{"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":"2026-10-25T11:44:29","modified_gmt":"2026-10-25T11:44:29","slug":"research","status":"publish","type":"page","link":"https:\/\/angle-lab.com\/site\/","title":{"rendered":"Research Areas"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Our research is on the geometry of data and machine learning models. We develop theory, algorithms and measures that help to create private, secure and accurate learning systems. In 2026 &#8211; 27 we are looking at the following topics.<\/p>\n\n\n<div role=\"navigation\" aria-label=\"Table of Contents\" class=\"simpletoc wp-block-simpletoc-toc\"><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_89 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\/#Generative_AI\" >Generative AI<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/angle-lab.com\/site\/#Study_of_internal_operation_of_generative_models\" >Study of internal operation of generative models<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/angle-lab.com\/site\/#Repeated_application_of_generative_models\" >Repeated application of generative models<\/a><\/li><\/ul><\/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\/#Geometry_Statistics_and_Theory_of_Neural_networks\" >Geometry, Statistics and Theory of Neural networks<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/angle-lab.com\/site\/#Neural_training_dynamics_and_stochastic_gradient_descent\" >Neural training dynamics and stochastic gradient descent<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/angle-lab.com\/site\/#Statistics_geometry_and_distances\" >Statistics geometry and distances<\/a><\/li><\/ul><\/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\/#Private_and_Secure_Machine_Learning_%E2%80%94_differential_privacy_cryptography_and_blockchains\" >Private and Secure Machine Learning &#8212; differential privacy, cryptography, and blockchains<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/angle-lab.com\/site\/#Biomedical_Engineering\" >Biomedical Engineering<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/angle-lab.com\/site\/#Protein_and_Drug_design_%E2%80%94_shapes_of_molecules\" >Protein and Drug design &#8212; shapes of molecules<\/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\/#Geometry_and_Topology_in_the_Human_body\" >Geometry and Topology in the Human body<\/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=\"#generative-ai\">Generative AI<\/a>\n\n<ul>\n<li><a href=\"#study-of-internal-operation-of-generative-models\">Study of internal operation of generative models<\/a>\n<\/li>\n<li><a href=\"#repeated-application-of-generative-models\">Repeated application of generative models<\/a>\n<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#geometry-statistics-and-theory-of-neural-networks\">Geometry, Statistics and Theory of Neural networks<\/a>\n\n<ul>\n<li><a href=\"#neural-training-dynamics-and-stochastic-gradient-descent\">Neural training dynamics and stochastic gradient descent<\/a>\n<\/li>\n<li><a href=\"#statistics-geometry-and-distances\">Statistics geometry and distances<\/a>\n<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#private-and-secure-machine-learning-differential-privacy-cryptography-and-blockchains\">Private and Secure Machine Learning &#8212; differential privacy, cryptography, and blockchains<\/a>\n<\/li>\n<li><a href=\"#biomedical-engineering\">Biomedical Engineering<\/a>\n\n<ul>\n<li><a href=\"#protein-and-drug-design-shapes-of-molecules\">Protein and Drug design &#8212; shapes of molecules<\/a>\n<\/li>\n<li><a href=\"#geometry-and-topology-in-the-human-body\">Geometry and Topology in the Human body<\/a>\n<\/li>\n<\/ul>\n<\/li><\/ul><\/div>\n\n\n<h3 id=\"generative-ai\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Generative_AI\"><\/span>Generative AI<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Generative models can now produce realistic text and images. But their internal mechanisms and imapacts are not well understood. We would like to understand why and when they work well, and when they do not. We also want to know what happens at the usage end of generative models. <\/p>\n\n\n\n<h4 id=\"study-of-internal-operation-of-generative-models\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Study_of_internal_operation_of_generative_models\"><\/span>Study of internal operation of generative models <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">When a model generates a new image step by step, we can study and compare these steps to try and understand their behaviour. We use this technique in our work on <em>Provenance of Fine Tuned Diffusion Models<\/em>. Fine tuning is a class of specialised techniques to modify a large model to work on a particular domain. For example, diffusion models for creating images can be modified to produce a particular type or style of images using these techniques. In the paper, we develop techniques to determine if images are generated from a particular model or its adaptations. <\/p>\n\n\n\n<h4 id=\"repeated-application-of-generative-models\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Repeated_application_of_generative_models\"><\/span>Repeated application of generative models<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The exciting current developments in AI are from generative model created with data found on the Internet. Now artifical data from these models is everywhere. What happens when next generation of generative models are trained in part on artificial data? <a href=\"https:\/\/www.scientificamerican.com\/article\/ai-generated-data-can-poison-future-ai-models\/\">See my interview at Scientific American for a discussion<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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-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 class=\"wp-block-paragraph\"><\/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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 id=\"geometry-statistics-and-theory-of-neural-networks\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Geometry_Statistics_and_Theory_of_Neural_networks\"><\/span>Geometry, Statistics and Theory of Neural networks<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">An x-ray look at neural network to understand their training and behaviour requires understanding their embeddings and operating geometry. <\/p>\n\n\n\n<h4 id=\"neural-training-dynamics-and-stochastic-gradient-descent\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Neural_training_dynamics_and_stochastic_gradient_descent\"><\/span>Neural training dynamics and stochastic gradient descent<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">While neural networks are the everywhere and the main basis of machine learning today, their internal operation and training process remain mysterious and poorly understood. Overparameterised neural networks generalise surprisingly well, which is not yet understood in terms of statistical theory.  On the other hand, after excess training, they can also memorise much of the data. Using a quantity called magnitude potential we can predict and analyse much of these changes during the training of a neural network. <\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"198\" src=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-1024x198.png\" alt=\"\" class=\"wp-image-219\" style=\"aspect-ratio:5.171803941384538;width:737px;height:auto\" srcset=\"https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-1024x198.png 1024w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-300x58.png 300w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-764x148.png 764w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-2048x397.png 2048w, https:\/\/angle-lab.com\/site\/wp-content\/uploads\/2026\/10\/image-1536x298.png 1536w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In this picture we see how Magnitude potential and Magnitude potential ratio separates red and blue points in their original embedding and in the logit layer of a classifier. You can find more in the paper <a href=\"https:\/\/arxiv.org\/abs\/2610.01633\">Generalization in Neural Networks Through the Lens of Magnitude Potential appearing at NeurIPS 2026<\/a>.<\/p>\n\n\n\n<h4 id=\"statistics-geometry-and-distances\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Statistics_geometry_and_distances\"><\/span>Statistics geometry and distances <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Developing our understanding of machine learning depends on finding new ides in statistics, geometry and algorithms. We regularly work on finding new algorithms and measures. We recently created <em>magnitude distance <\/em>as a way ot measure the distance between two datasets. In the paper <em><a href=\"https:\/\/icml.cc\/virtual\/2026\/poster\/65802\">Magnitude Distance: A Geometric Measure of Dataset Similarity (ICML 2026)<\/a><\/em> we use define distance and use as a loss function in flow models for image generation. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 id=\"private-and-secure-machine-learning-differential-privacy-cryptography-and-blockchains\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Private_and_Secure_Machine_Learning_%E2%80%94_differential_privacy_cryptography_and_blockchains\"><\/span>Private and Secure Machine Learning &#8212; differential privacy, cryptography, and blockchains<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">In a recent paper called <a href=\"https:\/\/arxiv.org\/abs\/2510.18109\">PrivaDE: Privacy-preserving Data Evaluation for Blockchain-based Data Marketplaces<\/a> we describe how data can be evaluated and shared securely, that is, someone buying data to update their models can first evaluate the quality of the data before paying or using it. This data valuation works using cryptographic techniques called Zero Knowledge Proofs, that ensure that the requirements are met, without leaking information about the data. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When it comes using large generative models, only big organisations alone have the resources to run large number of queries. But if we can pool our resources to share the workload, we can run many queries and make good use of generative models without requiring to pay for proprietary systems. We described a new blockchain system called <em>Proof of machine learning<\/em> where everyone can participate and instead of using wasteful hash mining in proof of work, the miner contribute by running generative AI queries. Thus they not only contribute to running the blockchain, in the process they also compute AI queries. You can find more in the paper <a href=\"https:\/\/arxiv.org\/abs\/2610.26713\">Proof-of-Machine-Learning-Inference: Mining Knowledge, Not Hashes<\/a>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 id=\"biomedical-engineering\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Biomedical_Engineering\"><\/span>Biomedical Engineering<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 id=\"protein-and-drug-design-shapes-of-molecules\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Protein_and_Drug_design_%E2%80%94_shapes_of_molecules\"><\/span>Protein and Drug design &#8212; shapes of molecules<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">AI applied to molecules is one of the most important areas of machine learning today. The 2024 Nobel prize in Chemistry went to the creators of Alphafold for contributing to the long standing open problem of predicting the folded shape of proteins. Major challenges these areas are about predicting the shapes of proteins and other molecules (e.g. drugs) and how they will interact. Various kinds of models exist to predict properties of proteins and other molecules, including language models and embedding models. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We analysed a large set of plant proteins and found a set that can be used as surfactants. Surfactants are chemicals widely used in industry to create emulsions, but are usually manufactured synthetically. Instead, plant protein based emulsifiers are natural and environment friendly. Read more in our paper about <a href=\"https:\/\/www.nature.com\/articles\/s42004-026-02173-6\">plant protein surfactants at Nature&#8217;s Communication Chemistry<\/a>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We are additionally starting to investigate various questions around drug design, protein design alphafold and other folding models, chirality and diffusion models. <\/p>\n\n\n\n<h4 id=\"geometry-and-topology-in-the-human-body\" class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Geometry_and_Topology_in_the_Human_body\"><\/span>Geometry and Topology in the Human body <span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Shape at a larger scale scale is also critical in understanding the human body, various conditions and developing remedies. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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 wp-block-paragraph\"><a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-030-87444-5_12\">The brain: young, old, and under Alzheimer&#8217;s disease<\/a>. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Our work on <a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC7645869\/\">3D meshes of the human tongue<\/a> 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 wp-block-paragraph\">The beautiful 3D geometry of the human tongue surface<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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","protected":false},"excerpt":{"rendered":"<p>Our research is on the geometry of data and machine learning models. We develop theory, algorithms and measures that help to create private, secure and accurate learning systems. In 2026 &#8211; 27 we are looking at the following topics. Generative AI Generative models can now produce realistic text and images. But their internal mechanisms and [&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":21,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages\/77\/revisions"}],"predecessor-version":[{"id":226,"href":"https:\/\/angle-lab.com\/site\/wp-json\/wp\/v2\/pages\/77\/revisions\/226"}],"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}]}}