Reaction rates and transport in neutron stars

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.

Representation of three-dimensional space in the auditory cortex of the echolocating bat P. discolor.

The auditory cortex is an essential center for sound localization. In echolocating bats, combination sensitive neurons tuned to specific delays between call emission and echo perception represent target distance. In many bats, these neurons are organized as a chronotopically organized map of echo delay. However, it is still unclear to what extend these neurons can process directional information and thereby form a three-dimensional representation of space. We investigated the representation of three-dimensional space in the auditory cortex of Phyllostomus discolor. Specifically, we hypothesized that combination sensitive neurons encoding target distance in the AC can also process directional information. We used typical echolocation pulses of P. discolor combined with simulated echoes from different positions in virtual 3D-space and measured the evoked neuronal responses in the AC of the anesthetized bats. Our results demonstrate that combination sensitive neurons in the AC responded selectively to specific positions in 3-D space. While these neurons were sharply tuned to echo delay and formed a precise target distance map, the neurons' specificity in azimuth and elevation depended on the presented sound pressure level. Our data further reveal a topographic distribution of best elevation of the combination sensitive neurons along the rostro-caudal axis i.e., neurons in the rostral part of the target distance map representing short delays prefer elevations below the horizon. Due to their spatial directionality and selectivity to specific echo delays representing target distance, combination sensitive cortical neurons are suited to encode three-dimensional spatial information

Cortical 3D-representation of auditory space

Representation of three-dimensional space in the auditory cortex of the echolocating bat P. discolo

Three-dimensional receptive field of cortical combination sensitive neuron.

<p>Spatial receptive fields of the same unit as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0182461#pone.0182461.g009" target="_blank">Fig 9</a> in tree-dimensional space. The receptive fields (50% contour line) at each echo delay step (3.8 ms, 4.8 ms, 6.0 ms = BD, 7.5 ms, 9.4 ms) are indicated by a black solid line, the colored area indicates the respective echo delay and the black asterisks mark BAZ/BEL. The response rate and consequently the size of the receptive fields normalized on the maximum response at BD decrease at shorter or longer echo delays than the unit’s BD. Because of this, the black outlines of the receptive fields at different delay steps indicate a three-dimensional response volume in space where the response with at least 50% of its maximum response. The dotted black line shows the linear regression through BAZ/BEL at the different echo delay steps and indicates the unit’s spatial directionality.</p

Delay tuning in the auditory cortex.

<p>(A,B) DRFs of a two cortical units with medium (A) and long (B) best delay. The spike count per repetition is color-coded; the black dotted contour line represents the response threshold at 50% of the units maximal spike count. The echo delay/echo level combination eliciting the maximal response is marked by a black asterisk (A: BD = 7 ms, BL = -20 dB, B: BD = 14 ms, BL = -20 dB). Note the different scaling of the abcissa in A and B. (C) Distribution of BDs along the rostro-caudal axis in the PDF of the AC. Units encoding short echo delays are located in the frontal part of the PDF, units with long best delays in the caudal part of the PDF. The dotted line indicates a linear regression. The position of the analyzed units in the cortex is sketched above the data points. Black lines indicate the bat’s brain, dashed lines indicate the position of the auditory cortex and red lines mark the rostro-caudal range from 7000–8500 μm as shown below. d: dorsal, v: ventral, r: rostral, c: caudal.</p

Simulated echo levels at different echo delays.

<p>Echo levels at 60 kHz relative to the presented pulse level at echo delays of 3 ms (A), 6 ms (B), 9 ms (C), 12 ms (D) and 15 ms (E). Relative echo levels are color-coded. The black lines correspond to differences of 5 dB. Echo levels at different spatial positions are calculated using the pulse emission characteristics of <i>P</i>. <i>discolor</i>, distance and frequency dependent sound damping (corresponding to the echo delay or physical distance in air) and the HRTF. For each echo delay, the maximum echo levels [dB] are indicated at the loudest position.</p

BAZ/BEL and centroid positions of all analyzed units.

<p>(A) Distribution of BAZ and BEL. The best responses were measured at discrete spatial positions (15° binning). Multiple units responding at the same position are grouped together in the figure. Each unit’s BD is color-coded. The lower histogram shows the distribution of BAZ and the left histogram the distribution of BEL. (B) Distribution of centroids of the spatial receptive fields. The lower histogram shows the distribution of the centroid positions in azimuth, the left histogram the distribution of the centroid positions in elevation (bin width 7.5°). All azimuth positions are normalized to one hemisphere. Azimuth positions > 0° correspond to positions contralateral to the recording site.</p

Systematic representation of target elevation and echo delay.

<p>Schematic drawing illustrating the possible implication of the covariation of BD and elevation for target representation in the cortical target-range map.. (A) At long distances to the target, neurons with long BDs in the caudal region of the PDF respond preferably to echoes from frontal positions. (B) At short distances to the target, neurons with short BDs in the rostral region of the PDF respond preferably to positions below the bat. Arrows represent the direction of best elevation. d: dorsal, v: ventral, r: rostral, c: caudal.</p

Azimuth and elevation at different best delays.

<p>Boxplots of BAZ (A), BEL (B), centroid positions in azimuth (C) and in elevation (D) for all analyzed units with best delays ≤ 7 ms (left box, n = 34) and > 7 ms (right box, n = 33). All boxes represent the median (red center line) and the interquartile range (IQR); whiskers indicate values within 1.5x IQR, black circles mark outliers. Significant differences between different groups are indicated by a black asterisk.</p

Influence of call/echo level on spatial tuning.

<p>(A) Boxplots of maximum spike count for all analyzed units (n = 40) and for each presented pulse/echo level. The boxes represent the median (red center line) and the interquartile range (IQR); whiskers indicate values within 1.5x IQR, black circles mark outliers. (B-D) Spatial receptive fields of a unit at the unit’s BD and echo levels of BL -10 dB (B), BL +0 dB (C) and BL +10 dB (D). The relative spike count in relation to the maximum response at each echo level is color-coded. The maximum spike count per repetition at each presented echo level is given on top of each figure. In each figure, the black asterisk marks the position of the maximum response and the black circle marks the centroid of the receptive field.</p