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The normalized state $\ket{\psi(t)}=c_1(t)\ket{1}+c_2(t)\ket{2}$ of a single two-level system performs oscillations under the influence of a resonant driving field. It is assumed that only one realization of this process is available. We…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible,…
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…
Factor-based Structural Equation Modeling (SEM) relies on likelihood-based estimation assuming a nonsingular sample covariance matrix, which breaks down in small-sample settings with $p>n$. To address this, we propose a novel estimation…
Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…
Simultaneous localization and mapping (SLAM) are essential in numerous robotics applications, such as autonomous navigation. Traditional SLAM approaches infer the metric state of the robot along with a metric map of the environment. While…
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on the Hilbert space of square integrable random variables. In…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
Consider the problem of simultaneous estimation and support recovery of the coefficient vector in a linear data model with additive Gaussian noise. We study the problem of estimating the model coefficients based on a recently proposed…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
A robust nonlinear stochastic observer for simultaneous localization and mapping (SLAM) is proposed using the available uncertain measurements of angular velocity, translational velocity, and features. The proposed observer is posed on the…