The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical results for the KPZ dynamics. We present direct evidence that the iso-height lines can be described by the family of conformal invariant curves called SchrammLoewner evolution (or SLEκ) with diffusivity κ = 8/3. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity κ from 8/3 to 4, indicating that the iso-height lines of the Edwards-Wilkinson (EW) surface are also conformally invariant, and belong to the universality class of the domain walls in the O(2) spin model. Evidence of conformal invariance in the geometrical features of such complex nonlinear systems have been provided, in the continuum limit, by stochastic (Schramm) Loewner evolution, i.e., SLE κ , where κ is the diffusivity [6,7]. Schramm and Sheffield showed that the contour lines in a two-dimensional discrete Gaussian free field are statistically equivalent to SLE 4 [8]. Moreover, it is shown that the restriction property only applies in the case for κ = 8/3 [9]. Since self-avoiding random walk (SAW) satisfies the restriction property, it is conjectured in the scaling limit to fall in the SLE class with κ = 8/3 [10]. The scaling limit of SAW in the half-plane has been proven to exist [11] but there is no general proof of its existence.In this Letter we investigate numerically the isoheight lines of the (2+1)-dimensional Kardar-ParisiZhang (KPZ) model [12], and study their possible conformal invariance. It is shown that the KPZ's iso-height lines are equivalent to self-avoiding walks, and that the iso-height lines in the 2D-KPZ surface are SLE 8/3 curves. For the Edwards-Wilkinson (EW) interface (the KPZ model without the nonlinear term) the iso-height lines fall in the universality class of the interfaces in the O(2) model, and can be described by SLE 4 .The KPZ equation is given byThe first term on the r.h.s describes relaxation of the interface caused by a surface tension ν, and the nonlinear term is due to the lateral growth. The noise η is uncorrelated Gaussian white noise in both space and time with zero average i.e., η(x, t) = 0 and η(x, t)η(The KPZ equation is invariant under translations along both growth direction and perpendicular to it, as well as time translation and rotation [13]. Rescaling the variables, h =h 2D/ν, and t =t/ν, changes Eq. (1) In the following, we work with the single parameter ǫ and drop all the tildes for simplicity.We have studied the rescaled KPZ equation on a square lattice with periodic boundary conditions. The numerical integration was done using the Runge-Kutta-Fehlberg scheme of orders O(4) and O(5) [14]. This scheme controls automatically the integration time step δt, such that the resulting height error δh (which is estimated by comparing the results obtained from the O(4) and O(5) integrations) can be ignored at each time step. We t...

Propagation of acoustic waves in strongly heterogeneous elastic media is studied using renormalization group analysis and extensive numerical simulations. The heterogeneities are characterized by a broad distribution of the local elastic constants. We consider both Gaussian-white distributed elastic constants, as well as those with long-range correlations with a nondecaying power-law correlation function. The study is motivated in part by recent analysis of experimental data for the spatial distribution of the elastic moduli of rock at large length scales, which indicated that the distribution contains the same type of longrange correlations as what we consider in the present paper. The problem that we formulate and the results are, however, applicable to acoustic wave propagation in any disordred elastic material that contains the types of heterogeneities that we consider in the present paper. Using the Martin-Siggia-Rose method, we analyze the problem analytically and find that, depending on the type of disorder, the renormalization group (RG) flows exhibit a transition to a localized or extended regime in any dimension. We also carry out extensive numerical simulations of acoustic wave propagation in one-, two-and three-dimensional systems. Both 1 isotropic and anisotropic media (with anisotropy being due to stratified) are considered. The results for the isotropic media are consistent with the RG predictions. While the RG analysis, in its present form, does not make any prediction for the anisotropic media, the results of our numerical simulations indicate the possibility of the existence of a regime of superlocalization in which the waves' amplitudes decay as exp[−(|x|/ξ) γ ], with γ > 1, where ξ is the localization length. However, further investigations may be necessary in order to establish the possible existence of such a localization regime.

Table of contentsA1 Functional advantages of cell-type heterogeneity in neural circuitsTatyana O. SharpeeA2 Mesoscopic modeling of propagating waves in visual cortexAlain DestexheA3 Dynamics and biomarkers of mental disordersMitsuo KawatoF1 Precise recruitment of spiking output at theta frequencies requires dendritic h-channels in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneuronsVladislav Sekulić, Frances K. SkinnerF2 Kernel methods in reconstruction of current sources from extracellular potentials for single cells and the whole brainsDaniel K. Wójcik, Chaitanya Chintaluri, Dorottya Cserpán, Zoltán SomogyváriF3 The synchronized periods depend on intracellular transcriptional repression mechanisms in circadian clocks.Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett, Kresimir JosićO1 Assessing irregularity and coordination of spiking-bursting rhythms in central pattern generatorsIrene Elices, David Arroyo, Rafael Levi, Francisco B. Rodriguez, Pablo VaronaO2 Regulation of top-down processing by cortically-projecting parvalbumin positive neurons in basal forebrainEunjin Hwang, Bowon Kim, Hio-Been Han, Tae Kim, James T. McKenna, Ritchie E. Brown, Robert W. McCarley, Jee Hyun ChoiO3 Modeling auditory stream segregation, build-up and bistabilityJames Rankin, Pamela Osborn Popp, John RinzelO4 Strong competition between tonotopic neural ensembles explains pitch-related dynamics of auditory cortex evoked fieldsAlejandro Tabas, André Rupp, Emili Balaguer-BallesterO5 A simple model of retinal response to multi-electrode stimulationMatias I. Maturana, David B. Grayden, Shaun L. Cloherty, Tatiana Kameneva, Michael R. Ibbotson, Hamish MeffinO6 Noise correlations in V4 area correlate with behavioral performance in visual discrimination taskVeronika Koren, Timm Lochmann, Valentin Dragoi, Klaus ObermayerO7 Input-location dependent gain modulation in cerebellar nucleus neuronsMaria Psarrou, Maria Schilstra, Neil Davey, Benjamin Torben-Nielsen, Volker SteuberO8 Analytic solution of cable energy function for cortical axons and dendritesHuiwen Ju, Jiao Yu, Michael L. Hines, Liang Chen, Yuguo YuO9 C. elegans interactome: interactive visualization of Caenorhabditis elegans worm neuronal networkJimin Kim, Will Leahy, Eli ShlizermanO10 Is the model any good? Objective criteria for computational neuroscience model selectionJustas Birgiolas, Richard C. Gerkin, Sharon M. CrookO11 Cooperation and competition of gamma oscillation mechanismsAtthaphon Viriyopase, Raoul-Martin Memmesheimer, Stan GielenO12 A discrete structure of the brain wavesYuri Dabaghian, Justin DeVito, Luca PerottiO13 Direction-specific silencing of the Drosophila gaze stabilization systemAnmo J. Kim, Lisa M. Fenk, Cheng Lyu, Gaby MaimonO14 What does the fruit fly think about values? A model of olfactory associative learningChang Zhao, Yves Widmer, Simon Sprecher,Walter SennO15 Effects of ionic diffusion on power spectra of local field potentials (LFP)Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H. Pettersen,Ole A. Andreassen...

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state and, moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects. In particular, we consider a two-dimensional Ising model at the critical temperature and investigate how its functional network changes with the increasing degree of structural defects. We show that the scale-free and small-world properties of the functional network at criticality are robust against large degrees of structural lesions while the system remains below the percolation limit. Although the Ising model is only a conceptual description of a two-state neuron, our research reveals fundamental robustness properties of functional networks derived from classical statistical mechanics models.

Formation and motion of the silver nanoparticles inside an ion-exchanged soda-lime glass in the presence of a focused high intensity continuous wave Ar+ laser beam (intensity: 9.2 × 104 W/cm2) have been studied in here. One-dimensional diffusion equation has been used to model the diffusion of the silver ions into the glass matrix, and a two-dimensional reverse diffusion model has been introduced to explain the motion of the silver clusters and their migration toward the glass surface in the presence of the laser beam. The results of the mentioned models were in agreement with our measurements on thickness of the ion-exchange layer by means of optical microscopy and recorded morphology of the glass surface around the laser beam axis by using a Mirau interferometer. SEM micrographs were used to extract the size distribution of the migrated silver particles over the glass surface.