arXiv subjects

Lucius Schoenbaum

Publications and source records attributed to Lucius Schoenbaum.

4 recordsLinked to original sources

arXiv2025

Development of grid-based and PINN solvers for electron kinetics in collisional non-thermal plasmas

We compare traditional finite volume and Physics Informed Neural Network (PINN) solvers for elliptic (Poisson), hyperbolic (advection), and parabolic (diffusion) equations in 2d settings. We describe the challenges of using traditional and PINN solvers for electron kinetic equations in collisional plasmas. The advantages and drawbacks of PINNs over state-of-the-art traditional solvers are discussed. We also consider angular moments in spherical velocity space and the potential use of ML algorithms for reduced kinetic models in the coordinate-energy phase space based on adaptive closure relations.

physics.plasm-ph↗

arXiv2021

Journalistic Voting System's Effects on Election Security Threats and Gerrymandering

The Journalistic Voting System is a proxy voting system in which journalists are delegated the task of voting on behalf of individual voters in a western-style democracy. We introduce the Journalistic Voting System and discuss its potential advantages and potential problems. In particular, we discuss its advantages to individuals in the system (voters, journalists, and politicians) and we discuss its effects relative to several widely discussed threats to election security, namely: cybersecurity, social media, big data, artificial intelligence (AI), and gerrymandering. The Journalistic Voting System is modeled on a predecessor system, called the Valence Voting System, which is reviewed.

physics.soc-ph↗

arXiv2016

A Generalization of the Curry-Howard Correspondence

We present a variant of the calculus of deductive systems developed in (Lambek 1972, 1974), and give a generalization of the Curry-Howard-Lambek theorem giving an equivalence between the category of typed lambda-calculi and the category of cartesian closed categories and exponential-preserving morphisms that leverages the theory of generalized categories (Schoenbaum 2016). We discuss potential applications and extensions.

cs.LO↗

arXiv2016

Towards Visual Type Theory as a Mathematical Tool and Mathematical User Interface

A visual type theory is a cognitive tool that has much in common with language, and may be regarded as an exceptional form of spatial text adjunct. A mathematical visual type theory, called NPM, has been under development that can be viewed as an early-stage project in mathematical knowledge management and mathematical user interface development. We discuss in greater detail the notion of a visual type theory, report on progress towards a usable mathematical visual type theory, and discuss the outlook for future work on this project.

cs.AI↗