Related papers: Best matching Barenblatt profiles are delayed
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Similarity solutions play an important role in many fields of science. The recent book of Barenblatt (1996) discusses many examples. Often, outstanding unresolved issues are whether a similarity solution is dynamically attractive, and if it…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a…
The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter…
The body plan of the fruit fly is determined by the expression of just a handful of genes. We show that the spatial patterns of expression for several of these genes scale precisely with the size of the embryo. Concretely, discrete…
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the…
Self-consistent theory for concentrated electrolytes is developed. Oscillatory decay of the charge-charge correlation function with the decay length that shows perfect agreement with the experimentally discovered and so far unexplained…
In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance $d_\mathcal{M}$ measures the difference between $2$-parameter persistence modules by taking the…
This paper is concerned with the Cauchy-Dirichlet problem for fast diffusion equations posed in bounded domains, where every energy solution vanishes in finite time and a suitably rescaled solution converges to an asymptotic profile.…
This paper quantifies the speed of convergence and higher- order asymptotics of fast diffusion dynamics on R^n to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the…
We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems…
We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…
In two-time-scale stochastic approximation (SA), two iterates are updated at varying speeds using different step sizes, with each update influencing the other. Previous studies on linear two-time-scale SA have shown that the convergence…
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…