{"id":77,"date":"2023-01-07T09:46:31","date_gmt":"2023-01-07T09:46:31","guid":{"rendered":"https:\/\/angle-lab.com\/?page_id=77"},"modified":"2023-12-14T20:37:37","modified_gmt":"2023-12-14T20:37:37","slug":"research","status":"publish","type":"page","link":"https:\/\/angle-lab.com\/site\/","title":{"rendered":"Research Areas"},"content":{"rendered":"\n<p>Our research combines theory and applications in Data Science and trustworthy machine learning. We develop theoretical results &#8212; algorithms, theorems, proofs that define new ideas and concepts. We implement and test these on real datasets and and applications. <\/p>\n\n\n\n<p>Our theoretical work includes deep mathematical and computational concepts derived from geometry, topology, theoretical machine learning, algorithms and many other areas. Below are a list of our current research interests, and our favourite application areas. Get in touch if you would like to work in these exciting areas. <\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\"><div class=\"wp-block-group__inner-container\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/angle-lab.com\/site\/#Table_of_Contents\" >Table of Contents<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/angle-lab.com\/site\/#Machine_Learning_Analysis_of_SGD_Neural_Networks_and_Optimisation\" >Machine Learning: Analysis of SGD, Neural Networks and Optimisation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/angle-lab.com\/site\/#Generative_Models_and_Impact_of_Artificial_Data\" >Generative Models and Impact of Artificial Data<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/angle-lab.com\/site\/#Value_of_Data\" >Value of Data<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/angle-lab.com\/site\/#Differential_Privacy_and_Private_Machine_Learning\" >Differential Privacy and Private Machine Learning.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/angle-lab.com\/site\/#Topological_Data_Analysis\" >Topological Data Analysis<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/angle-lab.com\/site\/#Computational_Fairness_and_Interpretability\" >Computational Fairness and Interpretability.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/angle-lab.com\/site\/#Application_Areas\" >Application Areas<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/angle-lab.com\/site\/#Network_Analysis_and_Graph_machine_learning\" >Network Analysis and Graph machine learning.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/angle-lab.com\/site\/#Biomedical_Engineering\" >Biomedical Engineering.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/angle-lab.com\/site\/#IoT_Sensors_and_decentralised_computation\" >IoT, Sensors and decentralised computation.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/angle-lab.com\/site\/#Chemistry_and_Drug_design\" >Chemistry and Drug design.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/angle-lab.com\/site\/#Mobility_trajectories_and_spatial_data\" >Mobility, trajectories and spatial data.<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h3 class=\"simpletoc-title\"><span class=\"ez-toc-section\" id=\"Table_of_Contents\"><\/span>Table of Contents<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul class=\"simpletoc-list\">\n<li><a href=\"#machine-learning-analysis-of-sgd-neural-networks-and-optimisation\">Machine Learning: Analysis of SGD, Neural Networks and Optimisation<\/a>\n\n<\/li>\n<li><a href=\"#generative-models-and-impact-of-artificial-data\">Generative Models and Impact of Artificial Data<\/a>\n\n<\/li>\n<li><a href=\"#value-of-data\">Value of Data<\/a>\n\n<\/li>\n<li><a href=\"#differential-privacy-and-private-machine-learning\">Differential Privacy and Private Machine Learning.<\/a>\n\n<\/li>\n<li><a href=\"#topological-data-analysis\">Topological Data Analysis<\/a>\n\n<\/li>\n<li><a href=\"#computational-fairness-and-interpretability\">Computational Fairness and Interpretability.<\/a>\n\n<\/li>\n<li><a href=\"#application-areas\">Application Areas<\/a>\n\n\n<ul><li>\n<a href=\"#network-analysis-and-graph-machine-learning\">Network Analysis and Graph machine learning.<\/a>\n\n<\/li>\n<li><a href=\"#biomedical-engineering\">Biomedical Engineering.<\/a>\n\n<\/li>\n<li><a href=\"#iot-sensors-and-decentralised-computation\">IoT, Sensors and decentralised computation.<\/a>\n\n<\/li>\n<li><a href=\"#chemistry-and-drug-design\">Chemistry and Drug design.<\/a>\n\n<\/li>\n<li><a href=\"#mobility-trajectories-and-spatial-data\">Mobility, trajectories and spatial data.<\/a>\n<\/li>\n<\/ul>\n<\/li><\/ul><\/div>\n<\/div>\n<\/div><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"machine-learning-analysis-of-sgd-neural-networks-and-optimisation\"><span class=\"ez-toc-section\" id=\"Machine_Learning_Analysis_of_SGD_Neural_Networks_and_Optimisation\"><\/span>Machine Learning: Analysis of SGD, Neural Networks and Optimisation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>Neural networks are mysterious things. They perform surprisingly well, and they also fail when no one expects them to. Big neural networks are behind all the recent successes in ML and the current hype in AI, but we don&#8217;t really understand what goes on in them. Where do they work? Why do they fail?<\/p>\n\n\n\n<p>Recent research has found many interesting behaviours in neural networks. For example, Network Pruning shows that large networks have small subnetworks that are really the core to the network&#8217;s actions. Study of the Stochastic Gradient descent algorithm has found that the trajectory in model space taken by the algorithm determines its properties through its mathematical invariants. Finally, neural networks behave strangely with respect to data &#8212; they frequently <em>forget<\/em> certain data points, and <em>memorise<\/em> certain points.<\/p>\n\n\n\n<p>We are looking at neural networks at finer scales than ever before \u2014 simultaneously analysing the network, the optimisation algorithm and the data to understand the subtle relations between them.<\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"generative-models-and-impact-of-artificial-data\"><span class=\"ez-toc-section\" id=\"Generative_Models_and_Impact_of_Artificial_Data\"><\/span>Generative Models and Impact of Artificial Data<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>The exciting current developments in AI are all based on generative model created with data found on the Internet. As AI and generative models become better and used more widely, artificial data will become more common everywhere. What happens when next generation of generative models are trained in part on artificial data? <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"616\" src=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-1-1024x616.png\" alt=\"\" class=\"wp-image-170\" style=\"width:612px;height:auto\" srcset=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-1-1024x616.png 1024w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-1-300x181.png 300w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-1-768x462.png 768w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-1.png 1426w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>We tried feeding artificial data to train generative models, and found that through generations, the models degrade until they start producing nonsense. <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"910\" height=\"586\" src=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-2.png\" alt=\"\" class=\"wp-image-171\" style=\"width:591px;height:auto\" srcset=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-2.png 910w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-2-300x193.png 300w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-2-768x495.png 768w\" sizes=\"auto, (max-width: 910px) 100vw, 910px\" \/><\/figure>\n\n\n\n<p>There are, of course, many a lot of even more exciting research to do in this area. What is really different in artificial data? Can we avoid this pitfall? What are the subtle differences in models trained with artificial data and what are their consequences? <\/p>\n\n\n\n<p>See my interview at Scientific American for a longer discussion:  <a href=\"https:\/\/www.scientificamerican.com\/article\/ai-generated-data-can-poison-future-ai-models\/\">https:\/\/www.scientificamerican.com\/article\/ai-generated-data-can-poison-future-ai-models\/<\/a><\/p>\n\n\n\n<p><\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"value-of-data\"><span class=\"ez-toc-section\" id=\"Value_of_Data\"><\/span>Value of Data<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>Some of the largest companies today run their businesses on data, and make enormous profits. So clearly, data is valuable. But how much exactly? Our personal data is used for building their core models and products, though we gain no knowledge of an individual&#8217;s contribution to these profit making products. Consider a company that uses our movie preferences, search behaviour or interactions with friends to improve their ML models. How much did <em>your<\/em> data contribute to the product? How much did the ML model improve by using your data? <\/p>\n\n\n\n<p>This is the problem of Data valuation. By assigning a value to each point, we can get a better idea of how much our data is worth. We can then make better decisions to share or not to share our data. We can perhaps ask for compensations from those using our data. This fundamental problem involves the study of a range of topics &#8212; economics, mathematics, game theory, interpretable machine learning, privacy and many others. It will have huge impact on the future of data science, technology and even economic policy. <\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"differential-privacy-and-private-machine-learning\"><span class=\"ez-toc-section\" id=\"Differential_Privacy_and_Private_Machine_Learning\"><\/span>Differential Privacy and Private Machine Learning.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>Privacy is a fundamental and difficult challenge in today&#8217;s world. As our data gets used in many products and services, the question is: can we hope to save some of our privacy while retaining the same applications of data science? Thus, instead of simply extracting as much knowledge as possible, privacy is a question of balancing what we can learn with what we can hide. <\/p>\n\n\n\n<p>Differential privacy is a way of measuring the loss of privacy due to a particular computation. Private ML models are those with guarantees of a certain level of differential privacy. In our research group we develop algorithms that provide guarantees of differential privacy to making queries to databases, training ML models and various other computations. We are currently investigating improved differential privacy for training neural networks and  data valuation. <\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"topological-data-analysis\"><span class=\"ez-toc-section\" id=\"Topological_Data_Analysis\"><\/span>Topological Data Analysis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>Topological data analysis deals with the <em>Shape of Data<\/em>. In data science, where the objective is to gain knowledge from data, this shape can reveal insights that are otherwise hard to see. In many real scenarios, the data is directly associated with shapes. In biological data for example, the shape of the organs and networks are the primary concern. In geospatial data, the 2-D shape of spatial functions and trajectories determine the properties of the system concerned. In such applications, Topological data analysis provide valuable features that act as input to machine learning models and the basis of analytics.<\/p>\n\n\n\n<p>Computational topology can be used to gain insights on machine learning itself. To understand the mysterious behaviour of neural networks, topology can be applied to the optimisation steps. This approach is currently being applied to gain deeper understanding of machine learning. <\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"computational-fairness-and-interpretability\"><span class=\"ez-toc-section\" id=\"Computational_Fairness_and_Interpretability\"><\/span>Computational Fairness and Interpretability. <span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>As complex computations, datascience and machine learning becomes common across many domains, we have to consider possible consequences and complexities. <\/p>\n\n\n\n<p>Complex computations and data driven decisions raise the question of fairness. Biases in the data may be cause the final decisions to be biased. This is a subtle issue, and biases are hard to catch, or even to define. What is fair from one perspective may be unfair from another. We study the topic of fairness in training ML models in conjunction with other issues like privacy and explainability\/interpretability. <\/p>\n\n\n\n<p>Complex models and datascience create another type of issue &#8212; explaining what is going one. Why did the AI decide to do what it did? Why did the self driving car turn at a certain point? Why did the classifier suggest the specific diagnosis? Interpretable machine learning is the topic of answering such questions &#8212; finding how features, model and data affect specific decisions and general behaviour of models. This requires close examination of models and their behaviours; combining technques from mathematics, economics and other areas. <\/p>\n\n\n<h3 class=\"wp-block-heading\" id=\"application-areas\"><span class=\"ez-toc-section\" id=\"Application_Areas\"><\/span>Application Areas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n<h4 class=\"wp-block-heading\" id=\"network-analysis-and-graph-machine-learning\"><span class=\"ez-toc-section\" id=\"Network_Analysis_and_Graph_machine_learning\"><\/span>Network Analysis and Graph machine learning.  <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n<p>Networks are ubiquitous from social networks to computer, transport and biological ones. We have developed algorithms specifically for networked data, including algorithms for embedding\/representation, classification and community detection. <\/p>\n\n\n\n<p>Our early work on hyperbolic embedding has led to a large body of work hyperbolic approaches for networks, knowledge graphs, and many other types of data. We have published many popular benchmark datasets, and award winning graph-ML libraries. <\/p>\n\n\n<h4 class=\"wp-block-heading\" id=\"biomedical-engineering\"><span class=\"ez-toc-section\" id=\"Biomedical_Engineering\"><\/span>Biomedical Engineering. <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n<p>We have applied network analysis and topological data analysis to detection go diabetic retinopathy and Azheimer&#8217;s disease. We have developed a realistic model of the human tongue surface, with analytical methods to measure its sensing and friction properties. Further works is in progress in these areas. <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"402\" src=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-3-1024x402.png\" alt=\"\" class=\"wp-image-175\" style=\"width:589px;height:auto\" srcset=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-3-1024x402.png 1024w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-3-300x118.png 300w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-3-768x302.png 768w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/image-3.png 1426w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">The brain: young, old, and under Alzheimer&#8217;s disease. <\/p>\n\n\n\n<p>Our work on 3D meshes of the human tongue has gained recognition in media all over the world. <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"732\" src=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-1024x732.png\" alt=\"\" class=\"wp-image-176\" style=\"width:484px;height:auto\" srcset=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-1024x732.png 1024w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-300x215.png 300w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-768x549.png 768w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-1536x1098.png 1536w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2023\/12\/filiform-PR-2048x1465.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center\">The beautiful 3D geometry of the human tongue surface<\/p>\n\n\n\n<p>See our most recent work on the features and <a href=\"https:\/\/angle-lab.com\/site\/2023\/12\/14\/the-distinct-and-unique-papillae-on-the-tongue-a-3d-study-with-ai-and-tda\/\" data-type=\"link\" data-id=\"https:\/\/angle-lab.com\/site\/2023\/12\/14\/the-distinct-and-unique-papillae-on-the-tongue-a-3d-study-with-ai-and-tda\/\">uniqueness of tongue papillae using ML and topological data analysis.<\/a><\/p>\n\n\n<h4 class=\"wp-block-heading\" id=\"iot-sensors-and-decentralised-computation\"><span class=\"ez-toc-section\" id=\"IoT_Sensors_and_decentralised_computation\"><\/span>IoT, Sensors and decentralised computation. <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n<p>We develop decentralised algorithms including decentralised model training algorithms. We have a line of well known works in the areas of information processing in IoT and sensor networks using deep mathematical concepts such as differential geometry and topology, Ricci flow and conformal geoemetry, hypoerbolic geometry and many others. <\/p>\n\n\n<h4 class=\"wp-block-heading\" id=\"chemistry-and-drug-design\"><span class=\"ez-toc-section\" id=\"Chemistry_and_Drug_design\"><\/span>Chemistry and Drug design. <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n<p>Machine learning and graph machine learning are being increasingly applied to predict chemical properties of molecules. We are combining ML with geometric ideas to predict drug interaction, reaction and other properties of molecules. <\/p>\n\n\n<h4 class=\"wp-block-heading\" id=\"mobility-trajectories-and-spatial-data\"><span class=\"ez-toc-section\" id=\"Mobility_trajectories_and_spatial_data\"><\/span>Mobility, trajectories and spatial data. <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n<p>We have developed several algorithms to process data from a 2-D space such as a map. We have developed Locality sensitive hashes for trajectories, topological sketches and differentially private query algorithms on maps. Typically these works combine geometric and topological ideas with datascience techniques. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Our research combines theory and applications in Data Science and trustworthy machine learning. We develop theoretical results &#8212; algorithms, theorems, proofs that define new ideas and concepts. We implement and test these on real datasets and and applications. Our theoretical work includes deep mathematical and computational concepts derived from geometry, topology, theoretical machine learning, algorithms [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-77","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/comments?post=77"}],"version-history":[{"count":17,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages\/77\/revisions"}],"predecessor-version":[{"id":189,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages\/77\/revisions\/189"}],"wp:attachment":[{"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/media?parent=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}