The Confessions of Montaigne

Montaigne rarely repented and he viewed confession—both juridical and ecclesiastical—with skepticism. Confession, Montaigne believed, forced a mode of self-representation onto the speaker that was inevitably distorting. Repentance, moreover, made claims about self-transformation that Montaigne found improbable. This article traces these themes in the context of Montaigne’s Essays, with particular attention to “On Some Verses of Virgil” and argues that, for Montaigne, a primary concern was finding a means of describing a self that he refused to reduce, as had Augustine and many other writers before and after him, to the homo interior

Can linear collocation ever beat quadratic?

Computational approaches are becoming increasingly important in neuroscience, where complex, nonlinear systems modelling neural activity across multiple spatial and temporal scales are the norm. This paper considers collocation techniques for solving neural field models, which typically take the form of a partial integro-dfferential equation. In particular, we investigate and compare the convergence properties of linear and quadratic collocation on both regular grids and more general meshes not fixed to the regular Cartesian grid points. For regular grids we perform a comparative analysis against more standard techniques, in which the convolution integral is computed either by using Fourier based methods or via the trapezoidal rule. Perhaps surprisingly, we find that on regular, periodic meshes, linear collocation displays better convergence properties than quadratic collocation, and is in fact comparable with the spectral convergence displayed by both the Fourier based and trapezoidal techniques. However, for more general meshes we obtain superior convergence of the convolution integral using higher order methods, as expected

A numerical simulation of neural fields on curved geometries

Despite the highly convoluted nature of the human brain, neural field models typically treat the cortex as a planar two-dimensional sheet of neurons. Here, we present an approach for solving neural field equations on surfaces more akin to the cortical geometries typically obtained from neuroimaging data. Our approach involves solving the integral form of the partial integro-differential equation directly using collocation techniques alongside efficient numerical procedures for determining geodesic distances between neural units. To illustrate our methods, we study localised activity patterns in a two-dimensional neural field equation posed on a periodic square domain, the curved surface of a torus, and the cortical surface of a rat brain, the latter of which is constructed using neuroimaging data. Our results are twofold: Firstly, we find that collocation techniques are able to replicate solutions obtained using more standard Fourier based methods on a flat, periodic domain, independent of the underlying mesh. This result is particularly significant given the highly irregular nature of the type of meshes derived from modern neuroimaging data. And secondly, by deploying efficient numerical schemes to compute geodesics, our approach is not only capable of modelling macroscopic pattern formation on realistic cortical geometries, but can also be extended to include cortical architectures of more physiological relevance. Importantly, such an approach provides a means by which to investigate the influence of cortical geometry upon the nucleation and propagation of spatially localised neural activity and beyond. It thus promises to provide model-based insights into disorders like epilepsy, or spreading depression, as well as healthy cognitive processes like working memory or attention

Refining the scalar and tensor contributions in τ→πππντ\tau\to \pi\pi\pi\nu_\tau decays

In this article we analyze the contribution from intermediate spin-0 and spin-2 resonances to the $\tau\to\nu \pi\pi\pi$ decay by means of a chiral invariant Lagrangian incorporating these mesons. In particular, we study the corresponding axial-vector form-factors. The advantage of this procedure with respect to previous analyses is that it incorporates chiral (and isospin) invariance and, hence, the partial conservation of the axial-vector current. This ensures the recovery of the right low-energy limit, described by chiral perturbation theory, and the transversality of the current in the chiral limit at all energies. Furthermore, the meson form-factors are further improved by requiring appropriate QCD high-energy conditions. We end up with a brief discussion on its implementation in the Tauola Monte Carlo and the prospects for future analyses of Belle's data.Comment: 32 pages, 13 figures. Extended discussion on the numerical importance of the tensor and scalar resonances and the parametrization of the scalar propagator. Version published in JHE

Boolean network model predicts cell cycle sequence of fission yeast

A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe) is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer, faithfully reproduces the known sequence of regulatory activity patterns along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.Comment: 10 pages, 3 figure