7 research outputs found
Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond
We present a simple construction method for Feller processes and a framework
for the generation of sample paths of Feller processes. The construction is
based on state space dependent mixing of L\'evy processes.
Brownian Motion is one of the most frequently used continuous time Markov
processes in applications. In recent years also L\'evy processes, of which
Brownian Motion is a special case, have become increasingly popular.
L\'evy processes are spatially homogeneous, but empirical data often suggest
the use of spatially inhomogeneous processes. Thus it seems necessary to go to
the next level of generalization: Feller processes. These include L\'evy
processes and in particular Brownian motion as special cases but allow spatial
inhomogeneities.
Many properties of Feller processes are known, but proving the very existence
is, in general, very technical. Moreover, an applicable framework for the
generation of sample paths of a Feller process was missing. We explain, with
practitioners in mind, how to overcome both of these obstacles. In particular
our simulation technique allows to apply Monte Carlo methods to Feller
processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the
generation of sample paths of Feller processe
Altered Disrupted-in-Schizophrenia-1 function affects the development of cortical parvalbumin interneurons by an indirect mechanism.
<div><p><i>Disrupted-in-Schizophrenia-1 (DISC1)</i> gene has been linked to schizophrenia and related major mental illness. Mouse Disc1 has been implicated in brain development, mainly in the proliferation, differentiation, lamination, neurite outgrowth and synapse formation and maintenance of cortical excitatory neurons. Here, the effects of two loss-of-function point mutations in the mouse <i>Disc1</i> sequence (Q31L and L100P) on cortical inhibitory interneurons were investigated. None of the mutations affected the overall number of interneurons. However, the 100P, but not the 31L, mutation resulted in a significant decrease in the numbers of interneurons expressing parvalbumin mRNA and protein across the sensory cortex. To investigate role of Disc1 in regulation of parvalbumin expression, mouse wild-type Disc-1 or the 100P mutant form were electroporated <i>in utero</i> into cortical excitatory neurons. Overexpression of wild-type Disc1 in these cells caused increased densities of parvalbumin-expressing interneurons in the electroporated area and in areas connected with it, whereas expression of Disc1-100P did not. We conclude that the 100P mutation prevents expression of parvalbumin by a normally sized cohort of interneurons and that altering Disc1 function in cortical excitatory neurons indirectly affects parvalbumin expression by cortical interneurons, perhaps as a result of altered functional input from the excitatory neurons.</p></div