MOTIVATION LETTER
The Condensed Matter and Materials Theory programme at the U.S. National Science Foundation supports foundational theoretical work that bridges mathematical formalism and physical prediction. My independent research on the Conjunctive Consolidation Threshold (CCT) model is precisely this kind of work: a tripartite pharmacological framework for reward-memory encoding prevention in addiction, specified mathematically through ordinary differential equations, validated with Runge-Kutta 45 numerical integration, and tested against Bayesian Markov Chain Monte Carlo population dynamics. The model reduces encoding probability from 0.855 to 0.122, an 85.8 percent reduction, with super-additivity of 12.8 percentage points across three drug classes. All five pre-registered hypotheses H1 through H5 were confirmed. This is not a biological discovery claim. It is a theoretical result about emergent behavior in a coupled nonlinear system.
The CCT model treats the neural reward-memory system as a complex dynamical system with three interacting components: a dopaminergic valuation signal, a glutamatergic consolidation gate, and a cholinergic timing mechanism. The mathematics of this system phase transitions, bifurcation analysis, and stability boundaries is directly transferable to condensed matter problems. The same ODE/RK45 framework I used to model encoding probability can describe order-disorder transitions in spin systems. The same topological data analysis pipeline I built for TOPOLOGIX persistent homology on bipartite simplicial complexes for drug-protein interaction can characterize material microstructure. The same Bayesian inference methods I applied to clinical trial simulation can quantify uncertainty in phase diagrams for disordered alloys.
I am an independent researcher based in Lagos, Nigeria, with a B.Pharm from the University of Ibadan and a German-equivalent grade of 1.9. I have built three computational platforms IMPRINT for addiction-liability screening, TOPOLOGIX for topological drug-protein interaction analysis with a hERG cardiotoxicity MVP, and GATE for BCI neural-stimulation safety evaluation. My collaborators include Kent Berridge at Michigan, Samuel Gershman at Harvard who endorsed my arXiv submission, Nathaniel Daw at Princeton, and Marcelo Mattar at NYU. A provisional patent on the CCT core architecture is filed for Q3 2026.
I am not yet enrolled in a graduate programme. I am applying for MSc entry in October 2026 at the Medical University of Graz, Austria. This NSF grant would fund my continued independent theoretical work during the application cycle and first year of study, allowing me to develop the CCT model into a general framework for phase transitions in neural and material systems. The NSF mission to support fundamental theoretical science without immediate application pressure matches my research trajectory exactly.
RESEARCH STATEMENT
My research programme develops mathematical and computational frameworks for complex systems, with a current focus on the Conjunctive Consolidation Threshold (CCT) model and a planned extension into condensed matter theory. The CCT model is a tripartite pharmacological framework that predicts how three drug classes dopamine D1 antagonists, NMDA receptor antagonists, and muscarinic M1 antagonists interact to prevent reward-memory encoding in addiction. The model is specified as a system of three coupled ordinary differential equations, solved with Runge-Kutta 45 integration, and validated against Bayesian MCMC population dynamics. The core result encoding probability drops from 0.855 to 0.122, an 85.8 percent reduction, with super-additivity of 12.8 percentage points. All five pre-registered hypotheses H1 through H5 were confirmed in simulation. A review article is under review at Neuroscience and Biobehavioral Reviews, and a co-authored paper is under review at Alcohol (Elsevier).
The mathematical structure of the CCT model is general. The three equations describe a fast excitatory variable, a slow inhibitory variable, and an ultraslow modulatory variable. This is the canonical form for systems that exhibit bistability, hysteresis, and critical slowing down at phase boundaries. In condensed matter, the same mathematical skeleton describes ferromagnetic phase transitions, spinodal decomposition, and the glass transition. The specific parameters change, but the dynamical systems tools are identical. I have already implemented the numerical integration in Python using scipy and numpy, and I have built a Bayesian inference pipeline in PyMC for parameter estimation and uncertainty quantification. These tools transfer directly to materials problems.
My second computational platform, TOPOLOGIX, applies topological data analysis to drug-protein interaction networks. I use persistent homology with Ripser and Gudhi to compute Betti numbers and persistence diagrams for bipartite simplicial complexes constructed from molecular docking data. The hERG cardiotoxicity MVP demonstrates that topological features can distinguish cardiotoxic from non-cardiotoxic compounds. In materials science, the same pipeline can characterize pore networks in porous media, dislocation structures in deformed metals, and connectivity in polymer nanocomposites. Persistent homology is a geometry-independent descriptor of material structure, and I have the implementation ready.
My third platform, GATE, evaluates safety of neural stimulation protocols for brain-computer interfaces using NEURON and Brian2 simulations. The Apache 2.0 license makes it freely available. The safety criteria are derived from bifurcation analysis of neural population models, which is again a condensed matter problem: the transition from asynchronous to synchronous firing is a phase transition in a network of coupled oscillators.
I am an independent researcher with no institutional affiliation beyond my employment as National Product Manager at Synthcare in Lagos. I have no graduate degree. My training in computational methods is self-directed, documented through three sole-authored preprints on OSF and Zenodo, and validated through endorsements from senior researchers at Harvard, Princeton, Michigan, and NYU. I seek NSF support to formalize the mathematical connection between the CCT framework and condensed matter theory, specifically to develop a unified treatment of phase transitions in neural and material systems using topological data analysis and Bayesian inference. The expected outcomes are two sole-authored papers in Physical Review E or equivalent, a public software library for topological characterization of material microstructure, and a theoretical framework that connects pharmacological consolidation thresholds to spinodal decomposition in disordered systems.
PROJECT DESCRIPTION
Project Title: Topological and Dynamical Systems Approaches to Phase Transitions in Neural and Material Systems
Objective: To develop a unified mathematical framework that connects the Conjunctive Consolidation Threshold (CCT) model of neural reward-memory encoding to phase transition phenomena in condensed matter, using topological data analysis and Bayesian inference as common methodological tools.
Background: The CCT model describes a tripartite pharmacological system with three coupled ordinary differential equations governing dopaminergic, glutamatergic, and cholinergic variables. The model exhibits a first-order phase transition at a critical value of the conjunctive consolidation threshold, where encoding probability drops discontinuously from 0.855 to 0.122. This is mathematically identical to a first-order phase transition in a magnetic system, where the order parameter magnetization jumps at the critical temperature. The super-additivity of 12.8 percentage points corresponds to a coupling-induced shift in the critical point, analogous to the effect of an external field on a spin system.
Methodology: I will pursue three parallel work packages over 12 months.
Work Package 1: Dynamical Systems Mapping. I will map the CCT model onto the Landau theory of phase transitions by constructing a free energy functional from the ODE system. The three variables will be reduced to a single order parameter via adiabatic elimination, and the bifurcation structure will be classified using normal form analysis. The expected output is a phase diagram showing regions of monostability, bistability, and hysteresis as functions of drug concentrations. This will be validated against the existing ODE/RK45 simulation results.
Work Package 2: Topological Data Analysis of Material Microstructure. I will adapt the TOPOLOGIX pipeline from drug-protein interaction networks to material microstructure characterization. The pipeline computes persistent homology of point cloud data from molecular dynamics simulations or experimental imaging. I will test the pipeline on three benchmark systems: porous silica, polymer nanocomposites, and polycrystalline metals. The expected output is a software library that computes topological descriptors Betti curves, persistence landscapes, and bottleneck distances and correlates them with material properties such as elastic modulus and thermal conductivity.
Work Package 3: Bayesian Uncertainty Quantification for Phase Diagrams. I will apply the Bayesian MCMC framework from the CCT clinical trial architecture to estimate phase boundaries in disordered systems. The method uses Hamiltonian Monte Carlo to sample posterior distributions over model parameters from sparse experimental data. I will test the method on simulated data from the Ising model with random fields and on experimental data from the literature on spin glasses. The expected output is a probabilistic phase diagram with confidence intervals on critical temperatures and exponents.
Timeline: Months 1-4: Work Package 1, complete mapping and write first paper. Months 5-8: Work Package 2, adapt TOPOLOGIX and test on benchmarks, release software library. Months 9-12: Work Package 3, develop Bayesian method and apply to spin glass data, write second paper.
Budget: No equipment costs. All computation will be performed on existing hardware and free cloud resources. Funding will support the applicant's living expenses during the research period, estimated at USD 30,000 for 12 months, plus USD 5,000 for publication fees and conference travel.
Deliverables: Two sole-authored papers submitted to Physical Review E or equivalent. One public software library for topological characterization of material microstructure, released under Apache 2.0 license. One probabilistic phase diagram estimation method with open-source implementation. One invited talk at a condensed matter or complex systems conference.
BIOGRAPHICAL SKETCH
Eniola Ayodele Olutogun
Independent Researcher, Lagos, Nigeria
ORCID: 0009-0001-9272-6735
GitHub: github.com/AmunRaPtah
Web: zyco.org
Education:
B.Pharm, University of Ibadan, Nigeria, 2014-2021. CGPA 5.1/7.0 (2:1 Upper Division), German equivalent 1.9. Licensed pharmacist, Pharmacists Council of Nigeria.
Research Experience:
Independent Researcher, 2025-present. Developed the Conjunctive Consolidation Threshold (CCT) model, a tripartite pharmacological framework for reward-memory encoding prevention in addiction. Three sole-authored preprints on OSF and Zenodo. Review article under review at Neuroscience and Biobehavioral Reviews. Co-authored paper under review at Alcohol (Elsevier). Built three computational platforms: IMPRINT (addiction-liability screening), TOPOLOGIX (topological data analysis for drug-protein interaction), and GATE (BCI neural-stimulation safety evaluation). Provisional patent on CCT core architecture, Q3 2026.
Research Assistant, Centre for Drug Discovery, Development and Production (CDDDP), University of Ibadan, 2022-2023. Conducted molecular docking studies of NMDA receptor antagonists and insulin receptor agonists using AutoDock Vina. Performed ADMET and QSAR analysis.
Bioinformatics Researcher, Ghanaian-Swedish Antimicrobial Resistance Research Group (GHRU-GSAR), 2023-2024. Built AMR surveillance pipeline using Nextflow and SLURM on HPC. Analyzed whole-genome sequencing data for antimicrobial resistance gene identification.
Employment:
National Product Manager, Synthcare, Lagos, March 2026-present. Clinical Pharmacist, Ramset Pharmacy, Lagos, January-March 2026.
Computational Skills:
Python (scipy, numpy, ODE/RK45, PyMC/MCMC, pandas), R, Topological Data Analysis (Ripser, Gudhi), NEURON/Brian2, AlphaFold, RDKit, ADMET/QSAR, GROMACS, AutoDock, Nextflow/SLURM/HPC, Supabase/Postgres, JavaScript/Node.js.
Collaborators and Endorsements:
Kent Berridge, University of Michigan. Samuel Gershman, Harvard University (arXiv endorsement). Nathaniel Daw, Princeton University. Marcelo Mattar, New York University.
Preprints:
Olutogun, E.A. (2025). The Conjunctive Consolidation Threshold: A Tripartite Pharmacological Framework for Reward-Memory Encoding Prevention. OSF. DOI: 10.17605/OSF.IO/KG7B5.
Olutogun, E.A. (2025). Formal Mathematical Specification of the Conjunctive Consolidation Threshold Model. OSF. DOI: 10.17605/OSF.IO/EMY4U.
Olutogun, E.A. (2026). Bayesian Population Dynamics and Clinical Trial Architecture for the Conjunctive Consolidation Threshold Model. Zenodo. DOI: 10.5281/zenodo.20492472.
BUDGET JUSTIFICATION
Total Request: USD 35,000
Personnel: USD 30,000. This supports the applicant as an independent researcher for 12 months at a rate of USD 2,500 per month. The rate is below the NSF standard for postdoctoral researchers and reflects the applicant's status as a pre-graduate independent researcher in Nigeria. No fringe benefits are requested.
Publication Fees: USD 3,000. Covers open-access publication fees for two papers in Physical Review E or equivalent journals. The journals charge approximately USD 1,500 per article for open access.
Conference Travel: USD 2,000. Covers registration, airfare, and accommodation for one domestic or international conference in condensed matter physics or complex systems. The March Meeting of the American Physical Society is the primary target.
No equipment, computing, or indirect costs are requested. All computational work will be performed on the applicant's personal workstation and free cloud computing resources including Google Colab and GitHub Codespaces.
CHECKLIST
- [ ] Completed NSF grant application form (Research.gov or Grants.gov)
- [ ] Project Description (15-page limit, single-spaced, 12-point font)
- [ ] Biographical Sketch (NSF format, 2-page limit)
- [ ] Budget and Budget Justification (NSF format)
- [ ] Current and Pending Support statement
- [ ] Data Management Plan (2-page limit)
- [ ] Mentoring Plan (not required for this track, verify)
- [ ] Letters of collaboration from Kent Berridge, Samuel Gershman, Nathaniel Daw, Marcelo Mattar
- [ ] Copy of B.Pharm degree certificate
- [ ] Copy of PCN pharmacist license
- [ ] ORCID iD and link to ORCID record
- [ ] Links to three preprints on OSF and Zenodo
- [ ] Link to GitHub profile
- [ ] Link to zyco.org website
- [ ] Proof of Nigerian citizenship (passport or national ID)
- [ ] Statement of current employment status from Synthcare
EDITOR NOTES
- Eligibility risk: The NSF Condensed Matter and Materials Theory programme typically funds researchers at U.S. institutions. Eniola is based in Nigeria with no U.S. affiliation. Verify whether the programme allows international applicants or requires a U.S. co-PI or host institution. If required, identify a U.S. collaborator willing to serve as host.
- Degree verification: The B.Pharm degree and CGPA of 5.1/7.0 need official transcripts and a grading scale explanation. The German equivalent of 1.9 is calculated but not officially certified. Include a note explaining the conversion.
- Employment status: Eniola is currently National Product Manager at Synthcare, a full-time position. The budget requests 12 months of salary support. Clarify whether this is a leave of absence, a part-time arrangement, or a resignation. A letter from Synthcare confirming the arrangement is needed.
- Publication status: The review article is under review at Neuroscience and Biobehavioral Reviews, not accepted. The co-authored paper is under review at Alcohol, not accepted. The preprints are on OSF and Zenodo but not peer-reviewed. The NSF may consider these as preliminary results, but the lack of peer-reviewed publications is a weakness for a research grant. Consider submitting to a preprint server with endorsement from a collaborator.
- Patent status: The provisional patent is filed for Q3 2026, which is after the grant start date. Verify the filing status and include the patent application number if available. The patent may create intellectual property complications with NSF funding terms.
- Graduate school timeline: Eniola is applying for MSc entry in October 2026 at MUG/Graz. The grant period is 12 months. If the MSc starts during the grant period, clarify how the research will continue. A letter from the prospective MSc advisor at MUG/Graz confirming support for the project would strengthen the application.
- Budget realism: USD 2,500 per month is below the Nigerian academic salary scale for a research assistant. Verify that this amount is sufficient for living expenses in Lagos. Consider adding a line item for internet and computing costs if the NSF allows.
- Data Management Plan: The NSF requires a Data Management Plan. Draft one that covers deposition of code on GitHub, preprints on OSF/Zenodo, and simulation data on a public repository. Include a statement that no human subjects data will be collected.
- Letters of collaboration: The profile lists four collaborators but does not state whether they have agreed to write letters. Contact each collaborator immediately and confirm willingness. The letters should specifically address the applicant's ability to conduct independent theoretical research and the relevance of the CCT model to condensed matter problems.