@article{harlim_mahdi_majda_2014, title={An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models}, volume={257}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2013.10.025}, abstractNote={A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Harlim, John and Mahdi, Adam and Majda, Andrew J.}, year={2014}, month={Jan}, pages={782–812} }
@article{mahdi_meshkat_sullivant_2014, title={Structural Identifiability of Viscoelastic Mechanical Systems}, volume={9}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0086411}, abstractNote={We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.}, number={2}, journal={PLOS ONE}, author={Mahdi, Adam and Meshkat, Nicolette and Sullivant, Seth}, year={2014}, month={Feb} }
@article{mahdi_2013, title={CENTER PROBLEM FOR THIRD-ORDER ODES}, volume={23}, ISSN={["1793-6551"]}, DOI={10.1142/s0218127413500788}, abstractNote={We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three 4-parameter families of quadratic systems on ℝ3. We also give a positive answer to an open question posed in [Dias & Mello, 2010] related to similar systems.}, number={5}, journal={INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS}, author={Mahdi, Adam}, year={2013}, month={May} }
@article{fercec_mahdi_2013, title={Center conditions and cyclicity for a family of cubic systems: Computer algebra approach}, volume={87}, ISSN={["0378-4754"]}, DOI={10.1016/j.matcom.2013.02.003}, abstractNote={Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. To that end we overcome the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we also determine the number of limit cycles bifurcating from each component of the center variety.}, journal={MATHEMATICS AND COMPUTERS IN SIMULATION}, author={Fercec, Brigita and Mahdi, Adam}, year={2013}, month={Jan}, pages={55–67} }
@article{llibre_mahdi_valls_2013, title={Darboux integrability of the Lu system}, volume={63}, ISSN={["1879-1662"]}, DOI={10.1016/j.geomphys.2012.10.003}, abstractNote={We characterize all the values of the parameters of the Lü system, for which it admits a Darboux first integral.}, journal={JOURNAL OF GEOMETRY AND PHYSICS}, author={Llibre, Jaume and Mahdi, Adam and Valls, Claudia}, year={2013}, month={Jan}, pages={118–128} }
@article{mahdi_sturdy_ottesen_olufsen_2013, title={Modeling the Afferent Dynamics of the Baroreflex Control System}, volume={9}, ISSN={1553-7358}, url={http://dx.doi.org/10.1371/journal.pcbi.1003384}, DOI={10.1371/journal.pcbi.1003384}, abstractNote={In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.}, number={12}, journal={PLoS Computational Biology}, publisher={Public Library of Science (PLoS)}, author={Mahdi, Adam and Sturdy, Jacob and Ottesen, Johnny T. and Olufsen, Mette S.}, editor={Arciero, Julia C.Editor}, year={2013}, month={Dec}, pages={e1003384} }
@article{mahdi_valls_2012, title={Analytic non-integrability of the Suslov problem}, volume={53}, ISSN={["0022-2488"]}, DOI={10.1063/1.4763464}, abstractNote={In this work, we consider the Suslov problem, which consists of a rotation motion of a rigid body, whose center of mass is located at one axis of inertia, around a fixed point O in a constant gravity field restricted to a nonholonomic constraint. The integrability and non-integrability has been established by a number of authors for the nongeneric values of b = (b1, b2, b3) which is the unit vector along the line connecting the point O with the center of mass of the body. Here, we prove the analytic non-integrability for the remaining (generic) values of b.}, number={12}, journal={JOURNAL OF MATHEMATICAL PHYSICS}, author={Mahdi, Adam and Valls, Claudia}, year={2012}, month={Dec} }