A Co-Embedding Model with Variational Auto-Encoder for Knowledge Graphs

Knowledge graph (KG) embedding has been widely studied to obtain low-dimensional representations for entities and relations. It serves as the basis for downstream tasks, such as KG completion and relation extraction. Traditional KG embedding techniques usually represent entities/relations as vectors or tensors, mapping them in different semantic spaces and ignoring the uncertainties. The affinities between entities and relations are ambiguous when they are not embedded in the same latent spaces. In this paper, we incorporate a co-embedding model for KG embedding, which learns low-dimensional representations of both entities and relations in the same semantic space. To address the issue of neglecting uncertainty for KG components, we propose a variational auto-encoder that represents KG components as Gaussian distributions. In addition, compared with previous methods, our method has the advantages of high quality and interpretability. Our experimental results on several benchmark datasets demonstrate our model’s superiority over the state-of-the-art baselines.

Statistical Analyses of the Energies of X-Ray Plateaus and Flares in Gamma-Ray Bursts

Distinct X-ray plateau and flare phases have been observed in the afterglows of gamma-ray bursts (GRBs), and most of them should be related to central engine activities. In this paper, we collect 174 GRBs with X-ray plateau phases and 106 GRBs with X-ray flares. There are 51 GRBs that overlap in the two selected samples. We analyze the distributions of the proportions of the plateau energy E plateau and the flare energy E flare relative to the isotropic prompt emission energy E γ,iso. The results indicate that they well meet the Gaussian distributions and the medians of the logarithmic ratios are ∼−0.96 and −1.39 in the two cases. Moreover, strong positive correlations between E plateau (or E flare ) and E γ,iso with slopes of ∼0.95 (or ∼0.80) are presented. For the overlapping sample, the slope is ∼0.80. We argue that most of X-ray plateaus and flares might have the same physical origin but appear with different features because of the different circumstances and radiation mechanisms. We also test the applicabilities of two models, i.e., black holes surrounded by fractured hyperaccretion disks and millisecond magnetars, on the origins of X-ray plateaus and flares.

Probabilistic Graphical Model for Continuous Variables

Most of the sampled data in complex industrial processes are sequential in time. Therefore, the traditional BN learning mechanisms have limitations on the value of probability and cannot be applied to the time series. The model established in Chap. 10.1007/978-981-16-8044-1_13 is a graphical model similar to a Bayesian network, but its parameter learning method can only handle the discrete variables. This chapter aims at the probabilistic graphical model directly for the continuous process variables, which avoids the assumption of discrete or Gaussian distributions.

Statistical Forecasting : Third Wave of COVID-19-With an Application to India

The pandemic due to the SARS-CoV-2 virus impacted the entire world in different waves. An important question that arise after witnessing the first and second waves of COVID-19 is - Will the third wave also arrive and if yes, then when. Various types of methodologies are being used to explore the arrival of third wave. A statistical methodology based on the fitting of mixture of Gaussian distributions is explored in this paper and the aim is to forecast the third wave using the data on the first two waves of pandemic. Utilizing the data of different countries that are already facing the third wave, modelling of their daily cases data and predicting the impact and timeline for the third wave in India is attempted in this paper. The Gaussian mixture model based on algorithm for clustering is used to estimate the parameters.

Mixture Density Regression reveals frequent recent adaptation in the human genome

How much genome differences between species reflect neutral or adaptive evolution is a central question in evolutionary genomics. In humans and other mammals, the prevalence of adaptive versus neutral genomic evolution has proven particularly difficult to quantify. The difficulty notably stems from the highly heterogenous organization of mammalian genomes at multiple levels (functional sequence density, recombination, etc.) that complicates the interpretation and distinction of adaptive vs. neutral evolution signals. Here, we introduce Mixture Density Regressions (MDRs) for the study of the determinants of recent adaptation in the human genome. MDRs provide a flexible regression model based on multiple Gaussian distributions. We use MDRs to model the association between recent selection signals and multiple genomic factors likely to affect positive selection, if the latter was common enough in the first place to generate these associations. We find that a MDR model with two Gaussian distributions provides an excellent fit to the genome-wide distribution of a common sweep summary statistic (iHS), with one of the two distributions likely capturing the positively selected component of the genome. We further find several factors associated with recent adaptation, including the recombination rate, the density of regulatory elements in immune cells and testis, GC-content, gene expression in immune cells, the density of mammal-wide conserved elements, and the distance to the nearest virus-interacting gene. These results support that strong positive selection was relatively common in recent human evolution and highlight MDRs as a powerful tool to make sense of signals of recent genomic adaptation.

Melanoma Detection by AFM Indentation of Histological Specimens

Melanoma is visible unlike other types of cancer, but it is still challenging to diagnose correctly because of the difficulty in distinguishing between benign nevus and melanoma. We conducted a robust investigation of melanoma, identifying considerable differences in local elastic properties between nevus and melanoma tissues by using atomic force microscopy (AFM) indentation of histological specimens. Specifically, the histograms of the elasticity of melanoma displayed multimodal Gaussian distributions, exhibiting the heterogeneous mechanical properties, in contrast with the unimodal distributions of elasticity in the benign nevus. We identified this notable signature was consistent regardless of blotch incidence by sex, age, anatomical site (e.g., thigh, calf, arm, eyelid, and cheek), or cancer stage (I, IV, and V). In addition, we found that the non-linearity of the force-distance curves for melanoma is increased compared to benign nevus. We believe that AFM indentation of histological specimens may technically complement conventional histopathological analysis for earlier and more precise melanoma detection.

Enhanced Mineral Quantification and Uncertainty Analysis from Downhole Spectroscopy Logs Using Variational Autoencoders

This paper describes an innovative machine-learning application, based on variational autoencoder frameworks, to quantify the concentrations and associated uncertainties of common minerals in sedimentary formations using the measurement of atomic element concentrations from geochemical spectroscopy logs as inputs. The algorithm comprises an input(s), encoder, decoder, output(s), and a novel cost function to optimize the model coefficients during training. The input to the algorithm is a set of dry-weight concentrations of atomic elements with their associated uncertainty. The first output is a set of dry-weight fractions of 14 minerals, and the second output is a set of reconstructed dry-weight concentrations of the original elements. Both sets of outputs include estimates of uncertainty on their predictions. The encoder and decoder are multilayer feed-forward artificial neural networks (ANN), with their coefficients (weights) optimized during calibration (training). The cost function simultaneously minimizes error (accuracy metric) and variance (precision or robustness metric) on the mineral and reconstructed elemental outputs. Training of the weights is done using a set of several-thousand core samples with independent, high-fidelity elemental and mineral (quartz, potassium-feldspar, plagioclase-feldspar, illite, smectite, kaolinite, chlorite, mica, calcite, dolomite, ankerite, siderite, pyrite, and anhydrite) data. The algorithm provides notable advantages over existing methods to estimate formation lithology or mineralogy relying on simple linear, empirical, or nearest-neighbor functions. The ANN numerically capture the multidimensional and nonlinear geochemical relationship (mapping) between elements and minerals that is insufficiently described by prior methods. Training is iterative via backpropagation and samples from Gaussian distributions on each of the elemental inputs, rather than single values, for every sample at each iteration (epoch). These Gaussian distributions are chosen to specifically represent the unique statistical uncertainty of the dry-weight elements in the logging measurements. Sampling from Gaussian distributions during training reduces the potential for overfitting, provides robustness for log interpretations, and further enables a calibrated estimate of uncertainty on the mineral and reconstructed elemental outputs, all of which are lacking in prior methods. The framework of the algorithm is purposefully generalizable so that it can be adapted across geochemical spectroscopy tools. The algorithm reasonably approximates a “global-average” model that requires neither different calibrations nor expert parameterization or intervention for interpreting common oilfield sedimentary formations, although the framework is again purposefully generalizable so it can be optimized for local environments where desirable. The paper showcases a field application of the method for estimating mineral type and abundance in oilfield formations from wellbore-logging measurements.