43,948 research outputs found
Model of the early development of thalamo-cortical connections and area patterning via signaling molecules
The mammalian cortex is divided into architectonic and functionally distinct
areas. There is growing experimental evidence that their emergence and
development is controlled by both epigenetic and genetic factors. The latter
were recently implicated as dominating the early cortical area specification.
In this paper, we present a theoretical model that explicitly considers the
genetic factors and that is able to explain several sets of experiments on
cortical area regulation involving transcription factors Emx2 and Pax6, and
fibroblast growth factor FGF8. The model consists of the dynamics of thalamo-
cortical connections modulated by signaling molecules that are regulated
genetically, and by axonal competition for neocortical space. The model can
make predictions and provides a basic mathematical framework for the early
development of the thalamo-cortical connections and area patterning that can be
further refined as more experimental facts become known.Comment: brain, model, neural development, cortical area patterning, signaling
molecule
Composition operators on Hilbert spaces of entire functions with analytic symbols
Composition operators with analytic symbols on some reproducing kernel
Hilbert spaces of entire functions on a complex Hilbert space are studied. The
questions of their boundedness, seminormality and positivity are investigated.
It is proved that if such an operator is bounded, then its symbol is a
polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type
model for composition operators with linear symbols is established. As a
consequence, explicit formulas for their polar decomposition, Aluthge transform
and powers with positive real exponents are provided. The theorem of Carswell,
MacCluer and Schuster is generalized to the case of Segal-Bargmann spaces of
infinite order. Some related questions are also discussed.Comment: This is a final version of our previous submissions. It consists of
48 page
Expressiveness of Generic Process Shape Types
Shape types are a general concept of process types which work for many
process calculi. We extend the previously published Poly* system of shape types
to support name restriction. We evaluate the expressiveness of the extended
system by showing that shape types are more expressive than an implicitly typed
pi-calculus and an explicitly typed Mobile Ambients. We demonstrate that the
extended system makes it easier to enjoy advantages of shape types which
include polymorphism, principal typings, and a type inference implementation.Comment: Submitted to Trustworthy Global Computing (TGC) 2010
Multiloop functional renormalization group for general models
We present multiloop flow equations in the functional renormalization group
(fRG) framework for the four-point vertex and self-energy, formulated for a
general fermionic many-body problem. This generalizes the previously introduced
vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403
(2018)] and provides the necessary corrections to the self-energy flow in order
to complete the derivative of all diagrams involved in the truncated fRG flow.
Due to its iterative one-loop structure, the multiloop flow is well-suited for
numerical algorithms, enabling improvement of many fRG computations. We
demonstrate its equivalence to a solution of the (first-order) parquet
equations in conjunction with the Schwinger-Dyson equation for the self-energy
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