Related papers: Why Adversarial Interaction Creates Non-Homogeneou…

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…

Reaction-diffusion systems are ubiquitous in nature and in engineering applications, and are often modeled using a non-linear system of governing equations. While robust numerical methods exist to solve them, deep learning-based reduced…

State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the perturbations can \textit{transfer across models}:…

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…

Many existing adversarial attacks generate $L_p$-norm perturbations on image RGB space. Despite some achievements in transferability and attack success rate, the crafted adversarial examples are easily perceived by human eyes. Towards…

The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…

Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

Adversarial examples have raised several open questions, such as why they can deceive classifiers and transfer between different models. A prevailing hypothesis to explain these phenomena suggests that adversarial perturbations appear as…

Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…

We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…

Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…

Adversarial examples are some special input that can perturb the output of a deep neural network, in order to make produce intentional errors in the learning algorithms in the production environment. Most of the present methods for…

The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (2008), pp. 1249--1267].…

Adversarial attacks dramatically change the output of an otherwise accurate learning system using a seemingly inconsequential modification to a piece of input data. Paradoxically, empirical evidence indicates that even systems which are…

This paper focuses on learning transferable adversarial examples specifically against defense models (models to defense adversarial attacks). In particular, we show that a simple universal perturbation can fool a series of state-of-the-art…

In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability…

Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…