Related papers: Einstein from Noise: Statistical Analysis
Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a…
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…
In recent years, more and more researchers in the field of neural networks are interested in creating hardware implementations where neurons and the connection between them are realized physically. The physical implementation of ANN…
We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window $[t_w,t_w+t_m]$, namely the observation started after a waiting time…
A very recent article [(1) E. Zakka-Bajjani et al., PRL104, 206802 (2010)] has addressed the problem of how the statistics of electrons crossing a quantum conductor influences that of the photons they emit. It is however not clear that the…
We develop a theory of spin noise spectroscopy of itinerant, noninteracting, spin-carrying fermions in different regimes of temperature and disorder. We use kinetic equations for the density matrix in spin variables. We find a general…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
In ultra-fast astronomical observations featuring fast transients on sub-$\mu$s time scales, the conventional Signal-to-Noise Ratio (SNR) threshold, often fixed at $5\sigma$, becomes inadequate as observational window timescales shorten,…
A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor P/I (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium.…
Fourier embedding has shown great promise in removing spectral bias during neural network training. However, it can still suffer from high generalization errors, especially when the labels or measurements are noisy. We demonstrate that…
The relation between noise and Fick's diffusion coefficient in barrier limited transport associated with hopping or tunneling mechanisms of particles obeying the asymmetric simple exclusion processes (ASEP) is physically assessed by Monte…
A modelling framework, based on the theory of signal processing, for characterising the dynamics of systems driven by the unravelling of information is outlined, and is applied to describe the process of decision making. The model input of…
Neutrino oscillations are precision probes of new physics beyond the Standard Model. Apart from neutrino masses and mixings, they are also sensitive to possible deviations of low-energy interactions between quarks and leptons from the…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
The over-damped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is…
Considerable effort in experimental quantum computing is devoted to noisy intermediate scale quantum computers (NISQ computers). Understanding the effect of noise is important for various aspects of this endeavor including notable claims…
Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…
We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to…