465 research outputs found
Coupling the reduced-order model and the generative model for an importance sampling estimator
In this work, we develop an importance sampling estimator by coupling the
reduced-order model and the generative model in a problem setting of
uncertainty quantification. The target is to estimate the probability that the
quantity of interest (QoI) in a complex system is beyond a given threshold. To
avoid the prohibitive cost of sampling a large scale system, the reduced-order
model is usually considered for a trade-off between efficiency and accuracy.
However, the Monte Carlo estimator given by the reduced-order model is biased
due to the error from dimension reduction. To correct the bias, we still need
to sample the fine model. An effective technique to reduce the variance
reduction is importance sampling, where we employ the generative model to
estimate the distribution of the data from the reduced-order model and use it
for the change of measure in the importance sampling estimator. To compensate
the approximation errors of the reduced-order model, more data that induce a
slightly smaller QoI than the threshold need to be included into the training
set. Although the amount of these data can be controlled by a posterior error
estimate, redundant data, which may outnumber the effective data, will be kept
due to the epistemic uncertainty. To deal with this issue, we introduce a
weighted empirical distribution to process the data from the reduced-order
model. The generative model is then trained by minimizing the cross entropy
between it and the weighted empirical distribution. We also introduce a penalty
term into the objective function to deal with the overfitting for more
robustness. Numerical results are presented to demonstrate the effectiveness of
the proposed methodology
Can crop yield risk be globally diversified?
In 2007 and 2008 world food markets observed a significant price boom. Crop failures simultaneously occurring in some of the world’s major production regions have been quoted as one factor among others for the price boom. Against this background, we analyse the stochasticity of crop yields in major production areas. The analysis is exemplified for wheat, which is one of the most important crops worldwide. Particular attention is given to the stochastic dependence of yields in different regions. Thereby we address the question of whether local fluctuations of yields can be smoothed by international agricultural trade, i.e. by global diversification. The analysis is based on the copula approach, which requires less restrictive assumptions compared with linear correlations. The use of copulas allows for a more reliable estimation of extreme yield shortfalls, which are of particular interest in this application. Our calculations reveal that a production shortfall, such as in 2007, is not a once in a lifetime event. Instead, from a statistical point of view, similar production conditions will occur every 15 years.crop yield risk, fully nested hierarchical Archimedean copulas (FNAC), price boom
Equilibrium of Heterogeneous Congestion Control: Optimality and Stability
When heterogeneous congestion control protocols
that react to different pricing signals share the same network,
the current theory based on utility maximization fails to predict
the network behavior. The pricing signals can be different types
of signals such as packet loss, queueing delay, etc, or different
values of the same type of signal such as different ECN marking
values based on the same actual link congestion level. Unlike in a
homogeneous network, the bandwidth allocation now depends on
router parameters and flow arrival patterns. It can be non-unique,
suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous
congestion control: Existence and uniqueness,” IEEE/ACM
Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and
uniqueness of equilibrium of heterogeneous protocols are investigated.
This paper extends the study with two objectives: analyzing
the optimality and stability of such networks and designing control
schemes to improve those properties. First, we demonstrate the
intricate behavior of a heterogeneous network through simulations
and present a framework to help understand its equilibrium
properties. Second, we propose a simple source-based algorithm
to decouple bandwidth allocation from router parameters and
flow arrival patterns by only updating a linear parameter in the
sources’ algorithms on a slow timescale. It steers a network to
the unique optimal equilibrium. The scheme can be deployed
incrementally as the existing protocol needs no change and only
new protocols need to adopt the slow timescale adaptation
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Central Dogma at the Single-Molecule Level in Living Cells
Gene expression originates from individual DNA molecules within living cells. Like many single-molecule processes, gene expression and regulation are stochastic, that is, sporadic in time. This leads to heterogeneity in the messenger RNA and protein copy numbers in a population of cells with identical genomes. With advanced single-cell fluorescence microscopy, it is now possible to quantify transcriptomes and proteomes with single-molecule sensitivity. Dynamic processes such as transcription factor binding, transcription and translation can be monitored in real time, providing quantitative descriptions of gene expression and regulation, and the demonstration that a single-molecule event can determine the phenotype of a cell.Chemistry and Chemical Biolog
Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations
Since Kopel's duopoly model was proposed about three decades ago, there are
almost no analytical results on the equilibria and their stability in the
asymmetric case. The first objective of our study is to fill this gap. This
paper analyzes the asymmetric duopoly model of Kopel analytically by using
several tools based on symbolic computations. We discuss the possibility of the
existence of multiple positive equilibria and establish necessary and
sufficient conditions for a given number of positive equilibria to exist. The
possible positions of the equilibria in Kopel's model are also explored.
Furthermore, if the duopolists adopt the best response reactions or homogeneous
adaptive expectations, we establish rigorous conditions for the existence of
distinct numbers of positive equilibria for the first time. The occurrence of
chaos in Kopel's model seems to be supported by observations through numerical
simulations, which, however, is challenging to prove rigorously. The second
objective is to prove the existence of snapback repellers in Kopel's map, which
implies the existence of chaos in the sense of Li-Yorke according to Marotto's
theorem.Comment: arXiv admin note: substantial text overlap with arXiv:2301.1262
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