Uncovering Hidden Factors in Electricity Consumption Based on Gaussian Mixture Estimation

Load characteristics play an essential role in the planning of power generation and distribution. Various undiscovered factors, which could be socioeconomic, geographic, or climatic, make it possible to describe the electricity demand by a multimodal distribution. This letter proposes a novel method based on multimodal distributions to characterize the hidden factors in electricity consumption. Consequently, a new approach is developed to evaluate the impact of the underlying factors of electricity consumption. Some quantifiable and predictable factors are analyzed in developing multimodal distribution to describe the expected demand. Simulations based on synthetic and real-world data have been conducted to demonstrate the usefulness and robustness of the proposed method.

Randomized maximum likelihood based posterior sampling

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples generated by minimization is not the desired target density, unless the observation operator is linear, but the distribution of samples is useful as a proposal density for importance sampling or for Markov chain Monte Carlo methods. In this paper, we focus on applications to sampling from multimodal posterior distributions in high dimensions. We first show that sampling from multimodal distributions is improved by computing all critical points instead of only minimizers of the objective function. For applications to high-dimensional geoscience inverse problems, we demonstrate an efficient approximate weighting that uses a low-rank Gauss-Newton approximation of the determinant of the Jacobian. The method is applied to two toy problems with known posterior distributions and a Darcy flow problem with multiple modes in the posterior.

Orientations of Mistaken Point Fronds Indicate Morphology Impacted Ability to Survive Turbulence

The Ediacaran fossils of the Mistaken Point E surface have provided crucial insight into early animal communities, including how they reproduced, the importance of Ediacaran height and what the most important factors were to their community dynamics. Here, we use this iconic community to investigate how morphological variation between eight taxa affected their ability to withstand different flow conditions. For each of Beothukis, Bradgatia, Charniodiscus procerus, Charniodiscus spinosus, Plumeropriscum, Primocandelabrum, Thectardis and Fractofusus we measured the orientation and length of their stems (if present) and their fronds. We statistically tested each taxon’s stem and frond orientation distributions to see whether they displayed a uniform or multimodal distribution. Where multimodal distributions were identified, the stem/frond length of each cohort was tested to identify if there were differences in size between different orientation groups. We find that Bradgatia and Thectardis show a bimodal felling direction, and infer that they were felled by the turbulent head of the felling flow. In contrast, the frondose rangeomorphs including Beothukis, Plumeropriscum, Primocandelabrum, and the arboreomorphs were felled in a single direction, indicating that they were upright in the water column, and were likely felled by the laminar tail of the felling flow. These differences in directionality suggests that an elongate habit, and particularly possession of a stem, lent greater resilience to frondose taxa against turbulent flows, suggesting that such taxa would have had improved survivability in conditions with higher background turbulence than taxa like Bradgatia and Thectardis, that lacked a stem and had a higher centre of mass, which may have fared better in quieter water conditions.

Orientations of Mistaken Point fronds indicate morphology impacted ability to survive turbulence

The Ediacaran organisms of the Mistaken Point E surface have provided crucial insight into early animal communities, including how they reproduced, the importance of Ediacaran height and what the most important factors were to their community dynamics. Here, we use this iconic community to investigate how morphological variation between eight taxa affected their ability to withstand different flow conditions. For each of Beothukis, Bradgatia, Charniodiscus procerus, Charniodiscus spinosus, Plumeropriscum, Primocandelabrum and Fractofusus we measured the orientation and length of their stems (if present) and their fronds. We statistically tested each taxon's stem and frond orientation distributions to see whether they displayed a uniform or multimodal distribution. Where multimodal distributions were identified, the stem/frond length of each cohort was tested to identify if there were differences in size between different orientation groups. We find that Bradgatia and Thectardis show a bimodal felling direction, and infer that they were felled by the turbulent head of the felling flow. In contrast, the frondose rangeomorphs including Beothukis, Plumeropriscum, Primocandelabrum, and the arboreomorphs were felled in a single direction, indicating that they were upright in the water column, and were likely felled by the laminar tail of the felling flow. These differences in directionality suggests that an elongate habit, and particularly possession of a stem, lent greater resilience to frondose taxa against turbulent flows, suggesting that such taxa would have had improved survivability in conditions with higher background turbulence than taxa like Bradgatia and Thectardis, which lacked a stem and which had a higher centre of mass, which may have fared better in quieter water conditions.

Direct Measurement of Sedimentation Coefficient Distributions in Multimodal Nanoparticle Mixtures

Differential centrifugal sedimentation (DCS) is based on physical separation of nanoparticles in a centrifugal field prior to their analysis. It is suitable for resolving particle populations, which only slightly differ in size or density. Agglomeration presents a common problem in many natural and engineered processes. Reliable data on the agglomeration state are also crucial for hazard and risk assessment of nanomaterials and for grouping and read-across of nanoforms. Agglomeration results in polydisperse mixtures of nanoparticle clusters with multimodal distributions in size, density, and shape. These key parameters affect the sedimentation coefficient, which is the actual physical quantity measured in DCS, although the method is better known for particle sizing. The conversion into a particle size distribution is, however, based on the assumption of spherical shapes. The latter disregards the influence of the actual shape on the sedimentation rate. Sizes obtained in this way refer to equivalent diameters of spheres that sediment at the same velocity. This problem can be circumvented by focusing on the sedimentation coefficient distribution of complex nanoparticle mixtures. Knowledge of the latter is essential to implement and optimize preparative centrifugal routines, enabling precise and efficient sorting of complex nanoparticle mixtures. The determination of sedimentation coefficient distributions by DCS is demonstrated based on supracolloidal assemblies, which are often referred to as “colloidal molecules”. The DCS results are compared with sedimentation coefficients obtained from hydrodynamic bead-shell modeling. Furthermore, the practical implementation of the analytical findings into preparative centrifugal separations is explored.

Statistical Characterization of Supraharmonics in Low-Voltage Distribution Networks

Modern power systems are subject to waveform distortions that include spectral components (supraharmonics) in the range of 2–150 kHz. Due to the lack of regulation in this range and since supraharmonics may follow time-varying patterns, the operators can take advantage of the statistical characterization of supraharmonics, e.g., for determining convenient power quality limits or to analyze the residual capacity of networks toward further installations of power electronic converters. This paper studies the statistical characterization of supraharmonics in low-voltage distribution networks, considering both the overall supraharmonic distortion (through the characterization of the total supraharmonic distortion index) and individual supraharmonic components. Several probability distributions are proposed and compared, also considering multimodal distributions that can fit more general scenarios in which the supraharmonic emissions follow regime patterns. The outcome of numerical experiments based on publicly available data collected at actual low-voltage distribution networks suggests that multimodal distributions are useful in characterizing supraharmonics in most cases, with acceptable goodness of fitting even in the presence of stair-shaped empirical distributions. This paper can serve as a starting point for the development of probabilistic power system analysis tools accounting for supraharmonic emissions and for the convergence toward standardization in the 2–150 kHz range.

‘Statistical Irreproducibility’ Does Not Improve with Larger Sample Size: How to Quantify and Address Disease Data Multimodality in Human and Animal Research

Poor study reproducibility is a concern in translational research. As a solution, it is recommended to increase sample size (N), i.e., add more subjects to experiments. The goal of this study was to examine/visualize data multimodality (data with >1 data peak/mode) as cause of study irreproducibility. To emulate the repetition of studies and random sampling of study subjects, we first used various simulation methods of random number generation based on preclinical published disease outcome data from human gut microbiota-transplantation rodent studies (e.g., intestinal inflammation and univariate/continuous). We first used unimodal distributions (one-mode, Gaussian, and binomial) to generate random numbers. We showed that increasing N does not reproducibly identify statistical differences when group comparisons are repeatedly simulated. We then used multimodal distributions (>1-modes and Markov chain Monte Carlo methods of random sampling) to simulate similar multimodal datasets A and B (t-test-p = 0.95; N = 100,000), and confirmed that increasing N does not improve the ‘reproducibility of statistical results or direction of the effects’. Data visualization with violin plots of categorical random data simulations with five-integer categories/five-groups illustrated how multimodality leads to irreproducibility. Re-analysis of data from a human clinical trial that used maltodextrin as dietary placebo illustrated multimodal responses between human groups, and after placebo consumption. In conclusion, increasing N does not necessarily ensure reproducible statistical findings across repeated simulations due to randomness and multimodality. Herein, we clarify how to quantify, visualize and address disease data multimodality in research. Data visualization could facilitate study designs focused on disease subtypes/modes to help understand person–person differences and personalized medicine.

Clustering Using Student t Mixture Copulas

Tewari et al. (Parametric characterization of multimodal distributions with non-Gaussian modes, pp 286–292, 2011) introduced Gaussian mixture copula models (GMCM) for clustering problems which do not assume normality of the mixture components as Gaussian mixture models (GMM) do. In this paper, we propose Student t mixture copula models (SMCM) as an extension of GMCMs. GMCMs require weak assumptions, yielding a flexible fit and a powerful cluster tool. Our SMCM extension offers, in a natural way, even more flexibility than the GMCM approach. We discuss estimation issues and compare Expectation-Maximization (EM)-based with numerical simplex optimization methods. We illustrate the SMCM as a tool for image segmentation.