70,323 research outputs found
A Method for the Combination of Stochastic Time Varying Load Effects
The problem of evaluating the probability that a structure becomes unsafe under a
combination of loads, over a given time period, is addressed. The loads and load effects
are modeled as either pulse (static problem) processes with random occurrence time, intensity and a specified shape or intermittent continuous (dynamic problem) processes which
are zero mean Gaussian processes superimposed 'on a pulse process. The load coincidence
method is extended to problems with both nonlinear limit states and dynamic responses,
including the case of correlated dynamic responses. The technique of linearization of a
nonlinear limit state commonly used in a time-invariant problem is investigated for timevarying
combination problems, with emphasis on selecting the linearization point. Results
are compared with other methods, namely the method based on upcrossing rate, simpler
combination rules such as Square Root of Sum of Squares and Turkstra's rule. Correlated
effects among dynamic loads are examined to see how results differ from correlated static
loads and to demonstrate which types of load dependencies are most important, i.e., affect'
the exceedance probabilities the most.
Application of the load coincidence method to code development is briefly discussed.National Science Foundation Grants CME 79-18053 and CEE 82-0759
Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density
We derive a closed-form expression for the orthogonal polynomials associated
with the general lognormal density. The result can be utilized to construct
easily computable approximations for probability density function of a product
of random variables, when the considered variates are either independent or
correlated. As an example, we have calculated the approximative distribution
for the product of Nakagami-m variables. Simulations indicate that accuracy of
the proposed approximation is good with small cross-correlations under light
fading condition.Comment: submitted to IEEE Communications Lette
A note on q-Gaussians and non-Gaussians in statistical mechanics
The sum of sufficiently strongly correlated random variables will not in
general be Gaussian distributed in the limit N\to\infty. We revisit examples of
sums x that have recently been put forward as instances of variables obeying a
q-Gaussian law, that is, one of type (cst)\times[1-(1-q)x^2]^{1/(1-q)}. We show
by explicit calculation that the probability distributions in the examples are
actually analytically different from q-Gaussians, in spite of numerically
resembling them very closely. Although q-Gaussians exhibit many interesting
properties, the examples investigated do not support the idea that they play a
special role as limit distributions of correlated sums.Comment: 17 pages including 3 figures. Introduction and references expande
The excursion set approach in non-Gaussian random fields
Insight into a number of interesting questions in cosmology can be obtained
from the first crossing distributions of physically motivated barriers by
random walks with correlated steps. We write the first crossing distribution as
a formal series, ordered by the number of times a walk upcrosses the barrier.
Since the fraction of walks with many upcrossings is negligible if the walk has
not taken many steps, the leading order term in this series is the most
relevant for understanding the massive objects of most interest in cosmology.
This first term only requires knowledge of the bivariate distribution of the
walk height and slope, and provides an excellent approximation to the first
crossing distribution for all barriers and smoothing filters of current
interest. We show that this simplicity survives when extending the approach to
the case of non-Gaussian random fields. For non-Gaussian fields which are
obtained by deterministic transformations of a Gaussian, the first crossing
distribution is simply related to that for Gaussian walks crossing a suitably
rescaled barrier. Our analysis shows that this is a useful way to think of the
generic case as well. Although our study is motivated by the possibility that
the primordial fluctuation field was non-Gaussian, our results are general. In
particular, they do not assume the non-Gaussianity is small, so they may be
viewed as the solution to an excursion set analysis of the late-time, nonlinear
fluctuation field rather than the initial one. They are also useful for models
in which the barrier height is determined by quantities other than the initial
density, since most other physically motivated variables (such as the shear)
are usually stochastic and non-Gaussian. We use the Lognormal transformation to
illustrate some of our arguments.Comment: 14 pages, new sections and figures describing new results, discussion
and references adde
Extreme value distributions for weakly correlated fitnesses in block model
We study the limit distribution of the largest fitness for two models of
weakly correlated and identically distributed random fitnesses. The correlated
fitness is given by a linear combination of a fixed number of independent
random variables drawn from a common parent distribution. We find that for
certain class of parent distributions, the extreme value distribution for
correlated random variables can be related either to one of the known limit
laws for independent variables or the parent distribution itself. For other
cases, new limiting distributions appear. The conditions under which these
results hold are identified.Comment: Expanded, added reference
Asymptotic Mutual Information Statistics of Separately-Correlated Rician Fading MIMO Channels
Precise characterization of the mutual information of MIMO systems is
required to assess the throughput of wireless communication channels in the
presence of Rician fading and spatial correlation. Here, we present an
asymptotic approach allowing to approximate the distribution of the mutual
information as a Gaussian distribution in order to provide both the average
achievable rate and the outage probability. More precisely, the mean and
variance of the mutual information of the separatelycorrelated Rician fading
MIMO channel are derived when the number of transmit and receive antennas grows
asymptotically large and their ratio approaches a finite constant. The
derivation is based on the replica method, an asymptotic technique widely used
in theoretical physics and, more recently, in the performance analysis of
communication (CDMA and MIMO) systems. The replica method allows to analyze
very difficult system cases in a comparatively simple way though some authors
pointed out that its assumptions are not always rigorous. Being aware of this,
we underline the key assumptions made in this setting, quite similar to the
assumptions made in the technical literature using the replica method in their
asymptotic analyses. As far as concerns the convergence of the mutual
information to the Gaussian distribution, it is shown that it holds under some
mild technical conditions, which are tantamount to assuming that the spatial
correlation structure has no asymptotically dominant eigenmodes. The accuracy
of the asymptotic approach is assessed by providing a sizeable number of
numerical results. It is shown that the approximation is very accurate in a
wide variety of system settings even when the number of transmit and receive
antennas is as small as a few units.Comment: - submitted to the IEEE Transactions on Information Theory on Nov.
19, 2006 - revised and submitted to the IEEE Transactions on Information
Theory on Dec. 19, 200
- …