It has become common to perform kinetic analysis using approximate Koopman operators that transforms high-dimensional time series of observables into ranked dynamical modes.
Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.
Ranked #12 on Image Generation on CelebA 64x64
We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori--Zwanzig formalism.
Here, we show that gene expression noise counter-intuitively accelerates the evolution of a biological oscillator and, thus, can impart a benefit to living organisms.
To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack).
Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable.
We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time.
To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population.
Using a sparsity inducing penalty in artificial neural networks (ANNs) avoids over-fitting, especially in situations where noise is high and the training set is small in comparison to the number of features.