Related papers: Machine Learning Analysis of Anomalous Diffusion
Anomaly detection has garnered extensive applications in real industrial manufacturing due to its remarkable effectiveness and efficiency. However, previous generative-based models have been limited by suboptimal reconstruction quality,…
In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium,…
Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…
We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong…
This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or diffusion models, for generative artificial intelligence. We…
Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and…
The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a…
We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
Diffusion Models~(DMs) have emerged as the dominant approach in Generative Artificial Intelligence (GenAI), owing to their remarkable performance in tasks such as text-to-image synthesis. However, practical DMs, such as stable diffusion,…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes undergoing in a range of materials including living cells and tissues. However, extracting that information is not a…
Anomaly detection in complex, high-dimensional data, such as UAV sensor readings, is essential for operational safety but challenging for existing methods due to their limited sensitivity, scalability, and inability to capture intricate…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
Medical image segmentation is crucial for accurate clinical diagnoses, yet it faces challenges such as low contrast between lesions and normal tissues, unclear boundaries, and high variability across patients. Deep learning has improved…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
The goal of anomaly detection is to identify anomalous samples from normal ones. In this paper, a small number of anomalies are assumed to be available at the training stage, but they are assumed to be collected only from several anomaly…
Anomaly detection for time-series data has been an important research field for a long time. Seminal work on anomaly detection methods has been focussing on statistical approaches. In recent years an increasing number of machine learning…