About — Rin Ray

ABOUT ME

My name is Rin Ray (they/them), and I’m a researcher-artist. My current math research is on arithmetic patterns in homotopy theory and physics.

Rin Ray
CV MATH CV SCIENCE PORTFOLIO
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Before the math and alongside: measurement and inference where the observable is missing, degraded, or not addressed to the observer — in biology, neural signals, robotics and physics.

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Here for… the science ↓ the math ↓ the art ↓

I build instruments for overhearing. Across mathematics, scientific computing, biological systems, robotics, and art, I am interested in things that cannot be observed directly: a neural intention, an animal’s affective state, a body’s internal signal, a physical parameter, a mathematical structure.

I look for the traces they leave behind, and build ways to make those traces legible.

THE PATH

I am currently a postdoc at Uni-Münster in the Arithmetic and Homotopy Theory Working Group led by Thomas Nikolaus and Christopher Deninger.

Interview — How an Inventor becomes a Mathematician

A blackboard of zeta function computations

Before that, I graduated from George Mason University at 16 with a B.S. in Computational Physics, and accepted the Thiel Fellowship in 2014 to develop medical technology and study mathematics under my mentor, Edward Frenkel.

I came to mathematics from the laboratory, and never really left: computational physics, robotics, machine learning on biological signals, and medical devices since 2011. That work is in The Lab, below.

Interview — WIRED, on Medical Tech

I graduated with my Master’s degree from UChicago working with Peter May and Kazuya Kato (加藤 和也), and with my PhD from Northwestern working with Paul Goerss. Yifeng Liu advised me too, without the title.

Here for the math? Skip to the research ↓

THE LAB

are you… No background assumed, one line per project. What I built, why I cared, and where the field has gone since. No story: what was done, how, and what limited it — grouped by method.

I build things, and I believe almost anything will answer you if you are willing to learn how it speaks. What I have spent my time building, mostly, is instruments for overhearing. A blinded robot, feeling for its own hand. Rats, telling each other how they are feeling. A cat, feeling for his colon. A brain, through the scar it grows around anything that listens. Half a page of Braille, about the missing half. Arithmetic, about superconductors nobody had made yet. A drone and a wheelchair, microwaved argon and a plate of food, a face, septic blood — and others. There are always others.

Most of this came before the mathematics found me — or before I found it. Two threads have remained in my hands: a cluster of diseases that keep showing up together and keep being treated apart, and a treatment that works and was never written down.

I build things, and I believe almost anything will answer you if you are willing to learn how it speaks. For over a decade I have studied the three kinds of silence: what is absent, what is fading, and what is spoken in another room. Three threads remain in my hands: a cluster of diseases that keep being treated apart, a treatment that was never written down, and a cheap drug for pain that nobody will test.

A decade of work on measurement and inference where the observable is missing, degraded, or not addressed to the observer: motor intention from a thinning population of cortical units, affective state from ultrasonic vocalization, proprioception without vision, lexical structure from partial parallelism, superconducting transition temperature from electronic structure.

Living things

Hidden states, read from the traces a system emits.

Sensory Sensitivity as a Unifying Mechanism2024 – ongoingcurrent

Sensory processing as an organizing principle · gut microbiome · autoimmunity · chronic pain · glutamate excitability · joint with Luca Estinto

An essay arguing that a cluster of conditions usually treated separately come from one mechanism.

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The people I interviewed about wheelchairs kept telling me about pain, and pain was the thing nobody had an answer for. Years later the same shape kept appearing: autoimmune conditions, gut trouble, chronic pain, sensory sensitivity, and certain neuropsychiatric diagnoses turning up together in the same people and being treated by five different specialists who never speak to each other.

A long essay written with Luca Estinto, treating these as a diseasome — a set of conditions linked not by the organ they present in but by the pathway underneath them — and arguing that sensory processing is a good deal of what that pathway is. A nervous system which never habituates, and keeps reporting a signal at full strength, produces consequences that cascade through the immune and digestive systems by way of stress. The piece pulls together imaging work on altered connectivity, the habituation literature, glutamate as a shared route to overexcitability, microbiome composition differences, and the enteric nervous system’s direct hand in immunoglobulin secretion.

Restarting the nerves that move a colon2026current

Feline idiopathic megacolon · enteric motility and cholinergic transmission · neostigmine · owner documentation of an unpublished treatment

A cat with a paralysed colon, and the treatment we found that is not in the literature.

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A cat of mine was dying because his colon was paralysed, and the two options put in front of me were surgery and euthanasia. He was too heavy and too unwell to survive the anesthetic, so in practice that was one option. There is a third, and it is not in the literature: it circulates as folklore between practitioners, never reaches a journal, and so whether it is offered to your animal depends almost entirely on who you happen to be standing in front of that day.

An owner-reported case study, written up in enough detail to take to a vet and ask. Recurrent idiopathic megacolon: the colon dilates and the nerves that should drive it stop producing any useful push. Enemas, manual deobstipation, laxatives and dietary modification all failed to prevent recurrence. The regime that held was neostigmine, an acetylcholinesterase inhibitor borrowed from equine practice, injected when palpation finds accumulation — it leaves acetylcholine in the junction longer, so the cholinergic signal telling the muscle to contract actually lands. Alongside it: daily lactulose to keep the stool soft, and an anti-NGF injection every six weeks for spinal spondylosis.

Sequencing matters more than the drug. Neostigmine is given only after the colon has been emptied under anesthetic and mechanical obstruction has been definitively excluded, because a drug that makes a bowel contract harder is dangerous if that bowel is genuinely blocked. Duration to treatment is the other variable: medical management succeeds in about two thirds of cats presenting under six months of symptoms, and in under six percent of those presenting later. Maintenance is injections every few weeks, indefinitely.

The six-cent drug nobody will test2026current

Memantine · NMDA receptor antagonism · central sensitization · opioid tolerance and hyperalgesia · drug repurposing · trial design

A cheap dementia drug that might treat chronic pain, and why nobody has paid to find out.

read the post

People who use mobility aids told me they were choosing every day between being stoned past the point of finishing a sentence and being lucid and in agony. I wanted to know whether anything avoids that choice.

An argument with references, written to be taken to a doctor or a funder. Memantine blocks the same channel as ketamine, gently enough to take daily for years, at six cents a tablet. The trial evidence is thin and mixed: it fails in old nerve injury and shows promise where pain is central and ongoing. The post lays out the mechanism, every trial including the negative ones, the commercial history that ended the research, and the trial that would settle it.

Learning the ultrasonic language of ratslate 2013 – mid 2014

Computational bioacoustics · unsupervised clustering of rodent ultrasonic vocalizations · quasi-real-time monitoring in the animal’s own cage · preclinical safety pharmacology · affective-state readout · 3Rs refinement

I taught a computer to sort what rats and mice say to each other, which became a way to test drugs before they reach people, and to bother the animals a good deal less while doing it.

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A mouse cannot report a symptom, but it is talking constantly in a register we cannot hear. Two things follow from listening properly. You get some understanding of what these animals are actually saying to each other. And you get far more out of each experiment while doing far less to the animals in it: a microphone over a cage takes readings continuously, at night, in the dark, from an animal nobody has touched, picked up, restrained or moved to a testing room — which is both a kinder life and a cleaner measurement, since a frightened mouse is not the animal you meant to study. More information out of every cohort, less disturbance per animal, and a clearer picture of what a compound does before it goes anywhere near a person.

Computational bioacoustics at Vium — unsupervised classification of ultrasonic vocalizations in quasi-real time, which is also how I dipped my toes into audio processing. This was early: several years before MUPET and DeepSqueak made unsupervised clustering the standard way to do this, and as far as I know the first to run it in quasi-real time on cages being monitored continuously rather than on a corpus after the fact. Letting the categories fall out of the recordings instead of deciding in advance what to listen for is the only way to hear a call nobody has named yet. The calls turned out to carry the animals’ libido and their stress, so I could discover and then implement a way of reading those off the audio directly. It was deployed in Vium’s preclinical studies, where it could tell you whether a compound shifts libido or stress before the drug ever reaches a human trial. Two write-ups came out of it, A New Female–Female Mouse Vocalization Discovered via Unlabeled Machine Learning and On the Detection and Prevention of Aggression in Lab Mice via Quasi-Real Time Analysis.

A multi-company validation in 2025 put three compounds that had passed conventional safety pharmacology under continuous non-invasive monitoring in their own cages and found signals anyway, some persisting for days after dosing. Quietly watching animals who are left alone turns out to see things that handling them on a schedule does not.

The signal under the scarSummer 2014

Intracortical brain–computer interfaces · decoder convergence analysis · foreign body response and chronic signal loss · optical recording

Work on reading the intention to move out of a brain, from the software side and then the hardware side.

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Neuroprosthetics have two major issues. At the tissue end, putting an electrode into a brain is an injury: microglia arrive, astrocytes proliferate, and a glial scar closes around it, pushing the neurons you wanted away from the thing that is listening — so the signal thins and gets noisier across the months in which a person is coming to depend on it. At the other end, any single neuron tells you almost nothing; the intention to move is legible only across a whole population of them. I came at this from the software side and assumed both were software problems. My first thought was that a decoder which recalibrated fast enough could just track the signal as it drifted — that convergence was the thing to fix. I worked on that for a while before accepting you cannot infer your way out of an electrode with fewer and fewer neurons left to hear.

The software half was convergence analysis of the decoders then in common use: how fast a Kalman-style filter settles onto a usable mapping from neural activity to intended movement, how far that mapping degrades as the underlying signal drifts, and how much of the loss you can claw back by letting the decoder keep adapting while somebody is using it. The number that matters to a user is not peak accuracy on a good day. It is how long recalibration takes every morning, and whether the thing is still working by the afternoon.

The hardware half was optical recording: instead of pushing metal into cortex and waiting for the scar, you get the neurons to express a fluorescent indicator that brightens when they fire, and read them with light. It buys cell-type specificity and thousands of cells at once. It costs you depth — a millimeter or so even with two-photon, in an organ several centimeters thick — and temporal resolution, because calcium rises and falls far more slowly than a spike does, and it requires getting a gene into somebody, which is a much larger request than a connector.

Most of the answer has been materials. The stiffness mismatch is absurd — silicon around 180 GPa against a brain of a few kPa — so the field went soft: ultraflexible polymer threads, mesh electronics injected through a syringe, carbon fibers seven microns across, substrates stiff enough to go in and then soften once wet. In mice it works beautifully. One open-mesh design tracked the same neurons for thirteen months, most of the animals’ adult lives. Coatings do the rest: PEDOT to drop impedance, neural adhesion proteins, dexamethasone eluted to quiet the response. Then the uncomfortable part. Across fourteen BrainGate participants and up to seven and a half years, the arrays held spiking on about a third of their electrodes and declined only about seven percent — and when arrays are taken out and examined, the leading failure is the silicon eroding and the metal coming away, not the tissue closing in. Softer probes may be the right fix for the wrong failure. “Scar-free” was a mouse result in 2017 and has been quoted a long way past its evidence. Meanwhile the thing these arrays turned out to decode best was not a limb but speech, which in 2014 I would not have guessed at all.

A laboratory on a keyring2011 – 2014

Point-of-consumption allergen detection · laser absorption spectroscopy · G12 antibody colorimetric assay · immunoassay cost and sampling limits

A keyring-sized scanner meant to tell you whether the food in front of you would hurt you.

read the post

For someone with celiac disease or a severe food allergy, every meal they did not cook themselves is an act of trust in a stranger, and the cost of that trust being misplaced runs from a ruined week to a funeral. The idea was to hand the judgment back to the person eating, in something small enough to live on a keyring.

I tried it twice. The first attempt was optical: a one-dimensional array of infrared and visible lasers with an avalanche photodiode, looking for gluten’s absorption signature, which would have read food about a centimeter deep without touching it. It drowned in noise. Gluten’s signal is faint against everything else going on in a protein-rich food, and protein-rich food is exactly where you need to look.

So I switched from physics to chemistry: G12 antibodies, which bind gliadin, read out by a colorimetric assay — a toothpick you poke into the food, or a strip that works like litmus paper. G12 is less sensitive than A1 and much cheaper, and cheap is what matters when the thing has to work at every meal. That is where it stopped, and the wall was the antibodies: short of bulk synthesis, a per-meal consumable costs more than the people who need it can spend.

In March 2014 I found GlutenTox, TellSpec and 6SensorLabs already at it — the good kind of disappointment. 6SensorLabs became Nima, which shipped in 2017, missed gluten at the legal threshold more than a fifth of the time, died in 2020, and came back in 2026 claiming 10 ppm, by its own measurement. My wall got routed around rather than climbed: the expensive part was the antibody, and the field swapped it for aptamers, synthetic DNA that folds around a target for a fraction of the cost. One 2024 design reads gliadin off gold nanoparticles with a phone camera. The part underneath is still unsolved: a negative on one bite does not clear the plate, and sampling error swamps measurement error.

Polyglass — reading a pulse off a face, and why I would not build it nowHackMIT 2013

Remote photoplethysmography from video · contactless physiological sensing on a head-mounted display · consent and surveillance ethics

A Google Glass app that read your pulse off your face without touching you. I would not build it now.

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The idea was to help autistic people read social communication: if the signals everyone else is supposedly picking up on are real, a machine ought to be able to surface them.

A Google Glass app that recovers a person’s pulse from the video feed alone, no contact and no cuff, and reads the changes in it while they talk. Joint with Kartik Talwar and Spencer Hewett.

I would not build this now. It takes a reading off someone’s body without their knowledge and gives them no way to refuse — the person being measured is the one person in the room with no say in it. The need was real; meeting it this way moves the cost onto somebody who never agreed to carry it.

Bodies in motion

A body reading the traces of its own movement.

Fixing what is wrong with wheelchairs2013 – 2015

Modular retrofit robotics for powered wheelchairs · automated pressure redistribution · powered seat elevation · assisted transfer · rough-terrain drive · user-led requirements · gaze-controlled assistive mobility · mentorship

I asked wheelchair users what they actually wanted, and built four attachments that bolt onto the chair they already own.

The wheelchair postInterview — WIRED

My grandfather lost his mobility, so I volunteered at a spinal cord injury rehabilitation unit and asked the people there: What would improve your quality of life? Three answers kept coming back: getting between bed and chair, being at eye level in a conversation, and ground rougher than the floor the chair was built for. Separately I went looking at what actually kills people with spinal cord injuries. Mostly infection, and an open pressure sore is one of the ways infection gets in. They are not the biggest killer — that is pneumonia; they are the biggest killer mechanical engineering can do anything about.

Everything was modular, and that was the point: not a new wheelchair, but parts that bolt onto the one somebody already owns. A chair gets fitted to a body over years, and asking someone to give that up in order to gain a feature is not a trade most people will take.

  • five robotic pressure-injury relief mechanisms, shifting the occupant’s load without them having to do anything — depending on someone to remember it, which many cannot, fails on exactly the days they are unwell
  • a transfer mechanism, for getting between bed and chair
  • a seat that rises, for talking at eye level
  • a drive and tires for ragged ground

The year after, I mentored Ada Rosa on the same problem from the other end: mobility assistance for people with ALS and spinal cord injuries, driven by gaze, for users whose remaining reliable movement is their eyes — here she is showing off the eye control.

I expected to hear about getting around. What I kept hearing about was pain — constant, and largely unaddressed by anyone they had seen.

It was not a thing I could answer with mechanical engineering. What I could do was make sure the mechanisms were not locked up: I wrote up all the mechanical engineering and soft robotics I’d invented as a nonprovisional patent application, Robotic Mobility Assistive Wheelchairs, and then decided not to file it, and they went out under a Creative Commons license instead. A patent would have meant the people I built them for waiting on somebody else to license it first.

Then I went to work on understanding and treating chronic pain, which I am still doing.

Both halves have since arrived, about a decade on. Medicare began covering powered seat elevation in 2023 — on the grounds of transfers and reach, not of meeting people at eye level, which is what the users I spoke to actually said. And automated pressure redistribution that asks nothing of the occupant is now a pilot study. I should say plainly that all of this, mine included, measures interface pressure, which is a proxy; nobody has shown it prevents an injury.

When the cameras die, the hands take overSummer 2012

Proprioception-only contact-rich manipulation · blind peg-in-hole insertion · two-arm load equalization · Willow Garage PR2 · human–robot interaction

I taught a robot arm to find a hole and fit a shape into it with every sense but its own body switched off.

code: PR2-positronics

Blindness in robots. A machine that stops dead the moment its camera fails is a machine you cannot trust around people, and sensors fail constantly.

So I programmed the PR2 to keep working with its other sensors switched fully off — no vision, no external feedback of any kind — and to learn, under those conditions, to place objects into the holes of the corresponding shape. All it had was its own past motor position commands and the finger gripper sensors, so the robot had to adapt to the task from its own sense of where its body had been.

Our team also smoothed joint movement of the Willow Garage Personal Robot 2 and improved load equalization — sharing the torque between its two arms so it could hold something bulky whose mass sat off to one side without one arm taking the whole of it. That is most of what carrying things for somebody actually is: a bag of shopping is heavier at one end, a box is packed unevenly, and a person handing it over expects the thing taking it to adjust.

What is recoverable once a sense is gone?

The Braille work, the following spring. Here, a robot reaching for a hole it cannot see and finding it by touch; there, a language meant to be read by touch, worked out from fragments by a machine that cannot see either. Both are asking what is recoverable when the channel everyone assumes you have is missing.

Drawing the map while flying through itFall 2012

Simultaneous localization and mapping · monocular visual SLAM with parallax bootstrapping · loop closure · scale from sonar and inertial fusion · motion planning on a partial map

I taught a toy drone to find its way outdoors while drawing its own map as it went.

To know where you are, you need a map. To build a map, you need to know where you are. So how does anything ever get off the ground?

You do not solve either one first. You estimate both at once and let them correct each other. Take two frames from slightly different positions, triangulate the handful of features visible in both, and you have a crude map — which means you have to move before you can know anything at all, because depth comes from parallax. After that it alternates: given the map, work out where the camera must be to be seeing what it sees; given the poses, add new points and refine the old ones. The tracker running underneath this was PTAM, whose trick was to split those two jobs across threads — follow the features every frame, rebuild the map in the background whenever there is time to spare.

Error accumulates the whole way, because every new position is measured against a map built out of the previous ones. You get it back by recognizing somewhere you have already been and closing the loop. And there is one thing a single camera can never tell you: scale. A large room far away and a small room close up produce the same picture. That number had to come from the sonar altimeter and the inertial unit.

All of it ran off-board, on a laptop, over WiFi. It held together where there was texture and steady light, and fell apart where there was not: repetitive ground, changing sun, and wind, which moves the aircraft between one frame and the next.

I would not take this on now. Navigating terrain nobody has surveyed is not a neutral capability — there is very little daylight between solving it for a toy quadcopter and solving it for something armed. I was treating it as a puzzle about maps and motion, not thinking of the consequences.

The homesickness robot2011

Mimicking animal motion and companionship · robot person following · gait-based re-identification · statically stable hexapedal locomotion

I missed my dog at university, so I built a six-legged robot that followed me around.

My first robotics project, and the motive was homesickness — I missed my dog at university, so I built something that would trail after me.

One told it to follow you by standing in front of it. Two problems follow from there: knowing who to keep following, and keeping up with them.

The first answer was color — lock onto the histogram of whatever the person was wearing and chase that — which works right up until they turn away, walk under a different lamp, or take their coat off. So it identified them by gait instead, from the way they walked rather than from their face or their clothes.

For keeping up I took what looked like the cheap way out. Six legs are statically stable: an alternating tripod keeps three feet on the ground with the body over its own support at every instant, so in principle the thing never has to balance at all. In practice it fell over constantly. Static stability is a promise about geometry, not about the world — it assumes the feet land where you expect, that the ground holds when they do, and that you are moving slowly enough for momentum not to count. A slope, a patch of gravel, a foot dropping into a dip a centimeter deeper than the controller believed, and the support polygon is not where it is supposed to be. Extra legs buy margin, not immunity.

The way out was not more legs, even though I personally find that cuter. Boston Dynamics went the other way with BigDog — four legs, which cannot fall back on geometry at all and so have to catch themselves, force-controlled limbs choosing where to put a foot in the next fraction of a second. That is the machine everybody remembers getting kicked sideways on ice and skittering back upright, and it is the approach that generalized. Quadrupeds now learn the recovery in simulation and cross ground I could never have got a hexapod over. Following a person around has a name now too — robot person following — with benchmarks, and re-identification that keeps learning your target as they change.

What if, rather than planning motion across a floor, you add flight to the problem? Three dimensions, no ground to stand on, and no option to stop and think.

Matter

Behaviour inferred from the traces that structure leaves.

Calculating a material into existence2012 – 2013

Electronic-structure calculation · augmented plane wave method · superconducting transition temperature of intermetallic compounds · computational materials screening

Working out on a computer which materials would superconduct, instead of making them one at a time to find out.

read the post

A superconductor carries current with no resistance: nothing lost, nothing turned to heat, and magnets far stronger than their power draw. Every one we have needs liquid helium, so the chase is for one that works warmer — and you cannot run that chase by building candidates one at a time.

Extending GMU’s simulation after transferring there, advised by Dimitrios Papaconstantopoulos, using electronic-structure calculation by the augmented plane wave method to predict the superconducting transition temperature of intermetallic compounds. This became one of my two undergraduate theses, Predicting Superconductivity Transition Temperature via the Augmented Plane Wave Model. Alongside it, algorithms of AI chess players.

The approach paid off, in other people’s hands. H3S was calculated to superconduct near 200 K and then measured at 203 K; LaH10 was predicted in 2017 and found at 250 K two years later. Materials predicted on a computer before anyone made them, which is the outcome the whole approach was betting on. They need megabar pressures, so nobody is wiring a city with them yet.

Nothing interesting happens at only one scaleJan 2015

Multiscale modeling · directed type systems · compositional model building · topology applied to complex biological systems

A proposal that multiphysics models, which are already fibrations, be written in a dependent type language and run faster for it.

A multiphysics simulation is several different physics solved over one domain at once, and it is expensive twice over: the run itself, and the human work of stitching solvers together without introducing errors. Both of those are structural costs, and the structure is already sitting there in the mathematics.

The proposal was to write these models in a dependent type language, because the mathematics is already the right shape for it. A classical field is a section of a bundle over the domain, and a gauge field is a connection on one; a bundle is a fibration. A dependent type is also a fibration — a family indexed over a base, which categorically is a map whose fibers are the types. The two are the same construction wearing different clothes, so a physics model can be carried in a type rather than in a comment, and the compiler can then see what the physicist knows.

The payoff I was after was run time, not just correctness. Once the structure is in the type, whole categories of runtime work become statically unnecessary — dimension and index checks, guards on couplings that cannot occur, dispatch that can be specialized away. That is not speculative: eliminating array bound checks through dependent types measurably speeds up ordinary numerical programs. A multiphysics solver has far more structure to exploit than a bubble sort does. Making direction of dependence part of the type — which physics feeds which — is what pushes it from ordinary dependent types toward the directed, cocartesian kind.

Other people were heading the same way, and one of my own co-authors on Toward Directed Collapsibility is among them: Nicole Sanderson now writes on topology and neural circuits. Persistent homology has reached the tumour microenvironment too, picking out rare T-cell states under checkpoint blockade. The immunotherapy daydream had other people in it all along.

Both halves have since been developed, independently of me. Directed type theory was rebuilt on synthetic simplicial foundations, where the objects under study are exactly cocartesian fibrations, and the proofs are going into a proof assistant. On the applied side, Decapodes composes systems of PDEs diagrammatically: you assemble a multiphysics simulation out of component models instead of editing a monolith, and the composite is a first-class object rather than a hand-merged file. They report a drastic drop in time-to-first-simulation, though they say plainly that the claim is qualitative and unmeasured, which is the honest state of it.

What shapes will a plasma hold?2012

Standing-wave mode structure of a 2.45 GHz argon discharge · conductive polyhedral cavity · deployable structures in ionospheric plasma

I filled a metal polyhedron with argon, put a microwave source inside, and looked at the shapes the plasma made.

Space is cool, and a satellite that folds is cooler: you launch something small and it opens into something large. But a deployed satellite is a geometric mesh sitting in the ionosphere, which is a plasma, and that plasma is part of the electrical environment the structure has to work in. So the question is what a given geometry does to the fields around it.

I was given access to a hollow aluminum polyhedron, a vacuum pump and a 2.45 GHz RF source: evacuate it, backfill with argon, and strike a discharge inside. The cavity’s geometry picks out which modes can live there, and the discharge organizes itself along the resulting standing wave. The point was the mode structure: which field patterns a given polyhedron will and will not permit. A benchtop analogue for mode selection rather than a faithful orbit — argon is the conventional stand-in for low-earth-orbit plasma, but it matches neither the ion mass nor the temperature, and a microwave discharge sits orders of magnitude above ionospheric density.

People do this deliberately now and call them plasma metasurfaces: discharges arranged so their geometry decides which electromagnetic modes get through, and reconfigured by changing the discharge rather than the hardware. I was making a very crude one and calling it a side project.

A thinking film you could bendSpring 2012

Flexible TiO2 resistive switching · memristive device fabrication and bend-cycle characterization · in-memory computing

A memristor is a resistor that remembers. I made bendable ones by hand and measured them until they failed.

A memristor is a resistor that remembers where you last left it. That sounds like a small thing and it is not: a component that stores a value and computes with it in the same place means a device built from them does not have to send its data somewhere else to be processed. Put a memristor on a flexible surface and that device can be worn: potentially as a non-invasive medical device.

Chua predicted the device in 1971; HP said they had built one in 2008; I was depositing titanium dioxide films in 2012, when the field was still mostly promise. What I did was make them and measure them — bench work, not simulation, a research assistantship in the materials science lab of the Chemistry and Physics Department at Mary Baldwin College — pushing each one until it switched, then bending it and doing it again to find where the behavior fell apart. It is also where I became interested in physical examples of nonlinear systems.

Years afterward, a group wired live rat neurons in Padova to silicon neurons in Zurich through memristors in Southampton, with the memristors holding the synaptic weights between them. The devices were Pt/TiOx/Pt — the same stack I had been making by hand. I had nothing to do with it, and it is still my favorite thing to have happened to a material I once held.

Fragments

Structure recovered from the traces a language leaves behind.

Reading a language from the fragments somebody already translatedSpring 2013

Unsupervised grammar and lexicon induction from partially parallel text · decipherment of incompletely understood scripts · contracted Braille as the test language · accessible signage

A method for working out a language you only partly have, tested on the Braille that gets signs wrong.

read the post code: MachLearn-G2Braille

This started because I read Braille and kept noticing that the signs around me were wrong. The one that decided it: a door labeled electrical room in print and safety exit in Braille. Whoever installed it could not read what they were mounting, and nobody downstream of them could catch it. So I wanted translation to be something a builder could get right at the point of installing a sign, rather than something they had to take on faith.

The mistakes are easy to make, because Grade 2 Braille is not a cipher you can look up letter by letter — it is contracted, with about a hundred and eighty contractions, and the same six dots can be a letter, a whole word, or a fragment glued to its neighbors depending on where in the word it falls and what sits beside it.

Which makes it a very good test case for a problem much older than Braille: you have a text in a script you only partly understand, and a translation of some of it, and you want the rest. The method does not care that the script is Braille. It builds probabilistic dictionaries from whatever parallel fragments exist and lets the grammar fall out of the alignment — the same shape of problem as an incompletely deciphered ancient script, where a handful of confident readings and a great deal of unread text is exactly the situation you are in. Braille simply has the advantage of a known answer to check against. It grew out of my automated computational semantics research at GMU and became my other undergraduate thesis, Contextual Machine Learning through the Analysis and Chunking of Partially Translated Grade 2 Braille.

The grammar was the problem, and the standards body agreed. When Unified English Braille replaced the older code, nine contractions were deliberately deleted — in BANA's own words, to enable accurate automatic translation and reduce the exceptions to the rules. They simplified the language rather than the model. It is still not solved: frontier language models today refuse, hallucinate, or emit malformed Braille, and a small fine-tuned model beats all of them.

Trying to keep clinical doctors up to date2013

Automated computational semantics · abstractive summarization of biomedical literature · evidence fidelity

A machine that reads a scientific paper and tells a busy doctor whether it is worth their evening.

I kept meeting working doctors who were further from the current literature than they wanted to be. Not for any want of caring: seeing patients all day and reading a stack of new papers every week are not two things one person can do. The volume is what defeats them, so the volume is what to go after.

Automated computational semantics research at George Mason, aimed at getting a machine to read a paper and return something faithful and short enough that a clinician between appointments could decide whether the whole thing was worth an evening.

This is the research CAMEL grew out of, pointed the other way round. There, meaning recovered from too little text; here, meaning kept intact while most of the text goes away.

Living things

Hidden states, read from the traces a system emits.

Sensory Sensitivity as a Unifying Mechanism2024–current

systems biologyneuroimmunologyevidence synthesis

Synthesis arguing that failure of habituation constitutes a shared upstream mechanism, drawing on connectivity imaging, glutamatergic excitability, microbiome composition and enteric regulation of immunoglobulin secretion. With L. Estinto.

Hypothesis-generating; not experimentally validated.

Neostigmine in feline idiopathic megacolon2026current

veterinary pharmacologycase documentationenteric motility

Owner-reported case study of an acetylcholinesterase inhibitor used off-label to restore colonic motility, with lactulose and anti-NGF analgesia, documented to a standard usable in consultation.

Contraindicated without prior deobstipation and exclusion of mechanical obstruction. Medical management succeeds in roughly two thirds of cases presenting under six months and under six percent thereafter.

Memantine as a candidate non-opioid analgesic in central sensitization2026current

pharmacologyevidence synthesishealth policy

Review of the mechanistic rationale, comparative pharmacology against ketamine and dextromethorphan, and the clinical trial record for memantine in chronic pain, with a proposed design for a publicly funded trial.

Evidence synthesis only. The pooled analysis of eleven trials is not significant; the positive signal rests on one 63-patient fibromyalgia trial.

Unsupervised classification of rodent ultrasonic vocalization for continuous preclinical monitoring2013–2014

computational bioacousticsunsupervised learningsafety pharmacology

Unsupervised classification of rodent ultrasonic vocalizations in quasi-real time, deployed as a preclinical readout for compound effects on stress and libido — the first continuous non-invasive behavioral phenotyping system at Vium, several years before MUPET and DeepSqueak made the approach standard. Two write-ups: A New Female–Female Mouse Vocalization Discovered via Unlabeled Machine Learning and On the Detection and Prevention of Aggression in Lab Mice via Quasi-Real Time Analysis.

Non-contact acquisition removes handling stress as a confound and increases information yield per cohort; later multi-company validation supports the approach. Prior unsupervised USV clustering exists (Grimsley et al., 2013).

Decoder convergence and optical recording for intracortical motor prostheses2014

brain–computer interfacesdecoder designneural interfaces

Convergence analysis of intracortical decoders under signal drift — how fast a Kalman-style filter settles onto a usable mapping from neural activity to intended movement, how far it degrades as glial scarring thins the neural population, and how much adaptive recalibration recovers. Then optical recording via fluorescent calcium indicators as an alternative to penetrating electrodes.

Foreign body response degrades yield; subsequent human longitudinal data indicates abiotic electrode failure may dominate. Optical methods remain depth- and delivery-limited.

Portable detection of gluten and common allergenic proteins2011–2014

immunoassayoptical spectroscopypoint-of-care

Two approaches: a laser and avalanche-photodiode optical assay, abandoned for insufficient SNR against protein-rich matrices; then a G12 antibody colorimetric assay in a toothpick or strip format.

Limiting factor was antibody cost per assay, not sensitivity. Sampling variance in heterogeneous food exceeds measurement variance, which bounds the device class; aptamer assays have since addressed the cost term.

Remote photoplethysmography on a head-mounted display2013

computer visionphysiological sensingresearch ethics

Recovery of cardiac pulse and its variation from video alone, without contact, intended as a social-signal aid. HackMIT, with K. Talwar and S. Hewett.

Withdrawn on ethical grounds: the measured party cannot detect or refuse the measurement.

Bodies in motion

A body reading the traces of its own movement.

Modular robotic retrofits for powered wheelchairs2013–2015

mechanism designrehabilitation engineeringuser-led requirements

Four assemblies designed to fit chairs already configured to their users: automated pressure redistribution, powered seat elevation, assisted bed-to-chair transfer, rough-terrain drive. Requirements elicited from wheelchair users with spinal cord injury; subsequent mentorship of gaze-controlled mobility assistance for ALS and SCI.

Written as a nonprovisional patent application and deliberately not filed; released under Creative Commons. Interface pressure is a surrogate endpoint.

Graceful degradation under sensor failure: contact-rich manipulation on proprioception alone2012

graceful degradationcontact-rich manipulationproprioceptive controlhuman–robot interaction

A robot that stops dead the moment its camera fails cannot be trusted around people, and sensors fail constantly. With vision and all external feedback disabled, a Willow Garage PR2 autonomously acquired a shape-matched insertion task from commanded joint positions and gripper sensing alone. Also two-arm load equalization for objects with off-center mass. HCI internship, George Washington University.

Demonstrates graceful degradation at the extreme: total loss of exteroception, not a partial fault. Learning was small-scale policy search.

Monocular visual SLAM with motion planning on a micro aerial vehicle2012

SLAMsensor fusionmotion planning

PTAM-class monocular SLAM, processed off-board, with metric scale recovered by fusing sonar altimetry and inertial measurement, coupled to frontier-based planning on a partially built map. Parrot ARDrone.

Bounded by repetitive texture, illumination change and airframe disturbance. Dual-use: unsurveyed autonomous navigation transfers directly to armed platforms.

Gait-based re-identification for robot person following2011

computer visionre-identificationlegged locomotion

Hexapedal platform; target enrollment by proximity, association by gait rather than appearance, steering on bearing. Alternating tripod gait for statically stable traversal.

Static stability is a guarantee over an idealized contact model and does not survive real terrain.

Matter

Behaviour inferred from the traces that structure leaves.

Electronic-structure prediction of superconducting transition temperature2012–2013

density functional methodselectronic structurematerials screening

Augmented plane wave band structure feeding an electron-phonon coupling estimate and a McMillan/Allen–Dynes transition temperature for intermetallic compounds. Advised by D. Papaconstantopoulos, George Mason University. Undergraduate thesis.

Subsequently validated at scale by the predicted-then-synthesized hydride superconductors, at megabar pressures.

Dependent and directed type systems for multiphysics models2015

type theorycategory theoryscientific computing

Proposal that multiphysics models be expressed in a dependent type language. Classical fields are sections of fiber bundles; dependent types are semantically fibrations; the correspondence permits model structure, including direction of coupling, to be carried in the type and exploited by the compiler. Visiting researcher, Santa Fe Institute.

Motivated by run time rather than correctness alone: dependently typed elimination of runtime checks measurably reduces execution time on ordinary numerical code. Directed variants correspond to cocartesian fibrations; a related applied line of work is diagrammatic composition of PDE systems, whose reported gains remain qualitative.

Standing-wave mode structure of an RF discharge in a polyhedral cavity2012

RF plasmaelectromagneticscavity resonance

2.45 GHz discharge in an evacuated aluminum polyhedron backfilled with argon; cavity geometry selects the supported resonant modes and the discharge organizes along the resulting standing wave. Motivated by deployable conductive structures in ionospheric plasma.

Benchtop analogue only: argon matches neither ion mass nor electron temperature, and discharge density sits orders of magnitude above ionospheric values.

Flexible TiO2 resistive-switching devices2012

thin-film devicesresistive switchingdevice physics

Fabrication and characterization of memristive devices on compliant substrates, including switching behavior under bend cycling. Research assistantship, Mary Baldwin College.

Motivation was colocated storage and computation for body-worn sensing; now termed in-sensor and near-sensor computing.

Fragments

Structure recovered from the traces a language leaves behind.

Unsupervised grammar and lexicon induction from partially parallel text2013

natural language processinglexicon inductiondecipherment

Probabilistic lexicon induction over weakly parallel corpora, evaluated on contracted Grade 2 Braille, chosen as a test language with a known ground truth. Undergraduate thesis, George Mason University. Code.

This grew out of automated computational semantics research at GMU, which also included work on abstractive summarization of biomedical literature — getting a machine to read a scientific paper and return something faithful and short enough that a clinician could decide whether the full paper was worth their evening.

Generalizes to incompletely deciphered scripts. Applied motivation: transcription error in installed accessible signage.

Automated abstractive summarization of biomedical literature for clinical readers2013

natural language processingsummarizationbiomedical text

Automated computational semantics directed at reducing a paper to a triage-sufficient summary. George Mason University.

Evaluation of evidence fidelity, rather than generation, remains the open problem.

THE PROOFS

PUBLICATIONS & PREPRINTS

Toward Directed Collapsibility2020published

joint with R. Belton, R. Brooks, S. Ebli, L. Fajstrup, B. T. Fasy, N. Sanderson, E. Vidaurre · Advances in Mathematical Sciences, vol. 21, pp. 255–271

arXiv

IN PROGRESS

Zeta Functions in Homotopy Theory

Syntomic cohomology of ring spectra and a \(T(h)\)-local zeta function

joint with Gabe Angelini-Knoll

Toward Categorifying the relationship of Symplectic L-functions and Reidemeister Torsion

Riemann–Roch for Reidemeister torsion in K-theory and L-theory

L-genera and Localizations in K-theory

joint with Daniel Berwick-Evans, Natalia Pacheco-Tallaj

All Bernoulli Numbers in Homotopy Theory Are Shifts

joint with Andres Mejia and Noah Riggenbach · connecting Kervaire–Milnor to Quillen–Lichtenbaum using the compatibility of \(K(\mathbb{S})\) and \(L_{K(1)}K(\mathbb{Z})\)

Moduli Stacks of Curves in Homotopy Theory

The group cohomology of the maximal finite subgroups of the Lubin–Tate action is the \(E_2\) page needed to capture all p-torsion information in the stable homotopy groups of spheres. My thesis (2023) attempts to resolve the 40-year-old open problem of describing the Lubin–Tate action for all maximal finite subgroups.

It does so by outlining a universal way to build a geometric model using a moduli stack of G-curves given a subgroup G. A key insight is to replace the role of level structures with higher ramification information. To make the thesis more digestible, I have broken it up into three parts, the last of which is forthcoming. The only nontrivial p-torsion for odd primes is found at heights \(p^{k-1}(p-1)\).

My thesis, explained for everyone (PDF) code: h-splitting

Writhing Jewels: A Conjectural Description of the Lubin–Tate Action via Moduli Stacks of G-Curves for \(h = p^{k-1}(p-1)\)

Lubin-Tate illustration

EXPOSITORY

K-theoretic Tate–Poitou Duality Seminarcoming soon

March 2025

My two Master’s theses

TEACHING

stub An updated teaching statement is on its way; this is the current one.

I came into academia from outside, so I go out of my way to present mathematics in ways that are accessible to everyone. For me it is a visual, interactive, intuitive and artistic experience, and above all a narrative one. I keep learning materials for students of all levels on my resources page. My teaching statement:

READ MY TEACHING STATEMENT →

THE STUDIO

Pastels, acrylic, spray-painted creature murals, tattoos, polaroids. A taste:

  • Open the gallery
  • Open the gallery
  • Open the gallery
  • Open the gallery
  • Open the gallery

And beyond the gallery:

CONTACT ME

Curiosity is welcome
fractalcows@gmail.com
My work email
cray@uni-muenster.de

You will find the name Cathe(rin)e Ray on old stuff and Rin Ray on my newer works — these both refer to the same person. I prefer Rin nowadays.

Comments from the old blog (5)

Recovered from the Wayback Machine of the old site after my back-up servers got black-hatted.

  1. Ibrahim

    I just wanna say that like this blog so much, and you remind me of the movie called: Proof 😉

  2. Mari

    Agreed. I don’t comment but visit and enjoy regularly.

  3. Adam Karlson

    Edward Frenkel was your mentor! WOW!

  4. Dr Rizvan Ghasura

    Hi
    Good Morning…
    Best of Luck for Future Work…
    If you will come to India ..I will meet you…
    Nice work

  5. Happy Raagas

    Hi Rin, just wanted to say how much you inspire to help young people like math. Keep it up. 🙂