Fractional cable models for spiny neuronal dendrites

Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that postsynaptic potentials propagating along dendrites with larger spine densities can arrive at the soma faster and be sustained at higher levels over longer times. Calibration and validation of the models should provide new insight into the functional implications of altered neuronal spine densities, a hallmark of normal aging and many neurodegenerative disorders

Multiple Disguises for the Same Party: The Concepts of Morphogenesis and Phenotypic Variations in Cryptococcus neoformans†

Although morphological transitions (such as hyphae and pseudohyphae formation) are a common feature among fungi, the encapsulated pathogenic yeast Cryptococcus neoformans is found during infection as blastoconidia. However, this fungus exhibits striking variations in cellular structure and size, which have important consequences during infection. This review will summarize the main aspects related with phenotypic and morphological variations in C. neoformans, which can be divided in three classes. Two of them are related to changes in the capsule, while the third one involves changes in the whole cell. The three morphological and phenotypic variations in C. neoformans can be classified as: (1) changes in capsule structure, (2) changes in capsule size, and (3) changes in the total size of the cell, which can be achieved by the formation of cryptococcal giant/titan cells or microforms. These changes have profound consequences on the interaction with the host, involving survival, phagocytosis escape and immune evasion and dissemination. This article will summarize the main features of these changes, and highlight their importance during the interaction with the host and how they contribute to the development of the disease

A simple finite-difference scheme for handling topography with the second-order wave equation

The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free surface can decrease that error. An existing approach requires extrapolation of interior solution values to the exterior while using the boundary condition at the free surface. However, schemes of this type occasionally become unstable and may be impossible to implement with highly irregular topography. One-dimensional extrapolation along coordinate lines results in a simple and efficient scheme. The stability of the 1D scheme is improved by ignoring the interior point nearest to the boundary during extrapolation in case its distance to the boundary is less than half a grid spacing. The generalization of the 1D scheme to more than one dimension requires a modification if the boundary intersects the finite-difference stencil on both sides of the central evaluation point and if there are not enough interior points to build the finite-difference stencil. Examples for the 2D constant-density acoustic case with a fourth-order finite-difference scheme demonstrate the method's capability. Because the 1D assumption is not valid in two dimensions if the boundary does not follow grid lines, the formal numerical accuracy is not always obtained, but the method can handle highly irregular topography.Applied Geophysics and Petrophysic

Higher-order source-wavefield reconstruction for reverse time migration from stored values in a boundary strip just one point wide

One way to deal with the storage problem for the forward source wavefield in reverse time migration and full-waveform inversion is the reconstruction of that wavefield during reverse time stepping along with the receiver wavefield. Apart from the final states of the source wavefield, this requires a strip of boundary values for the whole time range in the presence of absorbing boundaries. The width of the stored boundary strip, positioned in between the interior domain of interest and the absorbing boundary region, usually equals about half that of the finite-difference stencil. The required storage in 3D with high frequencies can still lead to a decrease in computational efficiency, despite the substantial reduction in data volume compared with storing the source wavefields at all or at appropriately subsampled time steps. We have developed a method that requires a boundary strip with a width of just one point and has a negligible loss of accuracy. Stored boundary values over time enable the computation of the second and higher even spatial derivatives normal to the boundary, which together with extrapolation from the interior provides stability and accuracy. Numerical tests show that the use of only the boundary values provides at most fourth-order accuracy for the reconstruction error in the sourcewavefield. The use of higher even normal derivatives, reconstructed from the stored boundary values, allows for higher orders as numerical examples up to order 26 demonstrate. Subsampling in time is feasible with highorder interpolation and provides even more storage reduction but at a higher computational cost.Applied Geophysics and Petrophysic

Performance of old and new mass-lumped triangular finite elements for wavefield modelling

Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In two dimensions on quadrilaterals, spectral elements are the obvious choice. Triangles offer more flexibility for meshing, but the construction of polynomial elements is less straightforward. The elements have to be augmented with higher-degree polynomials in the interior to preserve accuracy after lumping of the mass matrix. With the classic accuracy criterion, triangular elements suitable for mass lumping up to a polynomial degree 9 were found. With a newer, less restrictive criterion, new elements were constructed of degree 5–7. Some of these are more efficient than the older ones. To assess which of all these elements performs best, the acoustic wave equation is solved for a homogeneous model on a square and on a domain with corners, as well as on a heterogeneous example with topography. The accuracy and runtimes are measured using either higher-order time stepping or second-order time stepping with dispersion correction. For elements of polynomial degree 2 and higher, the latter is more efficient. Among the various finite elements, the degree-4 element appears to be a good choice.Applied Geophysics and Petrophysic

A numerically exact nonreflecting boundary condition applied to the acoustic Helmholtz equation

ABSTRACTWhen modeling wave propagation, truncation of the computational domain to a manageable size requires nonreflecting boundaries. To construct such a boundary condition on one side of a rectangular domain for a finite-difference discretization of the acoustic wave equation in the frequency domain, the domain is extended on that one side to infinity. Constant extrapolation in the direction perpendicular to the boundary provides the material properties in the exterior. Domain decomposition can split the enlarged domain into the original one and its exterior. Because the boundary-value problem for the latter is translation-invariant, the boundary Green functions obey a quadratic matrix equation. Selection of the solvent that corresponds to the outgoing waves provides the input for the remaining problem in the interior. The result is a numerically exact nonreflecting boundary condition on one side of the domain. When two nonreflecting sides have a common corner, the translation invariance is lost. Treating each side independently in combination with a classic absorbing condition in the other direction restores the translation invariance and enables application of the method at the expense of numerical exactness. Solving the quadratic matrix equation with Newton?s method turns out to be more costly than solving the Helmholtz equation and may select unwanted incoming waves. A proposed direct method has a much lower cost and selects the correct branch. A test on a 2D acoustic marine seismic problem with a free surface at the top, a classic second-order Higdon condition at the bottom, and numerically exact boundaries at the two lateral sides demonstrates the capability of the method. Numerically exact boundaries on each side, each computed independently with a free-surface or Higdon condition, provide even better results.Applied Geophysics and Petrophysic

Time-shift extended imaging for estimating depth errors

The stationary-phase method applied to migration with a time-shift extension in a 2-D constant-velocity model with a dipped reflector produces two solutions in the domain of the extended image: one a straight line and the other a curve. If the velocity differs from the true one, the depth error follows from the depth and apparent dip of the reflector as well as the depth of the amplitude peak at a non-zero time shift, where the two solutions meet and the extended image focuses. The results are compared to finite-frequency results from a finite-difference code. A 2-D synthetic example with a salt diapir illustrates how depth errors can be estimated in an inhomogeneous model after inverting the seismic data for the velocity model.Applied Geophysics and Petrophysic

Stationary-phase analysis of time-shift extended imaging in a constant-velocity model

To estimate the depth errors in a subsurface model obtained from the inversion of seismic data, the stationary-phase approximation in a two-dimensional constant-velocity model with a dipped reflector is applied to migration with a time-shift extension. This produces two asymptotic solutions: one is a straight line, and the other is a curve. If the velocity differs from the true one, a closed-form expression of the depth error follows from the depth and apparent dip of the reflector as well as the position of the amplitude peak at a non-zero time shift, where the two solutions meet and the extended migration image focuses. The results are compared to finite-frequency results from a finite-difference code. A two-dimensional synthetic example with a salt diapir illustrates how depth errors can be estimated in an inhomogeneous model after inverting the seismic data for the velocity model.Applied Geophysics and Petrophysic

On the error behaviour of force andmoment sources in tetrahedral spectral finite elements

The representation of a force or of a moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on 1-D elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in 3D on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the 1-D case, although in 3D, the loss of accuracy for the moment source is not a severe as a full order.Accepted Author ManuscriptApplied Geophysics and Petrophysic

Efficiency of Old and New Triangular Finite Elements for Wavefield Modelling in Time

Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In 2D on quadrilaterals, spectral elements are the obvious choice. Triangles are more flexible for meshing, but the construction of polynomial elements is less straightforward. So far, elements up to degree 9 have been found. Some years ago, an accuracy criterion that is sharper and less restrictive than the customary one led to new tetrahedral elements that are considerably more efficient than those previously known. Applying the same criterion to triangular elements provides infinitely many new elements of degree 5, with the same number of nodes as the old one, and two elements of degree 6 with less nodes than the known ones. Their efficiency, measured in terms of the compute time needed to obtain a solution with a given accuracy, is determined for a homogeneous problem and compared to that of the old elements of degree 1 to 8. For moderate accuracy, elements of degree 3 are the most efficient. For high accuracy, one of the new degree-6 elements performs best.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic