Related papers: Morphogen Gradient from a Noisy Source
Noise is source of ambiguity for fuzzy systems. Although being an important aspect, the effects of noise in fuzzy modeling have been little investigated. This paper presents a set of tests using three well-known fuzzy modeling algorithms.…
Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…
Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model…
Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task, both in developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional…
The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform.…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
A system of coherently-driven two-level atoms is analyzed in presence of two independent stochastic perturbations: one due to collisions and a second one due to phase fluctuations of the driving field. The behaviour of the quantum…
The probability of transition between levels of a quantum bouncer, induced by a noise-like perturbation, is calculated. The results are applied to two sources of noise (vibrations and mirror surface waviness) which might play an important…
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we…
We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
With increased adoption of supervised deep learning methods for processing and analysis of cosmological survey data, the assessment of data perturbation effects (that can naturally occur in the data processing and analysis pipelines) and…
Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this…
The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory.…
Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…
The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic…
It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…
To sample from an unconditionally trained Denoising Diffusion Probabilistic Model (DDPM), classifier guidance adds conditional information during sampling, but the gradients from classifiers, especially those not trained on noisy images,…