Related papers: Best matching Barenblatt profiles are delayed
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity,…
The statistical properties of local alignment algorithms with gaps are analyzed theoretically for uncorrelated and correlated DNA sequences. In the vicinity of the log-linear phase transition, the statistics of alignment with gaps is shown…
This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation (RGLE) with periodic boundary conditions on monotonically growing or shrinking domains. First, we obtain closed-form expressions…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph…
Many predictions are probabilistic in nature; for example, a prediction could be for precipitation tomorrow, but with only a 30 percent chance. Given both the predictions and the actual outcomes, "reliability diagrams" (also known as…
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in…
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…
We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
Allocating extra computation at inference time has recently improved sample quality in large language models and diffusion-based image generation. In parallel, Flow Matching (FM) has gained traction in language, vision, and scientific…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…