12,749 research outputs found
Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras
For a commutative algebra the shuffle product is a morphism of complexes. We
generalize this result to the quantum shuffle product, associated to a class of
non-commutative algebras (for example all the Hopf algebras). As a first
application we show that the Hochschild-Serre identity is the dual statement of
our result. In particular, we extend this identity to Hopf algebras. Secondly,
we clarify the construction of a class of quasi-Hopf algebras.Comment: 23 pages, 7 Postscript figures (uses epsfig.sty
Small-x effects in forward-jet production at HERA
We investigate small-x effects in forward-jet production at HERA in the
two-hard-scale region kT ~ Q>>Lambda_QCD. We show that, despite describing
different energy regimes, both a BFKL parametrization and saturation
parametrizations describe well the H1 and ZEUS data for dsigma/dx published a
few years ago. This is confirmed when comparing the predictions to the latest
data.Comment: 4 pages, 2 figures, Proceedings of the XIIIth International Workshop
on Deep Inelastic Scattering (DIS05), Madison, Wisconsin, USA, April 27-May 1
200
Leader neurons in leaky integrate and fire neural network simulations
Several experimental studies show the existence of leader neurons in
population bursts of 2D living neural networks. A leader neuron is, basically,
a neuron which fires at the beginning of a burst (respectively network spike)
more often that we expect by looking at its whole mean neural activity. This
means that leader neurons have some burst triggering power beyond a simple
statistical effect. In this study, we characterize these leader neuron
properties. This naturally leads us to simulate neural 2D networks. To build
our simulations, we choose the leaky integrate and fire (lIF) neuron model. Our
lIF model has got stable leader neurons in the burst population that we
simulate. These leader neurons are excitatory neurons and have a low membrane
potential firing threshold. Except for these two first properties, the
conditions required for a neuron to be a leader neuron are difficult to
identify and seem to depend on several parameters involved in the simulations
themself. However, a detailed linear analysis shows a trend of the properties
required for a neuron to be a leader neuron. Our main finding is: A leader
neuron sends a signal to many excitatory neurons as well as to a few inhibitory
neurons and a leader neuron receives only a few signals from other excitatory
neurons. Our linear analysis exhibits five essential properties for leader
neurons with relative importance. This means that considering a given neural
network with a fixed mean number of connections per neuron, our analysis gives
us a way of predicting which neuron can be a good leader neuron and which
cannot. Our prediction formula gives us a good statistical prediction even if,
considering a single given neuron, the success rate does not reach hundred
percent.Comment: 25 pages, 13 figures, 2 table
A lattice formulation of the F4 completion procedure
We write a procedure for constructing noncommutative Groebner bases.
Reductions are done by particular linear projectors, called reduction
operators. The operators enable us to use a lattice construction to reduce
simultaneously each S-polynomial into a unique normal form. We write an
implementation as well as an example to illustrate our procedure. Moreover, the
lattice construction is done by Gaussian elimination, which relates our
procedure to the F4 algorithm for constructing commutative Groebner bases
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