329 research outputs found
On C*-algebras related to constrained representations of a free group
We consider representations of the free group on two generators such
that the norm of the sum of the generators and their inverses is bounded by
. These -constrained representations determine a C*-algebra
for each . We prove that these C*-algebras form a
continuous bundle of C*-algebras over and calculate their K-groups.Comment: 9 page
Basal Chromospheric Flux and Maunder Minimum-type Stars: The quiet-Sun Chromosphere as a Universal Phenomenon
Aims: We demonstrate the universal character of the quiet-Sun chromosphere
among inactive stars (solar-type and giants). By assessing the main physical
processes, we shed new light on some common observational phenomena. Methods:
We discuss measurements of the solar Mt. Wilson S-index, obtained by the
Hamburg Robotic Telescope around the extreme minimum year 2009, and compare the
established chromospheric basal Ca II K line flux to the Mt. Wilson S-index
data of inactive ("flat activity") stars, including giants. Results: During the
unusually deep and extended activity minimum of 2009, the Sun reached S-index
values considerably lower than in any of its previously observed minima. In
several brief periods, the Sun coincided exactly with the S-indices of inactive
("flat", presumed Maunder Minimum-type) solar analogues of the Mt. Wilson
sample; at the same time, the solar visible surface was also free of any plages
or remaining weak activity regions. The corresponding minimum Ca II K flux of
the quiet Sun and of the presumed Maunder Minimum-type stars in the Mt. Wilson
sample are found to be identical to the corresponding Ca II K chromospheric
basal flux limit. Conclusions: We conclude that the quiet-Sun chromosphere is a
universal phenomenon among inactive stars. Its mixed-polarity magnetic field,
generated by a local, "fast" turbulent dynamo finally provides a natural
explanation for the minimal soft X-ray emission observed for inactive stars.
Given such a local dynamo also works for giant chromospheres, albeit on larger
length scales, i.e., l ~ R/g, with R and g as stellar radius and surface
gravity, respectively, the existence of giant spicular phenomena and the
guidance of mechanical energy toward the acceleration zone of cool stellar
winds along flux-tubes have now become traceable.Comment: 6 pages, 4 figures; Astronomy & Astrophysics (Research Note), in
pres
One rule to grow them all: A general theory of neuronal branching and its practical application
Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramon y Cajal's laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the "TREES toolbox," which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks
Computing the local field potential (LFP) from integrate-and-fire network models
Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best "LFP proxy", we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with "ground-truth" LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo
A New Version of Reimers' law of Mass Loss Based on a Physical Approach
We present a new semi-empirical relation for the mass loss of cool stellar
winds, which so far has frequently been described by "Reimers' law".
Originally, this relation was based solely on dimensional scaling arguments
without any physical interpretation. In our approach, the wind is assumed to
result from the spill-over of the extended chromosphere, possibly associated
with the action of waves, especially Alfven waves, which are used as guidance
in the derivation of the new formula. We obtain a relation akin to the original
Reimers law, but which includes two new factors. They reflect how the
chromospheric height depends on gravity and how the mechanical energy flux
depends, mainly, on effective temperature. The new relation is tested and
sensitively calibrated by modelling the blue end of the Horizontal Branch of
globular clusters. The most significant difference from mass loss rates
predicted by the Reimers relation is an increase by up to a factor of 3 for
luminous late-type (super-)giants, in good agreement with observations.Comment: 12 pages, 4 figures, accepted by ApJ Letter
Robust coding of flow-field parameters by axo-axonal gap junctions between fly visual interneurons
Complex flight maneuvers require a sophisticated system to exploit the optic flow resulting from moving images of the environment projected onto the retina. In the fly's visual course control center, the lobula plate, 10 so-called vertical system (VS) cells are thought to match, with their complex receptive fields, the optic flow resulting from rotation around different body axes. However, signals of single VS cells are unreliable indicators of such optic flow parameters in the context of their noisy, texture-dependent input from local motion measurements. Here we propose an alternative encoding scheme based on network simulations of biophysically realistic compartmental models of VS cells. The simulations incorporate recent data about the highly selective connectivity between VS cells consisting of an electrical axo-axonal coupling between adjacent cells and a reciprocal inhibition between the most distant cells. We find that this particular wiring performs a linear interpolation between the output signals of VS cells, leading to a robust representation of the axis of rotation even in the presence of textureless patches of the visual surround
Coronal properties of planet-bearing stars
Do extrasolar planets affect the activity of their host stars? Indications
for chromospheric activity enhancement have been found for a handful of
targets, but in the X-ray regime, conclusive observational evidence is still
missing. We want to establish a sound observational basis to confirm or reject
major effects of Star-Planet Interactions (SPI) in stellar X-ray emissions. We
therefore conduct a statistical analysis of stellar X-ray activity of all known
planet-bearing stars within 30pc distance for dependencies on planetary
parameters such as mass and semimajor axis. We find that in our sample, there
are no significant correlations of X-ray luminosity or the activity indicator
L_X/L_bol with planetary parameters which cannot be explained by selection
effects. Coronal SPI seems to be a phenomenon which might only manifest itself
as a strong effect for a few individual targets, but not to have a major effect
on planet-bearing stars in general.Comment: accepted by A&
X-ray Activity on the Star-Planet Interaction Candidate HD 179949
We carry out detailed spectral and timing analyses of the X-ray
data of HD 179949, a prototypical example of a star with a close-in giant
planet with possible star-planet interaction (SPI) effects. We find a low
coronal abundance Fe/H0.2 relative to the solar photosphere, as well
as lower abundances of high FIP elements O/Fe 1, Ne/Fe
0.1, but with indications of higher abundances of N and Al. This star also has
an anomalous FIP bias of , larger than expected for
stars of this type. We detect significant intensity variability over time
scales ranging from 100~s - 10~ks, and also evidence for spectral variability
over time scales of 1-10~ks. We combine the flux measurements with
and measurements to detect periodicities, and determine
that the dominant signal is tied to the stellar polar rotational period,
consistent with expectations that the corona is rotational-pole dominated. We
also find evidence for periodicity at both the planetary orbital frequency and
at its beat frequency with the stellar polar rotational period, suggesting the
presence of a magnetic connection between the planet and the stellar pole. If
these periodicities represent an SPI signal, the lack of phase dependence in
coronal temperature or flaring suggests that the SPI in this system is driven
by a quasi-continuous form of heating (e.g., magnetic field stretching) rather
than a highly sporadic, hot, impulsive form (e.g., flare-like reconnection).Comment: 23 pages, 12 figures, 9 tables. Submitted to the Astrophysical
Journal. Comments welcome
- …