Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed

Abstract: Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting values of other chemical species. The broad goal of this nascent field is to develop systems that can operate in the niche of a (wet) cellular environment, rather than to directly compete with modern digital computers.

There have been numerous works that design reaction networks that carry out basic arithmetic. However, in general, these constructions have speeds of computation (i.e., a rates of convergence) that depend intimately upon the inputs to the computation itself, sometimes making them unusably slow. In this talk, I will discuss how we designed a full suite of “elementary” chemical systems that carry out arithmetic computations (such as inversion, addition, roots, multiplication, rectified subtraction, absolute difference, etc.) over the real numbers, and that have speeds of computation that are independent of the inputs to the computations. Moreover, we proved that finite sequences of such elementary modules, running in parallel, can carry out composite arithmetic over real numbers, also at a rate that is independent of inputs. I will close with a number of open questions and directions for future work.

This is all joint work with Badal Joshi, and the relevant paper can be found here: arxiv.org/abs/2404.04396.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom!

The organizers.

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