SaaS Metrics
Biological Modeling
Differential Equation
AI Synthesis & Market Narrative
Differential equations are extensively applied in modeling complex biological systems and fundamental engineering mechanics. Current AI models demonstrate limitations in accurately solving these problems without explicit domain knowledge.
Correlated Linguistic Patterns
["kinetics-based model"
"haematopoiesis"
"C\u2013N exchange model"
"legume\u2013Rhizobium symbiosis"
"Dynamics of trachoma infection"
"hidden state model"
"simply supported beam"
"fourth-order ODE"
"ChatGPT"]
Driving Media Context
A kinetics-based model of haematopoiesis reveals extrinsic regulation of skewed lineage output from stem cells
Single-cell transplantations of long-term haematopoietic stem cells (HSCs), in-depth phenotyping and mathematical modelling identify reconstitution kinetics ...
C–N exchange model of legume–Rhizobium symbiosis incorporating ATP budget constraints and energy–mass balance between the species
We present a comparative advantage model of carbon–nitrogen exchange in legume–Rhizobium symbiosis that incorporates ATP budget constraints and the energy–ma...
Simply supported beam—fourth-order ODE
In the introductory post to this series, I mentioned that the shear is the derivative of the moment. It’s easy to see that for our specific problem, the simp...
Dynamics of trachoma infection in West Africa revealed by a hidden state model
Author summary Trachoma is an infectious disease that can lead to blindness through repeated infections over time. Understanding trachoma transmission is imp...
Areas of my expertise
A few years ago, I wrote a post describing how I asked ChatGPT to solve a couple of elementary beam bending problems and how its answers were persistently wr...
A differential approach to Ax-Schanuel, I
In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic re...
Network structure induced bias in estimates of intrinsic generation times
Author summary When a new infectious disease outbreak starts, mathematical epidemiologists find themselves building or using mathematical models to understan...
Soliton dynamics, overlapping phenomena, multistability, and chaotic nature of a nonlinear model in relativistic wave mechanics
Scientific Reports - Soliton dynamics, overlapping phenomena, multistability, and chaotic nature of a nonlinear model in relativistic wave mechanics
Strategies of high-accuracy memristor-based analogue computing in memory for artificial intelligence
Noise and non-ideal characteristics at the device and circuit levels lead to errors in memristor-based analogue computing. This Review dissects the computing...
Learning the Integral of a Diffusion Model
A deep dive on flow maps.