arXiv subjects

Martin Lorenz

Publications and source records attributed to Martin Lorenz.

At least 19 recordsLinked to original sources

arXiv2026

CR-Eyes: A Computational Rational Model of Visual Sampling Behavior in Atari Games

Designing mobile and interactive technologies requires understanding how users sample dynamic environments to acquire information and make decisions under time pressure. However, existing computational user models either rely on hand-crafted task representations or are limited to static or non-interactive visual inputs, restricting their applicability to realistic, pixel-based environments. We present CR-Eyes, a computationally rational model that simulates visual sampling and gameplay behavior in Atari games. Trained via reinforcement learning, CR-Eyes operates under perceptual and cognitive constraints and jointly learns where to look and how to act in a time-sensitive setting. By explicitly closing the perception-action loop, the model treats eye movements as goal-directed actions rather than as isolated saliency predictions. Our evaluation shows strong alignment with human data in task performance and aggregate saliency patterns, while also revealing systematic differences in scanpaths. CR-Eyes is a step toward scalable, theory-grounded user models that support design and evaluation of interactive systems.

cs.HC↗

arXiv2026

MRDrive: An Open Source Mixed Reality Driving Simulator for Automotive User Research

Designing and evaluating in-vehicle interfaces requires experimental platforms that combine ecological validity with experimental control. Driving simulators are widely used for this purpose. However, they face a fundamental trade-off: high-fidelity physical simulators are costly and difficult to adapt, while virtual reality simulators provide flexibility at the expense of physical interaction with the vehicle. In this work, we present MRDrive, an open mixed-reality driving simulator designed to support HCI research on in-vehicle interaction, attention, and explainability in manual and automated driving contexts. MRDrive enables drivers and passengers to interact with a real vehicle cabin while being fully immersed in a virtual driving environment. We demonstrate the capabilities of MRDrive through a small pilot study that illustrates how the simulator can be used to collect and analyze eye-tracking and touch interaction data in an automated driving scenario. MRDRive is available at: https://github.com/ciao-group/mrdrive

cs.HC↗

arXiv2025

Combining Molecular Dynamics and Experimental Methods for the Parametrization of Binary Carbonate-Based Electrolytes

Modelling the ionic transport in battery cells requires precise parametrization of the involved electrolytes. For carbonate-based electrolytes, however, the evaluation of their parameters suffers from interphase effects between the bulk electrolyte and the Li metal electrode, commonly present in the usual electrochemical polarization experiments. In this work, we combine measurements on conductivity and concentration cells with molecular dynamic simulations, avoiding these difficulties and thus, allowing for a more accurate determination of the parameters. We determine the conductivity, the transference number, the thermodynamic factor and the salt diffusion coefficient for three different electrolytes, i.e mixtures of ethylene carbonate (EC), ethyl methyl carbonate (EMC), methyl propionate (MP), dimethyl carbonate (DMC) and propylene carbonate (PC), containing LiPF$_6$ at various concentrations and temperatures. In order to validate the simulated transference numbers, we employ electrophoretic Nuclear Magnetic Resonance spectroscopy (eNMR).

physics.chem-ph↗

arXiv2023

A Volume-based Description of Transport in Incompressible Liquid Electrolytes and its Application to Ionic Liquids

Transference numbers play an important role for understanding the dynamics of electrolytes and assessing their performance in batteries. Unfortunately, these transport parameters are difficult to measure in highly concentrated, liquid electrolytes such as ionic liquids. Also, the interpretation of their sign and magnitude has provoked an ongoing debate in the literature further complicated by the use of different language. In this work, we highlight the role of the reference frame for the interpretation of transport parameters using our novel thermodynamically consistent theory for highly correlated electrolytes. We argue that local volume conservation is a key principle in incompressible liquid electrolytes and use the volume-based drift velocity as reference. We apply our general framework to electrophoretic NMR experiments. For ionic liquid based electrolytes, we find that the results of the eNMR measurements can be best described using this volume-based description. This highlights the limitations of the widely used center-of-mass reference frame which for example forms the basis for molecular dynamics simulations - a standard tool for the theoretical calculation of transport parameters. It shows that the assumption of local momentum conservation is incorrect in those systems on the macroscopic scale.

physics.chem-ph↗

arXiv2022

Local volume conservation in concentrated electrolytes is governing charge transport in electric fields

While ion transport processes in concentrated electrolytes, e.g. based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employ-ing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to deter-mine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found as zero, implying a non-zero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incom-pressibility, but not with a local application of momentum conservation. The constraint affects the calcu-lation of transference numbers as well as comparisons of MD results to experimental findings.

cond-mat.soft↗

arXiv2021

A note on affine representable algebras

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial algebra. We also prove a refined version of a theorem of V.T. Markov stating that the Gelfand-Kirillov dimension of any affine representable algebra is an integer.

math.RA↗

arXiv2020

Hopf algebra actions and rational ideals

This note discusses a framework for the investigation of the prime spectrum of an associative algebra A that is equipped with an action of a Hopf algebra H. In particular, we study a notion of H-rationality for ideals of A and comment on a possible Dixmier-Moeglin equivalence for H-prime ideals of A.

math.RA↗

arXiv2019

Actions of cocommutative Hopf algebras

Let $H$ be a cocommutative Hopf algebra acting on an algebra $A$. Assuming the base field to be algebraically closed and the $H$-action on $A$ to be integral, that is, it is given by a coaction of some Hopf subalgebra of the finite dual $H^\circ$ that is an integral domain, we stratify the prime spectrum $\mbox{Spec}\, A$ in terms of the prime spectra of certain commutative algebras. For arbitrary $H$-actions in characteristic $0$, we show that the largest $H$-stable ideal of $A$ that is contained in a given semiprime ideal of $A$ is semiprime as well.

math.RA↗

arXiv2019

On the Adjoint Representation of a Hopf Algebra

We consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{\text{adfin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as module over a cocommutative Hopf subalgebra), we show that $H_{\text{adfin}}$ is a Hopf subalgebra of $H$. This is a consequence of the fact, proved here, that locally finite parts yield a tensor functor on the module category of any virtually pointed Hopf algebra. For general Hopf algebras, $H_{\text{adfin}}$ is shown to be a left coideal subalgebra. We also prove a version of Dietzmann's Lemma from group theory for Hopf algebras.

math.RT↗

arXiv2015

Frobenius Divisibility for Hopf Algebras

We present a unified ring theoretic approach, based on properties of the Casimir element of a symmetric algebra, to a variety of known divisibility results for the degrees of irreducible representations of semisimple Hopf algebras in characteristic 0. All these results are motivated by a classical theorem of Frobenius on the degrees of irreducible complex representations of finite groups.

math.RA↗

arXiv2012

On the stratification of noncommutative prime spectra

We study rational actions of an algebraic torus G by automorphisms on an associative algebra R. The G-action on R induces a stratification of the prime spectrum of R which was introduced by Goodearl and Letzter. For a noetherian algebra R, Goodearl and Letzter showed that the strata of the spectrum of R are isomorphic to the spectra of certain commutative Laurent polynomial algebras. The purpose of this note is to give a new proof of this result which works for arbitrary algebras R.

math.RA↗

arXiv2011

Rational group actions on affine PI-algebras

Let R be an affine PI-algebra over an algebraically closed field k and let G be an affine algebraic k-group that acts rationally by algebra automorphisms on R. For R prime and G a torus, we show that R has only finitely many G-prime ideals if and only if the action of G on the center of R is multiplicity free. This extends a standard result on affine algebraic G-varieties. Under suitable hypotheses on R and G, we also prove a PI-version of a well-known result on spherical varieties and a version of Schelter's catenarity theorem for G-primes.

math.RA↗

arXiv2010

Some applications of Frobenius algebras to Hopf algebras

This expository article presents a unified ring theoretic approach, based on the theory of Frobenius algebras, to a variety of results on Hopf algebras. These include a theorem of S. Zhu on the degrees of irreducible representations, the so-called class equation, the determination of the semisimplicity locus of the Grothendieck ring, the spectrum of the adjoint class and a non-vanishing result for the adjoint character.

math.RA↗

arXiv2010

Projective modules over Frobenius algebras and Hopf comodule algebras

This note presents some results on projective modules and the Grothendieck groups K_0 and G_0 for Frobenius algebras and for certain Hopf Galois extensions. Our principal technical tools are the Higman trace for Frobenius algebras and a product formula for Hattori-Stallings ranks of projectives over Hopf Galois extensions.

math.RA↗

arXiv2009

Group actions and rational ideals

We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring of quotients replaces the classical ring of quotients which underlies the previous definition of rational ideals but is not available in a general setting. Our main result concerns rational actions of an affine algebraic group G on R. Working over an algebraically closed base field, we prove an existence and uniqueness result for generic rational ideals: for every G-rational ideal I of R, the closed subset of the rational spectrum Rat R that is defined by I is the closure of a unique G-orbit in Rat R. Under additional Goldie hypotheses, this was established earlier by Moeglin and Rentschler (in characteristic zero) and by Vonessen (in arbitrary characteristic), answering a question of Dixmier.

math.RA↗

arXiv2009

Algebraic group actions on noncommutative spectra

Let G be an affine algebraic group and let R be an associative algebra with a rational action of G by algebra automorphisms. We study the induced G-action on the spectrum Spec R of all prime ideals of R, viewed as a topological space with the Jacobson-Zariski topology, and on the subspace consisting of all rational ideals of R. Here, a prime ideal P of R is said to be rational if the extended centroid of R/P is equal to the base field. The main themes of the article are local closedness of G-orbits in Spec R and the so-called G-stratification of Spec R. This stratification plays a central role in the recent investigation of algebraic quantum groups, in particular in the work of Goodearl and Letzter. We describe the G-strata in terms of certain commutative spectra. Our principal results are based on prior work of Moeglin & Rentschler and Vonessen. We generalize the theory arbitrary associative algebras while also simplifying some of the earlier proofs.

math.RA↗

arXiv2007

N-homogeneous superalgebras

We develop the theory of N-homogeneous algebras in a super setting, with particular emphasis on the Koszul property. To any Hecke operator on a vector superspace, we associate certain superalgebras and generalizing the ordinary symmetric and Grassmann algebra, respectively. We prove that these algebras are N-Koszul. For the special case where the Hecke operator is the ordinary supersymmetry, we derive an $N$-generalized super-version of MacMahon's classical "master theorem".

math.QA↗

arXiv2006

Koszul algebras and the quantum MacMahon Master Theorem

We give a new proof of the quantum version of MacMahon's Master Theorem due to Garoufalidis, Le and Zeilberger (one-parameter case) and to Konvalinka and Pak (multiparameter case) by deriving it from known facts about Koszul algebras.

math.QA↗