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Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
This paper addresses the critical and challenging task of developing emulators for simulating human operational motions in industrial workplaces. We conceptualize human motion as a sequence of human body shapes and develop statistical…
This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near…
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
We study the impedance spectra of woodwind instruments with arbitrary axisymmetric geometry. We perform piecewise interpolations of the instruments' profile, using interpolating functions amenable to analytic solutions of the Webster…
Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
This paper considers the analysis of partial differential equations (PDE) containing multiple random variables. Recently developed collocation methods enable the construction of high-order stochastic solutions by converting a stochastic PDE…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Trajectory modeling of dense points usually employs implicit deformation fields, represented as neural networks that map coordinates to relate canonical spatial positions to temporal offsets. However, the inductive biases inherent in neural…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…
The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…