6,471 research outputs found
Succinct Indexable Dictionaries with Applications to Encoding -ary Trees, Prefix Sums and Multisets
We consider the {\it indexable dictionary} problem, which consists of storing
a set for some integer , while supporting the
operations of \Rank(x), which returns the number of elements in that are
less than if , and -1 otherwise; and \Select(i) which returns
the -th smallest element in . We give a data structure that supports both
operations in O(1) time on the RAM model and requires bits to store a set of size , where {\cal B}(n,m) = \ceil{\lg
{m \choose n}} is the minimum number of bits required to store any -element
subset from a universe of size . Previous dictionaries taking this space
only supported (yes/no) membership queries in O(1) time. In the cell probe
model we can remove the additive term in the space bound,
answering a question raised by Fich and Miltersen, and Pagh.
We present extensions and applications of our indexable dictionary data
structure, including:
An information-theoretically optimal representation of a -ary cardinal
tree that supports standard operations in constant time,
A representation of a multiset of size from in bits that supports (appropriate generalizations of) \Rank
and \Select operations in constant time, and
A representation of a sequence of non-negative integers summing up to
in bits that supports prefix sum queries in constant
time.Comment: Final version of SODA 2002 paper; supersedes Leicester Tech report
2002/1
Tropical rainforest bird community structure in relation to altitude, tree species composition, and null models in the Western Ghats, India
Studies of species distributions on elevational gradients are essential to
understand principles of community organisation as well as to conserve species
in montane regions. This study examined the patterns of species richness,
abundance, composition, range sizes, and distribution of rainforest birds at 14
sites along an elevational gradient (500-1400 m) in the Kalakad-Mundanthurai
Tiger Reserve (KMTR) of the Western Ghats, India. In contrast to theoretical
expectation, resident bird species richness did not change significantly with
elevation although the species composition changed substantially (<10%
similarity) between the lowest and highest elevation sites. Constancy in
species richness was possibly due to relative constancy in productivity and
lack of elevational trends in vegetation structure. Elevational range size of
birds, expected to increase with elevation according to Rapoport's rule, was
found to show a contrasting inverse U-shaped pattern because species with
narrow elevational distributions, including endemics, occurred at both ends of
the gradient (below 800 m and above 1,200 m). Bird species composition also did
not vary randomly along the gradient as assessed using a hierarchy of null
models of community assembly, from completely unconstrained models to ones with
species richness and range-size distribution restrictions. Instead, bird
community composition was significantly correlated with elevation and tree
species composition of sites, indicating the influence of deterministic factors
on bird community structure. Conservation of low- and high-elevation areas and
maintenance of tree species composition against habitat alteration are
important for bird conservation in the southern Western Ghats rainforests.Comment: 36 pages, 5 figures, two tables (including one in the appendix)
Submitted to the Journal of the Bombay Natural History Society (JBNHS
Interpolation of Non-abelian Lattice Gauge Fields
We propose a method for interpolating non-abelian lattice gauge fields to the
continuum, or to a finer lattice, which satisfies the properties of (i)
transverse continuity, (ii) (lattice) rotation and translation covariance,
(iii) gauge covariance, (iv) locality. These are the properties required for
use in our earlier proposal for non-perturbative formulation and simulation of
chiral gauge theories.Comment: A few typos corrected, a reference and a clarifying comment added. To
appear in Nuclear Physics B. 16 pages, LateX, 1 figure. This interpolation
scheme is intended for use in our formulation of lattice chiral gauge theory,
Nucl. Phys. B455 (1990) 287, hep-ph/950633
On the developmental morphology of the rosette galls of Acacia leucophloea Willd., (Mimosaceae) induced by Thilakothrips hablu Ramk. (Thysanoptera: Insecta)
Thilakothrips babuli induces rosette (artichoke) galls on the axillary buds of Acacia leucophloea. As a result of feeding by the building populations of thrips, axillary shoot meristems are destroyed, and primordial palisade tissues of the leaflets and cortical tissues of the shoot axis are transformed into nutritive cells of specialised morphology. Very similar to the galls induced by mites, midges, chalcids, and chloropids, Thilakothrips-induced Acacia galls also have a characteristic morphology, involving the inhibition of elongation of the shoot axis and crowding of maldeveloped leaflets. While describing the cecidogenesis in relation to the biology of the gall maker, an attempt has been made to discuss the morphological convergence among shoot apex galls
On the development morphology of the leaf fold galls of Maytenus senegalensis (Lam) Excel!., (Celastraceae), induced by Alocothrips hadrocerus (Karny)(Thysanoptera:Insecta)
The galls of Maytenus senegalensis (=Gymnosporia heyneana Lawson) induced by Alocothrips hadrocerus are histologically unique when compared with the other thrip galls. Principal cecidogenetic phenomena are hypertrophy and hyperplasia. The incidence of tannin containing as well as sclerenchymatous cells, and the epidermal proliferation are discussed in relation to gall development
Cecidogenous Crotonothrips (Thysanoptera)- Memecylon interactions: host relations, nutritive tissue, tissue dynamics and cecidogenetic patterns
The host relations of Crotonothrips with Memecylon on the criterion of gall formation appear interesting. In the light of the morphogenetic courses that the susceptible host organ, the leaf, show, an attempt has been made to assess their functional efficiency in terms of structural adaptations envisaging the organisation of a nutritive zone, and tissue dynamics taking Memecylon edule, Memecylon lushingtonii, and Memecylon umbellatum as models
The eigenspectra of Indian musical drums
In a family of drums used in the Indian subcontinent, the circular drum head
is made of material of non-uniform density. Remarkably, and in contrast to a
circular membrane of uniform density, the low eigenmodes of the non-uniform
membrane are harmonic. In this work we model the drum head by a non-uniform
membrane whose density varies smoothly between two prescribed values. Using a
Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and
eigenvalues of the drum head. For a suitable choice of parameters, which we
find by optimising a cost function, the eigenspectra obtained from our model
are in excellent agreement with experimental values. Our model and the
numerical method should find application in numerical sound synthesis
Succinct Partial Sums and Fenwick Trees
We consider the well-studied partial sums problem in succint space where one
is to maintain an array of n k-bit integers subject to updates such that
partial sums queries can be efficiently answered. We present two succint
versions of the Fenwick Tree - which is known for its simplicity and
practicality. Our results hold in the encoding model where one is allowed to
reuse the space from the input data. Our main result is the first that only
requires nk + o(n) bits of space while still supporting sum/update in O(log_b
n) / O(b log_b n) time where 2 <= b <= log^O(1) n. The second result shows how
optimal time for sum/update can be achieved while only slightly increasing the
space usage to nk + o(nk) bits. Beyond Fenwick Trees, the results are primarily
based on bit-packing and sampling - making them very practical - and they also
allow for simple optimal parallelization
Quantum thermodynamics at critical points during melting and solidification processes
We systematically explore and show the existence of finite-temperature
continuous quantum phase transition (CTQPT) at a critical point, namely, during
solidification or melting such that the first-order thermal phase transition is
a special case within CTQPT. Infact, CTQPT is related to chemical reaction
where quantum fluctuation (due to wavefunction transformation) is caused by
thermal energy and it can occur maximally for temperatures much higher than
zero Kelvin. To extract the quantity related to CTQPT, we use the ionization
energy theory and the energy-level spacing renormalization group method to
derive the energy-level spacing entropy, renormalized Bose-Einstein
distribution and the time-dependent specific heat capacity. This work
unambiguously shows that the quantum phase transition applies for any finite
temperatures.Comment: To be published in Indian Journal of Physics (Kolkata
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