Retrieval-Augmented Generation (RAG) systems enhance large language models by grounding responses in retrieved documents from external knowledge sources at inference time. However, this reliance on retrieved content introduces vulnerabilities to poisoning attacks, in which adversarial documents can manipulate both the retrieval process and the generated outputs. This paper investigates poisoning robustness in RAG through a full factorial experimental study covering 432 configurations. We analyze the impacts of dataset, retriever type, retrieval depth, database composition, chunking strategy, and generator model on retrieval-level and generation-level metrics. The results show that retriever architecture, dataset, and retrieval depth are the strongest factors affecting poisoning exposure, while generator choice and database composition have a major impact on downstream attack success. Dense and graph-based retrievers generally improve robustness relative to BM25, whereas larger retrieval depth increases the likelihood of retrieving poisoned passages. We further show that replicating poisoned content across multiple databases amplifies adversarial influence, while additional clean sources can mitigate it. These findings highlight that poisoning vulnerability in RAG is not attributable to a single component, but instead arises from the interaction of retrieval, generation, and knowledge-base configuration.

This is a continuation of a previous report on an experiment in autoformalisation of Gödel's second incompleteness theorem in Agda using Claude. Using the framework built in this experiment, Claude could ``automformalise'' Chaitin's proof of the first incompleteness theorem and then the Kritchman-Raz surprise examination paradox version of the second incompleteness. As the first experiment, the project provides a case study of the strengths and limitations of current large language models in mathematics. Since Chaitin's proof involves coding programs, Claude had to represent code as ternary string and could build autonomously a parser and a continuation stack evaluation machine. The fact that we can simulate computations as expected is not completely trivial and we suggested a Gandy/Howard majorisation argument, that Claude had no problem to follow. The resulting formalisation clarifies a number of details left implicit in the original presentation and provides a fully machine-checked proof of these arguments for Church's Basic Recursive Arithmetic.

Problem: Despite growing interest in project-based learning, little is known about how a master-level course can be continuously evolved toward research-oriented approaches over several years and how students perceive this development. Method: We conducted a longitudinal mixed-methods study of a master-level course in Information Systems at the University of Applied Sciences and Arts Hannover (Germany). The analysis covers six years between 2019 and 2025 and draws on teaching evaluations, course documentation, and reflective teaching artifacts. Results: The course evolved from a practice-oriented project format toward a more explicitly research-oriented learning environment. Despite this change, students' perceived course quality remained positive. Authentic projects, external collaboration, lecturer support, structured scaffolding, and visible relevance supported positive student perceptions. Contribution: This paper shows how a master-level course can be continuously evolved toward research-oriented learning while maintaining positive student perceptions. It further identifies the course design decisions that supported this transition.

Context: Generative Artificial Intelligence (GenAI) tools such as ChatGPT are increasingly integrated into students learning practices. While previous research mainly examines adoption rates and attitudes, students awareness of institutional regulations and their perceived compliance remain unexplored. Understanding whether regulatory awareness influences student behavior is therefore important as higher education institutions create and apply AI policies. Objective: This study investigates how students awareness of GenAI regulations relates to their perceived compliance and actual usage behavior. Our research objective is to examine the association between regulatory knowledge, GenAI use, and perceived rule conformity among students in computer science related study programs. Method: A survey with 151 undergraduate students in Business Information Systems and E-Government programs at the University of Applied Sciences and Arts Hannover (Germany) collected data on GenAI usage, tools used, awareness of institutional regulations, and perceived compliance. Descriptive statistics, cross-tabulations, and correlation analyzes were applied. Results: Most students actively use GenAI tools, but over half are uncertain whether their usage complies with institutional regulations. Regulatory awareness shows only weak to moderate associations with actual usage behavior. Students primarily rely on privately accessed GenAI tools rather than institutionally provided solutions. Contributions: The study contributes empirical evidence on the relationship between regulatory awareness and GenAI usage in higher education. Our findings highlight a gap between institutional regulations and student practices and provide insights for educators and institutions on improving policy communication and integrating GenAI more effectively into teaching and learning contexts.

Municipal agencies increasingly use machine learning to inventory sidewalks, score streetscapes, and generate visualizations of public-space interventions. These systems produce outputs that enter budgeting, design iteration, and public justification, yet judgments about inclusion, safety, and belonging remain contested. This paper proposes Pluralistic-Alignment Urbanism (PAU), a procedural governance framework that treats public-space AI systems as civic infrastructure and formulates a procedural Right to AI for municipal uses of such systems. Drawing on two participatory case studies with community organizations in Montreal, Canada, the paper examines how disagreement, subgroup variation, bounded predictive scaling, and neutral preference judgments can inform municipal AI governance. Street Review elicits resident criteria for streetscape evaluation and trains a subgroup-aware scaling model for co-produced judgments, achieving an R2 of 0.89 on a held-out test set. LIVS, a Local Intersectional Visual Spaces dataset, constructs pluralistic preference data for aligning text-to-image models and treats neutral selections as evidence of indeterminacy. Across the cases, disagreement appears structured, deliberation changes what counts as evidence, scaling is feasible but limited by modality and coverage, and neutrality constrains what preference tuning can justify. PAU translates these constraints into a municipal governance architecture with disaggregated reporting, a versioned value register, standing deliberative cells, procurement clauses, and defined pause and rollback authority.

AI governance frameworks primarily focus on risks during the development and deployment phases, implicitly treating system withdrawal as a technical shutdown. This paper argues that decommissioned AI systems generate residual risk, termed AI debris, that persists after model removal and continues to shape institutional behaviour, accountability, and trust. AI debris is defined as the post-withdrawal socio-technical residue of AI systems, including workflow dependency, data contamination, capability displacement (deskilling), legitimacy erosion, and accountability breakdown. The paper develops a typology of debris domains and identifies mechanisms through which debris persists, including institutional memory, path dependency, blame avoidance, and feedback effects in organisational data. To operationalise the concept, the paper proposes an evaluator-ready AI Debris Decommissioning Protocol (AIDP), a stepwise checklist specifying auditable evidence for freezing decision footprints, incident review, remediation, contestability, and post-withdrawal accountability assignment. A brief vignette of Amazon's discontinued hiring tool illustrates how algorithmic decision categories and screening heuristics can persist after system rollback. The paper contributes a practical governance instrument for regulators, auditors, and organisations seeking to prevent paper compliance, strengthen AI lifecycle governance, and improve institutional resilience in high-stakes decision environments.

Background and Context. Problem decomposition is a core concern of computing education. It has also become increasingly relevant: in response to GenAI, many CS1 educators are advocating for shifting instructional emphasis away from code writing and towards decomposition and higher-level planning. Currently, there is a lack of knowledge in how novices do decomposition in large, multifunction tasks. Objectives. In this study, we describe how students represent solutions to a decomposition task, and characterize common issues that arise in those representations. Method. In a 50-minute lab, students were given a description of a word game and asked to draw (with pencil and paper) a decomposition diagram for a program that would implement this game. We performed an inductive thematic analysis with negotiated agreement on 55 of the diagrams, coding salient elements (e.g. functions and the relationships between them) and issues that arose. Findings. Students used multiple representational strategies, including hierarchical function calls and sequencing (order of execution). We identified issues in notation (including use of differing, incompatible notations within the same diagram), order of execution, abstraction and reuse, encapsulation, clarity, and problem-specific misunderstandings. Implications. These findings suggest that novice decomposition is shaped by multiple underlying models of program behavior, with tensions between structural and sequence-focused reasoning. We discuss implications for decomposition instruction and future work, including clarifying representational constraints and plan tracing as simulation.

As artificial intelligence (AI) pervades many decision-making domains, AI bias grows in importance. Although there is increasing awareness of the social and ethical consequences of biased AI, understanding bias from the perspective of those who develop these systems, such as the AI research community, is less clear. In this study, we employ topic modeling on 6520 articles to explore how the AI research community interprets the concept of bias. Our results show that the definition of bias is dispersed and complex within the community, often exhibiting even divergent conceptions (some even view and introduce bias as a tunable statistical parameter rather than an undesirable issue). The research community as a whole needs to engage more effectively with the concept of bias and establish a more cohesive understanding of it. We specifically argue that, although some sub-communities view bias as an issue that can be captured and mitigated through technical, computational, or statistical methods, it is not solely a technical problem. It instead involves contextual, social, and ethical factors that require broader sociotechnical perspectives and solutions.

Computer science students are expected to be able to look at a problem and select an appropriate algorithm design paradigm to use to produce a solution. However, there is little research on how students determine which algorithmic paradigm to use. Historically, researchers have relied on free-response questions or interviews to assess students' knowledge of algorithmic paradigm selection. To successfully evaluate and scale teaching interventions for selecting an algorithmic design paradigm, we need to efficiently test a student's ability to select among different design paradigms. Here, we present the first attempts to assess student knowledge to select an algorithm design paradigm using multiple-choice questions. We present the construction of the \textit{algorithmic paradigm selection assessment} (APSA) and preliminary data demonstrating its effectiveness as an assessment. We discuss the key points we learned during this process to write multiple-choice questions for Algorithm Design Paradigms. We tested the internal consistency of our assessment using Cronbach's $α$ and obtained a score of $0.73$, which is above the required threshold of $0.7$. APSA can be used across institutions as a standardized way to assess students' ability to select different algorithm design paradigms. APSA will assist researchers in evaluating whether a theory helps students improve their knowledge of different Algorithm Design Paradigms.

AI in education is stuck between two failed responses: banning AI and building content-only tutors. Both fail because they ignore what decades of research has established: that personality, motivation, and emotional state shape learning outcomes as strongly as cognitive ability. This paper proposes behavioural architecture as an alternative. In the proposed architecture, the system adapts to how a student learns, not only to what they learn next. The student co-authors the record the system keeps, can read it, revise it, and revoke it. The designer role, what the system treats as true about the student, shifts from the AI vendor alone to a distribution among educator, student, and system. The paper argues that this architecture requires governance at EU level: the institution operating the system is the same one assessing the student, and individual institutions cannot provide the structural protections this configuration demands. Five empirical questions are proposed to test whether the architecture delivers on its claims. The contribution is naming a vacancy: the designer role in AI-in-education is currently unoccupied, and occupying it requires infrastructure that does not yet exist.

AI governance still tends to assume that the relevant object is a bounded model or a bounded agent. That assumption is getting weaker. Real systems increasingly distribute cognition across models, tools, humans, context stores, retrieval layers, runtime policies, authorization boundaries, and delegated institutional roles. In such systems, the central governance problem is no longer only what the system did, but whether later institutions can still read what the system was. This paper introduces the khipu problem for distributed AI: the record can survive while the reading practice needed to interpret it decays. Logs, traces, model versions, tool calls, outputs, and approval artifacts may remain available while the institutional capacity to read them as parts of one coherent cognitive episode disappears. We argue that this failure is better understood as loss of interpretive continuity than as ordinary lack of observability. The result is a distinct governance failure. Institutions must classify, trust, audit, and constrain systems whose relevant identity is distributed across components and whose legibility depends on surrounding interpretive scaffolding. The problem is not merely missing data. It is a structural mismatch between what can be represented and what must still be decided under consequential conditions. We therefore argue that governance for distributed AI requires preservation of interpretive continuity, not only trace retention. The paper distinguishes missing evidence, ambiguous evidence, and structurally unreadable evidence; argues that many consequential outcomes are better understood as distributed cognitive episodes than as bounded model outputs; and proposes governance workspaces together with receipt-bearing governance surfaces as interpretive infrastructure for preserving action identity, authority, boundary truth, evidential scope, and consequential outcomes.

In this paper, we investigate a secure integrated sensing and communication (ISAC) system in which multiple communication users (CUs) coexist with multiple untrusted sensing users (SUs) that may eavesdrop on the confidential information intended for the CUs. To promote security fairness among users, we formulate a max-min secrecy rate optimization problem subject to a transmit power budget and sensing quality requirements characterized by beampattern matching error constraints. The resulting design problem is highly non-convex due to the secrecy rate expressions and non-convex sensing constraints. To address these challenges, we first reformulate the problem using semidefinite relaxation (SDR). Based on the reformulated problem, we develop a branch-and-bound (BB) framework combined with convex relaxations to obtain the globally optimal solution within a prescribed accuracy. To further reduce computational complexity, we propose a low-complexity algorithm based on successive convex approximation (SCA), which iteratively solves a sequence of convex subproblems and converges to a local solution. Numerical results demonstrate that the proposed BB algorithm achieves the global optimum and provides a benchmark for performance evaluation. Moreover, the proposed SCA-based algorithm attains near-optimal secrecy performance with significantly lower computational complexity, making it attractive for practical ISAC deployments.

The voter model is a classical stochastic process that models how opinions might spread through a network: at each step, every node lazily adopts the opinion of a random neighbour; eventually all nodes share the same opinion (consensus). Stronger connectivity should yield faster consensus. Berenbrink, Giakkoupis, Kermarrec, and Mallmann-Trenn (ICALP 2016) make this precise via the network's conductance: if the network has $m$ edges, minimum degree $d_{\min}$, and conductance at least $ϕ$, then the voter model reaches consensus in expected $O(m/(d_{\min}ϕ))$ steps. Their results extend to dynamic networks with fixed vertex degrees by considering the network's conductance at each time step. We introduce temporal conductance $Φ$, a more general connectivity measure for dynamic networks. Unlike static conductance, which collapses to $0$ whenever some snapshot is disconnected, $Φ$ captures connectivity through edges that appear at different times. We generalise the results of Berenbrink et al. from static conductance to temporal conductance, showing that the expected consensus time of the standard voter model is at most $O(m/(d_{\min}Φ))$. Moreover, we prove that this bound is tight up to constant factors. We expect temporal conductance to be a useful primitive for analysing other dynamics on temporal networks, and potentially time-inhomogeneous Markov chains more generally.

This paper applies a subdivision-based isogeometric method to solve the axisymmetric Maxwell eigenvalue problem. The reduction to an $H^1$-formulation allows to use a Catmull-Clark construction for both geometry and field discretization. The approach yields a numerical solution for the electric field, which is $C^1$-continuous everywhere except at extraordinary vertices. This is demonstrated by computing the eigenmodes of a TESLA 9-cell cavity, showing smoother fields with less numerical noise than conventional methods. The convergence rate of the method is numerically analyzed and is in agreement with rates observed in the literature.

The solution of large, sparse linear systems often dominates the computational effort of scientific applications and is a frequent optimization target. Modern libraries provide numerous solver and preconditioner configurations, but their performance varies significantly across problem instances. Previous works have addressed the selection of an optimal solver, but are typically limited by the problem set addressed (e.g., only symmetric positive definite matrices), the use of expensive matrix features, or the complexity of the approach. This work proposes a modular, low-cost embedding-based framework for solver selection that decouples performance modeling from feature representation and downstream prediction. Solver-problem relationships are learned directly from observed performance data, while inexpensive numerical features are used to project unseen problems into the learned embedding space. The framework focuses on multilabel prediction and evaluation using user-centric metrics, such as MAPE and nDCG, which better reflect relative performance. Experiments on 621 matrices from the SuiteSparse matrix collection across 101 PETSc solver configurations demonstrate a 17% increase in top-prediction accuracy over classical feature-based models when expensive numerical features are included, along with reductions of 37% in mean average percentage error (MAPE) and 46% in top-prediction error (1-error). When restricted to a reduced feature set, the embedding approach remains competitive, while still consistently achieving ca. 24% lower MAPE and 1-error across a broad range of problems.

We introduce a switching Hamiltonian Monte Carlo method for sampling from finite mixture Boltzmann-Gibbs distributions. We propose symmetric numerical integrators to approximate switching Hamiltonian dynamics interlaced with Poisson jumps, where the regime-switching chain is simulated using the uniformization technique or the stochastic simulation algorithm. We prove geometric ergodicity of the resulting Markov chain. We develop an approach based on the discrete Poisson equation associated with numerical schemes to estimate the error in computing ergodic averages. Using this approach we prove that the proposed numerical integrators have second-order bias. This approach is simple and can be generalized to other settings, for example, kinetic Langevin equations. Finally, we verify the convergence result via numerical experiment.

We prove that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations. We also study some families of finite configurations that have interesting period functions.

The uniform generation of k Hamming weight binary words, equivalent to sampling k-subsets from n elements, relies on random bits, which can be expensive. We introduce a novel paradigm, random bit recycling, and use it to generate such binary words in linear time while consuming as few random bits as possible. The resulting algorithm is nearly optimal in terms of random bit consumption, meaning that it closely matches the Shannon entropic lower bound coming from information theory.

A symmetric function is called Schur-positive if it admits an expansion in the Schur basis with nonnegative coefficients. In this paper, we study the Schur-positivity of symmetric functions naturally associated with set partitions, with respect to a descent set function that considers i as descent, if i and i+1 share a block in the partition. The Schur expansion involves hook-shaped Young diagrams, and the corresponding coefficients are given by Touchard-Riordan polynomials, which enumerate matchings by their number of crossings.

This paper studies feedback Nash equilibria (FNE) in scalar discounted linear quadratic (LQ) games with $N$ players. By explicitly incorporating the discount factor, we show that finite-cost equilibria may fail to stabilize the original system, motivating a distinction between FNE and stable FNE together with a sufficient stability condition. Based on a parametric characterization of the policies, we propose numerical methods for computing all equilibria. Particular attention is devoted to the symmetric game, where a closed-form expression of the symmetric FNE and conditions for the existence of up to $M\leq2^N-2$ equilibria are derived. Numerical experiments illustrate how equilibrium multiplicity depends on the game configuration and highlight the emergence of finite-cost non-stabilizing equilibria.

This paper studies a variation of the classic network alignment problem, named diffusion-network alignment. The goal is to align the vertices of a rooted diffusion tree to the vertices of a network, where the diffusion tree could be from a communication trace or contact tracing, and the network could be an online or offline social network. Different from the classic network alignment where both networks are fully observed, this model captures the information asymmetry of two networks. To solve this problem, this paper presents an efficient algorithm based on tree correlation tests to extract alignment information from local neighborhoods. We analyze the performance of the algorithm in the sparse graph regime and show that with high probability, all matched pairs are correct. Furthermore, for each vertex on the diffusion tree, this paper establishes an explicit lower bound on the probability that the vertex is correctly matched. These lower bounds are depth-dependent and increase as vertices get closer to the root.

Neural assemblies, transiently coordinated groups of neurons, observed in the hippocampus are thought to underlie the formation of episodic memories. Acetylcholine (ACh), a neuromodulator, that is received by the hippocampus, plays a critical role in memory and learning. A well supported hypothesis suggests that high levels of ACh during active exploration and rapid eye movement (REM) sleep promote memory encoding, while low levels during quiet waking and slow-wave sleep (SWS) support memory consolidation. We study this bidirectional role of ACh in neural assembly formation through its effect on the synchrony among neurons. We consider a network model of pyramidal neurons, each equipped with a slow, voltage-dependent, non-inactivating potassium current (M-current), which is downregulated in the presence of ACh. Neural assemblies are represented as cluster solutions to this system. Using a one-dimensional phase model reduction of a pair of weakly coupled pyramidal neurons under different levels of the M-current, we predict the symmetric cluster solutions that may emerge in larger networks equipped with all-to-all globally homogeneous, symmetric distance-dependent and nearest-neighbours coupling architectures. We find that under low ACh conditions, the network can fully synchronize, whereas high levels can desynchronize the network into multiple stable symmetric cluster solutions representing distinct neural assemblies.

Performing statistical inference is an essential component of data science. Our focus in this work is on two inference techniques, viz. regression and interpolation. We propose a reaction network based approach that can implement linear regression (both univariate and multivariate) and linear interpolation. We do this by encoding the steady state concentration of species as the output of these inference techniques. Towards this, we use a novel generalized division module that can handle division of negative numbers. We verify our results by comparing them with in-silico implementation on standard synthetic datasets.

We study a forward-time formulation of the Black-Scholes equation with state-dependent volatility. In contrast to the classical terminal-value pricing problem, where the option payoff is prescribed at maturity and the price is computed backward in time, the present problem prescribes the current option-price profile and seeks to recover the option-price profile at the expiration date T. This formulation is ill-posed, since the equation evolves in the unstable direction of the parabolic operator and high-frequency perturbations in the initial data may be strongly amplified. To address this difficulty, we introduce a price-dimensional reduction based on shifted Legendre polynomials. The original Black-Scholes equation is projected onto a finite-dimensional Legendre basis in the asset-price variable, leading to a system of ordinary differential equations in time for the expansion coefficients. This reduction acts as a spectral cutoff and also relaxes the degeneracy caused by the factor S^2 at the zero-price boundary. The main reconstruction method is a dimension-reduced Legendre--Tikhonov method. We prove existence, uniqueness, data stability, and convergence for each fixed truncation level. We also include a reduced PINN solver as a secondary computational comparison after the Legendre reduction. Numerical experiments with smooth, butterfly-spread, and European put payoffs show that the Legendre--Tikhonov method recovers the terminal option-price profile from noisy initial data, while the reduced PINN solver provides a useful additional benchmark. Comparisons with the conventional physical-space quasi-reversibility method demonstrate the stabilizing effect of the Legendre reduction.

Sunflowerability, or the infinite sunflower property, was introduced and studied by Ackerman, Karker and Mirabi as a structural generalization of the well-known Δ-system lemma for sets. It turns out that for relational Fra\''issé limits with strong amalgamation, this property is equivalent to the so-called galah property, which was introduced by Sullivan and Winkel as an asymmetric variation of indivisibility. This paper is about these two properties and is divided into three parts. In the first part, we show that the conjecture proposed by Ackerman, Karker and Mirabi about the infinite sunflower property in higher dimensions is far from being true by proving that no infinite structure has the infinite n-sunflower property in dimension k for any n, k \geq 2. In the second part, we give a complete characterization of the galah property for Henson directed graphs, homogeneous metric spaces and homogeneous ultrametric spaces, thereby answering the second question asked by Sullivan and Winkel. The third part contains several additional results about the finite sunflower property, including a strengthening of recent results about indivisibility for some classes of undirected graphs obtained by Guingona et al..

At first glance, one would imagine that the energy field of the Ising model, the set of edges whose endpoints share the same spin, is stochastically monotone as a function of the coupling constants. However, this is not generally the case. In this paper, we introduce two weaker notions of stochastic domination that make this result true: $p$--weak and $p$--weak$^\dagger$ domination. Both of these notions depend on a parameter $p$ and we find the optimal values $p$ and $p^\dagger$ so that these dominations hold. One of the key ingredient to obtain some of the results is a new stochastic domination relating FK percolations with different parameters $q,\tilde{q}\geq 1$ that is of independent interest.

There exist an absolute constant $c>0$ and arbitrarily large finite sets $A\subset \mathbb{R}$ with $$\left| \left\{x+y+(x-y)^2:\ x, y \in A\right\}\right| \le|A|^{2-c}.$$ Since $x+y+(x-y)^2 \in \mathbb{R}[x,y]$ is a polynomial which is neither additive nor multiplicative, this provides a counterexample for the Elekes-Rónyai problem.

Let $p \colon \mathcal{A} \to G$ be a Fell bundle over a locally compact Hausdorff second countable groupoid $G$ equipped with a Haar system, and let $Γ$ be a discrete group. Given a continuous $1$-cocycle $c \colon G \to Γ$, we show that the $\mathrm{C}^*$-algebra of the restricted Fell bundle $\mathcal{A}|_{G_e}$ embeds isometrically into $\mathrm{C}^*(G;\mathcal{A})$, where $G_e = c^{-1}(e)$ is the clopen subgroupoid corresponding to the identity element. We exploit this embedding to show that $\mathrm{C}^*(G;\mathcal{A})$ admits a natural structure of a topologically graded $\mathrm{C}^*$-algebra in the sense of Exel. As a consequence, we obtain a canonical coaction $δ$ of $Γ$ on $\mathrm{C}^*(G; \mathcal{A})$. We further show that the associated coaction crossed product $\mathrm{C}^*(G; \mathcal{A})\rtimes_δΓ$ is naturally isomorphic to the $\mathrm{C}^*$-algebra of a Fell bundle constructed from the cocycle data.

We study the problem of diffusion parameter estimation for stochastic differential equation (SDE) models in scenarios where data and model are compatible only on specific scales that have yet to be determined. We introduce a simple and efficient method for selecting suitable rates at which given time series data should be subsampled in order to ensure that the statistical structure of the subsampled data is consistent with the behavior of the SDE model on an infinitesimal scale. Our approach is based on analyzing the statistics of the lengths of monotonically increasing or decreasing segments in the subsampled data sequence, which we refer to as monotone runs. As an analytical foundation, we prove for a large class of SDEs with additive noise that the lengths of monotone runs at an infinitesimal scale are approximately geometrically distributed with success probability $1/2$. This universal characterization is employed to derive an automated method for selecting appropriate subsampling rates for given time series data that is directly applicable in real-world scenarios and does not rely on an asymptotic framework of multiscale diffusions. The approach is demonstrated using an application from industrial mathematics concerning surrogate models for fiber lay-down curves in production processes of nonwoven textiles.

We discover six new families of modular Nahm sums in ranks 3 and 4. Two of them are rank three sums obtained by modifying two of Zagier's rank three examples. Three rank four families are derived by applying the lift-dual operation to the rank three tadpole Nahm sums studied by Milas and Wang, while the other rank four family is found by the constant term method. To prove modularity, we establish Rogers-Ramanujan type identities that express these Nahm sums as infinite products which are modular.