Published in Magnetic resonance in medicine
To develop a denoising strategy leveraging redundancy in high-dimensional data. The SNR fundamentally limits the information accessible by MRI. This limitation has been addressed by a host of denoising techniques, recently including the so-called MPPCA: principal component analysis of the signal followed by automated rank estimation, exploiting the...
Published in Journal of Statistical Mechanics: Theory and Experiment
We propose a data-driven, model-free, way to reduce the noise of covariance matrices of time-varying systems. If the true covariance matrix is time-invariant, non-linear shrinkage of the eigenvalues is known to yield the optimal estimator for large matrices. Such a method outputs eigenvalues that are highly dependent on the inputs, as common sense ...
Published in Journal of Physics: Complexity
The sinoatrial node (SAN) is the pacemaker of the heart. Recently calcium signals, believed to be crucially important in rhythm generation, have been imaged in intact SAN and shown to be heterogeneous in various regions of the SAN with a lot of analysis relying on visual inspection rather than mathematical tools. Here we apply methods of random mat...
Published in Journal of Physics A: Mathematical and Theoretical
As an alternative to entanglement entropies, the capacity of entanglement becomes a promising candidate to probe and estimate the degree of entanglement of quantum bipartite systems. In this work, we study the statistical behavior of entanglement capacity over major models of random states. In particular, the exact and asymptotic formulas of averag...
Published in Journal of Physics: Complexity
In this work we analyze structural and spectral properties of a model of directed random geometric graphs: given n vertices uniformly and independently distributed on the unit square, a directed edge is set between two vertices if their distance is smaller than the connection radius ℓ , which is randomly drawn from a Pareto distribution. This Paret...
Published in Journal of Physics A: Mathematical and Theoretical
This paper considers several aspects of random matrix universality in deep neural networks (DNNs). Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for DNNs based on a realistic model of their Hessians. In particular we derive universal aspects of outl...
Published in Frontiers in Physics
Published in Journal of Physics A: Mathematical and Theoretical
Quantum chaos of many-body (MB) systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classi...
Published in Journal of Physics A: Mathematical and Theoretical
We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the GOE to the Gaussian unitary ensemble (GUE) fo...
Published in Journal of Physics A: Mathematical and Theoretical
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These ensembles of Dirac operators are constructed as toy models of Euclidean quantum gravity on finite noncommutative ...
