2,530 research outputs found
A framework for evaluating statistical dependencies and rank correlations in power law graphs
We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. To the best of our knowledge, this is the first attempt to apply the well developed theory of regular variation to graph data. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between different graph parameters, such as in-degree and PageRank. Based on the proposed methodology, we suggest a new measure for rank correlations. Unlike most known methods, this measure is especially sensitive to rank permutations for topranked nodes. Using this method, we demonstrate that the PageRank ranking is not sensitive to moderate changes in the damping factor
Dirac structures and boundary control systems associated with skew-symmetric differential operators
Associated with a skew-symmetric linear operator on the spatial domain we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimensional system. We parameterize the boundary port variables for which the -semigroup associated to this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko Beam. \u
Rice Intensification in a Changing Environment: Impact on Water Availability in Inland Valley Landscapes in Benin
This study assesses the impact of climate change on hydrological processes under rice intensification in three headwater inland valley watersheds characterized by different land conditions. The Soil and Water Assessment Tool was used to simulate the combined impacts of two land use scenarios defined as converting 25% and 75% of lowland savannah into rice cultivation, and two climate scenarios (A1B and B1) of the Intergovernmental Panel on Climate Change Special Report on Emissions Scenarios. The simulations were performed based on the traditional and the rainfed-bunded rice cultivation systems and analyzed up to the year 2049 with a special focus on the period of 2030ā2049. Compared to land use, climate change impact on hydrological processes was overwhelming at all watersheds. The watersheds with a high portion of cultivated areas are more sensitive to changes in climate resulting in a decrease of water yield of up to 50% (145 mm). Bunded fields cause a rise in surface runoff projected to be up to 28% (18 mm) in their lowlands, while processes were insignificantly affected at the vegetation dominated-watershed. Analyzing three watersheds instead of one as is usually done provides further insight into the natural variability and therefore gives more evidence of possible future processes and management strategie
A triple origin for the lack of tight coplanar circumbinary planets around short-period binaries
Transiting circumbinary planets are more easily detected around short-period
than long-period binaries, but none have yet been observed by {\it Kepler}
orbiting binaries with periods shorter than seven days. In triple systems,
secular Kozai-Lidov cycles and tidal friction (KLCTF) have been shown to reduce
the inner orbital period from to a few days. Indeed, the majority
of short-period binaries are observed to possess a third stellar companion.
Using secular evolution analysis and population synthesis, we show that KLCTF
makes it unlikely for circumbinary transiting planets to exist around
short-period binaries. We find the following outcomes. (1) Sufficiently massive
planets in tight and/or coplanar orbits around the inner binary can quench the
KL evolution because they induce precession in the inner binary. The KLCTF
process does not take place, preventing the formation of a short-period binary.
(2) Secular evolution is not quenched and it drives the planetary orbit into a
high eccentricity, giving rise to an unstable configuration, in which the
planet is most likely ejected from the system. (3) Secular evolution is not
quenched but the planet survives the KLCTF evolution. Its orbit is likely to be
much wider than the currently observed inner binary orbit, and is likely to be
eccentric and inclined with respect to the inner binary. These outcomes lead to
two main conclusions: (1) it is unlikely to find a massive planet on a tight
and coplanar orbit around a short-period binary, and (2) the properties of
circumbinary planets in short-period binaries are constrained by secular
evolution.Comment: Revised to match MNRAS publication. 24 pages, 22 figure
On the accuracy of phase-type approximations of heavy-tailed risk models
Numerical evaluation of ruin probabilities in the classical risk model is an
important problem. If claim sizes are heavy-tailed, then such evaluations are
challenging. To overcome this, an attractive way is to approximate the claim
sizes with a phase-type distribution. What is not clear though is how many
phases are enough in order to achieve a specific accuracy in the approximation
of the ruin probability. The goals of this paper are to investigate the number
of phases required so that we can achieve a pre-specified accuracy for the ruin
probability and to provide error bounds. Also, in the special case of a
completely monotone claim size distribution we develop an algorithm to estimate
the ruin probability by approximating the excess claim size distribution with a
hyperexponential one. Finally, we compare our approximation with the heavy
traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference
Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment
Significant correlations between arrivals of load-generating events make the
numerical evaluation of the workload of a system a challenging problem. In this
paper, we construct highly accurate approximations of the workload distribution
of the MAP/G/1 queue that capture the tail behavior of the exact workload
distribution and provide a bounded relative error. Motivated by statistical
analysis, we consider the service times as a mixture of a phase-type and a
heavy-tailed distribution. With the aid of perturbation analysis, we derive our
approximations as a sum of the workload distribution of the MAP/PH/1 queue and
a heavy-tailed component that depends on the perturbation parameter. We refer
to our approximations as corrected phase-type approximations, and we exhibit
their performance with a numerical study.Comment: Received the Marcel Neuts Student Paper Award at the 8th
International Conference on Matrix Analytic Methods in Stochastic Models 201
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