The purpose of this paper is to formulate a dynamical model of an auditory hair-cell synapse, coupled to a model of the hair cell's receptor potential through intracellular calcium concentration. The synaptic model includes a mechanism for auditory nerve discharge, which allows for the determination of the afferent nerve's firing rate from stimulation of the receptor cell's hair bundle. We show that the synaptic model has a periodic solution under certain conditions, given a constant current stimulus. We also show that the firing rate undergoes adaptation.
The connections between the error function used in multilinear regression and the expected, or assumed, properties of the data are investigated. It is shown that two of the most basic properties often required in data analysis, scale and rotational invariance, are incompatible. With this, it is established that multilinear regression using an error function derived from a geometric mean is both scale and reflectively invariant. The resulting error function is also shown to have the property that its minimizer, under certain conditions, is well approximated using the centroid of the error simplex. It is then applied to several multidimensional real world data sets, and compared to other regression methods.
We present a demonstration based on SAP HANA to show a novel approach to churn risk scoring. Our focus is customer retention within a telecommunications setting. The purpose of this demonstration is to help identify customers who should be targeted for a customer retention marketing campaign. The data analysis considers multiple factors - churn likelihood (based on incoming and outgoing communications), customer influence (based on social connections) and the average revenue per customer. The results are presented using skyline visualization and advanced UI techniques to easily and intuitively interpret the analysis.
Abstract The non‐linear response of soft hydrated tissues under physiologically relevant levels of mechanical loading can be represented by a two‐phase continuum model based on the theory of mixtures. The governing equations for a biphasic soft tissue, consisting of an incompressible solid and an incompressible, inviscid fluid, under finite deformation are presented and a finite element formulation of this highly non‐linear problem is developed. The solid phase is assumed to be hyperelastic, and the stress‐strain relations for the solid phase are defined in terms of the free energy function. A finite element model is formulated via the Galerkin weighted residual method coupled with a penalty treatment of the continuity equation for the mixture. Using a total Lagrangian formulation, the non‐linear weighted residual statement, expressed with respect to the reference configuration, leads to a coupled non‐linear system of first order differential equations. The non‐linear constitutive equation for the solid phase elasticity is incrementally linearized in terms of the second Piola‐Kirchhoff stress and the corresponding Lagrangian strain. A tangent stiffness matrix is defined in terms of the free energy function; this matrix definition can be applied to any free energy function, and will yield a symmetric matrix when the free energy function is convex. An unconditionally stable implicit predictor‐corrector algorithm is used to obtain the temporal response histories. The confined compression mechanical test of soft tissue in stress relaxation is used as an example problem. Results are presented for moderate and rapid rates of loading, as well as small and large applied strains. Comparison of the finite element solution with an independent finite difference solution demonstrates the accuracy of the formulation.
Viscoelastic constitutive models can predict transient phenomena like creep and stress relaxation. Among the materials that can exhibit such effects in finite strain are biological soft tissues which are commonly modeled using a multiphasic continuum theory. Under infinitesimal strain, the classical 1-D Standard Linear Model (1-D SLM) is a simple law containing a stress rate and exhibiting the desired transient and equilibrium behavior observable in many soft tissues. The derivation of a rate-type constitutive law appropriate for modeling the non-linear viscoelasticity of soft tissues is the focus of this study. Well-posed laws should be objective and consistent with thermodynamic considerations of dissipation and energy. Infinitesimal models are not objective, while many non-linear analogies to the 1-D SLM fail to address dissipation. In the current study, internal variables are introduced, and employed in the derivation of a 3-D non-linear rate-type viscoelastic constitutive law. Evolution of the internal variables is assumed to involve first order rates. Properties of the 1-D SLM as well as existing non-linear models of soft tissues are used to motivate the constitutive assumptions and additional requirements. These requirements include symmetry of the stress, isotropy, reduction to hyperelasticity (via material parameters) and the existence of a hyperelastic equilibrium state. A class of objective rate-type constitutive laws satisfying dissipation and the additional requirements is derived. As an illustration, a compressible finite linear model is formulated. In infinitesimal strain, this model provides a 3-D analogy to the 1-D SLM with a set of constraints on the material parameters. The finite linear model is analyzed under simple time-dependent compression, extension and shear and shown to be consistent with expected behavior.
A three-dimensional hydroelastic model of the dynamical motion in the cochlea is analysed. The fluid is Newtonian and incompressible, and the basilar membrane is modelled as an orthotropic elastic plate. Asymptotic expansions are introduced, based on slender-body theory and the relative high frequencies in the hearing range, which reduce the problem to an eigenvalue problem in the transverse cross-section. After this, an example is worked out and a comparison is made with experiment and the earlier low-frequency theory.
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