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Visual illusion is the fallacious perception of reality or some actually existing object. In this paper, we imitate the mechanism of Ehrenstein illusion, neon color spreading illusion, watercolor illusion, Kanizsa illusion, shifted edges illusion, and hybrid image illusion using the Open Source Computer Vision Library (OpenCV). We also imitate these illusions using Cellular Neural Networks (CNNs). These imitations suggest that some illusions are processed by high-level brain functions. We next apply the morphological gradient operation to anomalous motion illusions. The processed images are classified into two kinds of images, which correspond to the central drift illusion and the peripheral drift illusion, respectively. It demonstrates that the contrast of the colors plays an important role in the anomalous motion illusion. We also imitate the anomalous motion illusions using both OpenCV and CNN. These imitations suggest that some visual illusions may be processed by the illusory movement of animations.

Consider a α-Hölder function A : Σ → ℝ and assume that it admits a unique maximizing measure μ_max. For each β, we denote μ_β, the unique equilibrium measure associated to βA. We show that (μ_β) satisfies a Large Deviation Principle, that is, for any cylinder C of Σ,

Almost isomorphism is an equivalence relation on countable state Markov shifts which provides a strong version of Borel conjugacy; still, for mixing SPR shifts, entropy is a complete invariant of almost isomorphism [2]. In this paper, we establish a class of potentials on countable state Markov shifts whose thermodynamic formalism is respected by almost isomorphism.

We show that for a ${\mathbb{Z}}^l$-action (or ${(\mathbb{N}\cup \{0\})}^l$-action) on a non-empty compact metrizable space $\mathrm{\Omega }$, the existence of a affine space dense in the set of continuous functions on $\mathrm{\Omega }$ constituted by elements admitting a unique equilibrium state implies that each invariant measure can be approximated weakly${}^{\ast }$ and in entropy by a sequence of measures which are unique equilibrium states.

We consider classical solutions to the initial boundary value problem for the non-isentropic compressible Euler equations with damping in several space dimensions. We establish a global existence theory for classical solutions to this system when the initial data are sufficiently small. We prove that the pressure and the velocity converge exponentially toward some constants, while the entropy and the density in general do not approach constants. Finally, we prove that, as the time goes to infinity, the pressure and the velocity components of the non-isentropic Euler equations with damping converge exponentially toward those of an associated nonlinear diffusion system, and the global existence of classical solutions to these nonlinear diffusion equations is also established.

A compartmental model is established for schistosomiasis infection in Qianzhou and Zimuzhou, two islets in the center of Yangtzi River near Nanjing, P. R. China. The model consists of five differential equations about the susceptible and infected subpopulations of mammalian Rattus norvegicus and Oncomelania snails. We calculate the basic reproductive number R₀ and discuss the global stability of the disease free equilibrium and the unique endemic equilibrium when it exists. The dynamics of the model can be characterized in terms of the basic reproductive number. The parameters in the model are estimated based on the data from the field study of the Nanjing Institute of Parasitic Diseases. Our analysis shows that in a natural isolated area where schistosomiasis is endemic, killing snails is more effective than killing Rattus norvegicus for the control of schistosomiasis.

The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions the LV model can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. The discrete analogy of LV model has been considered by many researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV models, LV type models can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors.

We introduce the notion of local perturbations for normalized energies and study their effect on the level of equilibrium measures. Using coupling technics and Kac's return time theorem, we obtain some -estimates for the equilibrium measures. These reveal stability of certain energies under local perturbations. They also show how some weak-⋆ convergence of equilibrium may be obtained in absence of ∥ ∥_∞-accuracy of the energies.