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Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
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 study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…
I describe a toy model of quantum measurement in which wave function collapse is described as a stochastic entropically-driven event guided by interactions between a measured two-state particle and an Ising-like measurement device. The…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
Standard diffusion models are flexible estimators of complex distributions, but they do not encode causal structures and therefore do not by themselves support causal analysis. We propose a causality-encoded diffusion framework that…
Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
A fundamental prediction of quantum theory that is derived from the "projection postulate" is that under continuous measurement, the state of a system traces out a "quantum trajectory" in time that depends upon its measurement record, and…
Recognition of objects from partial information presents a significant challenge for theories of vision because it requires spatial integration and extrapolation from prior knowledge. We combined neurophysiological recordings in human…
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework…
The development of mathematically complete and consistent models solving the so-called "measurement problem", strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical…
The internal validity of observational study is often subject to debate. In this study, we define the unobserved sample based on the counterfactuals and formalize its relationship with the null hypothesis statistical testing (NHST) for…
Protocols have been previously proposed to certify the presence of an entangled measurement in a fully device-independent manner. Here, I provide models for these protocols in which the claimed measurement is not entangled, and demonstrate…
We present a detailed description of the experiment realising for the first time a protective measurement, a novel measurement protocol which combines weak interactions with a ``protection mechanism'' preserving the measured state coherence…
This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observations) may be vitiated by a…
The proximal causal inference framework enables the identification and estimation of causal effects in the presence of unmeasured confounding by leveraging two disjoint sets of observed strong proxies: negative control treatments and…