132 research outputs found
The oscillatory distribution of distances in random tries
We investigate \Delta_n, the distance between randomly selected pairs of
nodes among n keys in a random trie, which is a kind of digital tree.
Analytical techniques, such as the Mellin transform and an excursion between
poissonization and depoissonization, capture small fluctuations in the mean and
variance of these random distances. The mean increases logarithmically in the
number of keys, but curiously enough the variance remains O(1), as n\to\infty.
It is demonstrated that the centered random variable
\Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution,
but rather oscillates between two distributions.Comment: Published at http://dx.doi.org/10.1214/105051605000000106 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Motor Learning Mechanism on the Neuron Scale
Based on existing data, we wish to put forward a biological model of motor
system on the neuron scale. Then we indicate its implications in statistics and
learning. Specifically, neuron firing frequency and synaptic strength are
probability estimates in essence. And the lateral inhibition also has
statistical implications. From the standpoint of learning, dendritic
competition through retrograde messengers is the foundation of conditional
reflex and grandmother cell coding. And they are the kernel mechanisms of motor
learning and sensory motor integration respectively. Finally, we compare motor
system with sensory system. In short, we would like to bridge the gap between
molecule evidences and computational models.Comment: 8 pages, 4 figure
Vanishing Minors in the Neutrino Mass Matrix from Abelian Gauge Symmetries
Augmenting the Standard Model by three right-handed neutrinos allows for an
anomaly-free gauge group extension G_max = U(1)_(B-L) x U(1)_(L_e-L_mu) x
U(1)_(L_mu-L_tau). While simple U(1) subgroups of G_max have already been
discussed in the context of approximate flavor symmetries, we show how two-zero
textures in the right-handed neutrino Majorana mass matrix can be enforced by
the flavor symmetry, which is spontaneously broken very economically by singlet
scalars. These zeros lead to two vanishing minors in the low-energy neutrino
mass matrix after the seesaw mechanism. This study may provide a new testing
ground for a zero-texture approach: the different classes of two-zero textures
with almost identical neutrino oscillation phenomenology can in principle be
distinguished by their different Z' interactions at colliders.Comment: 12 pages; Extended and clarified discussion; comments on finetuning
in the textures; matches published versio
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