The PDF corresponds to the maximum possible stationary value of the fourth-order moment of amplitude κ_4=4 and yields a probability to meet intensity above the rogue wave threshold that is higher by 1.5 orders of magnitude than that for a random superposition of linear waves. We routinely observe rogue waves with amplitudes ten times larger than the average one, and all of the largest waves that we have studied are very well approximated by the amplitude-scaled rational breather solutions of either the first (Peregrine breather) or the second orders.In this work we study the structure-transport property relationships of small ligand intercalated DNA molecules using a multiscale modeling approach where extensive ab initio calculations are performed on numerous MD-simulated configurations of dsDNA and dsDNA intercalated with two different intercalators, ethidium and daunomycin. DNA conductance is found to increase by one order of magnitude upon drug intercalation due to the local unwinding of the DNA base pairs adjacent to the intercalated sites, which leads to modifications of the density of states in the near-Fermi-energy region of the ligand-DNA complex. Our study suggests that the intercalators can be used to enhance or tune the DNA conductance, which opens new possibilities for their potential applications in nanoelectronics.The local microenvironment of a tumor plays an important and commonly observed role in cancer development and progression. Dynamic changes in the tissue microenvironment are thought to epigenetically disrupt healthy cellular phenotypes and drive cancer incidence. Despite the experimental work in this area there are no conceptual models to understand the interplay between the epigenetic dysregulation in the microenvironment of early tumors and the appearance of cancer driver mutations. Here, we develop a minimal model of the tissue microenvironment which considers three interacting subpopulations healthy, phenotypically dysregulated, and mutated cancer cells. Healthy cells can epigenetically (reversibly) transition to the dysregulated phenotype, and from there to the cancer state. The epigenetic transition rates of noncancer cells can be influenced by the number of cancer cells in the microenvironment (termed microenvironment feedback). Our model delineates the regime in which microenvironment feedback accelerates the rate of cancer initiation. In addition, the model shows when and how microenvironment feedback may inhibit cancer progression. We discuss how our framework may provide resolution to some of the puzzling experimental observations of slow cancer progression.Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not yet been demonstrated. Here we quantitatively analyze virion accumulation by accounting for aerosolized virion emission and destabilization. check details Reported superspreading events analyzed within this framework point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure calculated for these events is found to trace out a single value, suggesting a universal minimum infective dose (MID) via aerosol that is comparable to the MIDs measured for other respiratory viruses; thus, the consistent infectious exposure levels and their commensurability to known aerosol-MIDs establishes the plausibility of aerosol transmission of SARS-CoV-2. Using filtration at a rate exceeding the destabilization rate of aerosolized SARS-CoV-2 can reduce exposure below this infective dose.We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in scale-free networks. This phenomenon is characterized by multiple peaks in the susceptibility as a function of the infection rate. It can be explained by that, even under the global epidemic threshold, a hub can sustain the epidemics for an extended period. Moreover, our approach improves theoretical calculations of prevalence close to the threshold in heterogeneous networks and also can predict the average risk of infection for neighbors of nodes with different degree and state on uncorrelated static networks.We consider a thin fluid film flowing down an inclined substrate subjected to localized external sources of momentum and heat flux that induce deformations of the fluid's free surface. This scenario is encountered in several industrial processes and of particular interest is the case where these deformations are undesirable. When the substrate is thin and the temperature along its underside is freely imposed by an active cooling mechanism, temperature gradients are generated at the fluid surface which drive a thermocapillary flow and influence the deformations. This naturally leads us to pose the optimal control problem of choosing the temperature profile that minimizes the unwanted free-surface deformations. Numerical computations reveal that the external forces generate deflections in a region near their peak beyond which all deflections are suppressed by the optimal control. Where nonzero deflections occur, the control is of bang-bang type (taking either its upper or lower bound), while the control is obtained in closed form for regions where the deflections are suppressed. Strikingly, in switching between these regions the optimal control chatters, that is, it switches infinitely many times over a finite interval. By appealing to Pontryagin's maximum principle and leveraging a symmetry embedded in the adjoint problem we uncover the underlying fractal structure of the chattering. Finally, we present practical approaches to avoid the infinite switching while retaining significantly reduced free-surface deformations.Voter models are well known in the interdisciplinary community, yet they have not been studied from the perspective of anomalous diffusion. In this paper, we show that the original voter model exhibits a ballistic regime. Nonlinear transformations of the observation variable and time scale allow us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.