Causal inference methods (instrumental variables, difference-in-differences, regression discontinuity, etc.) are primary tools used across many social science milieus. One area where their application has lagged however, is in the study of productivity and efficiency. A main reason for this is that the nature of the stochastic frontier model does not immediately lend itself to a causal framework when interest hinges on an error component of the model. This paper reviews the nascent literature on attempts to merge the stochastic frontier literature with causal inference methods. We discuss modeling approaches and empirical issues that are likely to be relevant for applied researchers in this area. This review shows how this model can be easily put within the confines of causal analysis, reviews existing work that has already made inroads in this area, addresses challenges that have yet to be met and discusses core findings.

This paper explores a version of the classical Ces`aro integral operator for the Lebesgue space L2(0, 1) where we discuss its norm, adjoint, spectral properties, and invariant subspaces. An important tool will be semigroups of weighted composition operators on L2(0, 1).

This study presents a multi-task machine learning framework for simultaneous morphology classification and physical parameter estimation of eclipsing binaries using photometric light curves. We train Random Forest and XGBoost ensemble models on 845 of 995 well-characterized systems comprising three morphological configurations by extracting 51 domain-specific features from each phase-folded light. To assess generalization, 15% of systems were withheld as an independent test set before any model training. On this held-out set, the XGBoost model yields $R^2$ values of 0.88 for the effective temperature ratio, 0.91 for the primary surface potential, 0.92 for the secondary surface potential, 0.89 for inclination, and 0.77 for the mass ratio. Morphology classification achieves 95.4% accuracy on the cross-validation set with per-class F1 scores exceeding 0.90, while the held-out test set confirms generalization with 90.7% accuracy. We present a catalog of estimated physical parameters and classifications for these systems, identifying thousands of high-confidence candidates. Morphological classifications are independently validated against the OGLE Online Catalog of Variable Stars (OCVS), achieving a contact recall of 0.99 across 104692 matched systems. The model's generalization capability is validated by cross-matching predictions with independent Kepler catalogs, achieving 77% classification accuracy and recovering physical parameters with systematic deviations consistent with known selection biases, third-light dilution, and methodological differences between photometric and spectroscopic approaches. This work confirms that machine learning ensembles, when coupled with physics guided post-processing, can effectively bridge the gap between massive photometric surveys and detailed astrophysical characterization.

Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) provide an efficient framework for implementing polynomials of block-encoded matrices, and thus offer a systematic approach to quantum algorithm design. However, despite a number of recent advances, important limitations remain. In particular, QSP can only transform unitary matrices, by applying a polynomial to their eigenvalues, while QSVT is a singular-value transformation and thus one can only obtain the polynomial of Hermitian matrices. As a consequence, these techniques do not directly apply to an arbitrary non-Hermitian matrix that is not diagonalizable. In this work, we propose a simple yet powerful method to extend these ideas to arbitrary square matrices by acting on their eigenvalues. To this end, we introduce the notion of an $n$-regular block encoding, namely, a block encoding whose $k$-th power reproduces the $k$-th power of the encoded matrix for every $0 < k < n$. We show that applying QSP to any unitary with this property is equivalent to applying a polynomial of degree at most $n$ to the block-encoded matrix, independently of its internal structure. Moreover, we provide a simple construction that transforms any block encoding into an $n$-regular one using only $O(\log n)$ ancillary qubits and operations. Finally, we show that this construction induces the desired transformation on the eigenvalues associated with the Jordan normal form of the matrix.

The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a clock transition in the spectrum of quadrupolar nuclei (having spin length $I\geq 1$) to achieve a first-order suppression of noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a $\mathbb{Z}_2$-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states. We compute the dephasing time of the spin Kerr-cat qubit under a model of $1/f$ noise, as well as relaxation of the qubit due to breaking of the $\mathbb{Z}_2$ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (${}^{123}\mathrm{Sb}$) donors in silicon, we estimate that a coherence time of $T_2^*=100$ s could be achieved with this encoding. We propose a two-qubit gate mediated by hopping electrons and estimate that with an enhancement of measured quadrupolar splittings by a factor of $\approx 4$, a gate fidelity of $99\%$ could be achieved for spin Kerr-cat qubits encoded in ${}^{123}\mathrm{Sb}$ nuclear spins, neglecting errors that impact the electron while it is being shuttled and read out.

Reproducibility, traceability, and transparency in testing cyber-physical energy systems are crucial for scientific advancement and cross-laboratory collaboration. Current experimentation and test documentation practices lack formal semantics, making it difficult to reproduce experiments, share data, and apply, for example, the artificial intelligence-driven analysis. A dataspace that relies on structured ontologies aims to address these gaps by providing machine-actionable descriptions. In this work, we outline an ontology-driven approach for reproducibility of cyber-physical energy systems testing and illustrate its applicability through representative cross-laboratory use cases, demonstrating feasibility while identifying remaining semantic and metadata gaps that limit reproducibility. Based on these observations, we propose an open three-viewpoint ontology framework to guide future ontology extensions.

Higher-order interaction networks are typically modeled using hypergraphs or simplicial complexes, where interactions explicitly involve more than two nodes. Here we demonstrate that effective higher-order dynamical constraints emerge naturally on the 1-skeleton of a graph, provided the interaction carries nontrivial topological structure. We study phase-oscillator dynamics with edge phase lags modeled as a $U(1)$-valued connection. This structure induces a gradient Sakaguchi--Kuramoto-type flow and an associated twisted Laplacian whose spectrum depends on the cohomology class of the connection. We prove that the associated twisted Laplacian admits a zero mode if and only if the connection is cohomologically trivial, that is, when all cycle holonomies vanish. Consequently, synchronization is obstructed not by local pairwise mismatches, but by intrinsic topological frustration on cycles. We derive that the smallest eigenvalue of the twisted Laplacian scales with the magnitude of the holonomy, and its spectral transitions accurately predict the loss of stability of the phase-locked state as frustration is increased. For the specific case of constant phase lag, we analytically derive the critical transition point, $α_c = π/3$ for a pentagonal cycle, which is in quantitative agreement with previously reported numerical thresholds. Our results establish a spectral framework linking dynamical frustration to network cohomology, and show that transitions in remote synchronization are shaped by cycle-level topological constraints.

We implement methods from the geometry of numbers to give explicit estimates for the number of integral ideals in a number field. We pay particular attention to minimising the effect of the degree $n$ of the number field on the error term and avoid terms on the order of $n^{n^2}$. We do this by studying fundamental domains for the action of multiplying with units of infinite order in Minkowski space. With some lattice theory we show that one can make different choices for such a fundamental domain, which yield a smaller error, especially when the degree of the field extension is large. We also adapt Schmidt's partition trick to this generalised setting.

Energy systems optimisation models are a leading tool for informing decisions in the energy transition. However, these models often remain opaque, and results are frequently presented without a clear discussion of their epistemic limitations. We propose Diagnostic Modelling as a framework wherein modellers critically interrogate their models and explore uncertainties to uncover mechanistic explanations that offer policy-relevant insights. Mechanistic explanations provide fundamental understanding that remains valid despite model uncertainty and does not depend on detailed knowledge of a specific model. By adopting a more open and transparent approach to engaging with energy systems models, Diagnostic Modelling encourages the participation of a broader range of decision-makers, thereby building consensus in support of the energy transition.

We use high-resolution UV-to-optical imaging from the Hubble Space Telescope (HST) to construct spatially resolved spectral energy distributions (SEDs) for seven nearby ($z<0.07$) hard (14--195$\,$keV) X-ray-selected broad-line active galactic nuclei (AGN) with $L_{\rm bol}=10^{43.26}-10^{45.34}\,\rm{erg\,s^{-1}}$. The high spatial resolution of HST, which physically resolves structures on the scale of $\sim$50$\,$pc at $z=0.05$, enables the separation of AGN and host-galaxy emission through morphological decomposition with GALFIT, yielding improved measurements of AGN properties compared to those obtained with lower-resolution Swift UV/Optical Telescope (UVOT) data. AGN UV magnitudes derived from HST imaging (e.g., F225W) can differ by more than a magnitude from those from Swift/UVOT UVM2 due to extended nuclear emission. Additionally, the inclusion of high-resolution data at longer wavelengths (e.g., F814W) can significantly affect the resulting SED fit. Comparing fits of accretion disk and extinction models using HST and Swift/UVOT data, we find significant differences in the resulting parameters, with average differences of 2.0$\,$eV in the maximum disk temperature and 2.2$\,$mag in the AGN host-galaxy extinction. These differences ultimately lead to significant changes in bolometric luminosities and X-ray bolometric corrections, with the HST-based fits yielding average increases of $\sim$0.57$\,$dex and $\sim$0.66$\,$dex respectively. This demonstrates host-galaxy contamination in unresolved UV--optical data can strongly bias SED-based estimates of disk temperatures, extinction, bolometric luminosities, and X-ray bolometric corrections in AGN. Large-area, high-resolution imaging surveys from Euclid and the Nancy Grace Roman Space Telescope will extend these techniques to much larger AGN samples, enabling uniform, high-precision SED measurements in the near-IR.

This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides the unifying framework for the entire thesis. In Chapter 3 we study the characteristic Cauchy problem from a fully detached perspective. Chapter 4 is devoted to the Killing initial data problem, also analyzed within this detached framework. In Chapter 5 we investigate the transverse (or asymptotic) expansion of the metric at a general null hypersurface. Finally, Chapter 6 addresses the geometry of conformal null infinity.

The concept of cavity funneling has emerged recently as a promising route towards creating indistinguishable photons from highly dephased emitters. So far, all suggested solutions are solely based on dielectric cavities that require extremely high quality factors that are difficult to reach at visible wavelengths. Here we suggest a hybrid funneling architecture where a dephased emitter is coupled to a plasmonic nanoresonator that is enclosed by an outer dielectric cavity. The estimated lower limit of the outer cavity quality factor is found to be $\sim2$ orders of magnitude lower compared to a cascaded cavity system. Furthermore, the surrounding topology of our approach allows for a partial direct coupling between the emitter and the outer cavity which in turn can increase the overall system extraction efficiency $\left(β\right)$ by a factor of 12, boosting the probability of photon collection.

The anomalous magnetic moment of the tau lepton, $a_τ$, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau's extremely short lifetime, traditional spin-precession measurements remain inaccessible, necessitating innovative experimental strategies at high-energy colliders. This review provides a comprehensive overview of the current experimental landscape, highlighting the recent paradigm shift from LEP-era constraints to the unprecedented precision reached at the LHC. We emphasize the importance of Ultra-Peripheral Heavy-Ion Collisions (UPCs), which act as a ``photon-photon collider'' of extreme intensity. By leveraging the $Z^4$ enhancement of the coherent photon flux in Lead-Lead ($PbPb$) interactions, these collisions provide a theoretically robust ``quasi-static'' environment. These results are critically compared with the latest measurements from proton-proton collisions, including the recent CMS observation of the $γγ\to ττ$ process and the ATLAS constraints from the high-mass Drell-Yan tail. We evaluate their complementarity and the challenges related to Effective Field Theory validity at the TeV scale. Finally, we outline the future prospects for $a_τ$ at Belle II and the Future Circular Collider (FCC) stages. While FCC-hh in $PbPb$ mode provides a theoretically clean environment, its sensitivity remains limited to $\mathcal{O}(10^{-2})$. Conversely, the next generation of lepton facilities, specifically Belle II and FCC-ee, aims for the $\mathcal{O}(10^{-5})$ level, required to probe SM electroweak loop corrections. Long-term projections for a high-energy Muon Collider suggest a potential reach of $\mathcal{O}(10^{-6})$.

Efficient semantic access to industrial product data is a key enabler for factory automation and emerging LLM-based agent workflows, where both human engineers and autonomous agents must identify suitable components from highly structured catalogs. However, the vocabulary mismatch between natural-language queries and attribute-centric product descriptions limits the effectiveness of traditional retrieval approaches, e.g., BM25. In this work, we present a systematic evaluation of LLM-assisted dense retrieval for semantic product search on industrial electronic components, and investigate the integration of hierarchical semantics from the ECLASS standard into embedding-based retrieval. Our results show that dense retrieval combined with re-ranking substantially outperforms classical lexical methods and foundation model web-search baselines. In particular, the proposed approach achieves a Hit_Rate@5 of 94.3 %, compared to 31.4 % for BM25 on expert queries, while also exceeding foundation model baselines in both effectiveness and efficiency. Furthermore, augmenting product representations with ECLASS semantics yields consistent performance gains across configurations, demonstrating that standardized hierarchical metadata provides a crucial semantic bridge between user intent and sparse product descriptions.

Perceptual judgments of sequential stimuli are systematically biased by prior expectations and by the temporal structure of sensory input. In haptic discrimination tasks, these effects often manifest as time-order asymmetries, whereby the perceived difference between two stimuli depends on their presentation order. Here, we introduce a dynamical Bayesian model that accounts for these biases by combining noisy sensory measurements with an evolving internal representation of stimulus intensity. The model formalizes perception as an inference process in which prior expectations are updated by incoming stimuli and propagate in time between observations. We test the model on psychophysical data from vibrotactile discrimination experiments, in which participants compare pairs of sequential stimuli with varying intensities. With a small number of parameters, the model quantitatively reproduces both the direction and magnitude of time-order effects across subjects, as well as the observed inter-individual variability. The inferred parameters provide a compact description of perceptual biases in terms of prior expectations and noise characteristics. Beyond fitting the data, the model induces a transformation of stimulus space, leading to a subject-dependent geometry of perceived stimuli. In this transformed space, perceptual judgments exhibit approximate symmetries that are absent in the physical stimulus coordinates. These results suggest that temporal biases in perception can be understood as a consequence of dynamical inference, and that they impose non-trivial geometric constraints on perceptual representations.

Altermagnets feature unconventional magnetism due to their momentum-dependent spin splitting purely driven by magnetic order, for which a variety of transition-metal-based d-wave altermagnets have been proposed. However, carbon-based altermagnets in graphene structures remain elusive, even though magnetism in graphene nanostructures has been widely demonstrated. Here, we establish a symmetry-guided design principle to engineer i-wave altermagnets in graphene antidot superlattices and demonstrate the emergence of altermagnetic states in specific monolayer and bilayer graphene superlattices. By combining first principles methods and atomistic tight binding models, we show the appearance of an interaction-induced i-wave altermagnetic splitting, stemming from the intrinsic magnetic instability of 2D graphene antidot superlattices. Our work establishes a strategy to engineer i-wave altermagnetism in a graphene platform, putting forward a carbon-based platform for altermagnetic spintronics.

This paper presents a sensing management frame- work for integrated sensing and communications (ISAC) within cell-free massive multiple-input multiple-output (MIMO) systems to reduce pilot-based channel state information (CSI) acquisition overhead. Conventional communication systems rely on frequent channel estimation procedures that impose significant signaling overhead, consuming valuable time-frequency resources. To ad- dress this inefficiency, we propose a state-based architecture that partitions users into communication and sensing groups based on service requirements. When users are not requesting data, the system utilizes sensing capabilities to track their location. Upon receiving a communication request, the system transitions to communication mode, leveraging the tracked state for predictive beamforming to eliminate the need for uplink pilot training. We develop an extended Kalman filter (EKF) based tracking algorithm coupled with adaptive resource allocation strategies. Furthermore, we analyze the impact of inter-target interference and design a sensing management protocol that performs sensing operations only when necessary to maintain the accuracy of user location estimates. Simulation results demonstrate that the pro- posed EKF-based tracking and sensing management can support predictive beamforming with downlink spectral efficiency close to the perfect-CSI case, while requiring sensing only occasionally after an initial convergence period. The results also indicate that this performance is robust in a cell-free massive MIMO setup and can be achieved with practical sensing waveforms.

This paper develops a conceptual extension of the Kinetic Theory of Active Particles, building upon the framework introduced in [2]. Living systems cannot be adequately described within classical single-scale paradigms, even when refined. To overcome this limitation, we introduce a Multiscale Kinetic Theory of Active Particles (MS-KTAP), in which a sub-microscopic scale of interacting entities is incorporated into the description of collective dynamics. In this framework, the activity variable is interpreted as an emergent quantity arising from lower-scale regulatory mechanisms and influenced by interactions across higher scales. The proposed framework captures key features of living systems, including heterogeneity, adaptive decision-making, nonlinear and non-conservative interactions, spatial dynamics, and cross-scale feedback, within a unified mathematical structure. Competition and cooperation are thus described across multiple levels of organization. The first part of the paper derives the mathematical framework, while the second presents how specific models can be obtained. The paper concludes with perspectives on further developments, including possible integrations with scientific machine learning.

We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switching to a potential variable to obtain a Lagrangian density for the Korteweg-de Vries (KdV) equation. Building on this concept, we present the Lagrangian structure for bi-Hamiltonian systems, discuss the Lenard scheme in the symplectic formalisms, and apply this to construct pairs of Lagrangian multiforms. We discuss the key model of the KdV equation and some dispersionless limits of it. We present a pair of Lagrangian multiforms for these equations, one of which is new. We also consider the examples of polytropic gas dynamics and the constant astigmatism equation, for which no Lagrangian multiforms were previously known.

Fine-grained, per-micro-batch load balancing is essential for efficient Mixture-of-Experts (MoE) training, yet every prior dynamic scheduling scheme pays for it with extra communication that is hard to hide. Especially on modern bulk-transfer backends such as DeepEP. We make a simple but consequential observation: on the NVIDIA Hopper architecture the NVLink Copy Engine can move data between intra-node GPUs without consuming any SM cycles, effectively providing a nearly free communication channel that runs in parallel with compute kernels. FEPLB turns this idle hardware into a new parallel dimension for MoE load rebalancing. Its Two-Phase Dispatch first routes tokens across nodes via the standard EP backend, then redistributes dynamic-expert tokens and weights within the NVLink domain through the Copy Engine at nearly zero cost, while a lightweight CPU scheduler runs concurrently with static expert computation. Because FEPLB uses only Copy Engine and CPU that are orthogonal to those consumed by EP and PP, it coexists with existing parallel strategies without reconfiguration. On GLM-5's MoE layers (128 experts, no auxiliary loss, up to 16 H100 GPUs), FEPLB reduces the token straggler by 51-70% and the GEMM straggler by 50-68% with no measurable EP communication overhead. Its advantage grows with the EP degree: at EP=8, it achieves 2x lower token straggler than FasterMoE.

We present the serendipitous discovery of an overdensity of submillimeter galaxies (SMGs) in the field of SDSSJ0909-0108, a massive z~0.7 post-starburst galaxy from the SQuIGGLE survey. ALMA observations at 870um and 2mm reveal six galaxies within a 35'' region with flux ratios consistent with emission from dust. Given the rarity of 870um sources and the small field-of-view of ALMA, we speculate that some of these sources are physically associated. None of the sources are at the same redshift as the post-starburst, and four do not have spectroscopic redshifts. We suggest that follow-up optical and/or ALMA observations be carried out to measure redshifts for the galaxies in this potential protocluster environment.

We study the impact of neutron-skin thickness on $J/ψ$ photoproduction in ultra-peripheral $^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ collisions. Within the Color Glass Condensate framework, we calculate coherent and incoherent cross sections and examine their dependence on the momentum transfer $|t|$ for different neutron-skin thicknesses. We find a clear imprint of the neutron skin on the $|t|$ spectra: a larger neutron skin leads to a smoother and more extended color-density profile, suppressing the coherent cross section at large $|t|$ while enhancing the incoherent cross section through increased event-by-event configurational fluctuations in the nuclear periphery. We further show that the ratio of incoherent to coherent integrated cross sections provides a particularly sensitive and robust observable, with reduced theoretical uncertainties. These results establish diffractive vector-meson photoproduction in ultra-peripheral collisions as a powerful tomographic tool to constrain the neutron-skin thickness and the transverse gluon distribution at the LHC and future Electron-Ion Colliders.

We present the results of continuum-extrapolated lattice simulations of quantum chromodynamics (QCD) above the crossover temperature and for unprecedentedly high baryon densities at the physical point, employing the complex Langevin equation. In particular, we determine the QCD equation of state by computing the baryon density as well as the pressure as functions of the baryon chemical potential and the temperature. Potential issues with wrong convergence of complex Langevin dynamics are under control and we indeed find agreement with previous lattice studies working at smaller chemical potentials, as well as with perturbative hard-thermal-loop calculations at high temperatures.

The complexity and significance of multiscale phenomena in fusion energy systems make advanced modeling necessary for designing, optimizing, and safely deploying fusion plants. Tritium accountancy is one of those challenges for deuterium-tritium fusion systems. Its availability is constrained by its short half-life (12.33 years) and limited natural abundance, which require fusion plants to breed tritium onsite. Therefore, accurate tritium accountancy is essential for effective resource management, safety, and economics in fusion plants. Through the U.S. Department of Energy milestone program, Tokamak Energy Ltd. is developing a fusion pilot plant design and evaluating tritium retention and loss in key components and their effect on the fuel cycle. To rapidly explore design trade-offs and quantify design decisions on tritium management, this study presents a multiscale analysis to investigate tritium diffusion, trapping, and recovery in key plasma-facing components. To enhance computational efficiency, we integrate surrogate models at the component-level within a fuel cycle model at the system-level, enabling rapid evaluation of tritium recycling dynamics and inventory under various operational scenarios. The goal of this study is twofold: (1) demonstrate the feasibility of utilizing surrogate models to increase the accuracy of fuel cycle modeling, and (2) rapidly evaluate the performance of fusion technologies to accelerate design iterations. This multiscale model provides the tritium transport and retention behavior and supports the plasma-facing components design optimization in normal and bake-out operations. The work is implemented using the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source application for tritium transport analysis in fusion systems.

Starting from pseudometrics and preorders on sets of integers, we extend the focus to sets of finite sequences of integers, in particular sequences of consecutive integers. We outline existing concepts for deriving centred pseudometrics and preorders in a given pseudometric space and their application to $\mathbb{Z}$ and develop approaches to generalize the ideas to $\mathbb{Z}^m$. Sequences of consecutive integers represent a special case here and are examined in more detail. Another main topic is the use of arithmetic functions in this context. The types of pseudometrics and preorders examined in this paper can be induced by suitable arithmetic functions. We derive fundamental conclusions about relationships between functions and preorders, as well as about equivalent and potentially distinct types of preorders.

Air Traffic Flow Management (ATFM) traffic regulations are being increasingly used as rising demand meets persistent workforce shortages. This operational strain has amplified a critical phenomenon that we call \emph{regulation cascading}: the compounding, non-linear interactions that occur when multiple regulations influence one another in unpredictable ways. As the number and complexity of regulations grow, cascading effects become more pronounced, undermining the network operator's ability to protect sectors reliably. To address this challenge, we introduce Regulation Zero 2, an updated sequential planning framework that natively operates in the regulation space, optimizing over ordered sequences of flow-level regulations that remain compatible as much as possible with existing slot-allocation systems such as CASA and RBS++. We equipped Regulation Zero 2 with new heuristics to render flow finding more efficient. At its core, the method employs a hierarchical Monte Carlo Tree Search (MCTS) that first samples congestion hotspots and then selects candidate regulations synthesized by a local proposal engine. Each proposal is evaluated by a fast First-Planned-First-Served (FPFS) allocator to estimate its reward, with these feedbacks guiding the subsequent MCTS exploration. Experiments on many pan-European summer-peak traffic days that Regulation Zero delivers promising and consistent performance. Compared to a flight-centric simulated-annealing and NSGA-II baselines, it achieves markedly higher objective improvements, while maintaining a tighter scope of impact on the network. Ablation studies also found that Regulation Cascading could reduce up to 50\% of potential effectiveness. RZ also preserves FPFS fairness and supports expert knowledge injection, offering a pragmatic and low-disruption pathway toward automation in operations.

The intrinsic incommensurate charge density wave in metal-organic frameworks has remained elusive due to the lack of direct evidence linking atomic-scale structural modulation to macroscopic electronic properties. Using high-quality Pr3HHTP2 (HHTP = 2,3,6,7,10,11-hexahydroxytriphenylene) single crystals as a model system, we precisely resolve, for the first time, the incommensurately modulated structure of a conductive metal-organic framework at 100 K (modulation vector q = 0.39143(12) c*) via temperature-dependent single-crystal X-ray diffraction. The subsequent observation of a reversible metal-semiconductor transition around 350 K, which perfectly synchronizes with the disappearance of the structural modulation, provides convincing evidence for the electronic origin of the lattice distortion. Guest water molecules stabilize the modulated phase by synergistically regulating the relative rotation of the linkers and the interlayer spacing, thereby optimizing the inter-linker interactions. This work establishes a concrete experimental criterion for one-dimensional charge density wave in metal-organic frameworks and provides an ideal platform for probing coupled electronic-lattice modulations.

Dusty plasmas, composed of electrons, ions, neutral particles, and charged dust grains, exhibit self-organization phenomena such as string-like structures observed in microgravity experiments. The formation of these structures is influenced by ion wakes generated by streaming ions under external electric fields, as well as by time-evolving plasma inhomogeneities such as ionization waves. Existing ion wake models, such as point charge and Gaussian-based representations, often rely on configuration-specific parameters, limiting their general applicability. In this work, we present a robust and general potential model for dust and ion wake systems under PK-4-like conditions. Using a small set of coefficients determined from molecular dynamics simulations, the model captures the potential distributions for multiple interparticle distances. Its application to test cases and implementation in a small scale dust dynamics simulation demonstrates its applicability to a wide range of dust arrangements beyond string-like configurations.

We study asymmetric orbifolds of the $E_8\times E_8$ heterotic string from the perspective of worldsheet Dai-Freed anomalies. Focusing on cyclic symmetries $G = \mathbb{Z}_m$ that act chirally on the fermions and symmetrically on the bosons, we compute the corresponding spin-bordism invariants and derive the conditions for the vanishing of global anomalies from this perspective. In the fermionic description, these conditions are exactly the familiar level-matching constraints, together with the additional mod-2 conditions that appear for even $m$. We then discuss the same conditions from the transformation properties of higher-genus fermion partition functions and explain how the anomaly is matched under bosonization for a large class of inner automorphisms of the $E_8\times E_8$ lattice theory. This gives an interpretation of the standard consistency conditions for asymmetric heterotic orbifolds from the Dai-Freed anomaly perspective.

Graphs of solutions to the minimal surface equation over simply connected domains with boundary values 0 can have at most exponential growth.