Related papers: SPHARMA approximations for stationary functional t…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in \mathbb{Z}}$ as…
Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distributions in the different classes are complex, with nonlinear,…
We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and perform numerical simulations of the model. Several interesting types of…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
We propose Polyra Swarms, a novel machine-learning approach that approximates shapes instead of functions. Our method enables general-purpose learning with very low bias. In particular, we show that depending on the task, Polyra Swarms can…
We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…
Sample Space Reducing (SSR) processes are simple stochastic processes that offer a new route to understand scaling in path-dependent processes. Here we define a cascading process that generalises the recently defined SSR processes and is…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
We investigate the scalar Green function for spherically symmetric spacetimes expressed as a coordinate series expansion in the separation of the points. We calculate the series expansion of the function $V(x,x')$ appearing in the Hadamard…
In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where…
We develop a semi-classical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes,…
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when analysing misaligned functional data with…
We analyze two theoretical approaches to ensemble averaging for integrable systems in quantum chaos - spectral averaging and parametric averaging. For spectral averaging, we introduce a new procedure - rescaled spectral averaging. Unlike…