Related papers: Optimal correlation order in super-resolution opti…
We consider composition orderings for linear functions of one variable. Given $n$ linear functions $f_1,\dots,f_n$ and a constant $c$, the objective is to find a permutation $\sigma$ that minimizes/maximizes $f_{\sigma(n)}\circ\dots\circ…
We introduce a superresolution technique that combines spatial mode demultiplexing (SPADE) with emitter blinking. We show that temporal fluctuations not only enhance the precision of SPADE imaging, but also drastically simplify the…
Creating arbitrary light patterns finds applications in various domains including lithography, beam shaping, metrology, sensing and imaging. We study the formation of high-contrast light patterns that are obtained by transmission through an…
Improving the resolution of fluorescence microscopy beyond the diffraction limit can be achievedby acquiring and processing multiple images of the sample under different illumination conditions.One of the simplest techniques, Random…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
An approach for compensating the influence of the interrogator noises on the readings of interferometric sensors, interrogated by means of spectral interferometry with wavelength tuning is proposed. Both theoretical analysis and a…
We theoretically explore the role of mesoscopic fluctuations and noise on the spectral and temporal properties of systems of $\mathcal{PT}$-symmetric coupled gain-loss resonators operating near the exceptional point, where eigenvalues and…
I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use…
Super-resolution fluorescence microscopy is an important tool in biomedical research for its ability to discern features smaller than the diffraction limit. However, due to its difficult implementation and high cost, the universal…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
Various techniques have been developed to measure the 2D and 3D positions and 2D and 3D orientations of fluorescent molecules with improved precision over standard epifluorescence microscopes. Due to the challenging signal-to-background…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…
General formulas are presented for higher order cumulants of the conserved charge statistical fluctuations inside the mixed phase. As a particular example the van der Waals model in the grand canonical ensemble is used. The higher order…
We present a stable procedure for defining and measuring the two point angular autocorrelation function, w, of faint (25 < V < 29), barely resolved and unresolved sources in the HST GOODS and UDF datasets. We construct catalogs that include…
We have recently proposed a new method of flow analysis, based on a cumulant expansion of multiparticle azimuthal correlations. Here, we describe the practical implementation of the method. The major improvement over traditional methods is…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
The measurement of the spatio-temporal correlations of light provides an interesting tool to overcome the traditional limitations of standard imaging, such as the strong trade-off between spatial resolution and depth of field. In…
Superoscillation is a counterintuitive phenomenon for its mathematical feature of ``faster-than-Fourier", which has allowed novel optical imaging beyond the diffraction limit. In this article, we introduce a superoscillating quantum control…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations when only a subregion of the full system can be observed, focusing…