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There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing on patterns that lie in a Euclidean space, typically planar and spatial data. Methodology for planar and spatial data thus…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
The measurement problem remains unaddressed in modern physics, with an array of proposed solutions but as of yet no agreed resolution. In this paper, we examine measurement using the Q-based, objective-field model for quantum mechanics.…
Determining whether neural models internalize physical laws as world models, rather than exploiting statistical shortcuts, remains challenging, especially under out-of-distribution (OOD) shifts. Standard evaluations often test latent…
Tsirelson's precession protocol is a nonclassicality witness that can be defined for both discrete and continuous variable systems. Its original version involves measuring a precessing observable, like the quadrature of a harmonic…
We consider a method of high-fidelity, spatially resolved position measurement of ultracold atoms in an optical lattice. We show that the atom-number distribution can be nondestructively determined at a spatial resolution beyond the…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
Some versions of quantum theory treat wave function collapse as a fundamental physical phenomenon to be described by explicit laws. One motivation is to find a consistent unification of quantum theory and gravity, in which collapse prevents…
Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models make predictions,…
We analyze the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects. This consists of coherently expanding the wave function of a ground-state-cooled…
We develop a backstepping-based observer design for a class of ODE - continuum-PDE cascade systems, which can be viewed as the limit, of a finite collection of ODE - $2 \times 2$ hyperbolic systems, as the number of individual PDE system…
New rules are proposed to govern the collapse of a wave function during measurement. These rules apply with or without an observer in the system. They overcome an absurdity that was previous found when an objective state reduction is…
Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effect obtained after all earlier tests have failed, and appends…
We are concerned with the problem of detecting with high probability whether a wave function has collapsed or not, in the following framework: A quantum system with a $d$-dimensional Hilbert space is initially in state $\psi$; with…
In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require…
Survival outcomes are common in comparative effectiveness studies and require unique handling because they are usually incompletely observed due to right-censoring. A ``once for all'' approach for causal inference with survival outcomes…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
In causal inference, whether through randomized controlled trials or observational studies, access to both treated and control units is essential for estimating the effect of a treatment on an outcome of interest. When treatment assignment…
This paper addresses the observability analysis and the optimal design of observation parameters in the presence of noisy measurements and parametric uncertainties. The main underlying frameworks are the nonlinear constrained moving horizon…
A new theoretical approach to study the properties in solids, which are sensitive to a change of densities of the valence electrons in atomic cores (hyperfine structure constants, parameters of space parity (P) and time reversal (T)…