{"id":335,"date":"2026-01-23T21:54:07","date_gmt":"2026-01-23T21:54:07","guid":{"rendered":"https:\/\/www.jeffnathanson.com\/NateHart\/?page_id=335"},"modified":"2026-01-23T21:54:07","modified_gmt":"2026-01-23T21:54:07","slug":"measuring-lyapunov-exponents-of-c-elegans","status":"publish","type":"page","link":"https:\/\/www.jeffnathanson.com\/NateHart\/measuring-lyapunov-exponents-of-c-elegans\/","title":{"rendered":"Measuring Lyapunov Exponents of C. elegans"},"content":{"rendered":"\n<p>In September 2025, I joined the Vassar Applied Optics Laboratory (VAOL) where I worked under Professor Jenny Magnes studying the chaotic behavior of <em>C. elegans<\/em>. Our work is at the intersection of optics, nonlinear dynamics, and neuroscience.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><em><em>Caenorhabditis elegans<\/em><\/em> (Roundworm)<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"2560\" src=\"https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-scaled.jpeg\" alt=\"\" class=\"wp-image-337\" srcset=\"https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-scaled.jpeg 2560w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-300x300.jpeg 300w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-1024x1024.jpeg 1024w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-150x150.jpeg 150w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-768x768.jpeg 768w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-1536x1536.jpeg 1536w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-2048x2048.jpeg 2048w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/IMG_8368-2-edited-1568x1568.jpeg 1568w\" sizes=\"auto, (max-width: 2560px) 100vw, 2560px\" \/><figcaption class=\"wp-element-caption\">A picture of <em>C. elegans<\/em> I took under a microscope.<\/figcaption><\/figure>\n\n\n\n<p><em>C. elegans<\/em> are small nematodes only 1mm in length. They have only  302 neurons which have been fully mapped out, making them widely studied. Our lab is interested in their chaotic locomotion which we quantify via the Largest Lyapunov Exponent (LLE). In order to calculate the nematode&#8217;s LLE we collect optical data and use techniques from non-linear time-series analysis. Ultimately, we hope to quantify how chaotic their locomotion is for different ages and under different external conditions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Dynamic Optical Diffraction<\/h2>\n\n\n\n<p>In order to employ the techniques of dynamical systems that are traditionally used to find the LLE, we must first have a single time-series variable that encapsulates all the dynamics of the worm&#8230; a seemingly difficult task. Our lab accomplishes this via <strong>dynamic optical diffraction<\/strong>, a technique developed in our lab. By directing a Helium-Neon Laser at our sample worm, we observe a Fraunhofer diffraction pattern that changes as the worm undulates. We collect intensity data by placing a single photodiode in the diffraction pattern, away from the 0th order beam. This intensity signal acts as our time-series data.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In September 2025, I joined the Vassar Applied Optics Laboratory (VAOL) where I worked under Professor Jenny Magnes studying the chaotic behavior of C. elegans. Our work is at the intersection of optics, nonlinear dynamics, and neuroscience. Caenorhabditis elegans (Roundworm) C. elegans are small nematodes only 1mm in length. They have only 302 neurons which [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-335","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/comments?post=335"}],"version-history":[{"count":1,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/335\/revisions"}],"predecessor-version":[{"id":338,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/335\/revisions\/338"}],"wp:attachment":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/media?parent=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}