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This manuscript is inspired by the paper [2]. In the paper, they investigate a method to detect existence of an object with arbitrarily small interaction. Below, we sketch their protocol to motivate the present manuscript. The object of…
In this paper, we consider a general partially observed diffusion model with periodic coefficients and with non-degenerate diffusion component. The coefficients of such a model depend on an unknown (static and deterministic) parameter which…
We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…
The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle…
Vision Transformers (ViTs) with self-attention modules have recently achieved great empirical success in many vision tasks. Due to non-convex interactions across layers, however, theoretical learning and generalization analysis is mostly…
We show using a realistic Hamiltonian-type model that definite outcomes of quantum measurements may emerge from quantum evolution of pure states, i.e quantum dynamics provides a deterministic collapse of the wavefunction in a quantum…
Data-driven inference was recently introduced as a protocol that, upon the input of a set of data, outputs a mathematical description for a physical device able to explain the data. The device so inferred is automatically self-consistent,…
The notion of collapse is discussed and refined within the Two-State-Vector Formalism (TSVF). We show how a definite result of a measurement can be fully determined when considering specific forward and backward-evolving quantum states.…
A sharp change in apparent mobility at a characteristic temperature that depends on the observation time has been reported in experiments and simulations of hydrated proteins. Such behavior is often discussed in the context of the protein…
In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
A new analysis of the measurement problem reveals the possibility that collapse of the wavefunction may now take place just before photoisomerization of the rhodopsin molecule in the retinal rods. It is known that when a photon is initially…
In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an…
Vision-language models (VLMs), such as CLIP, have gained popularity for their strong open vocabulary classification performance, but they are prone to assigning high confidence scores to misclassifications, limiting their reliability in…
We develop a new statistical ideal observer model that performs holistic visual search (or gist) processing in part by placing thresholds on minimum extractable image features. In this model, the ideal observer reduces the number of free…
A novel test of time-reversal invariance in proton-deuteron scattering is planned as an internal target transmission experiment at the cooler synchrotron COSY. The P-even, T-odd observable is the polarization correlation $A_{y,xz}$ of the…
Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both…
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…
Liquid crystals are materials that experience an intermediate phase where the material can flow like a liquid, but the molecules maintain an orientation order. The Frank-Oseen model is a continuum model of a liquid crystal. The model…
Quantum mechanics allows for coherent control over the order in which different processes take place on a target system, giving rise to a new feature known as indefinite causal order. Indefinite causal order provides a resource for quantum…