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Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, i.e., sudden changes in the wavelength…
Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this…
Energy dispersive X-ray (EDX) spectrum imaging yields compositional information with a spatial resolution down to the atomic level. However, experimental limitations often produce extremely sparse and noisy EDX spectra. Under such…
We report measurements of counting statistics, average and variance, of microwave photons of ill-defined frequency : bichromatic photons, i.e. photons involving two well separated frequencies, and "white" broadband photons. Our setup allows…
We study the full field and frequency filtered output photon statistics of a resonator in thermal equilibrium with a bath and containing an arbitrarily large quartic nonlinearity. According to the general theory of photodetection, we derive…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We present a feature-resolved methodology to analyse the photoluminescence dynamics of single emitters using a combination of lifetime, spectral, and photon correlation analyses. By integrating conventional ensemble photon statistics…
Coherent control is extended to macroscopic processes under continuous pulsed laser irradiation. Here, this approach is used to analyze the experimentally measured two-photon phase control of currents emanating from a living brain cells…
The analysis of panel count data has garnered considerable attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most works focus on leveraging estimating equation-based…
In high-energy astrophysics, it is common practice to account for the background overlaid with the counts from the source of interest with the help of auxiliary measurements carried on by pointing off-source. In this "on/off" measurement,…
Detection and controlling of acoustic (AC) phonon phase have been strenuous tasks although such capability is crucial for further manipulating thermal properties. Here, we present a versatile formalism for tracing AC nanowaves with…
Despite their widespread use in cell biology, fluorescence lifetime imaging microscopy (FLIM) data-sets are challenging to analyse, because each spatial position can contain a superposition of multiple fluorescent components. Here, we…
The present dissertation covers two related research projects. The first topic was initiated with the ultimate goal of observing quantum degeneracy in ultrashort free electron pulses. This constitutes a thorough theoretical analysis of the…
Time-resolved coincidence imaging of photoelectrons and photoions represents the most complete experimental measurement of ultrafast excited state dynamics, a multi-dimensional measurement for a multi-dimensional problem. Here we present…
We present a rigorous description of the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability…
We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode. Experimentally detectable emission properties are taken into account by parametrizing the corresponding…
We show that the complete photoemission dynamics in situations of electron-ion entanglement can be retrieved from photoelectron spectral measurements without information on the ion. To this end, we develop an energy-time analysis of the…
Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a PDE model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A…
A theory is presented for the photodetection statistics of radiation produced by current fluctuations in a phase-coherent conductor. Deviations are found from the Poisson statistics that would result from a classical current. For detection…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…