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      {
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        "content": "  “The pleasure of finding things out.” — Richard FeynmanWelcome.I’m an undergrad wandering (somewhat aimlessly) through a bunch of ideas in — physics, biology, algorithms — without staying long enough to unpack my bags. I like to occasionally dabble into anything else that looks like it might someday self-organize into meaning. This site is a my semi-structured attempt at documenting such trails.I have recently started working on my Master’s Thesis projects on investigating aspects of Hopfield Models of Neural Networks (and its variations) using Spin-glass models. I’ll update more on this in coming time.📝 Recent Blog Posts              Aug 11, 2025:      Perspective on 'Why Sex'?                May 24, 2025:      First Blog      📢 Latest Updates              Aug 01, 2025:       Attended ICTS Program on UHDB                May 24, 2025:       Launched New Website!      Check out the News Archive for all past updates!",
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        "content": "(Detailed CV)📄Education  BSMS in Physics (minor in Computer Science), NISER, 2026 (expected)  High School, Kendriya Vidyalaya, Mumbai Region, 2021Research experience  Summer 2025: Internship          TIFR, Mumbai      Deriving Statistics of Single-File Diffusion      Supervisor: Prof. Tridib Sadhu        Summer 2024: Internship          Simons @ NCBS, Bengaluru      Cell-fate decision modelling      Supervisor: Dr. Archishman Raju        Summer 2023: Internship          IISER, Trivandrum      Hamiltonian Neural Network      Supervisor: Dr. Chandrakala Meena      Skills  Python (scipy, numpy, pytorch)  LaTeX  Mathematica (beginner)",
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        "tags": null,
        "type": "page"
      },
    
  
  
  
  
  
  
  
  
      {
        "title": "",
        "url": "/news/",
        "content": "📢 News Archive              Aug 01, 2025:       Attended ICTS Program on UHDB                May 24, 2025:       Launched New Website!      ",
        "tags": null,
        "type": "news"
      },
    
  
  
  
  
  
  
  
  
  
  
  
  
      {
        "title": "Portfolio",
        "url": "/portfolio/",
        "content": "This page contains various things that are/were of interest apart from Academia.                          Portfolio item number 1                                    Published: September 28, 2025                Short description of portfolio item number 1                                        Portfolio item number 2                                    Published: September 28, 2025                Short description of portfolio item number 2               ",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": "Publications",
        "url": "/publications/",
        "content": "                                                                                                              Journal Articles                                            Paper Title Number 3                                    Published in Journal 1, 2015                 This paper is about the number 3. The number 4 is left for future work.                  Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3).Download Paper | Download Slides                                                    Paper Title Number 2                                    Published in Journal 1, 2010                 This paper is about the number 2. The number 3 is left for future work.                  Recommended citation: Your Name, You. (2010). "Paper Title Number 2." Journal 1. 1(2).Download Paper | Download Slides                                                    Paper Title Number 1                                    Published in Journal 1, 2009                 This paper is about the number 1. The number 2 is left for future work.                  Recommended citation: Your Name, You. (2009). "Paper Title Number 1." Journal 1. 1(1).Download Paper | Download Slides | Download Bibtex                                        Conference Papers                                            Paper Title Number 4                                    Published in GitHub Journal of Bugs, 2024                 This paper is about fixing template issue #693.                  Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).Download Paper                                                      ",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/search.json",
        "content": "[  {% assign all_docs = site.pages | concat: site.posts | concat: site.portfolio | concat: site.publications | concat: site.teaching | concat: site.news | concat: site.talks %}  {% assign filtered_docs = all_docs | where_exp: \"doc\", \"doc.url contains 'sitemap'\" | map: \"url\" %}  {% for doc in all_docs %}  {% assign exclude_titles = \"Posts by Collection,Posts by Tags,Terms and Privacy Policy,Page Archive,Academic Pages is a ready-to-fork GitHub Pages template for academic personal websites,Archive Layout with Content,Markdown,Home,Talk Map,Non-Menu Page,CV (JSON),Page Not Found,Page not in menu\" | split: \",\" %}  {% assign exclude_urls = \"sitemap,archive-layout-with-content,markdown,terms,privacy,academic-pages,page-archive,posts-by-collection,posts-by-tags,index,talkmap,non-menu-page,404,cv-json,/non-menu-page/,/cv-json/\" | split: \",\" %}  {% unless doc.url contains 'sitemap' or exclude_titles contains doc.title or exclude_urls contains doc.url %}      {        \"title\": {{ doc.title | jsonify }},        \"url\": {{ doc.url | relative_url | jsonify }},        \"content\": {{ doc.content | strip_html | strip_newlines | jsonify }},        \"tags\": {{ doc.tags | jsonify }},        \"type\": \"{{ doc.collection | default: 'page' }}\"      }{% if forloop.last == false %},{% endif %}    {% endunless %}  {% endfor %}]",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
  
  
  
  
  
  
  
  
      {
        "title": "Talk map",
        "url": "/talkmap.html",
        "content": "This map is generated from a Jupyter Notebook file in talkmap.ipynb, which mines the location fields in the .md files in _talks/.",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": "Talks and presentations",
        "url": "/talks/",
        "content": "{% if site.talkmap_link == true %}See a map of all the places I've given a talk!{% endif %}{% for post in site.talks reversed %}  {% include archive-single-talk.html %}{% endfor %}See a map of all the places I've given a talk!",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": "Teaching",
        "url": "/teaching/",
        "content": "{% include base_path %}{% for post in site.teaching reversed %}  {% include archive-single.html %}{% endfor %}",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
  
  
  
  
      {
        "title": "Blog posts",
        "url": "/year-archive/",
        "content": "{% include base_path %}{% capture written_year %}'None'{% endcapture %}{% for post in site.posts %}  {% capture year %}{{ post.date | date: '%Y' }}{% endcapture %}  {% if year != written_year %}    {{ year }}    {% capture written_year %}{{ year }}{% endcapture %}  {% endif %}  {% include archive-single.html %}{% endfor %}",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/assets/css/style.css",
        "content": "@import \"jekyll-theme-primer\";",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/about/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/about.html",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/about/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/about.html",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/resume-json",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/resume",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/md/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/markdown.html",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/nmp/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/nmp.html",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/wordpress/blog-posts/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/redirects.json",
        "content": "{\"/about/\":\"https://abhixphys.github.io/\",\"/about.html\":\"https://abhixphys.github.io/\",\"/resume-json\":\"https://abhixphys.github.io/cv-json/\",\"/resume\":\"https://abhixphys.github.io/cv/\",\"/md/\":\"https://abhixphys.github.io/markdown/\",\"/markdown.html\":\"https://abhixphys.github.io/markdown/\",\"/nmp/\":\"https://abhixphys.github.io/non-menu-page/\",\"/nmp.html\":\"https://abhixphys.github.io/non-menu-page/\",\"/wordpress/blog-posts/\":\"https://abhixphys.github.io/year-archive/\"}",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/_pages/",
        "content": "",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": "Jupyter notebook markdown generator",
        "url": "/markdown_generator/",
        "content": "# Jupyter notebook markdown generatorThese .ipynb files are Jupyter notebook files that convert a TSV containing structured data about talks (`talks.tsv`) or presentations (`presentations.tsv`) into individual markdown files that will be properly formatted for the academicpages template. The notebooks contain a lot of documentation about the process. The .py files are pure python that do the same things if they are executed in a terminal, they just don't have pretty documentation.",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": null,
        "url": "/feed.xml",
        "content": "{% if page.xsl %}{% endif %}Jekyll{{ site.time | date_to_xmlschema }}{{ page.url | absolute_url | xml_escape }}{% assign title = site.title | default: site.name %}{% if page.collection != \"posts\" %}{% assign collection = page.collection | capitalize %}{% assign title = title | append: \" | \" | append: collection %}{% endif %}{% if page.category %}{% assign category = page.category | capitalize %}{% assign title = title | append: \" | \" | append: category %}{% endif %}{% if title %}{{ title | smartify | xml_escape }}{% endif %}{% if site.description %}{{ site.description | xml_escape }}{% endif %}{% if site.author %}{{ site.author.name | default: site.author | xml_escape }}{% if site.author.email %}{{ site.author.email | xml_escape }}{% endif %}{% if site.author.uri %}{{ site.author.uri | xml_escape }}{% endif %}{% endif %}{% if page.tags %}{% assign posts = site.tags[page.tags] %}{% else %}{% assign posts = site[page.collection] %}{% endif %}{% if page.category %}{% assign posts = posts | where: \"categories\", page.category %}{% endif %}{% unless site.show_drafts %}{% assign posts = posts | where_exp: \"post\", \"post.draft != true\" %}{% endunless %}{% assign posts = posts | sort: \"date\" | reverse %}{% assign posts_limit = site.feed.posts_limit | default: 10 %}{% for post in posts limit: posts_limit %}{% assign post_title = post.title | smartify | strip_html | normalize_whitespace | xml_escape %}{{ post_title }}{{ post.date | date_to_xmlschema }}{{ post.last_modified_at | default: post.date | date_to_xmlschema }}{{ post.id | absolute_url | xml_escape }}{% assign excerpt_only = post.feed.excerpt_only | default: site.feed.excerpt_only %}{% unless excerpt_only %}{% endunless %}{% assign post_author = post.author | default: post.authors[0] | default: site.author %}{% assign post_author = site.data.authors[post_author] | default: post_author %}{% assign post_author_email = post_author.email | default: nil %}{% assign post_author_uri = post_author.uri | default: nil %}{% assign post_author_name = post_author.name | default: post_author %}{{ post_author_name | default: \"\" | xml_escape }}{% if post_author_email %}{{ post_author_email | xml_escape }}{% endif %}{% if post_author_uri %}{{ post_author_uri | xml_escape }}{% endif %}{% if post.category %}{% elsif post.categories %}{% for category in post.categories %}{% endfor %}{% endif %}{% for tag in post.tags %}{% endfor %}{% assign post_summary = post.description | default: post.excerpt %}{% if post_summary and post_summary != empty %}{% endif %}{% assign post_image = post.image.path | default: post.image %}{% if post_image %}{% unless post_image contains \"://\" %}{% assign post_image = post_image | absolute_url %}{% endunless %}{% endif %}{% endfor %}",
        "tags": null,
        "type": "posts"
      },
    
  
  
  
  
  
  
  
  
      {
        "title": null,
        "url": "/robots.txt",
        "content": "Sitemap: {{ \"sitemap.xml\" | absolute_url }}",
        "tags": null,
        "type": "page"
      },
    
  
  
  
  
      {
        "title": "Perspective on 'Why Sex'?",
        "url": "/posts/2025/blog-post-2/",
        "content": "Multiplicative Updates and Sexual ReproductionThis blog is primarily derived from Multiplicative Updates in Coordination Games and the Theory of Evolution (2012) (arXiv:1208.3160) authored by E. Chastain, A. Livnat, C. Papadimitriou & U. Vazirani. The paper takes a crack on the famous enigma in evolutionary biology.The longstanding puzzle of ‘Why sex?’ remains one of the widely debated upon questions in evolutionary biology. Sexual reproduction is everywhere in nature — yet, from a cost–benefit point of view, it looks almost irrational.Consider the drawbacks:  It’s complex, risky, and energy-hungry.  It breaks apart well-adapted gene combinations.  It halves/dilutes a parent’s genetic contribution to offspring.Classic explanations — like faster adaptation, removal of deleterious mutations, or Red Queen–style arms races — have been insightful, but none have perfectly nailed down why sex consistently wins out despite these costs.A Different Angle: MixabilityThe authors propose reframing the problem. Under sexual reproduction, natural selection doesn’t chase the single “fittest” combination of alleles. Instead, it rewards alleles that play well with others.  Mixability of an Allele: An allele’s ability to work reasonably well with a wide range of genetic partners.From this angle, what used to be called sex’s biggest flaw — constantly breaking apart “lucky” genetic combinations — becomes its central feature. The shuffling keeps the focus on robustness and flexibility, not on a brittle, perfect match.The central result is proved in the weak selection regime, where fitness differences are small (think fitness values in \\([1-s,\\, 1+s]\\) with small \\(s\\)).Key points:      Quick drift to the Wright manifoldThe system rapidly settles into a state with no linkage disequilibrium — meaning genes behave as if inherited independently. Genotype distributions can then be     written as products of allele frequencies, which simplifies the analysis.        Evolution ≡ Multiplicative UpdatesIn weak selection, the population genetics dynamics are exactly the same as the multiplicative update rule from online learning (classes of learning algorithm that Netflix might be using  for optimizing the recommendations) and game theory.          Genes are the players.      Alleles are strategies.      Allele frequencies are strategy probabilities.      The payoff is mixability.        The paper is very emphatic:          “We are not saying the equilibrium can be found through multiplicative updates — we are saying something stronger: Evolution is multiplicative updates.”            Robust convergenceThis process converges to an equilibrium and remains stable even under small random perturbations to fitness values.  The Diversity QuestionBut simply convergence to equilibrium is not good enough for a population. One of the most appealing outcomes of this framework is that it ensures that diversity can persist at equilibrium (opposed to the case where a population of a bacterium would become uniform eventually).It’s not obvious — multiplicative updates often converge to narrow supports in other contexts — so the authors go further:  They show that for two genes, there are exponentially many equilibria where the support (the set of alleles with nonzero frequency) contains a significant fraction of the alleles for each gene.  This “exponential support” result means the loss of diversity is not inevitable — the dynamics can sustain large, mixed populations.The proof uses a neat trick:  Represent the differential fitness between allele combinations as a random matrix.  Show (via a potential function argument) that, with high probability, the inverse of this matrix has non-negative row and column sums.  This property guarantees the existence of large-support equilibria.The potential function argument is simple but clever: Flip the sign of any row or column whose sum is negative, track a global measure or potential (here the sum of all the elements of the matrix), and observe that it always increases. Eventually, one end up in a state where all row/column sums are non-negative.Limitations & Open QuestionsThe framework is elegant but comes with boundaries:      The proof relies on small fitness differences (weak-selection). It’s unclear which other fitness landscapes would yield the same multiplicative-update dynamics.        The results assume that linkage disequilibrium disappears quickly (Wright manifold assumption). A characterization of landscapes that stay on or return to this manifold still remains open.        Once an allele is lost, it’s gone (unless mutation reintroduces it). Real evolution, of course, never stabilizes — mutations are a slow but constant background force.        The equilibrium reached may not be a Nash equilibrium of the full game, but of a smaller ‘subgame’ containing only the alleles that survived.        The formal diversity result is proved for the two-gene case. Extending it to three or more genes is mathematically tough beacuse it would involve tensors of higher order, though simulations hint that large-support equilibria still exist.  A Computational Detour: The PLS QuestionHere’s where things get unexpectedly fun for anyone who likes computational complexity theory. The row/column-flipping step above isn’t just a neat trick — it’s also a search problem in disguise:  Given a nonsingular square matrix, can one flip rows and columns so that its inverse has non-negative row and column sums?The authors point out that this problem lives in the complexity class PLS — Polynomial Local Search. PLS problems have three key traits:  A solution always exists.  One can check the quality of a solution efficiently (in polynomial time).  One can move to a better solution by a small local change.The authors ask:  Is this matrix-flipping problem PLS-complete?  PLS-complete problems are the ‘hardest’ in PLS. If one can solve a single such problem efficiently, one solve all of them.  But if this matrix problem were PLS-complete, it would mean the computational challenge of predicting diversity-maintaining equilibria is as hard as any local search problem we know.In other words: If this is PLS-complete, the challenge of predicting/determining evolution’s equilibrium won’t be just due to messy biology and bad data— it’d be a fundamentally (or more aptly computationally) hard..Closing ThoughtsThis work reframes sexual mode of reproduction as a coordination game between genes, where multiplicative updates naturally push the system toward alleles with strong mixability. It’s a clean, learning-theoretic way to capture the why of sex — at least in the weak selection regime — and it opens the window into other questions.Me and my friend Pritipriya redid the calculations of the paper as a part of project in our ‘Theoretical ML’ coursework. The blog was one of the attempts at commentary on the article. For technical details on calculations/proof one can take a look at the preliminary project report we wrote.",
        "tags": ["evolution","theo bio","theo cs"],
        "type": "posts"
      },
    
  
  
  
  
      {
        "title": "First Blog",
        "url": "/posts/2025/blog-post-1/",
        "content": "This is to try out blog features in jekyll.Headings are coolYou can have many headingsAren’t headings cool?",
        "tags": ["cool posts","category1","category2"],
        "type": "posts"
      },
    
  
  
  
  
      {
        "title": "Portfolio item number 1",
        "url": "/portfolio/portfolio-1/",
        "content": "This is an item in your portfolio. It can be have images or nice text. If you name the file .md, it will be parsed as markdown. If you name the file .html, it will be parsed as HTML.",
        "tags": [],
        "type": "portfolio"
      },
    
  
  
  
  
      {
        "title": "Portfolio item number 2",
        "url": "/portfolio/portfolio-2/",
        "content": "This is an item in your portfolio. It can be have images or nice text. If you name the file .md, it will be parsed as markdown. If you name the file .html, it will be parsed as HTML. ",
        "tags": [],
        "type": "portfolio"
      },
    
  
  
  
  
      {
        "title": "Paper Title Number 1",
        "url": "/publication/2009-10-01-paper-title-number-1",
        "content": "The contents above will be part of a list of publications, if the user clicks the link for the publication than the contents of section will be rendered as a full page, allowing you to provide more information about the paper for the reader. When publications are displayed as a single page, the contents of the above “citation” field will automatically be included below this section in a smaller font.",
        "tags": [],
        "type": "publications"
      },
    
  
  
  
  
      {
        "title": "Paper Title Number 2",
        "url": "/publication/2010-10-01-paper-title-number-2",
        "content": "The contents above will be part of a list of publications, if the user clicks the link for the publication than the contents of section will be rendered as a full page, allowing you to provide more information about the paper for the reader. When publications are displayed as a single page, the contents of the above “citation” field will automatically be included below this section in a smaller font.",
        "tags": [],
        "type": "publications"
      },
    
  
  
  
  
      {
        "title": "Paper Title Number 3",
        "url": "/publication/2015-10-01-paper-title-number-3",
        "content": "The contents above will be part of a list of publications, if the user clicks the link for the publication than the contents of section will be rendered as a full page, allowing you to provide more information about the paper for the reader. When publications are displayed as a single page, the contents of the above “citation” field will automatically be included below this section in a smaller font.",
        "tags": [],
        "type": "publications"
      },
    
  
  
  
  
      {
        "title": "Paper Title Number 4",
        "url": "/publication/2024-02-17-paper-title-number-4",
        "content": "The contents above will be part of a list of publications, if the user clicks the link for the publication than the contents of section will be rendered as a full page, allowing you to provide more information about the paper for the reader. When publications are displayed as a single page, the contents of the above “citation” field will automatically be included below this section in a smaller font.",
        "tags": [],
        "type": "publications"
      },
    
  
  
  
  
      {
        "title": "Teaching experience 1",
        "url": "/teaching/2014-spring-teaching-1",
        "content": "This is a description of a teaching experience. You can use markdown like any other post.Heading 1Heading 2Heading 3",
        "tags": [],
        "type": "teaching"
      },
    
  
  
  
  
      {
        "title": "Teaching experience 2",
        "url": "/teaching/2015-spring-teaching-1",
        "content": "This is a description of a teaching experience. You can use markdown like any other post.Heading 1Heading 2Heading 3",
        "tags": [],
        "type": "teaching"
      },
    
  
  
  
  
      {
        "title": "Launched New Website!",
        "url": "/news/2025/05",
        "content": "Excited to share my new personal website built with Jekyll and Minimal Mistakes!",
        "tags": [],
        "type": "news"
      },
    
  
  
  
  
      {
        "title": "Attended ICTS Program on UHDB",
        "url": "/news/2025/08",
        "content": "Excited to share that I had recently been to ICTS Bengaluru to attend program on Unifying Theories in High-Dimensional Biology (UHDB). I met many really brilliant and interesting people there. I am thankful to all the organizers for setting up this wonderful program.A short blog will shortly follow.Gallery",
        "tags": [],
        "type": "news"
      },
    
  
  
  
  
      {
        "title": "Tutorial 1 on Relevant Topic in Your Field",
        "url": "/talks/2013-03-01-tutorial-1",
        "content": "More information hereThis is a description of your tutorial, note the different field in type. This is a markdown files that can be all markdown-ified like any other post. Yay markdown!",
        "tags": [],
        "type": "talks"
      },
    
  
  
  
  
      {
        "title": "Talk 2 on Relevant Topic in Your Field",
        "url": "/talks/2014-02-01-talk-2",
        "content": "More information hereThis is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!",
        "tags": [],
        "type": "talks"
      },
    
  
  
  
  
      {
        "title": "Conference Proceeding talk 3 on Relevant Topic in Your Field",
        "url": "/talks/2014-03-01-talk-3",
        "content": "This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.",
        "tags": [],
        "type": "talks"
      },
    
  
  
  
  
      {
        "title": "ML4PHY: Physics-Informed Machine Learning",
        "url": "/talks/2024-01-15-talk-1",
        "content": "The talk was aimed at introducing audience to a class of neural network achitecture called PINN. The talk can mainly be divided into three parts. First and foremost, introduction to ML including definition of some standard terms. An idea of bias-variance trade-off was also provided. This takes us to next part of talk, what are PINN exactly, and how does it hep reduce variance (or generalization error). The talk concludes with showing application of this architecture and its close relatives- Hamiltonian Neural Network & Lagrangian Neural Network to show how these techniques can be leveraged to learn dynamics of system from data itself.Note that this talk was mostly chalk-board, while PPT was only used to demonstrate the last part.",
        "tags": [],
        "type": "talks"
      }
    
  
]