Backreaction in Axion Monodromy, 4-forms and the Swampland

Axion monodromy models can always be described in terms of an axion coupled to 3-form gauge fields with non-canonical kinetic terms. The presence of the saxions parametrising the kinetic metrics of the 3-form fields leads to backreaction effects in the inflationary dynamics. We review the case in which saxions backreact on the K\"ahler metric of the inflaton leading to a logarithmic scaling of the proper field distance at large field. This behaviour is universal in Type II string flux compactifications and consistent with a refinement of the Swampland Conjecture. The critical point at which this behaviour appears depends on the mass hierarchy between the inflaton and the saxions. However, in tractable compactifications, such a hierarchy cannot be realised without leaving the regime of validity of the effective theory, disfavouring transplanckian excursions in string theory.Comment: Proceedings prepared for the "Workshop on Geometry and Physics", November 2016, Ringberg Castl

The asymmetric properties of surround suppression.

<p>Distributions of ASI, ASI_a (A), and AD, AD_a (B) are differentiated by color. Red and blue represent asymmetric properties for MFR and gLFP. Yellow and green represent axial asymmetric properties for MFR and gLFP. AD and AD_a analyses were only performed when corresponding ASI or ASI_a was larger than 0.2. The horizontal arrow indicates the optimal direction. (C) AD difference between the MFR and gLFP when the corresponding ASIs were both larger than 0.2. (D) ASI correlation of MFR and gLFP (r = 0.36, P = 0.048, t-test).</p

Spatial distribution of surround suppression of a sample recording site.

<p>Surround suppression was not always uniform for the firing rate (A) and gLFP (B). In this recording site, both responses had a distinct LSR of similar sizes. These LSRs did not overlap, but were aligned to the optimal direction. The dashed circle indicates the SSF size and position. The dashed arrow indicates the optimal direction of firing rate, which was also the drifting direction of all stimuli. For the sake of illustration, the data were interpolated four times by a 2D third-order spline.</p

Size-tuning responses of a sample recording site.

<p>(A–C) Multi-unit and LFP responses to the enlarging drifting gratings. Black vertical lines indicate the stimulus onset and offset times. The gray horizontal bars indicate the sustained response windows. (D) Size-tuning curve of the sustained response of mean firing rate. The data points indicate the mean ± SE. The solid line is the DoG function fitted from the data, with Adjust-R² = 0.951. The dashed line indicates the response level of uniform background control. (E) LFP power spectrum of different stimulus sizes. The gray bar indicates gamma band. (F) Normalized spike power spectrum of different stimulus sizes. The color code is identical to that of (E). (G) Size-tuning curve of sustained gLFP. The Adjust-R² of the fitted DoG was 0.871. The legends are identical to those of (D).</p

A Nonparametric Graphical Model for Functional Data With Application to Brain Networks Based on fMRI

<p>We introduce a nonparametric graphical model whose observations on vertices are functions. Many modern applications, such as electroencephalogram and functional magnetic resonance imaging (fMRI), produce data are of this type. The model is based on additive conditional independence (ACI), a statistical relation that captures the spirit of conditional independence without resorting to multi-dimensional kernels. The random functions are assumed to reside in a Hilbert space. No distributional assumption is imposed on the random functions: instead, their statistical relations are characterized nonparametrically by a second Hilbert space, which is a reproducing kernel Hilbert space whose kernel is determined by the inner product of the first Hilbert space. A precision operator is then constructed based on the second space, which characterizes ACI, and hence also the graph. The resulting estimator is relatively easy to compute, requiring no iterative optimization or inversion of large matrices. We establish the consistency and the convergence rate of the estimator. Through simulation studies we demonstrate that the estimator performs better than the functional Gaussian graphical model when the relations among vertices are nonlinear or heteroscedastic. The method is applied to an fMRI dataset to construct brain networks for patients with attention-deficit/hyperactivity disorder. Supplementary materials for this article are available online</p

Comparison of firing rate and gLFP surround suppression characteristics.

<p>(A) Pairwise comparison of suppression indexes. Black lines in histograms represent the median. The two distributions were significantly different and correlated (Wilcoxon signed-rank test, r_s is the Spearman rank correlation coefficient). (B) Distributions of stimulus size that produce maximum response. No significant differences were observed, although, they were significantly correlated. The legends are identical to those in (A).</p

Asymmetry vector and axial asymmetry vector of firing rate and gLFP.

<p>Population distributions of the AV of the firing rate (red circle) and gLFP (blue cycle), as well as the AV_a of the firing rate (yellow square) and gLFP (green square). The AV angle was rotated so that the optimal direction always horizontally points to the right (black arrow).</p

Stimulus paradigm.

<p>(A) Center-surround compound stimulus set. The center orientation selectivity was tested under different surround orientations in each column. The orientation selectivity of surround suppression was tested under different center orientations in each row. Surround orientation was the relative angle to the center orientation. (B) Spatial organization of surround modulation was tested by co-stimulation of grid center and other positions. The center stimulus response was chosen as the control level of surround suppression. See text for details.</p

Population-averaged orientation tuning of surround modulation.

<p>Horizontal lines and shadings indicate the mean ± SE of CRF stimulation without the surround stimulus. The Data points represent the mean ± SE under different surround orientations.</p

Responses of a sample recording site to the center-surround compound stimulus set.

<p>The upper row (A–C) shows firing rate responses and the lower row (D–F) shows the gLFP responses. (A, D) Response of center-surround compound stimulus set. For the sake of illustration, data were interpolated four times by a 2D third-order spline. (B, E) Center orientation tuning curves of firing rate and gLFP under different surround orientations. The data points represent the mean ± SE. The dashed lines indicate responses with no center stimulus. (C, F) Orientation tuning of surround suppression under different center orientations. The dashed lines indicate responses with no surround stimulus.</p