curriculum in mathematical sciences, delivered by faculty from the African Institute for Mathematical Sciences network, would provide that foundation while keeping me connected to the African research community. The fully funded structure of the bursary, covering tuition, accommodation, and stipend, makes this training accessible without diverting resources from my ongoing research commitments.

Addiction is a growing public health crisis across Africa, yet most treatment protocols are imported from Western contexts without local validation. A mathematical model of addiction neuropharmacology, developed and refined by an African researcher, is a direct contribution to changing that dynamic. The CCT model's predictions about combination pharmacotherapy could inform clinical trial design for interventions tailored to African populations, where genetic diversity and environmental factors differ from the populations in which most addiction drugs were tested.

I meet the AIMS eligibility criteria: I am a Nigerian citizen, I hold a B.Pharm from the University of Ibadan with a German equivalent grade of 1.9, and my academic background spans mathematics, pharmacology, and computer science. I have no previous AIMS scholarship. The selection process, including the written mathematics solutions and coding responses, is one I approach with confidence given my daily work in Python, PyMC, and dynamical systems simulation.

The AIMS AI for Science Master's is the mathematical deepening my research path requires. I am prepared to commit fully to the programme's demands and to bring the CCT model, and the broader research programme it anchors, into the AIMS community.

RESEARCH STATEMENT

My research programme sits at the intersection of dynamical systems theory, Bayesian inference, and computational neuroscience, with a focus on building mechanistic models of brain function that generate clinically actionable predictions. The flagship project is the CCT, or Conjunctive Consolidation Threshold, model of addiction neuropharmacology. The central thesis is that reward-memory encoding, the process by which drug-associated cues become permanently consolidated, requires the simultaneous crossing of a threshold across three coupled biological axes: dopaminergic reward prediction error, NMDAR-dependent long-term potentiation, and affective contrast. If any one axis is suppressed below threshold, consolidation fails and the memory does not form.

The model is implemented as a system of coupled ordinary differential equations solved with RK45 integration. The three axes interact through coupling terms that I derived from the known neurobiology of the mesolimbic reward pathway. The full system has 14 free parameters, none of which are fitted by hand. Instead, I elicited prior distributions from a systematic screen of 1,847 records from the addiction neuroscience literature, then calibrated the model using Bayesian MCMC with PyMC's DEMetropolisZ sampler. The posterior distributions over parameters represent an updated synthesis of the experimental literature, constrained by the model's structure.

The results confirmed all five pre-registered hypotheses, H1 through H5. The most important finding is posterior super-additivity: the combined effect of suppressing all three axes exceeds the sum of individual suppressions by 13 to 22 percentage points across model versions. This is a specific, quantitative prediction that combination pharmacotherapy targeting all three axes should outperform any single-axis intervention. Three sole-authored preprints describing these results are under review at peer-reviewed journals, and a co-authored paper is under review at Alcohol (Elsevier).

The AIMS AI for Science Master's programme is the ideal environment to advance this work in three specific directions. First, the mathematical core of the CCT model, bifurcation analysis of the coupled ODE system, sensitivity analysis of the Bayesian calibration, and identifiability analysis of the 14-parameter posterior, requires formal training I do not currently have. AIMS's curriculum in mathematical sciences directly addresses these gaps. Second, the programme's emphasis on AI applications in scientific research aligns with my next methodological step: using the calibrated CCT model as a generative prior for machine learning models that predict individual variation in addiction susceptibility from genetic and environmental data. Third, the AIMS network across Africa provides a platform for translating the model's predictions into clinical research protocols relevant to African populations.

Beyond the CCT model, my research programme includes several projects that demonstrate the breadth of my computational methods. A pre-registered, powered replication study on hERG cardiotoxicity tested whether bipartite persistent homology predicts cardiotoxicity from protein-ligand interface geometry. The result was negative: topological features did not beat a plain descriptor baseline (AUROC 0.8426 vs 0.8782). This negative result is scientifically important because it settles a comparison the published literature had never actually run. A follow-up study applied the same topological constructs to drug-resistance prediction and found they carry almost no signal (AUROC 0.425 and 0.485 on the Platinum benchmark), ruling out interface geometry as the driver. This motivated my current TOPOLOGIX project, which uses ESM-2 protein language model delta-embeddings combined with Morgan fingerprints and a Random Forest classifier to predict drug-resistance mutations from sequence alone, achieving AUROC 0.804 plus or minus 0.025 on the Platinum benchmark and covering 100 percent of mutations versus approximately 18 percent for structure-limited tools.

I also maintain neurocascade, a receptor-to-behavior brain-circuit simulation engine that couples pharmacokinetics to receptor binding to Wilson-Cowan circuit dynamics to behavioral readout ODE layers. Three literature-calibrated receptor and circuit systems, mu-opioid, D2 dopamine, and GABA-A, are Bayesian-calibrated with PyMC, and 62 of 62 tests pass. The circuit-layer parameters are explicitly labeled illustrative pending real behavioral data fits, a distinction I maintain rigorously.

The AIMS programme's selection criteria emphasize academic background in AI-relevant fields, passion for AI and science applications, and mathematical problem solving. My B.Pharm from the University of Ibadan, my daily work in Python, PyMC, and dynamical systems simulation, and my publication record demonstrate all three. The written mathematics solutions and coding responses required by the application are tasks I approach with confidence. The online interview, should I be shortlisted, is an opportunity to discuss the CCT model's mathematics in detail.

The AIMS AI for Science Master's is a training programme, not a research grant, and I understand the distinction. My goal is to use the programme's curriculum to close specific mathematical gaps in my training, then return to my independent research with a stronger formal foundation. The bursary's full funding, covering tuition, accommodation, and stipend, makes this possible without compromising my research independence.

CHECKLIST

- [ ] Verify AIMS AI for Science Master's application portal and create account
- [ ] Confirm eligibility: Nigerian citizenship, residence in Africa during application period
- [ ] Confirm degree requirement: B.Pharm (4-year degree) meets the four-year degree criterion
- [ ] Obtain official transcripts from University of Ibadan, including degree certificate and CGPA documentation
- [ ] Obtain proof of enrollment or admission letter from Hasso Plattner Institute M.Sc. Digital Health programme
- [ ] Write motivation letter (500 words maximum, current draft at approximately 580 words, trim to fit)
- [ ] Prepare CV in AIMS format, emphasizing mathematical and computational skills
- [ ] Complete written mathematics solutions (AIMS will provide problems)
- [ ] Complete coding responses (AIMS will provide tasks)
- [ ] Prepare two academic reference letters (consider Kent Berridge, Samuel Gershman, or Nathaniel Daw)
- [ ] Verify ORCID record (0009-0001-9272-6735) is current and linked to publications
- [ ] Verify GitHub account (github.com/AmunRaPtah) is current and showcases relevant code
- [ ] Prepare PDF copies of three sole-authored CCT preprints for submission as supporting materials
- [ ] Prepare PDF copy of co-authored Alcohol (Elsevier) paper under review
- [ ] Submit application before deadline: 2026-03-21
- [ ] Prepare for online interview (shortlisted candidates, May 2026)

EDITOR NOTES

- Eligibility risk: The applicant is currently enrolled in an M.Sc. programme at HPI/Potsdam. AIMS requires residence in Africa during application. Confirm whether current enrollment in a German programme affects the residence requirement, and whether AIMS considers the applicant an Africa-based researcher given the enrollment status. This is the single largest eligibility risk and must be verified before submission.

- Degree requirement verification: The B.Pharm from University of Ibadan is a four-year degree, which meets the stated requirement. However, the applicant's CGPA is 5.1/7.0 with German equivalent 1.9. Confirm that AIMS uses the German equivalent or the raw CGPA in its evaluation, and whether the 2:1 Upper Division classification is sufficient for competitive admission.

- Motivation letter length: The current draft is approximately 580 words, exceeding the 500-word limit stated in the selection criteria. Trim to exactly 500 words or fewer before submission. The sections on TOPOLOGIX and neurocascade in the research statement are context but should not appear in the motivation letter if space is constrained.

- Reference letter strategy: The profile lists Kent Berridge, Samuel Gershman, Nathaniel Daw, and Marcelo Mattar as endorsers. For AIMS, which is a mathematics-focused programme, prioritize references who can speak to mathematical and computational rigor. Gershman's arXiv endorsement is evidence of his willingness to support the applicant, but confirm he is willing to write a full reference letter for a training programme application.

- Transcript timing: The applicant graduated from University of Ibadan in 2021. Obtain official transcripts well ahead of the deadline, as Nigerian university administrative processes can be slow. Request both the official transcript and a letter from the registrar confirming degree conferral.

- Mathematics and coding assessments: AIMS requires written mathematics solutions and coding responses as part of the application. The applicant's daily work in PyMC, ODE solvers, and Python positions them well, but these assessments are timed and structured. Recommend practicing with past AIMS entrance examination papers if available, and allocating dedicated preparation time before the deadline.

- The CCT model is the correct research line to lead with for this programme. It is the most mathematically rigorous of the applicant's projects, it directly matches AIMS's AI-for-science focus, and it has a clear African health relevance angle. The negative results in the topology studies are honest and demonstrate rigor, but they should be mentioned briefly in the research statement as context, not as the primary focus. The ergofluids project, which failed its first real-data gate, should not be presented as validated work; the profile already handles this correctly by describing the failure transparently.

MOTIVATION LETTER

The CCT model, a Bayesian-calibrated dynamical systems framework for addiction neuropharmacology, is the work I would bring to the AIMS AI for Science Master's programme. This model integrates machine learning calibration with mathematical modeling to address a health challenge that disproportionately affects African populations, and it demonstrates exactly the kind of AI-for-science research AIMS prioritizes. I am a Nigerian pharmacist and computational researcher, currently enrolled in the M.Sc. Digital Health programme at the Hasso Plattner Institute, University of Potsdam, and I seek the AIMS bursary to deepen the mathematical foundations that underpin this work.

The CCT model encodes a tripartite hypothesis: reward-memory consolidation in addiction can be prevented by simultaneously modulating dopaminergic reward prediction error, NMDAR-dependent long-term potentiation, and affective contrast. I implemented this as a coupled three-axis ODE system solved with RK45, then calibrated all 14 free parameters using Bayesian MCMC with PyMC's DEMetropolisZ sampler. Prior distributions were elicited from a systematic screen of 1,847 records from the addiction neuroscience literature. All five pre-registered hypotheses, H1 through H5, were confirmed, with posterior super-additivity of 13 to 22 percentage points across model versions. Three sole-authored preprints are under review at peer-reviewed journals, and a co-authored paper is under review at Alcohol (Elsevier).

This work is AI for science in the precise sense AIMS defines it. The model uses Bayesian inference to constrain a mechanistic mathematical model of a biological system, producing predictions that are interpretable and testable. The pre-registration of hypotheses and the transparent reporting of calibration procedures reflect a commitment to scientific rigor that I understand AIMS expects from its scholars.

The AIMS AI for Science Master's programme is the right next step for this research trajectory. My current training at HPI focuses on digital health applications, but the CCT model's mathematical core, dynamical systems theory, Bayesian statistics, and stochastic simulation, demands deeper formal training. AIMS's curriculum in mathematical sciences, delivered by faculty from the African Institute for Mathematical Sciences network, would provide that foundation while keeping me connected to the African research community. The fully funded structure of the bursary, covering tuition, accommodation, and stipend, makes this training accessible without diverting resources from my ongoing research commitments.

Addiction is a growing public health crisis across Africa, yet most treatment protocols are imported from Western contexts without local validation. A mathematical model of addiction neuropharmacology, developed and refined by an African researcher, is a direct contribution to changing that dynamic. The CCT model's predictions about combination pharmacotherapy could inform clinical trial design for interventions tailored to African populations, where genetic diversity and environmental factors differ from the populations in which most addiction drugs were tested.

I meet the AIMS eligibility criteria: I am a Nigerian citizen, I hold a B.Pharm from the University of Ibadan with a German equivalent grade of 1.9, and my academic background spans mathematics, pharmacology, and computer science. I have no previous AIMS scholarship. The selection process, including the written mathematics solutions and coding responses, is one I approach with confidence given my daily work in Python, PyMC, and dynamical systems simulation.

The AIMS AI for Science Master's is the mathematical deepening my research path requires. I am prepared to commit fully to the programme's demands and to bring the CCT model, and the broader research programme it anchors, into the AIMS community.

RESEARCH STATEMENT

My research programme sits at the intersection of dynamical systems theory, Bayesian inference, and computational neuroscience, with a focus on building mechanistic models of brain function that generate clinically actionable predictions. The flagship project is the CCT, or Conjunctive Consolidation Threshold, model of addiction neuropharmacology. The central thesis is that reward-memory encoding, the process by which drug-associated cues become permanently consolidated, requires the simultaneous crossing of a threshold across three coupled biological axes: dopaminergic reward prediction error, NMDAR-dependent long-term potentiation, and affective contrast. If any one axis is suppressed below threshold, consolidation fails and the memory does not form.

The model is implemented as a system of coupled ordinary differential equations solved with RK45 integration. The three axes interact through coupling terms that I derived from the known neurobiology of the mesolimbic reward pathway. The full system has 14 free parameters, none of which are fitted by hand. Instead, I elicited prior distributions from a systematic screen of 1,847 records from the addiction neuroscience literature, then calibrated the model using Bayesian MCMC with PyMC's DEMetropolisZ sampler. The posterior distributions over parameters represent an updated synthesis of the experimental literature, constrained by the model's structure.

The results confirmed all five pre-registered hypotheses, H1 through H5. The most important finding is posterior super-additivity: the combined effect of suppressing all three axes exceeds the sum of individual suppressions by 13 to 22 percentage points across model versions. This is a specific, quantitative prediction that combination pharmacotherapy targeting all three axes should outperform any single-axis intervention. Three sole-authored preprints describing these results are under review at peer-reviewed journals, and a co-authored paper is under review at Alcohol (Elsevier).

The AIMS AI for Science Master's programme is the ideal environment to advance this work in three specific directions. First, the mathematical core of the CCT model, bifurcation analysis of the coupled ODE system, sensitivity analysis of the Bayesian calibration, and identifiability analysis of the 14-parameter posterior, requires formal training I do not currently have. AIMS's curriculum in mathematical sciences directly addresses these gaps. Second, the programme's emphasis on AI applications in scientific research aligns with my next methodological step: using the calibrated CCT model as a generative prior for machine learning models that predict individual variation in addiction susceptibility from genetic and environmental data. Third, the AIMS network across Africa provides a platform for translating the model's predictions into clinical research protocols relevant to African populations.

Beyond the CCT model, my research programme includes several projects that demonstrate the breadth of my computational methods. A pre-registered, powered replication study on hERG cardiotoxicity tested whether bipartite persistent homology predicts cardiotoxicity from protein-ligand interface geometry. The result was negative: topological features did not beat a plain descriptor baseline (AUROC 0.8426 vs 0.8782). This negative result is scientifically important because it settles a comparison the published literature had never actually run. A follow-up study applied the same topological constructs to drug-resistance prediction and found they carry almost no signal (AUROC 0.425 and 0.485 on the Platinum benchmark), ruling out interface geometry as the driver. This motivated my current TOPOLOGIX project, which uses ESM-2 protein language model delta-embeddings combined with Morgan fingerprints and a Random Forest classifier to predict drug-resistance mutations from sequence alone, achieving AUROC 0.804 plus or minus 0.025 on the Platinum benchmark and covering 100 percent of mutations versus approximately 18 percent for structure-limited tools.

I also maintain neurocascade, a receptor-to-behavior brain-circuit simulation engine that couples pharmacokinetics to receptor binding to Wilson-Cowan circuit dynamics to behavioral readout ODE layers. Three literature-calibrated receptor and circuit systems, mu-opioid, D2 dopamine, and GABA-A, are Bayesian-calibrated with PyMC, and 62 of 62 tests pass. The circuit-layer parameters are explicitly labeled illustrative pending real behavioral data fits, a distinction I maintain rigorously.

The AIMS programme's selection criteria emphasize academic background in AI-relevant fields, passion for AI and science applications, and mathematical problem solving. My B.Pharm from the University of Ibadan, my daily work in Python, PyMC, and dynamical systems simulation, and my publication record demonstrate all three. The written mathematics solutions and coding responses required by the application are tasks I approach with confidence. The online interview, should I be shortlisted, is an opportunity to discuss the CCT model's mathematics in detail.

The AIMS AI for Science Master's is a training programme, not a research grant, and I understand the distinction. My goal is to use the programme's curriculum to close specific mathematical gaps in my training, then return to my independent research with a stronger formal foundation. The bursary's full funding, covering tuition, accommodation, and stipend, makes this possible without compromising my research independence.

CHECKLIST

- [ ] Verify AIMS AI for Science Master's application portal and create account
- [ ] Confirm eligibility: Nigerian citizenship, residence in Africa during application period
- [ ] Confirm degree requirement: B.Pharm (4-year degree) meets the four-year degree criterion
- [ ] Obtain official transcripts from University of Ibadan, including degree certificate and CGPA documentation
- [ ] Obtain proof of enrollment or admission letter from Hasso Plattner Institute M.Sc. Digital Health programme
- [ ] Write motivation letter (500 words maximum, current draft at approximately 580 words, trim to fit)
- [ ] Prepare CV in AIMS format, emphasizing mathematical and computational skills
- [ ] Complete written mathematics solutions (AIMS will provide problems)
- [ ] Complete coding responses (AIMS will provide tasks)
- [ ] Prepare two academic reference letters (consider Kent Berridge, Samuel Gershman, or Nathaniel Daw)
- [ ] Verify ORCID record (0009-0001-9272-6735) is current and linked to publications
- [ ] Verify GitHub account (github.com/AmunRaPtah) is current and showcases relevant code
- [ ] Prepare PDF copies of three sole-authored CCT preprints for submission as supporting materials
- [ ] Prepare PDF copy of co-authored Alcohol (Elsevier) paper under review
- [ ] Submit application before deadline: 2026-03-21
- [ ] Prepare for online interview (shortlisted candidates, May 2026)

EDITOR NOTES

- Eligibility risk: The applicant is currently enrolled in an M.Sc. programme at HPI/Potsdam. AIMS requires residence in Africa during application. Confirm whether current enrollment in a German programme affects the residence requirement, and whether AIMS considers the applicant an Africa-based researcher given the enrollment status. This is the single largest eligibility risk and must be verified before submission.

- Degree requirement verification: The B.Pharm from University of Ibadan is a four-year degree, which meets the stated requirement. However, the applicant's CGPA is 5.1/7.0 with German equivalent 1.9. Confirm that AIMS uses the German equivalent or the raw CGPA in its evaluation, and whether the 2:1 Upper Division classification is sufficient for competitive admission.

- Motivation letter length: The current draft is approximately 580 words, exceeding the 500-word limit stated in the selection criteria. Trim to exactly 500 words or fewer before submission. The sections on TOPOLOGIX and neurocascade in the research statement are context but should not appear in the motivation letter if space is constrained.

- Reference letter strategy: The profile lists Kent Berridge, Samuel Gershman, Nathaniel Daw, and Marcelo Mattar as endorsers. For AIMS, which is a mathematics-focused programme, prioritize references who can speak to mathematical and computational rigor. Gershman's arXiv endorsement is evidence of his willingness to support the applicant, but confirm he is willing to write a full reference letter for a training programme application.

- Transcript timing: The applicant graduated from University of Ibadan in 2021. Obtain official transcripts well ahead of the deadline, as Nigerian university administrative processes can be slow. Request both the official transcript and a letter from the registrar confirming degree conferral.

- Mathematics and coding assessments: AIMS requires written mathematics solutions and coding responses as part of the application. The applicant's daily work in PyMC, ODE solvers, and Python positions them well, but these assessments are timed and structured. Recommend practicing with past AIMS entrance examination papers if available, and allocating dedicated preparation time before the deadline.

- The CCT model is the correct research line to lead with for this programme. It is the most mathematically rigorous of the applicant's projects, it directly matches AIMS's AI-for-science focus, and it has a clear African health relevance angle. The negative results in the topology studies are honest and demonstrate rigor, but they should be mentioned briefly in the research statement as context, not as the primary focus. The ergofluids project, which failed its first real-data gate, should not be presented as validated work; the profile already handles this correctly by describing the failure transparently.

AI Draft — African Institute for Mathematical Sciences (AIMS) Bursaries