Finite generation of the cohomology rings for the extension algebras of monomial algebras

We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [Formula: see text] is finitely generated [Formula: see text] is [Formula: see text] is, where [Formula: see text] is the dual extension of a monomial algebra [Formula: see text] and [Formula: see text] is the opposite algebra of [Formula: see text].

Understanding the Facies Architecture of a Fluvial-Aeolian of Tensleep Formation Using a Machine Learning Approach

Many aeolian dune reservoirs are built from various dune types, and many may remain unrecognized in subsurface work. The challenge is to tackle the complex geological architecture of dune types within the Teapot Dome dataset caused by wind and water erosion. Machine Learning (ML) helps predict facies architecture away from boreholes using seismic attributes and facies logs. It provides a detailed understanding of the facies architecture analysis of the relationship between the fluvial–aeolian environment in Tensleep Formation based on seismic and well data. It allows operators to wisely assess their hydrocarbon reservoir, improve safety, and maximize oil and gas production investment. The data from the Teapot Dome field (Naval Petroleum Reserve No.3 - NPR-3) provides a good testing ground for Machine Learning, as it is easy to validate and prove its value. This study will show how the ML supervised learning method incorporating Neural Network Seismic Inversion (NNSI) can successfully create porosity log and facies volumes. Moreover, unsupervised learning using Multi-Resolution Graph-based clustering (MRGC) can be used to classify the facies logs. NNSI has 0.963 for the cross-correlation coefficients for all wells. The ML approach was used to help recognize the type of aeolian dune reservoirs in the subsurface and correlate the well log and facies volumes. In addition, ML allowed the distinct sequences and reconstruction of their depositional history in the Tensleep Formation. This study also refers briefly to other examples of fluvial-aeolian facies architecture worldwide. It successfully found the ancient model in an existing modern fluvial-aeolian environment, revealing hidden information about facies architecture based on the geometrical shape of geobodies in the oil-producing reservoir in the Tensleep Formation.

Electrofacies as a Tool for the Prediction of True Resistivity Using Advanced Statistical Methods—Case Study

Statistical analysis methods have been widely used in all industries. In well logs analyses, they have been used from the very beginning to predict petrophysical parameters such as permeability and porosity or to generate synthetic curves such as density or sonic logs. Initially, logs were generated as simple functions of other measurements. Then, as a result of the popularisation of algorithms such as the k-nearest neighbours (k-NN) or artificial neural networks (ANN), logs were created based on other logs. In this study, various industry and general scientific programmes were used for statistical data analysis, treating the well logs data as individual data sets, obtaining very convergent results. The methods developed for processing well logs data, such as Multi-Resolution Graph-Based Clustering (MRGBC), as well as algorithms commonly used in statistical analysis such as Kohonen self-organising maps (SOM), k-NN, and ANN were applied. The use of the aforementioned statis-tical methods allows for the electrofacies determination and prediction of an Rt log based on the other recorded well logs. Correct determination of Rt in resistivity measurements made with the Dual Laterolog tool in the conditions of the Groningen effect is often problematic. The applied calculation methods allow for the correct estimation of Rt in the tested well.

The Power of Predictive Analytics in Oil Field Development: Integrating Machine Learning with Reservoir Hydrocarbon Data to Enable Enhanced Oil Recovery of Hugin Formation within the Theta Vest Structure

Machine learning is an algorithm based on pattern recognition and the concept that computers can learn without being programmed to perform specific tasks. Machine learning applications that are commonly used in the oil and gas companies are petrophysical estimation and well log classification, seismic structural identification, production forecasting, and artificial intelligence tasks. The goal of this study is to integrate machine learning workflows to evaluate how reservoir hydrocarbon distribution can help prospecting, field development, and production optimization, especially 4D seismic studies. Also to observe the fluid flow and to detect bypassed oil pockets changes during the production. The workflow consists of three phases: planning, execution, and delivery. The first phase consists of collecting and preprocessing wells, seismic and interpretation data. Once the plan is considered satisfactory, it will be followed by the execution that is started with data cleaning, processing, classification, and data validation. Machine learning methods are then deployed to build an electrofacies and reservoir distribution model for the Hugin Formation using Multi-Resolution Graph-Based Clustering (MRGC). After these models reach a satisfactory level, seismic attribute analysis is performed using Principal Component Analysis (PCA) and Democratic Neural Network Association (DNNA) to create a facies probability volume. The last step in this phase is to detect geobodies of oil sand and propose an infill well or injection strategy to enable the enhancement of the oil recovery. Once the machine learning results are satisfying, tthe status of the workflow will change from execution to the delivery phase to create the final project presentation. In our study, DNNA has demonstrated excellent prediction and facies classification to image a large volume encompassing some wellbores, changes in the fluid flow during production between baseline, and monitoring seismic surveys with a good Matthews correlation coefficient of 0.849554. It allows the operator to observe the dynamic processes in and around the reservoir to help the placement of infill wells more effectively, increas development and production success, reduce risk when following proposed infill wells. The integration of machine learning can also improve the understanding of hydrocarbons in the field. It shapes E&P business strategies in a way that may increase profit revenues, such as enhanced oil recovery of an effective and efficient infill well and optimizing an injection strategy.

Amyloid-β and tau pathologies relate to distinctive brain dysconnectomics in preclinical autosomal-dominant Alzheimer's disease

Amyloid-β and tau pathology in preclinical Alzheimers disease (AD) are hypothesized to propagate through brain networks that are critical for neural communication. We used high- resolution graph-based network analyses to test whether in vivo amyloid-β and tau burden related to segregation and integration of functional brain connections, and their association with memory, in cognitively-unimpaired Presenilin-1 E280A carriers who will develop early-onset AD dementia. Greater tau burden predicted weaker functional segregation and integration of the precuneus with other densely connected regions like the insula and entorhinal cortex, a site of early tau accumulation that is critical for memory. We also observed greater segregation and integration in the striatum and multimodal integrated networks that harbor amyloid-β early. Findings enlighten our understanding of how AD-related pathology distinctly alter the brains functional architecture to interfere with information processing within and across neural systems, possibly contributing to the spread of pathology and ultimately resulting in dementia.

A Deep Molecular Generative Model Based on Multi-Resolution Graph Variational Autoencoders

Deep generative models have recently emerged as encouraging tools for the de novo molecular structure generation. Even though considerable advances have been achieved in recent years, the field of generative molecular design is still in its infancy. One potential solution may be to integrate domain knowledge of structural or medicinal chemistry into the data-driven machine learning process to address specific deep molecule generation goals. This manuscript proposes a new graph-based hierarchical variational autoencoder (VAE) model for molecular generation. Training molecules are first decomposed into small molecular fragments. Unlike other motif-based molecular graph generative models, we further group decomposed fragments into different interchangeable fragment clusters according to their local structural environment around the attachment points where the bond-breaking occurs. In this way, each chemical structure can be transformed into a three-layer graph, in which individual atoms, decomposed fragments, or obtained fragment clusters act as graph nodes at each corresponding layer, respectively. We construct a hierarchical VAE model to learn such three-layer hierarchical graph representations of chemical structures in a fine-to-coarse order, in which atoms, decomposed fragments, and related fragment clusters act as graph nodes at each corresponding graph layer. The decoder component is designed to iteratively select a fragment out of a predicted fragment cluster vocabulary and then attach it to the preceding substructure. The newly introduced third graph layer will allow us to incorporate specific chemical structural knowledge, e.g., interchangeable fragments sharing similar local chemical environments or bioisosteres derived from matched molecular pair analysis information, into the molecular generation process. It will increase the odds of assembling new chemical moieties absent in the original training set and enhance structural diversity/novelty scores of generated structures. Our proposed approach demonstrates comparatively good performance in terms of model efficiency and other molecular evaluation metrics when compared with several other graph- and SMILES-based generative molecular models. We also analyze how our generative models' performance varies when choosing different fragment sampling techniques and radius parameters that determine the local structural environment of interchangeable fragment clusters. Hopefully, our multi-level hierarchical VAE prototyping model might promote more sophisticated works of knowledge-augmented deep molecular generation in the future.

A Deep Molecular Generative Model Based on Multi-Resolution Graph Variational Autoencoders

Deep generative models have recently emerged as encouraging tools for the de novo molecular structure generation. Even though considerable advances have been achieved in recent years, the field of generative molecular design is still in its infancy. One potential solution may be to integrate domain knowledge of structural or medicinal chemistry into the data-driven machine learning process to address specific deep molecule generation goals. This manuscript proposes a new graph-based hierarchical variational autoencoder (VAE) model for molecular generation. Training molecules are first decomposed into small molecular fragments. Unlike other motif-based molecular graph generative models, we further group decomposed fragments into different interchangeable fragment clusters according to their local structural environment around the attachment points where the bond-breaking occurs. In this way, each chemical structure can be transformed into a three-layer graph, in which individual atoms, decomposed fragments, or obtained fragment clusters act as graph nodes at each corresponding layer, respectively. We construct a hierarchical VAE model to learn such three-layer hierarchical graph representations of chemical structures in a fine-to-coarse order, in which atoms, decomposed fragments, and related fragment clusters act as graph nodes at each corresponding graph layer. The decoder component is designed to iteratively select a fragment out of a predicted fragment cluster vocabulary and then attach it to the preceding substructure. The newly introduced third graph layer will allow us to incorporate specific chemical structural knowledge, e.g., interchangeable fragments sharing similar local chemical environments or bioisosteres derived from matched molecular pair analysis information, into the molecular generation process. It will increase the odds of assembling new chemical moieties absent in the original training set and enhance structural diversity/novelty scores of generated structures. Our proposed approach demonstrates comparatively good performance in terms of model efficiency and other molecular evaluation metrics when compared with several other graph- and SMILES-based generative molecular models. We also analyze how our generative models' performance varies when choosing different fragment sampling techniques and radius parameters that determine the local structural environment of interchangeable fragment clusters. Hopefully, our multi-level hierarchical VAE prototyping model might promote more sophisticated works of knowledge-augmented deep molecular generation in the future.