17,983 research outputs found
Bivariate p-boxes
A p-box is a simple generalization of a distribution function, useful to study a random number in the presence of imprecision. We propose an extension of p-boxes to cover imprecise evaluations of pairs of random numbers and term them bivariate p-boxes. We analyze their rather weak consistency properties, since they are at best (but generally not) equivalent to 2-coherence. We therefore focus on the relevant subclass of coherent p-boxes, corresponding to coherent lower probabilities on special domains. Several properties of coherent p-boxes are investigated and compared with those of (one-dimensional) p-boxes or of bivariate distribution functions
A full scale Sklar's theorem in the imprecise setting
In this paper we present a surprisingly general extension of the main result
of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in
an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main
tools we develop in order to do so are: (1) a theory on quasi-distributions
based on an idea presented in a paper by R. Nelsen with collaborators; (2)
starting from what is called (bivariate) -box in the above mentioned paper
we propose some new techniques based on what we call restricted (bivariate)
-box; and (3) a substantial extension of a theory on coherent imprecise
copulas developed by M. Omladi\v{c} and N. Stopar in a previous paper in order
to handle coherence of restricted (bivariate) -boxes. A side result of ours
of possibly even greater importance is the following: Every bivariate
distribution whether obtained on a usual -additive probability space or
on an additive space can be obtained as a copula of its margins meaning that
its possible extraordinariness depends solely on its margins. This might
indicate that copulas are a stronger probability concept than probability
itself.Comment: 16 pages, minor change
A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems
We improve the local generic position method for isolating the real roots of
a zero-dimensional bivariate polynomial system with two polynomials and extend
the method to general zero-dimensional polynomial systems. The method mainly
involves resultant computation and real root isolation of univariate polynomial
equations. The roots of the system have a linear univariate representation. The
complexity of the method is for the bivariate case, where
, resp., is an upper bound on the degree, resp., the
maximal coefficient bitsize of the input polynomials. The algorithm is
certified with probability 1 in the multivariate case. The implementation shows
that the method is efficient, especially for bivariate polynomial systems.Comment: 24 pages, 5 figure
An Elimination Method for Solving Bivariate Polynomial Systems: Eliminating the Usual Drawbacks
We present an exact and complete algorithm to isolate the real solutions of a
zero-dimensional bivariate polynomial system. The proposed algorithm
constitutes an elimination method which improves upon existing approaches in a
number of points. First, the amount of purely symbolic operations is
significantly reduced, that is, only resultant computation and square-free
factorization is still needed. Second, our algorithm neither assumes generic
position of the input system nor demands for any change of the coordinate
system. The latter is due to a novel inclusion predicate to certify that a
certain region is isolating for a solution. Our implementation exploits
graphics hardware to expedite the resultant computation. Furthermore, we
integrate a number of filtering techniques to improve the overall performance.
Efficiency of the proposed method is proven by a comparison of our
implementation with two state-of-the-art implementations, that is, LPG and
Maple's isolate. For a series of challenging benchmark instances, experiments
show that our implementation outperforms both contestants.Comment: 16 pages with appendix, 1 figure, submitted to ALENEX 201
Constructing copulas from shock models with imprecise distributions
The omnipotence of copulas when modeling dependence given marg\-inal
distributions in a multivariate stochastic situation is assured by the Sklar's
theorem. Montes et al.\ (2015) suggest the notion of what they call an
\emph{imprecise copula} that brings some of its power in bivariate case to the
imprecise setting. When there is imprecision about the marginals, one can model
the available information by means of -boxes, that are pairs of ordered
distribution functions. By analogy they introduce pairs of bivariate functions
satisfying certain conditions. In this paper we introduce the imprecise
versions of some classes of copulas emerging from shock models that are
important in applications. The so obtained pairs of functions are not only
imprecise copulas but satisfy an even stronger condition. The fact that this
condition really is stronger is shown in Omladi\v{c} and Stopar (2019) thus
raising the importance of our results. The main technical difficulty in
developing our imprecise copulas lies in introducing an appropriate stochastic
order on these bivariate objects
Fine-Scale Plant Species Identification in a Poor Fen and Integration of Techniques and Instrumentation in a Classroom Setting
Refining carbon flux measurements in the carbon cycle is an ongoing challenge. This study attempted to identify plant species in Sallie’s Fen, a nutrient-poor fen in Barrington, New Hampshire, at a fine scale in order to better model and understand carbon exchange between plants and the atmosphere in this type of ecosystem. A protocol for estimating percent cover of species in plots via ground measurements was developed. The next stage of this project was to compare these measurements with measurements derived from spectral images using ImageJ computer software. Statistical tests of the ground measurement data revealed that patterns of seasonal defoliation had a strong effect on the apparent species richness, evenness, and biodiversity of plants as seen aerially. The presence of Sphagnum mosses excluded the presence of other species, but the presence of other plants only excluded the visibility of Sphagnum since it resides in the understory of the layered community. A regression comparing percent cover of the vascular plant functional group and fractal dimensions from a digital camera was statistically significant, indicating that ground and aerial measurements agree and that spectral imaging can be used to save time in the field in place of ground measurements. Additionally, since ecosystem science is such an interdisciplinary field, it provides the perfect platform around which students can apply their scientific knowledge and understanding. Modifications to this project were suggested so that it can be carried out in a secondary school classroom setting while aligning with the Next Generation Science Standards
Asymptotic distribution of fixed points of pattern-avoiding involutions
For a variety of pattern-avoiding classes, we describe the limiting
distribution for the number of fixed points for involutions chosen uniformly at
random from that class. In particular we consider monotone patterns of
arbitrary length as well as all patterns of length 3. For monotone patterns we
utilize the connection with standard Young tableaux with at most rows and
involutions avoiding a monotone pattern of length . For every pattern of
length 3 we give the bivariate generating function with respect to fixed points
for the involutions that avoid that pattern, and where applicable apply tools
from analytic combinatorics to extract information about the limiting
distribution from the generating function. Many well-known distributions
appear.Comment: 16 page
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