In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

We present an efficient method for the reduction of model equations in the linearized diffuse optical tomography (DOT) problem. We first implement the maximum a posteriori (MAP) estimator and Tikhonov regularization, which are based on applying preconditioners to linear perturbation equations. For model reduction, the precondition is split into two parts: the principal components are consid...

Growth condition perturbation or gene function disruption are commonly used strategies to study cellular systems. Although it is widely appreciated that such experiments may involve indirect effects, these frequently remain uncharacterized. Here, analysis of functionally unrelated Saccharyomyces cerevisiae deletion strains reveals a common gene expression signature. One property shared by these...

We study the interplay between motor programs and their timing in the brain by using precise pulses of transcranial magnetic stimulation (TMS) applied to the primary motor cortex. The movement of the finger performing a tapping task is periodically perturbed in synchronization with a metronome. TMS perturbation can profoundly affect both the finger trajectory and its kinematics, but the tapping...

Population activity measurement by calcium imaging can be combined with cellular resolution optogenetic activity perturbations to enable the mapping of neural connectivity in vivo. This requires accurate inference of perturbed and unperturbed neural activity from calcium imaging measurements, which are noisy and indirect, and can also be contaminated by photostimulation artifacts. We have devel...

Free-ocean CO2 enrichment (FOCE) systems are designed to assess the impact of ocean acidification on biological communities in situ for extended periods of time (weeks to months). They overcome some of the drawbacks of laboratory experiments and field observations by enabling (1) precise control of CO2 enrichment by monitoring pH as an offset of ambient pH, (2) consideration of indirect effects...

Inferring causal structures of real world complex networks from measured time series signals remains an open issue. The current approaches are inadequate to discern between direct versus indirect influences (i.e., the presence or absence of a directed arc connecting two nodes) in the presence of noise, sparse interactions, as well as nonlinear and transient dynamics of real world processes. We ...

MOTIVATION Quantification of cellular changes to perturbations can provide a powerful approach to infer crosstalk among molecular components in biological networks. Existing crosstalk inference methods conduct network-structure learning based on a single phenotypic feature (e.g. abundance) of a biomarker. These approaches are insufficient for analyzing perturbation data that can contain informa...

Coupling of local chemical processes over the globe by atmospheric transport leads to the existence of chemical modes that are a fundamental characterization of global atmospheric chemistry and provide a true description of the atmospheric response to small changes in trace-gas emissions. Such coupled chemistry-transport modes in global tropospheric chemistry are an inherent feature of three-di...