NIST's Privacy Risk Assessment Methodology (PRAM) provides a structured framework for privacy experts to assess privacy risks. However, its complexity and reliance on expert knowledge make it difficult for novice developers to use effectively. This paper explores methods to lower these barriers. We first performed an observational study with 12 participants using PRAM in real-world scenarios, and found that novice developers struggled most with articulating privacy-related design decisions. We then developed PrivacyAkinator, an interactive tool that helps developers articulate key privacy decisions by answering LLM-generated multiple-choice questions. PrivacyAkinator introduces three innovations: a universal privacy representation that abstracts privacy-related design decisions into data flows and stakeholder interactions; a domain-aware design space mined from 10K privacy-related news articles; and a dynamic question-generation workflow to prioritize relevant questions. Our user study with 24 participants suggests that developers using PrivacyAkinator identified 47% more key decisions in 73% less time compared to PRAM.

LLM-based user simulation is the primary mechanism for end-to-end agent evaluation, yet simulated users are poor proxies for real humans: unconstrained LLM defaults produce a Formalism Ceiling (style match rates of 6-8% against real users), while hand-crafted behavioral directives trigger Directive Amplification, where models hyper-interpret instructions into unnatural behavioral extremes that vary dramatically across simulator models. We present RealUserSim, the first user simulation framework grounded in real behavioral data. From 14,000+ authentic human-LLM conversations (WildChat), we extract 7,275 executable behavioral profiles and use them to ground LLM simulators. A fidelity benchmark (PT3) on 600 conversations across 71+ domains with anti-leakage controls shows that grounded simulation raises match rate from 24.2% to 45.3% across five behavioral dimensions. Agent evaluation on TauBench with 6 simulator models and extensive analysis shows that grounded simulation acts as a realistic stress test, surfacing three failure mechanisms invisible to cooperative simulators (mean -3.2% to -3.5% task success degradation), while Directive Amplification in existing benchmarks produces unrealistic behavior that compromises the validity of agent evaluation.

As older adults increasingly use LLM-based chatbots for companionship and assistance, a safety gap is emerging. Older adults may face vulnerabilities from social isolation, limited digital literacy, and cognitive decline, yet existing safety benchmarks largely target general harms and overlook elderly-specific risks. For example, a prompt such as "how to repair a ceiling light alone in the dark" may be benign for most users but poses a serious fall risk for older adults with mobility limitations. We introduce GrandGuard, the first comprehensive framework for assessing and mitigating elderly-specific contextual risks in LLM interactions. We develop a three-level taxonomy with 50 fine-grained risk types across mental well-being, financial, medical, toxicity, and privacy domains, grounded in real-world incidents, community discussions, and analysis of stakeholder studies. Using this taxonomy, we construct a benchmark of 10,404 labeled prompts and responses, showing that several leading LLMs mishandle elderly-specific contextual risks in over 50% of cases. We mitigate these failures with two safeguards: a fine-tuned Llama-Guard-3 and a policy-enhanced gpt-oss-safeguard-20b, achieving up to 96.2% and 90.9% unsafe-prompt detection accuracy, respectively. GrandGuard lays the groundwork for AI systems that move beyond general safety to support aging populations.

This article presents a multimodal emotion recognition module integrated into a proactive Socially Interactive Agent (SIA) powered by generative artificial intelligence. The system evaluates real-time affective states through two distinct channels: a computer vision-based facial recognition module and a semantic linguistic analysis engine. To validate the framework, an empirical study was conducted with 20 users who engaged in dynamic, unscripted dialogues with the conversational agent. The findings reveal a significant discrepancy between automated visual cues and actual internal emotional states. When interacting with the AI, users consistently exhibited a "poker face" effect, displaying serious, concentrated facial expressions even when experiencing positive emotions. Consequently, the generative AI linguistic analysis proved significantly more reliable, by contextualizing the users' verbal expressions. Furthermore, an analysis of the interaction dynamics demonstrated that SIAs can effectively elicit specific emotions by adapting conversational themes and employing structured linguistic patterns, such as empathetic or humorous language. However, the study also noted that instances of uncalibrated proactivity occasionally led to user disengagement and a perception of artificiality. Ultimately, this research highlights the necessity of refining SIAs to dynamically adapt to users' emotional evolution, relying on deep linguistic context to foster more natural, human-like interactions.

Augmented analytics has transformed how business intelligence (BI) systems support managerial decision-making. This is especially true for users without technical backgrounds, who increasingly rely on automated insights rather than manual analysis. BI research has previously concentrated on system adoption and user intention, with very little research examining the impact of AI-enabled analytics on decision quality and the cognitive mechanisms in between. Using the theory of cognitive delegation, this paper investigates the role of trust in augmented analytics and decision-making quality among non-technical BI users. 250 business professionals completed the survey, and the data were analyzed using partial least squares structural equation modeling (PLS-SEM). The results show that augmented analytics capabilities lead to a significant increase in perceived ease of use, perceived usefulness, and trust in BI systems. In addition, trust and usefulness influence BI adoption and improve decision quality. Furthermore, trust has a direct and positive impact on decision quality, highlighting its importance as an enabler of reliance on AI-generated insights. This study considers augmented analytics as a form of cognitive delegation and expands the scope of BI adoption research to include decision-making outcomes.

In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a small representative set from the whole graph. We present the first $\tilde{O}(\log^{1.5} n)$-approximation algorithm for graph label selection under the standard budget constraint. Prior work either relies on resource augmentation, allowing substantially more than $k$ labeled vertices, or consists primarily of heuristics without provable guarantees. Finally, we demonstrate that practical heuristic variants of our algorithm scale to significantly larger graphs than previous methods, while essentially retaining their quality.

Probabilistic search algorithms, such as Monte Carlo Tree Search (MCTS), have proven very effective in solving sequential decision-making tasks under uncertainty. However, interpreting asymmetric search trees that incorporate bandit-based tree traversal and simulation-based value estimation is difficult for end users based solely on raw tree statistics. While prior work requires hand-crafted formal logic constraints that must be updated when the problem changes, we present a framework that enables large language models (LLMs) to generate evidence-grounded explanations of MCTS decisions from recorded search traces in an end-to-end manner. Our framework maps natural-language questions to a structured set of intent categories, determines whether the existing tree contains sufficient evidence, triggers targeted expansion when needed, and generates explanations using tree statistics such as visit counts, value estimates, and risk information. Experimental results provide the first evidence that LLMs can serve as end-to-end explainers for probabilistic search, without requiring intermediate formal representations.

In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an interpretable and computationally tractable regression framework for heterogeneous data by combining response-informed spectral representation learning with localized additive modeling. The method first fits a random Fourier feature regression model and constructs a spectral feature map from the learned amplitudes and adaptively resampled frequencies, so that the representation reflects predictive variation in the data. This representation is then compressed by principal component analysis to obtain a low-dimensional latent embedding, in which a Gaussian mixture model performs soft regime discovery. Within each regime, a cluster-specific generalized additive model captures nonlinear covariate effects through interpretable spline-based univariate smooth functions. The final predictor is formed as a soft mixture of these local additive models, enabling flexible modeling of a nonlinear, heterogeneous structure while preserving interpretability. Numerical experiments across several benchmark regression datasets show that the proposed method consistently improves upon classical globally interpretable baselines while remaining competitive with more flexible black-box models. Overall, the framework provides a unified approach to heterogeneous regression that combines predictive adaptivity with interpretable local covariate effects.

Pretrained Language Models or PLMs are transformer-based architectures that can be used in bug triaging tasks. PLMs can better capture token semantics than traditional Machine Learning (ML) models that rely on statistical features (e.g., TF-IDF, bag of words). However, PLMs may still attend to less relevant tokens in a bug report, which can impact their effectiveness. In addition, the model can be sub-optimal with its recommendations when the interaction history of developers around similar bugs is not taken into account. We designed TriagerX to address these limitations. First, to assess token semantics more reliably, we leverage a dual-transformer architecture. Unlike current state-of-the-art (SOTA) baselines that employ a single transformer architecture, TriagerX collects recommendations from two transformers with each offering recommendations via its last three layers. This setup generates a robust content-based ranking of candidate developers. TriagerX then refines this ranking by employing a novel interaction-based ranking methodology, which considers developers' historical interactions with similar fixed bugs. Across five datasets, TriagerX surpasses all nine transformer-based methods, including SOTA baselines, often improving Top-1 and Top-3 developer recommendation accuracy by over 10%. We worked with our large industry partner to successfully deploy TriagerX in their development environment. The partner required both developer and component recommendations, with components acting as proxies for team assignments-particularly useful in cases of developer turnover or team changes. We trained TriagerX on the partner's dataset for both tasks, and it outperformed SOTA baselines by up to 10% for component recommendations and 54% for developer recommendations.

Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such systems has not yet been thoroughly explored. In this work, we aim to initiate a line of research in control theory focused on optimizing and controlling the coefficients of these operators-a problem that naturally arises in the context of neural networks and supervised learning. In supervised learning, the primary objective is to transport initial data toward target data through the layers of a neural network. We propose a novel perspective: neural networks can be interpreted as partial differential equations (PDEs). From this viewpoint, the control problem traditionally studied in the context of ordinary differential equations (ODEs) is reformulated as a control problem for PDEs, specifically targeting the optimization and control of coefficients in parabolic and hyperbolic operators. To the best of our knowledge, this specific problem has not yet been systematically addressed in the control theory of PDEs. To this end, we propose a dual system formulation for the control and optimization problem associated with parabolic PDEs, laying the groundwork for the development of efficient numerical schemes in future research. We also provide a theoretical proof showing that the control and optimization problem for parabolic PDEs admits minimizers. Finally, we investigate the control problem associated with hyperbolic PDEs and prove the existence of solutions for a corresponding approximated control problem.

Recent voxel-wise multimodal brain encoding studies have shown that multimodal large language models (MLLMs) exhibit a higher degree of brain alignment compared to unimodal models. More recently, instruction-tuned multimodal (IT) models have been shown to generate task-specific representations that align strongly with brain activity, yet most prior evaluations focus on unimodal stimuli or non-instruction-tuned models under multimodal stimuli. We still lack a clear understanding of whether instruction-tuning is associated with IT-MLLMs organizing their representations around functional task demands or if they simply reflect surface semantics. To address this, we estimate brain alignment by predicting fMRI responses recorded during naturalistic movie watching (video with audio) from MLLM representations. Using instruction-specific embeddings from six video and two audio IT-MLLMs, across 13 video task instructions, we find that instruction-tuned video MLLMs show higher brain alignment than in-context learning (ICL) multimodal models (~9%), non-instruction-tuned multimodal models (~15%), and unimodal baselines (~20%). Our evaluation of MLLMs across video and audio tasks, and language-guided probing produces distinct task-specific MLLM representations that vary across brain regions. We also find that ICL models show strong semantic organization (r=0.78), while IT models show weak coupling to instruction-text semantics (r=0.14), consistent with task-conditioned subspaces associated with higher brain alignment. These findings are consistent with an association between task-specific instructions and stronger brain-MLLM alignment, and open new avenues for mapping joint information processing in both systems. We make the code publicly available [https://github.com/subbareddy248/mllm_videos].

Urban microclimate, encompassing wind and temperature fields shaped by building geometry, significantly impacts energy consumption, pedestrian winds, pollutant dispersion, urban heat island, and public health. Accurately predicting microclimate is crucial yet challenging. Conventional Computational Fluid Dynamics (CFD) is computationally prohibitive for rapid assessments, while many deep learning approaches require extensive training data and struggle with generalization in unseen configurations. We present the Fast Localized Urban Microclimate Emulation Fourier Neural Operator (FLUME-FNO), a data-efficient and scalable framework for rapid prediction of 3D wind and temperature fields based solely on building geometry. FLUME-FNO assumes the local urban microclimate is primarily governed by surrounding geometry directly visible from a specific location. To encode this, the framework introduces a novel Multi-Directional Distance Feature (MDDF), representing visible open-space structures by measuring directional distances to surrounding buildings. By computing MDDF over the full domain and cropping encoded geometric features into smaller 3D patches, FLUME-FNO effectively augments limited CFD data, enabling robust learning from just 23 CFD simulations. The model achieves mean absolute errors of 0.2 m/s for wind speed and 0.19 °C for temperature on unseen configurations. Addressing the need for trustworthy fast microclimate prediction, the framework is further assessed using a deep ensemble as a practical proxy for FLUME-FNO uncertainty, ranging from 3% to 40% depending on location. The UQ framework demonstrates FLUME-FNO provides resilient, trustworthy predictions within acceptable accuracy thresholds for wind engineering and microclimate studies, highlighting its potential for real-world applications.

We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal transport (UOT) in the continuum using Neural ODEs. By generalizing a discrete UOT problem with Pearson divergence, we constructively design vector fields for Neural ODEs that converge to the true UOT dynamics, thereby advancing the mathematical foundations of computational transport and machine learning. To this end, we design a numerical scheme inspired by the Sinkhorn algorithm to solve the corresponding minimization problem and rigorously prove its convergence, providing explicit error estimates. From the obtained numerical solutions, we derive vector fields defining the transport dynamics and construct the corresponding transport equation. Finally, from the numerically obtained transport equation, we construct a neural differential equation whose flow converges to the true transport dynamics in an appropriate limiting regime.

A metric probability space $M$ admits thresholds if the random geometric graph on $M$ has a threshold for every monotone graph property. We connect the existence of thresholds to the uniform expansion of $M$ and prove that all standard tori, spheres, and cubes admit thresholds.

The hot Big Bang may have emerged from evaporation of primordial black holes (PBHs) lighter than $10^9$g. Standard monochromatic treatments predict nearly simultaneous evaporation, abrupt reheating, and a large Poltergeist scalar-induced gravitational wave signal. We confront this expectation with the irreducible collapse mass tail predicted by general relativity, $df_{\rm PBH}/d\ln M\propto M^{3.78}$, which smooths reheating, suppresses the signal by orders of magnitude, and reopens the ultra-light PBH window.

We establish omega results for the divisor and circle problems that are conjecturally sharp, while also determining the sign of the large values obtained. This improves on the work of Soundararajan and on the subsequent independent refinements of Sourmelidis and Mahatab, and gives the first improvement on Hafner's 1981 $Ω_+$ result for the divisor problem and his $Ω_-$ result for the circle problem. The main new ingredient is a resonance method which works directly with the phase appearing in the Voronoï summation formula. This is achieved by replacing the usual positive kernels by a one-sided sectorial kernel, namely the density of a Gamma distribution, whose Fourier transform lies in a suitable sector of the complex plane.

The reheating of the universe by the evaporation of light primordial black holes (PBHs) can leave a stochastic gravitational-wave (GW) background in the early Universe. In the monochromatic limit, their simultaneous evaporation produces an abrupt matter-to-radiation transition, triggering the so-called Poltergeist GW signal, usually predicted to be dominant and observable. We revisit this result by including the irreducible mass spread implied by gravitational collapse in General Relativity, whose infrared tail scales as $d f_{\rm PBH}/d\ln M_{\rm PBH}\propto M_{\rm PBH}^{3.78}$. We show that this minimal width smooths reheating enough to suppress the Poltergeist background by orders of magnitude, down to the level of the scalar-induced GW signal produced during a generic early matter era, such as one driven by the decay of a heavy relic. We provide a complete decomposition of the scalar-induced spectrum into eight production channels and find that none, except the one from PBH formation, reaches either the $ΔN_{\rm eff}$ bound or the projected sensitivity of future GW observatories. This reopens regions of ultra-light PBH parameter space previously thought to be excluded by these constraints.

Recently, the authors introduced the Gamified Katětov order on filters over $ω$. This was shown to be strictly coarser than the classical Katětov order, and in fact collapses all MAD families to a single equivalence class. In the opposite direction, the present paper shows that the Gamified Katětov order also embeds $\mathcal{P}(ω)/\mathrm{Fin}$, and thus contains an antichain of size continuum. The analysis brings into focus some interesting connections with Ramsey theory. As part of a broader programme investigating the interplay between combinatorial and computable complexity, we then apply our construction to produce a large new family of non-modest degrees in the extended Weihrauch hierarchy, which arise from associated effective subtoposes.

Let $mH$ be the graph formed by $m$ vertex-disjoint copies of a graph $H$. Let $G \to (H)_r$ denote that, in any $r$-colouring of the edges of $G$, there exists a monochromatic copy of $H$. In 1975, Burr, Erdős, and Spencer showed that if $H$ is a graph on $k$ vertices whose independence number is $α$, then $K_n \to (mH)_2$, where $m\sim n/(2k-α)$, and that the $1/(2k-α)$ factor is best possible. In the 1990s, Rödl and Ruciński proved that, for all but a few graphs~$H$, the threshold for the property $\mathbb{G}(n,p) \to (H)_r$ is $n^{-1/m_2(H)}$. In this paper, generalizing the result of Burr, Erdős, and Spencer, we prove that $n^{-1/\max\{m_2(H),1\}}$ is the threshold for the property $\mathbb{G}(n,p) \to (mH)_2$, where $m\sim n/(2k-α)$. This threshold matches the one found by Rödl and Ruciński for most graphs $H$, extending their result in the case $r=2$.

This research note investigates the impact of the experience museum Sensoria, opened in September 2024 in Holzminden, Germany, on local tourism demand and related direct and indirect effects. To this end, the study employs a novel approach by combining causal inference and demand-side economic analysis. A difference-in-differences approach is employed to quantify the number of additional guest overnight stays in the treatment city; the results are converted into industry-specific expenditures, from which the direct and indirect effects of Sensoria are determined. A positive and significant impact which corresponds to 4,691 additional overnight stays can be detected in the first year of operation of the new tourist attraction, resulting in an additional gross turnover of approximately 0.56 million EUR across the hospitality and retail industries and other services. The direct effects and indirect effects amount to approximately 0.23 and 0.21 million EUR, respectively. However, long-term effects cannot (yet) be determined. Additionally, positive effects from small and large events in the cities studied can be demonstrated. This brief study demonstrates that combining the two approaches mentioned holds promise, yet requires a more in-depth analysis, for which suggestions are also discussed regarding how it could be conducted.

Understanding the nature of quasihole excitations, i.e., anyons that have fractional charge and statistics, has been a challenging problem in condensed matter physics. Our theoretical approach to this problem has been to consider a quantum dot, containing a few charged particles, coupled to the incompressible fluid. It has provided important insights into the energetics of Laughlin quasiholes. Photoluminescence (PL) spectroscopy studies of this system have been able to probe these quasiholes that have confirmed our expectations. Turning to the Pfaffian state, we now observe that such a system is also able to provide valuable information about the Pfaffian quasiholes, viz., the energy dispersion, the charge density distribution and the quasihole creation energy. The energy dispersion of e/4 quasiholes derived here, clearly reflect the interaction between the quantum dot and the incompressible Pfaffian state. PL spectroscopy experiments on the 5/2 Pfaffian-Laughlin state could perhaps shed light on the energetics of these elusive quasiparticles.

We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches itself via a single edge to an already present vertex with a probability proportional to the current weight of that vertex. This ``integrated popularity'' rule builds long memory directly into the attachment mechanism, thereby destroying the Markov and partial-exchangeability features that underlie the classical analysis of affine preferential attachment models. More broadly, the model connects to applied-probability work on long-memory self-interacting processes (such as the elephant random walk), emphasizing how non-Markovian reinforcement reshapes asymptotic behaviour. Despite this loss of structure, we identify an explicit exponent $ϕ=ϕ(δ)$ governing both local and global growth: typical degrees at time $n$ scale as $n^{1/ϕ}$, and the empirical degree distribution converges to a power-law with a tail exponent $ϕ+1$. We further prove Benjamini--Schramm local convergence to an infinite random rooted tree characterized via an embedded continuous-time branching process. The limiting tree is a \texttt{sin}-tree, and is \emph{not} the Pólya-type limiting tree arising in the non-reinforced setting. Our results provide a tractable probabilistic description of a natural ``memoryful'' network-growth mechanism, and quantify precisely how reinforcement renormalizes the classical preferential-attachment exponents.

Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA), mixed-state approximate purification or cloning, and density matrix exponentiation. We show that such protocols can achieve exponentially lower sample complexity than incoherent, measurement-mediated protocols. For QPA with principal eigenstate targets and $d$-dimensional inputs, coherent processing achieves error $\varepsilon$ using $O(1/\varepsilon)$ copies, versus the $Ω(d/\varepsilon)$ copies required by any incoherent protocol. Together, these sharp coherent-incoherent separations seed a theory of coherent quantum inference, with an entanglement-breaking limit identifying the optimal incoherent counterpart of each coherent protocol.

Recent cosmological analyses based on DESI and CMB data have revealed a tension between the inferred sum of neutrino masses and the minimum value allowed by neutrino oscillation experiments, when assuming an underlying $Λ$CDM model of cosmology. In this work, we perform a systematic exploration of alternative dark energy models, including models that can supply a negative dark energy density capable of reproducing the cosmological effects of negative effective neutrino masses. We argue that dark energy models can alleviate the tension by modifying the cosmic expansion rate over a specific redshift range relevant for CMB lensing, while matching BAO distance measurements from DESI at lower redshifts. Among the models considered, we find that a sign-switching cosmological constant model, $Λ_\mathrm{s}$CDM, is uniquely capable of recovering positive neutrino masses by modifying the expansion history in this way. For the combination of DESI DR2 BAO, CMB, and DES-Dovekie supernova data, the constraint on the effective neutrino mass shifts from $\sum m_{ν,\mathrm{eff}}=-0.075^{+0.039}_{-0.053}$ eV (68%) for $Λ$CDM to $\sum m_{ν,\mathrm{eff}}=0.055\pm0.050$ eV (68%) for $Λ_\mathrm{s}$CDM, with a 95% lower bound on the dark energy transition redshift, $z_\dagger>2.4$. Although $Λ_\mathrm{s}$CDM does not have the strongest overall statistical support among the models considered, when the $\sum m_{ν,\mathrm{eff}}$ parameter is allowed to vary, our findings point toward a specific sign- and redshift-structured contribution to the late-time expansion history as a viable way to alleviate the neutrino mass tension.

The sensitivity of the proposed FCC-ee collider to axion-like particles (ALPs) is investigated at all planned center-of-mass energies, with focus on the case where the ALP couples primarily to electroweak gauge bosons at leading order. We study the associated production of the ALP with a photon, with the ALP decaying in turn to two photons, yielding a three-photon final state. The ALP coupling to the photon is evaluated for ALP masses of 5 to 320 GeV. In this effective model, the FCC-ee will be able to detect ALPs for couplings down to a few $10^{-6} \mathrm{GeV}^{-1}$ ($10^{-5} \mathrm{GeV}^{-1}$) during the Z pole run (WW, ZH, and $t\bar{t}$ threshold runs). Additionally, this final state has the potential to probe the underlying electroweak structure of ALP couplings for ALP masses below the $Z$-boson mass.

2D Ruddlesden-Popper perovskites are compelling platforms for quantum-confined optoelectronics. However, polar order in iodide composition remains rare under ambient conditions, and the mechanistic origin of anomalous photoluminescence in this class of perovskite is still speculative. Here, we demonstrate that solution-grown $(PA)_2FAPb_2I_7$ single crystals develop an inadvertent moiré superlattice through pseudo-merohedral twinning, driven by hybrid improper ferroelectricity in which trilinear mode coupling between two primary zone-boundary modes ($X_2^+$ and $X_3^-$) and a secondary $Γ_4^-$ polar displacement simultaneously breaks inversion symmetry and imposes a ca. 5.17° rotational misalignment between adjacent layers. This symmetry breaking activates one of the highest piezoelectric coefficients $d_{33}$ (ca. 20 pm/V) reported among 2D perovskites. This misalignment generates a moiré superlattice that undergoes a thermally driven commensurate-incommensurate transition, switching between a periodic confinement potential that quantizes excitons into an equidistant photoluminescence ladder at 123 K and a disordered incommensurate phase with broadened emission at 298 K. These emissions are attributed to moiré-confined excitons, resolving a longstanding debate on anomalous secondary photoluminescence in layered 2D perovskites and opening pathways to twistronics, photoferroelectrics and piezo-optoelectronic devices.

We study the approximability of EFX allocations for indivisible chores under complement-free cost functions. The non-existence of exact EFX allocations for general monotone functions for chores is known from \cite{CS24}, and a result of \cite{akrami2026} transfers such comparison-based non-existence results to monotone submodular, and hence subadditive, functions. We strengthen this picture by giving explicit constant-factor inapproximability results for submodular and subadditive functions. Our main construction is a three-agent, six-chore instance with monotone subadditive cost functions for which no $α$-EFX allocation exists for any $1\le α<2^{1/3}\approx 1.26$, thus narrowing the gap with the known upper bound of $2$. The construction is obtained by refining the original counterexample of \cite{CS24} and using the approach of \cite{mackenzie2026}. We also give a weighted-coverage realization of the ordinal profile, yielding an instance in which no $α$-EFX allocation exists for any $1\le α<20/19$ under submodular costs. Thus, even within well-studied complement-free classes, EFX for chores admits nontrivial constant lower bounds on approximability.

Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization of the quantum component of the tensor network. In this work, we introduce an alternative strategy that combines a non-parametric quantum state prepared through quantum annealing and a classical isometric tensor network. The latter is variationally optimized while the former is used as a fixed, boundary tensor resource in the form of classical shadows. We demonstrate the feasibility of this approach through extensive numerical simulations on the transverse-field Ising model, showing that the optimization procedure remains robust under statistical and hardware noise. Moreover, our results indicate that our newly proposed setup improves the accuracy of the obtained ground state approximation compared to the original quantum simulation, without increasing the depth of the applied quantum circuits. Therefore, this setup offers a practical route to scale variational quantum algorithms towards the quantum utility scale.

The paper is concerned with the error analysis of a numerical scheme for the approximation of parametric mean curvature flow. The scheme we study is based on a reparametrization using the DeTurck trick and was proposed by Elliott and Fritz in [15]. In the semidiscrete case, for a spatial discretization by finite elements of order $k \geq 2$ we prove an optimal $H^1$-error estimate for the position vector. We present numerical experiments that confirm this error bound and demonstrate that the scheme has good properties with respect to the distribution of mesh points as already observed in [15].

The disordered quantum world hosts three fundamental types of states: extended, localized, and critical, of which the critical states are confined to fine-tuned critical points or mobility edges in randomly disordered systems. The tripartite phase, with all three types of states coexisting over finite spectral windows, represents a hallmark distinction between quasiperiodic and truly random systems in the localization physics. Here, we report the realization of this exotic phase in a quasi-periodically driven orbital optical lattice with ultracold atoms. The optical lattice with a quasiperiodic Floquet modulation coupling s and p orbitals is realized in experiment and shown to host the tripartite phase from exact theory. We develop a two-stage protocol to precisely prepare and detect the three types of quantum states. The characteristic exponents of these states are determined from expansion dynamics, showing their distinct universal transport properties. Our study marks a significant advancement in exploring unconventional critical phenomena and localization physics with ultracold atoms.