相关论文: Intrinsic Location Parameter of a Diffusion Proces…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process.…
Uncertainty calibration in pre-trained transformers is critical for their reliable deployment in risk-sensitive applications. Yet, most existing pre-trained transformers do not have a principled mechanism for uncertainty propagation through…
Diffusion models often degrade when trained in latent spaces (e.g., VAEs), yet the formal causes remain poorly understood. We quantify latent-space diffusability through the rate of change of the Minimum Mean Squared Error (MMSE) along the…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
Diffusion mechanism design, which investigate how to incentivise agents to invite as many colleagues to a multi-agent decision making as possible, is a new research paradigm at the intersection between microeconomics and computer science.…
This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of…
This paper focuses on designing a particle filter for randomly delayed measurements with an unknown latency probability. A generalized measurement model is adopted which includes measurements that are delayed randomly by an arbitrary but…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function. We establish…
We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the…
It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these…