1,304 research outputs found
Shortest Unique Substring Query Revisited
We revisit the problem of finding shortest unique substring (SUS) proposed
recently by [6]. We propose an optimal time and space algorithm that can
find an SUS for every location of a string of size . Our algorithm
significantly improves the time complexity needed by [6]. We also
support finding all the SUSes covering every location, whereas the solution in
[6] can find only one SUS for every location. Further, our solution is simpler
and easier to implement and can also be more space efficient in practice, since
we only use the inverse suffix array and longest common prefix array of the
string, while the algorithm in [6] uses the suffix tree of the string and other
auxiliary data structures. Our theoretical results are validated by an
empirical study that shows our algorithm is much faster and more space-saving
than the one in [6]
Bulk Fermions in Warped Models with a Soft Wall
We study bulk fermions in models with warped extra dimensions in the presence
of a soft wall. Fermions can acquire a position dependent bulk Dirac mass that
shields them from the deep infrared, allowing for a systematic expansion in
which electroweak symmetry breaking effects are treated perturbatively. Using
this expansion, we analyze properties of bulk fermions in the soft wall
background. These properties include the realization of non-trivial boundary
conditions that simulate the ones commonly used in hard wall models, the
analysis of the flavor structure of the model and the implications of a heavy
top. We implement a soft wall model of electroweak symmetry breaking with
custodial symmetry and fermions propagating in the bulk. We find a lower bound
on the masses of the first bosonic resonances, after including the effects of
the top sector on electroweak precision observables for the first time, of
m_{KK} \gtrsim 1-3 TeV at the 95% C.L., depending on the details of the Higgs,
and discuss the implications of our results for LHC phenomenology.Comment: 34 pages, 8 figure
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