207 research outputs found
Effect of the Hydraulic Characteristics of a Stream Channel and its Surroundings on the Runoff Hydrograph
The course and magnitude of a rainfall flood depends primarily on the intensity and duration of the rainfall event, on the morphological parameters of the watershed (e.g. its slope and shape), and on how to watershed has been exploited. A flood wave develops in the stream channel that drains the watershed, and it transforms while passing along the channel. This is particularly the case if the water spreads into floodplains and/or storage reservoirs while passing through the channel. This paper addresses an additional effect that has a significant influence on the magnitude and course of the flood wave but has not previously been addressed adequately, namely the effect of the hydraulic parameters of the stream channel itself on the transformation of a flood wave. The paper explains theoretically and shows on a practical example that a smooth channel with a high capacity significantly increases the magnitude and speed of a flood wave.Many flood events are unnecessarily severe just because the watershed is drained by a hydraulically inappropriate channel. The channel is large and smooth and therefore it gathers most of the flowing water during the flood event, producing high water velocity in the channel. As a result, the large and smooth channel accelerates the runoff from the watershed and constrains the spread of water into the floodplain. A high and steep flood wave is developed in the channel, and this floods areas with a limited water-throughput capacity (e.g. urban areas in the vicinity of hydraulic structures) downstream the channel. This paper offers a methodology for evaluating the ability of a channel to convey a flood wave safely and for recognizing whether a regulated channel should be subjected to restoration due to its inability to convey flood waves safely.
Quantum Algorithms for Matrix Products over Semirings
In this paper we construct quantum algorithms for matrix products over
several algebraic structures called semirings, including the (max,min)-matrix
product, the distance matrix product and the Boolean matrix product. In
particular, we obtain the following results.
We construct a quantum algorithm computing the product of two n x n matrices
over the (max,min) semiring with time complexity O(n^{2.473}). In comparison,
the best known classical algorithm for the same problem, by Duan and Pettie,
has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time
quantum algorithm for computing the all-pairs bottleneck paths of a graph with
n vertices, while classically the best upper bound for this task is
O(n^{2.687}), again by Duan and Pettie.
We construct a quantum algorithm computing the L most significant bits of
each entry of the distance product of two n x n matrices in time O(2^{0.64L}
n^{2.46}). In comparison, prior to the present work, the best known classical
algorithm for the same problem, by Vassilevska and Williams and Yuster, had
complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for
classical algorithms as well, reducing the classical complexity to
O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L.
The above two algorithms are the first quantum algorithms that perform better
than the -time straightforward quantum algorithm based on
quantum search for matrix multiplication over these semirings. We also consider
the Boolean semiring, and construct a quantum algorithm computing the product
of two n x n Boolean matrices that outperforms the best known classical
algorithms for sparse matrices. For instance, if the input matrices have
O(n^{1.686...}) non-zero entries, then our algorithm has time complexity
O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page
Subsampling in Smoothed Range Spaces
We consider smoothed versions of geometric range spaces, so an element of the
ground set (e.g. a point) can be contained in a range with a non-binary value
in . Similar notions have been considered for kernels; we extend them to
more general types of ranges. We then consider approximations of these range
spaces through -nets and -samples (aka
-approximations). We characterize when size bounds for
-samples on kernels can be extended to these more general
smoothed range spaces. We also describe new generalizations for -nets to these range spaces and show when results from binary range spaces can
carry over to these smoothed ones.Comment: This is the full version of the paper which appeared in ALT 2015. 16
pages, 3 figures. In Algorithmic Learning Theory, pp. 224-238. Springer
International Publishing, 201
Analogues of the central point theorem for families with -intersection property in
In this paper we consider families of compact convex sets in
such that any subfamily of size at most has a nonempty intersection. We
prove some analogues of the central point theorem and Tverberg's theorem for
such families
Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension
We study the combinatorial complexity of D-dimensional polyhedra defined as
the intersection of n halfspaces, with the property that the highest dimension
of any bounded face is much smaller than D. We show that, if d is the maximum
dimension of a bounded face, then the number of vertices of the polyhedron is
O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For
inputs in general position the number of bounded faces is O(n^d). For any fixed
d, we show how to compute the set of all vertices, how to determine the maximum
dimension of a bounded face of the polyhedron, and how to compute the set of
bounded faces in polynomial time, by solving a polynomial number of linear
programs
Incremental dimension reduction of tensors with random index
We present an incremental, scalable and efficient dimension reduction
technique for tensors that is based on sparse random linear coding. Data is
stored in a compactified representation with fixed size, which makes memory
requirements low and predictable. Component encoding and decoding are performed
on-line without computationally expensive re-analysis of the data set. The
range of tensor indices can be extended dynamically without modifying the
component representation. This idea originates from a mathematical model of
semantic memory and a method known as random indexing in natural language
processing. We generalize the random-indexing algorithm to tensors and present
signal-to-noise-ratio simulations for representations of vectors and matrices.
We present also a mathematical analysis of the approximate orthogonality of
high-dimensional ternary vectors, which is a property that underpins this and
other similar random-coding approaches to dimension reduction. To further
demonstrate the properties of random indexing we present results of a synonym
identification task. The method presented here has some similarities with
random projection and Tucker decomposition, but it performs well at high
dimensionality only (n>10^3). Random indexing is useful for a range of complex
practical problems, e.g., in natural language processing, data mining, pattern
recognition, event detection, graph searching and search engines. Prototype
software is provided. It supports encoding and decoding of tensors of order >=
1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure
Nonlinear spectral calculus and super-expanders
Nonlinear spectral gaps with respect to uniformly convex normed spaces are
shown to satisfy a spectral calculus inequality that establishes their decay
along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to
behave sub-multiplicatively under zigzag products. These results yield a
combinatorial construction of super-expanders, i.e., a sequence of 3-regular
graphs that does not admit a coarse embedding into any uniformly convex normed
space.Comment: Typos fixed based on referee comments. Some of the results of this
paper were announced in arXiv:0910.2041. The corresponding parts of
arXiv:0910.2041 are subsumed by the current pape
On the chromatic number of random geometric graphs
Given independent random points X_1,...,X_n\in\eR^d with common probability
distribution , and a positive distance , we construct a random
geometric graph with vertex set where distinct and
are adjacent when \norm{X_i-X_j}\leq r. Here \norm{.} may be any norm on
\eR^d, and may be any probability distribution on \eR^d with a
bounded density function. We consider the chromatic number of
and its relation to the clique number as . Both
McDiarmid and Penrose considered the range of when and the range when , and their
results showed a dramatic difference between these two cases. Here we sharpen
and extend the earlier results, and in particular we consider the `phase
change' range when with a fixed
constant. Both McDiarmid and Penrose asked for the behaviour of the chromatic
number in this range. We determine constants such that
almost surely. Further, we find a "sharp
threshold" (except for less interesting choices of the norm when the unit ball
tiles -space): there is a constant such that if then
tends to 1 almost surely, but if then
tends to a limit almost surely.Comment: 56 pages, to appear in Combinatorica. Some typos correcte
Longitudinal double spin asymmetries in single hadron quasi-real photoproduction at high
We measured the longitudinal double spin asymmetries for single
hadron muo-production off protons and deuterons at photon virtuality <
1(GeV/) for transverse hadron momenta in the range 0.7
GeV/ to 4 GeV/ . They were determined using COMPASS data taken
with a polarised muon beam of 160 GeV/ or 200 GeV/ impinging on
polarised or targets. The experimental
asymmetries are compared to next-to-leading order pQCD calculations, and are
sensitive to the gluon polarisation inside the nucleon in the range
of the nucleon momentum fraction carried by gluons
Leading-order determination of the gluon polarisation from semi-inclusive deep inelastic scattering data
Using a novel analysis technique, the gluon polarisation in the nucleon is
re-evaluated using the longitudinal double-spin asymmetry measured in the cross
section of semi-inclusive single-hadron muoproduction with photon virtuality
. The data were obtained by the COMPASS experiment at
CERN using a 160 GeV/ polarised muon beam impinging on a polarised LiD
target. By analysing the full range in hadron transverse momentum ,
the different -dependences of the underlying processes are separated
using a neural-network approach. In the absence of pQCD calculations at
next-to-leading order in the selected kinematic domain, the gluon polarisation
is evaluated at leading order in pQCD at a hard scale of . It is determined in three intervals
of the nucleon momentum fraction carried by gluons, , covering the
range ~ and does not exhibit a significant
dependence on . The average over the three intervals, at
, suggests that the gluon polarisation
is positive in the measured range.Comment: 14 pages, 6 figure
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