Related papers: Fitting an Elephant with Four non-Zero Parameters
If neutrinos are Majorana fermions, the lepton mixing parameter space consists of six mixing parameters: three mixing angles and three CP-odd phases. A related issue concerns the physical range of the mixing parameters. What values should…
We present a brief numerical study of the Darwin-Fowler method applied to the analysis of the energy partition of essembles of bosons and fermions. We analyze the assertion of the existence of a "strong maximum" made in the original paper…
Given independent standard Gaussian points $v_1, \ldots, v_n$ in dimension $d$, for what values of $(n, d)$ does there exist with high probability an origin-symmetric ellipsoid that simultaneously passes through all of the points? This…
In this paper, we consider a generalization of the elephant random walk model. Compared to the usual elephant random walk, an interesting feature of this model is that the step sizes form a sequence of positive independent and identically…
Discrepancies between measurements of decay modes with an underlying quark level transition $b\to s \ell^+\ell^-$ and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of…
Inspired by the dexterous handling ability of an elephant's trunk, we propose a pneumatic actuator that generates diverse bending and extension motions in a flexible arm. The actuator consists of two flexible tubes. Each flexible tube is…
The paradox of enrichment was observed by M. Rosenzweig in a class of predator-prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation…
We establish some limit theorems for one-dimensional elephant random walk, including Berry-Esseen bounds, Cram\'{e}r moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit…
The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…
Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…
In this paper, we introduce a variation of the elephant random walk whose steps are polynomially decaying. At each time $k$, the walker's step size is $k^{-\gamma}$ with $\gamma>0$. We investigate effects of the step size exponent $\gamma$…
We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many…
We consider the elephant random walk with general step distribution. We calculate the first four moments of the limiting distribution of the position rescaled by $n^\alpha$ in the superdiffusive regime where $\alpha$ is the memory…
In 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for elliptic operators in divergence form with bounded measurable coefficients. In the Fermi lectures in 1998, Caffarelli stated a much simpler mean value theorem for…
Alignment faking is a form of strategic deception in AI in which models selectively comply with training objectives when they infer that they are in training, while preserving different behavior outside training. The phenomenon was first…
Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data…
The foraging behavior of animals is a paradigm of target search in nature. Understanding which foraging strategies are optimal and how animals learn them are central challenges in modeling animal foraging. While the question of optimality…
We have shown that commonly used model-fitting methods fail when the underlying ecological system is chaotic. Importantly, Hartig & Dormann [arXiv:1305.3544] suggest an alternative method that is able to overcome this problem for the…
In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have…
We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96…