39,712 research outputs found
Critical Point in Self-Organized Tissue Growth
We present a theory of pattern formation in growing domains inspired by
biological examples of tissue development. Gradients of signaling molecules
regulate growth, while growth changes these graded chemical patterns by
dilution and advection. We identify a critical point of this feedback dynamics,
which is characterized by spatially homogeneous growth and proportional scaling
of patterns with tissue length. We apply this theory to the biological model
system of the developing wing of the fruit fly \textit{Drosophila melanogaster}
and quantitatively identify signatures of the critical point.Comment: 5 pages, 3 figure
Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains
Coherent neural spiking and local field potentials are believed to be
signatures of the binding and transfer of information in the brain. Coherent
activity has now been measured experimentally in many regions of mammalian
cortex. Synfire chains are one of the main theoretical constructs that have
been appealed to to describe coherent spiking phenomena. However, for some
time, it has been known that synchronous activity in feedforward networks
asymptotically either approaches an attractor with fixed waveform and
amplitude, or fails to propagate. This has limited their ability to explain
graded neuronal responses. Recently, we have shown that pulse-gated synfire
chains are capable of propagating graded information coded in mean population
current or firing rate amplitudes. In particular, we showed that it is possible
to use one synfire chain to provide gating pulses and a second, pulse-gated
synfire chain to propagate graded information. We called these circuits
synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded
information can rapidly cascade through a neural circuit, and show a
correspondence between this type of transfer and a mean-field model in which
gating pulses overlap in time. We show that SGSCs are robust in the presence of
variability in population size, pulse timing and synaptic strength. Finally, we
demonstrate the computational capabilities of SGSC-based information coding by
implementing a self-contained, spike-based, modular neural circuit that is
triggered by, then reads in streaming input, processes the input, then makes a
decision based on the processed information and shuts itself down
Graded Majorana spinors
In many mathematical and physical contexts spinors are treated as Grassmann
odd valued fields. We show that it is possible to extend the classification of
reality conditions on such spinors by a new type of Majorana condition. In
order to define this graded Majorana condition we make use of
pseudo-conjugation, a rather unfamiliar extension of complex conjugation to
supernumbers. Like the symplectic Majorana condition, the graded Majorana
condition may be imposed, for example, in spacetimes in which the standard
Majorana condition is inconsistent. However, in contrast to the symplectic
condition, which requires duplicating the number of spinor fields, the graded
condition can be imposed on a single Dirac spinor. We illustrate how graded
Majorana spinors can be applied to supersymmetry by constructing a globally
supersymmetric field theory in three-dimensional Euclidean space, an example of
a spacetime where standard Majorana spinors do not exist.Comment: 16 pages, version to appear in J. Phys. A; AFK previously published
under the name A. F. Schunc
Hermitian forms for affine Hecke algebras
We study star operations for Iwahori-Hecke algebras and invariant hermitian
forms for finite dimensional modules over (graded) affine Hecke algebras with a
view towards a unitarity algorithm.Comment: 29 pages, preliminary version. v2: the classification of star
operations for the graded Hecke algebras and the construction of hermitian
forms in the Iwahori case via Bernstein's projectives have been removed from
this preprint and they will make the basis of a new pape
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