2,353 research outputs found
Secondary Indexing in One Dimension: Beyond B-trees and Bitmap Indexes
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string
over S. A "secondary index" for x answers alphabet range queries of the form:
Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in
[a_l; a_r]}. Secondary indexes are heavily used in relational databases and
scientific data analysis. It is well-known that the obvious solution, storing a
dictionary for the position set associated with each character, does not always
give optimal query time. In this paper we give the first theoretically optimal
data structure for the secondary indexing problem. In the I/O model, the amount
of data read when answering a query is within a constant factor of the minimum
space needed to represent I_{[a_l;a_r]}, assuming that the size of internal
memory is (|S| log n)^{delta} blocks, for some constant delta > 0. The space
usage of the data structure is O(n log |S|) bits in the worst case, and we
further show how to bound the size of the data structure in terms of the 0-th
order entropy of x. We show how to support updates achieving various time-space
trade-offs.
We also consider an approximate version of the basic secondary indexing
problem where a query reports a superset of I_{[a_l;a_r]} containing each
element not in I_{[a_l;a_r]} with probability at most epsilon, where epsilon >
0 is the false positive probability. For this problem the amount of data that
needs to be read by the query algorithm is reduced to O(|I_{[a_l;a_r]}|
log(1/epsilon)) bits.Comment: 16 page
Stability of three neutrino flavor conversion in supernovae
Neutrino-neutrino interactions can lead to collective flavor conversion in
the dense parts of a core collapse supernova. Growing instabilities that lead
to collective conversions have been studied intensely in the limit of
two-neutrino species and occur for inverted mass ordering in the case of a
perfectly spherical supernova. We examine two simple models of colliding and
intersecting neutrino beams and show, that for three neutrino species
instabilities exist also for normal mass ordering even in the case of a fully
symmetric system. Whereas the instability for inverted mass ordering is
associated with , the new instability we find for normal mass
ordering is associated with . As a consequence, the growth
rate of these new instabilities for normal ordering is smaller by about an
order of magnitude compared to the rates of the well studied case of inverted
ordering.Comment: 18 pages, 5 figures Minor update on the consistency of the formulae
and prefactors, actualized plot
Finite-temperature behavior of the Bose polaron
We consider a mobile impurity immersed in a Bose gas at finite temperature.
Using perturbation theory valid for weak coupling between the impurity and the
bosons, we derive analytical results for the energy and damping of the impurity
for low and high temperatures, as well as for temperatures close to the
critical temperature for Bose-Einstein condensation. These results show
that the properties of the impurity vary strongly with temperature. In
particular, the energy exhibits a non-monotonic behavior close to , and
the damping rises sharply close to . We argue that this behaviour is
generic for impurities immersed in an environment undergoing a phase transition
that breaks a continuous symmetry. Finally, we discuss how these effects can be
detected experimentally.Comment: 10 pages and 6 figure
IceCube Flavor Ratios with Identified Astrophysical Sources: Towards Improving New Physics Testability
Motivated by the discovery of the first high-energy astrophysical neutrino
source, the blazar TXS 0506+056, we revisit the IceCube flavor ratio analysis.
Assuming large statistics from identified blazars, collected in the forthcoming
years by the IceCube detector and its successor IceCube-Gen2, we demonstrate
that the constraints on several new physics scenarios in which the baseline
dependent terms in neutrino oscillation probabilities are not averaged, can be
improved. As a representative case, we consider pseudo-Dirac neutrinos while
neutrino decay is also discussed.Comment: 17 pages, 5 figure
EEG source imaging assists decoding in a face recognition task
EEG based brain state decoding has numerous applications. State of the art
decoding is based on processing of the multivariate sensor space signal,
however evidence is mounting that EEG source reconstruction can assist
decoding. EEG source imaging leads to high-dimensional representations and
rather strong a priori information must be invoked. Recent work by Edelman et
al. (2016) has demonstrated that introduction of a spatially focal source space
representation can improve decoding of motor imagery. In this work we explore
the generality of Edelman et al. hypothesis by considering decoding of face
recognition. This task concerns the differentiation of brain responses to
images of faces and scrambled faces and poses a rather difficult decoding
problem at the single trial level. We implement the pipeline using spatially
focused features and show that this approach is challenged and source imaging
does not lead to an improved decoding. We design a distributed pipeline in
which the classifier has access to brain wide features which in turn does lead
to a 15% reduction in the error rate using source space features. Hence, our
work presents supporting evidence for the hypothesis that source imaging
improves decoding
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