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Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
Measurement-based entanglement is a method for entangling quantum systems through the state projection that accompanies a parity measurement. We derive a stochastic master equation describing measurement-based entanglement of a pair of…
Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows…
In order to develop predictive wear laws, relevant material parameters and their influence on the wear rate need to be identified. Despite decades of research, there is no agreement on the mathematical form of wear equations and even the…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Measurement-only models offer an ideal platform for exploring entanglement dynamics in the absence of unitary evolution. Despite extensive numerical evidence for entanglement phase transitions in measurement-only dynamics, the underlying…
Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received an increasing attention during the last decades, thanks to the information…
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…
The Winfree model is a phase-coupled synchronization model which simplifies pulse-coupled models such as the Peskin model on pacemaker cells. It is well-known that the Winfree ensemble with the first-order coupling exhibits discrete…
Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key…
Dynamic benchmarks interweave model fitting and data collection in an attempt to mitigate the limitations of static benchmarks. In contrast to an extensive theoretical and empirical study of the static setting, the dynamic counterpart lags…
Bayesian model comparison relies upon the model evidence, yet for many models of interest the model evidence is unavailable in closed form and must be approximated. Many of the estimators for evidence that have been proposed in the Monte…
For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…
Design, control, and estimation for dynamic systems require accurate and analytically tractable models. However, modern engineered systems contain components that are described with heterogeneous modeling paradigms, as well as subsystems…
The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary…
It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and…
In high dimensional analysis, effects of explanatory variables on responses sometimes rely on certain exposure variables, such as time or environmental factors. In this paper, to characterize the importance of each predictor, we utilize its…
We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e.\ particle diameter), maximum…
Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through…
We present an alternative proof of asymptotic freeness of independent sample covariance matrices, when the dimension and the sample size grow at the same rate, by embedding these matrices into Wigner matrices of a larger order and using…