We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a ...nonlinear function of the flow, dissipation, and Gaussian, additive noise. For a given set of parameters and finite noise amplitudes, the network self-organizes into one of several metastable configurations, according to a probability distribution that depends on the noise amplitude α. At a finite value α, we find a resonantlike behavior for which one network topology is the most probable stationary state. This specific topology maximizes the robustness and transport efficiency, it is reached with the maximal convergence rate, and it is not found by the noiseless dynamics. We argue that this behavior is a manifestation of noise-induced resonances in network self-organization. Our findings show that stochastic dynamics can boost transport on a nonlinear network and, further, suggest a change of paradigm about the role of noise in optimization algorithms.
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2.
A confusion of curves Raper, Simon
Significance (Oxford, England),
June 2022, 2022-06-01, 20220601, Volume:
19, Issue:
3
Journal Article
Francis Galton was beguiled by the normal distribution, believing it could split the natural world into a spectrum of types – with each type represented by its own “bell curve”. But he was wrong in ...this belief, and his ideas for separating and shifting the bell curves of human types helped pave a dark path. By Simon Raper
Francis Galton was beguiled by the normal distribution, believing it could split the natural world into a spectrum of types — with each type represented by its own “bell curve”. But he was wrong in this belief, and his ideas for separating and shifting the bell curves of human types helped pave a dark path. By Simon Raper.
Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated ...multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online.
Purpose
The purpose of this study is to extend the classical noncentral
F
-distribution under normal settings to noncentral closed skew
F
-distribution for dealing with independent samples from ...multivariate skew normal (SN) distributions.
Design/methodology/approach
Based on generalized Hotelling's
T
2
statistics, confidence regions are constructed for the difference between location parameters in two independent multivariate SN distributions. Simulation studies show that the confidence regions based on the closed SN model outperform the classical multivariate normal model if the vectors of skewness parameters are not zero. A real data analysis is given for illustrating the effectiveness of our proposed methods.
Findings
This study’s approach is the first one in literature for the inferences in difference of location parameters under multivariate SN settings. Real data analysis shows the preference of this new approach than the classical method.
Research limitations/implications
For the real data applications, the authors need to remove outliers first before applying this approach.
Practical implications
This study’s approach may apply many multivariate skewed data using SN fittings instead of classical normal fittings.
Originality/value
This paper is the research paper and the authors’ new approach has many applications for analyzing the multivariate skewed data.
Category:
Hindfoot; Midfoot/Forefoot; Other
Introduction/Purpose:
The key pathology of Müller-Weiss Disease (MWD) is fragmentation of the lateral pole of the navicular which leads to lateral rotation ...of the talar head, inversion of the subtalar joint, and eventually collapse of the medial arch with a paradoxical flatfoot deformity since the varus heel persists. Treatment for MWD should be based on an understanding of this unusual hind and midfoot deformity in order to achieve ideal outcomes. For years however, some authors have treated MWD as a flatfoot deformity instead of correction of the varus heel. This study used weightbearing CT (WBCT) images to demonstrate the structural and alignment changes of the hindfoot and medial arch in patients with MWD compared to those of controls and patients with adult acquired flatfoot deformity (AAFD).
Methods:
Twelve patients with 17 feet from two medical centers with a clinical diagnosis of MWD were retrospectively reviewed. Ten feet with flexible AAFD were chosen as the flatfoot control group. Ten feet without deformity, arthritis, a history of trauma, or prior surgical history in the foot and ankle were chosen as normal controls. The hindfoot moment arm (HMA), foot and ankle offset (FAO), middle facet subluxation (MFS), talonavicular joint coverage angle (TNCA), and the percentage of calcaneocuboid joint subluxation (CCS) measured on WBCT were used to assess the alignment of the hindfoot and peritalar joints. The arch height index was used to assess the height of the medial arch. Positive was used to reflect lateral subluxations and negative was for the medial ones. ANOVA test were used to compare data among the three groups with a normal distribution, while Wilcoxon test were used for non normal distribution.
Results:
According to WBCT analysis, patients with MWD showed totally different hindfoot alignment and peritalar subluxation characteristics compared to the AAFD and the normal control groups. In the order of MWD, AAFD and control, the mean HMA values were -3.44 mm, 15.75 mm, and 3.19 mm, FAO values were -0.72%, 7.42%, and 2.63%. TNCA values were -7.18, 22.11, and 11.37; MFS values were 14%, 45%, and 23%; CCS values were -0.19, 0 and -0.04. The arch height index values were 0.46, 0.45, and 0.58. There was statistically significant difference among the three groups in all the above parameters except the middle facet subluxation and fifth metatarsal medial cuneiform height ratios between the MWD group and the normal controls.
Conclusion:
This study confirmed that hindfoot varus is a typical feature of MWD. And this is the first study to demonstrate that peritalar subluxation is an important marker. With lateral rotation of the talar head, the subtalar joint is driven into varus, with medial subluxation of both the middle facet and the calcaneocuboid joint, resulting in peritalar subluxation opposite to that of AAFD. No significant difference between the medial arch of the MWD group and the controls was present. In conclusion, structural changes of the midfoot and hindfoot totally different from the characteristics of AAFD are present in MWD.
•The paper presents a reliability-based learning function for adaptive Kriging surrogate models.•The modulating effect of the scatting geometry of random samples is considered.•The use of ...low-discrepancy samples and truncated sampling regions initiates efficient active-learning results.•Case studies have shown the proposed method has engineering applications.
Structural reliability analysis is typically evaluated based on a multivariate function that describes underlying failure mechanisms of a structural system. It is necessary for a surrogate model to mimic the true performance function as the brute-force Monte-Carlo simulation is computationally intensive for rare failure probabilities. To this end, the paper presents an effective active-learning based Kriging method for structural reliability analysis. The reliability-based expected improvement function (REIF) is first derived based on the folded-normal distribution. To account for the modulating effect of the joint probability density function of input random variables on the scattering geometry of candidate samples, an improvement of the REIF active-learning function, i.e., the REIF2 is further presented. Then, the low-discrepancy samples and adaptively truncated sampling regions are combined together to initiate efficient active-learning iterations. The truncated sampling region is directly related to a structural failure probability result, rather than subjectively fixed by an analyst. Numerical validity of the proposed active-learning functions in conjunction with adaptively truncated sampling region and low-discrepancy samples is demonstrated by several structural reliability examples in the literature.
Convolutional Networks have been demonstrated to be particularly useful for extracting high level feature in structural data. Temporal convolutional network (TCN) is a framework which employs casual ...convolutions and dilations so that it is adaptive for sequential data with its temporality and large receptive fields. In this paper, we apply TCN for anomaly detection in time series. We train the TCN on normal sequences and use it to predict trend in a number of time steps. Prediction errors are fitted by a multivariate Gaussian distribution and used to calculate the anomaly scores of points. In addition, a multi-scale feature mixture method is raised to promote performance. The validity of this method is confirmed on three real-world datasets.
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