Mathematical Modeling seminars

Why do dorsal raphe serotonin neurons respond to reward, surprise, salience and uncertainty in ways that resist a single explanation? This talk proposes that serotonin activity encodes prospective value: a prediction of cumulative future reward. The model is motivated by the unusually strong and persistent spike-frequency adaptation of these neurons, which may support efficient and accurate predictions. It reproduces important qualitative features of serotonergic responses that earlier models miss and predicts measured in vivo firing rates more accurately than competing accounts. By treating previously separate responses as manifestations of one prospective value code, the work connects serotonin physiology to its computational roles in learning and behaviour.

Uri Cohen examines how stable memories can emerge in recurrent networks without imposing specially engineered dynamics such as a Lyapunov gradient. The analysis concerns discrete fixed points in networks with graded activity and noise. Random matrix methods characterize both the bulk and outlier eigenvalues of the local Jacobians. This yields a stability threshold: either all fixed points are stable or all are unstable, depending on their number. That threshold differs from the usual storage capacity, which counts achievable fixed points irrespective of stability. Relating the stability threshold to measurable pattern statistics and activation functions predicts advantages for sparse-like memories and threshold-linear responses. The talk connects these predictions to hippocampal CA3, a proposed auto-associative memory circuit. An assembled dataset of in-vivo patch-clamp recordings from CA3 pyramidal cells in behaving mice provides preliminary support for the predicted threshold-linear activation.

Amber Smith examines immune mechanisms underlying respiratory infections using mechanistic mathematical models combined with multimodal data. Using influenza, the seminar shows how models can expose biological processes that measurements alone do not reveal, explain why similar biomarker profiles can reflect different disease states, and improve predictions of outcomes. The approach links otherwise inaccessible mechanisms to a foundation for predictive, mechanism-based precision medicine.

Mammalian brains increasingly reuse the same neurons and regions for different tasks, while maintaining robust performance when the environment or stimulus context changes. Udo Ernst combines theoretical modelling with quantitative physiological observations to investigate the mechanisms that support both flexibility and resilience. Selective processing in the primate visual system provides the central example. One analytically tractable framework routes attended external signals through avalanches of spikes in recurrent neuronal networks; a second examines control circuits that preserve reliable routing across stimulus contexts. Mathematical analysis clarifies both mechanisms and how their operating ranges depend on physiological parameters.

Shadi Sharif Azadeh examines how artificial intelligence is turning operations research into a learning-enabled approach to decisions in dynamic, uncertain and data-rich systems. The talk develops two directions: integrating prediction, optimization and learning sequentially, and embedding AI within optimization algorithms. Applications address demand and supply in multimodal mobility with uncertain resources, train scheduling and modular autonomous vehicle operations. Rather than replacing optimization, AI can predict changing states, learn from operational feedback, improve computational efficiency and support adaptation where static models are inadequate.

Tito Homem-de-Mello presents decision-focused learning for two-stage stochastic optimization conditioned on contextual data. Recent theory shows that some two-stage stochastic linear programs can be solved using a single, initially unknown scenario. The talk establishes when learned scenario generators induce optimal policies and why one scenario component outside the observed support can suffice. A log-barrier smoothing operator makes that learning possible. The resulting method draws on interior-point optimization and is evaluated on standard contextual stochastic-programming benchmarks.

The brain adjusts its internal activity to direct visual and auditory attention and regulate responses to external stimuli. Appropriate endogenous activity may support normal cognition and behaviour, while its modulation can also produce dysfunction. Beginning with mathematical models of general anaesthesia, this talk examines how changes in noisy endogenous activity can fragment functional brain organization and account for loss of consciousness. Anaesthesia experiments in ferrets support the theoretical result. Further experimental examples are discussed to show how underlying internal noise may help explain observed transitions between brain states.