Related papers: The Fourth-Order Correlation Function of a Randoml…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d<\theta^2>/dt$ of the scalar…
We propose a method to obtain physical quantities in the theta vacuum from those at fixed topology, which are different by finite size effects. Extending the work by Brower et al., we derive the formula to estimate these finite size…
We have applied the gaussian auxiliary field method introduced by Mazenko to the ordering dynamics of a non-conserved scalar system with attractive long-range interactions. This study provides a test-bed for the approach and shows some of…
The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom…
Derivation of two-time second-order correlation function by following approaches such as stochastic differential equation, coherent-state propagator, and quasi-statistical distribution function is presented. In the process, the time…
Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <f(i)>: sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
The field-theoretic renormalization group (RG) and the operator product expansion are applied to the model of a divergence-free vector quantity, passively advected by the ``synthetic'' turbulent flow with a finite correlation time. The…
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…
Trace anomaly for conformally invariant higher derivative 4D scalar-dilaton theory is obtained by means of calculating divergent part of one-loop effective action for such system. Its applications are briefly mentioned
We consider the model of random sequential adsorption, with depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…
We study the predictions for the matter redshift-space power spectrum and correlation function of a Lagrangian-space Gaussian ansatz introduced in a previous work. This model is a natural extension of the Zeldovich approximation, where the…
Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
This work investigates the long-time asymptotic behavior of a diffusing passive scalar advected by fluid flow in a straight channel with a periodically varying cross-section. The goal is to derive an asymptotic expansion for the scalar…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…