Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics

Infrastructure monitoring is critical for safe operations and sustainability. Like many networked systems, water distribution networks (WDNs) exhibit both graph topological structure and complex embedded flow dynamics. The resulting networked cascade dynamics are difficult to predict without extensive sensor data. However, ubiquitous sensor monitoring in underground situations is expensive, and a key challenge is to infer the contaminant dynamics from partial sparse monitoring data. Existing approaches use multi-objective optimization to find the minimum set of essential monitoring points but lack performance guarantees and a theoretical framework. Here, we first develop a novel Graph Fourier Transform (GFT) operator to compress networked contamination dynamics to identify the essential principal data collection points with inference performance guarantees. As such, the GFT approach provides the theoretical sampling bound. We then achieve under-sampling performance by building auto-encoder (AE) neural networks (NN) to generalize the GFT sampling process and under-sample further from the initial sampling set, allowing a very small set of data points to largely reconstruct the contamination dynamics over real and artificial WDNs. Various sources of the contamination are tested, and we obtain high accuracy reconstruction using around 5%–10% of the network nodes for known contaminant sources, and 50%–75% for unknown source cases, which although larger than that of the schemes for contaminant detection and source identifications, is smaller than the current sampling schemes for contaminant data recovery. This general approach of compression and under-sampled recovery via NN can be applied to a wide range of networked infrastructures to enable efficient data sampling for digital twins.

Design of SkSP-R Plan for Popular Statistical Distributions

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.

Identification of causal effects in case-control studies

Background Case-control designs are an important yet commonly misunderstood tool in the epidemiologist’s arsenal for causal inference. We reconsider classical concepts, assumptions and principles and explore when the results of case-control studies can be endowed a causal interpretation. Results We establish how, and under which conditions, various causal estimands relating to intention-to-treat or per-protocol effects can be identified based on the data that are collected under popular sampling schemes (case-base, survivor, and risk-set sampling, with or without matching). We present a concise summary of our identification results that link the estimands to the (distribution of the) available data and articulate under which conditions these links hold. Conclusion The modern epidemiologist’s arsenal for causal inference is well-suited to make transparent for case-control designs what assumptions are necessary or sufficient to endow the respective study results with a causal interpretation and, in turn, help resolve or prevent misunderstanding. Our approach may inform future research on different estimands, other variations of the case-control design or settings with additional complexities.

On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

In this chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

In the chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use of ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

Clinically significant prostate cancer (csPCa) detection with various prostate sampling schemes based on different csPCa definitions

Background Combining targeted biopsy (TB) with systematic biopsy (SB) is currently recommended as the first-line biopsy method by the European Association of Urology (EAU) guidelines in patients diagnosed with prostate cancer (PCa) with an abnormal magnetic resonance imaging (MRI). The combined SB and TB indeed detected an additional number of patients with clinically significant prostate cancer (csPCa); however, it did so at the expense of a concomitant increase in biopsy cores. Our study aimed to evaluate if ipsilateral SB (ipsi-SB) + TB or contralateral SB (contra-SB) + TB could achieve almost equal csPCa detection rates as SB + TB using fewer cores based on a different csPCa definition. Methods Patients with at least one positive prostate lesion were prospectively diagnosed by MRI. The combination of TB and SB was conducted in all patients. We compared the csPCa detection rates of the following four hypothetical biopsy sampling schemes with those of SB + TB: SB, TB, ipsi-SB + TB, and contra-SB + TB. Results The study enrolled 279 men. The median core of SB, TB, ipsi-SB + TB, and contra-SB + TB was 10, 2, 7 and 7, respectively (P < 0.001). ipsi-SB + TB detected significantly more patients with csPCa than contra-SB + TB based on the EAU guidelines (P = 0.042). They were almost equal on the basis of the Epstein criteria (P = 1.000). Compared with SB + TB, each remaining method detected significantly fewer patients with csPCa regardless of the definition (P < 0.001) except ipsi-SB + TB on the grounds of D1 (P = 0.066). Ten additional subjects were identified with a higher Gleason score (GS) on contra-SB + TB, and only one was considered as significantly upgraded (GS = 6 on ipsi-SB + TB to a GS of 8 on contra-SB + TB). Conclusions Ipsi-SB + TB could acquire an almost equivalent csPCa detection value to SB + TB using significantly fewer cores when csPCa was defined according to the EAU guidelines. Given that there was only one significantly upgrading patient on contra-SB, our results suggested that contra-SB could be avoided.

Impacts of Taxon-Sampling Schemes on Bayesian Molecular Dating under the Unresolved Fossilized Birth-Death Process

Evolutionary timescales can be estimated using a combination of genetic data and fossil evidence based on the molecular clock. Bayesian phylogenetic methods such as tip dating and total-evidence dating provide a powerful framework for inferring evolutionary timescales, but the most widely used priors for tree topologies and node times often assume that present-day taxa have been sampled randomly or exhaustively. In practice, taxon sampling is often carried out so as to include representatives of major lineages, such as orders or families. We examined the impacts of these diversified sampling schemes on Bayesian molecular dating under the unresolved fossilized birth-death (FBD) process, in which fossil taxa are topologically constrained but their exact placements are not inferred. We used synthetic data generated by simulation of nucleotide sequence evolution, fossil occurrences, and diversified taxon sampling. Our analyses show that increasing sampling density does not substantially improve divergence-time estimates under benign conditions. However, when the tree topologies were fixed to those used for simulation or when evolutionary rates varied among lineages, the performance of Bayesian tip dating improves with sampling density. By exploring three situations of model mismatches, we find that including all relevant fossils without pruning off those inappropriate for the FBD process can lead to underestimation of divergence times. Our reanalysis of a eutherian mammal data set confirms some of the findings from our simulation study, and reveals the complexity of diversified taxon sampling in phylogenomic data sets. In highlighting the interplay of taxon-sampling density and other factors, the results of our study have useful implications for Bayesian molecular dating in the era of phylogenomics.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.