Related papers: Single-Observation Uniformity Testing under Increa…
We present methods which allow orders of magnitude increase in the number of modes in linear optics experiments by moving from spatial encoding to temporal encoding and using dispersion. This enables significant practical advantages for…
Tests of the stability of nature's fundamental constants are one of the cornerstones of the ongoing search for the new physics which is required to explain the recent acceleration of the universe. The two main settings for these tests are…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
Quantum-enhanced measurements use highly non-classical quantum states in order to enhance the precision of the measurement of classical quantities, like the length of an optical cavity. The major goal is to beat the standard quantum limit…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
We present a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, we establish scale invariant absolute continuity of harmonic measure with respect to surface measure, along with higher…
In the medical fields, ultrasound detection is often performed with piezoelectric arrays that enable one to simultaneously map the acoustic fields at several positions. In this work, we develop a novel method for transforming a…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
As with all measurements, the measurement of examinee ability, in terms of scores that the examinee obtains in a test, is also error-ridden. The quantification of such error or uncertainty in the test score data--or rather the complementary…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…
Quantum instruments derived from composite systems allow greater measurement precision than their classical counterparts due to coherences maintained between N components; spins, atoms or photons. Decoherence that plagues real-world devices…
The standard method of transforming a continuous distribution on the line to the uniform distribution on the unit interval is the probability integral transform. Analogous transforms exist on compact Riemannian manifolds, in that, for each…
We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…
The recent success of deep learning models in solving complex problems and in different domains has increased interest in understanding what they learn. Therefore, different approaches have been employed to explain these models, one of…
An extended aperture has the potential to greatly improve ultrasound imaging performance. This work extends the effective aperture size by coherently compounding the received radio frequency data from multiple transducers. A framework is…
Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be…
Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of…