Related papers: Caveat on the Boltzmann distribution function use …
Consider a one-parameter family of Boltzmann distributions $p_t(x) = \tfrac{1}{Z_t}e^{-S_t(x)}$. This work studies the problem of sampling from $p_{t_0}$ by first sampling from $p_{t_1}$ and then applying a transformation $\Psi_{t_1}^{t_0}$…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no…
A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
Predicting the change in binding free energy ($\Delta \Delta G$) is crucial for understanding and modulating protein-protein interactions, which are critical in drug design. Due to the scarcity of experimental $\Delta \Delta G$ data,…
This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization…
Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current…
Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…
This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and…
In the recent years, scientific workflows gained more and more popularity. In scientific workflows, tasks are typically treated as black boxes. Dealing with their complex interrelations to identify optimization potentials and bottlenecks is…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…
It is strange but fruitful to think about the functions as random processes. Any function can be viewed as a martingale (in many different ways) with discrete time. But it can be useful to have continuous time too. Processes can emulate…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…