We construct Igusa stacks for all Shimura varieties of abelian type and derive consequences for the cohomology of these Shimura varieties. As an application, we prove that the Fargues--Scholze local Langlands correspondence agrees with the semi-simplification of the local Langlands correspondences constructed by Arthur, Mok and others, for all classical groups of type $A$, $B$ and $D$; this extends work of Hamann, Bertoloni Meli--Hamann--Nguyen and Peng.

Locality-sensitive hashing (LSH) is a well-known solution for approximate nearest neighbor (ANN) search with theoretical guarantees. Traditional LSH-based methods mainly focus on improving the efficiency and accuracy of query phase by designing different query strategies, but pay little attention to improving the efficiency of the indexing phase. They typically fine-tune existing data-oriented partitioning trees to index data points and support their query strategies. However, their strategy to directly partition the multidimensional space is time-consuming, and performance degrades as the space dimensionality increases. In this paper, we design an encoding-based tree called Dynamic Encoding Tree (DE-Tree) to improve the indexing efficiency and support efficient range queries. Based on DE-Tree, we propose a novel LSH scheme called DET-LSH. DET-LSH adopts a novel query strategy, which performs range queries in multiple independent index DE-Trees to reduce the probability of missing exact NN points. Extensive experiments demonstrate that while achieving best query accuracy, DET-LSH achieves up to 6x speedup in indexing time and 2x speedup in query time over the state-of-the-art LSH-based methods. In addition, to further improve the performance of DET-LSH, we propose PDET-LSH, an in-memory method adopting the parallelization opportunities provided by multicore CPUs. PDET-LSH exhibits considerable advantages in indexing and query efficiency, especially on large-scale datasets. Extensive experiments show that, while achieving the same query accuracy as DET-LSH, PDET-LSH offers up to 40x speedup in indexing time and 62x speedup in query answering time over the state-of-the-art LSH-based methods. Our theoretical analysis demonstrates that DET-LSH and PDET-LSH offer probabilistic guarantees on query answering accuracy. This paper was published in TKDE.

Approximate Nearest Neighbor Search (ANNS) in high-dimensional Euclidean spaces is a fundamental problem with broad applications. Subspace Collision is a newly proposed ANNS framework that provides a novel paradigm for similarity search and achieves superior indexing and query performance. However, the subspace collision framework remains data-agnostic and query-oblivious, resulting in imbalanced index construction and wasted query overhead. In this paper, we address these limitations from two aspects: first, we design a subspace-oriented data transformation mechanism by averaging the entropies computed over each subspace of the transformed data, which ensures balanced subspace partitioning (in an information theoretical sense) and enables data-adaptive subspace collision; second, we present query-aware and scalable query strategies that dynamically allocate overhead for each query and accelerate collision probing within subspaces. Building on these ideas, we propose a novel data-adaptive and query-aware subspace collision method, abbreviated as TaCo, which achieves efficient and accurate ANN search while maintaining an excellent balance between indexing and query performance. Extensive experiments on real-world datasets demonstrate that, when compared to state-of-the-art subspace collision methods, TaCo achieves up to 8x speedup in indexing and reduces to 0.6x memory footprint, while achieving over 1.5x query throughput. Moreover, TaCo achieves state-of-the-art indexing performance and provides an effective balance between indexing and query efficiency, even when compared with advanced methods beyond the subspace-collision paradigm. This paper was published in SIGMOD 2026.

Motivated by growing evidence for the significance of the third-nearest-neighbor Heisenberg ($J_3$) interaction in candidate Kitaev materials, we investigate the dynamical properties of the Kitaev spin liquid (KSL) under a $J_3$ perturbation, focusing on its spin dynamical structure factor (DSF) and Raman scattering. Within a self-consistent parton mean-field plus random-phase approximation framework, we find that $J_3$ induces coherent, paramagnon-like collective modes that coexist with a high-energy Majorana continuum in the spin DSF. The softening of these modes with increasing $|J_3|$ signals a quantum phase transition to magnetic order. Remarkably, magnetic ordering sets in at a common critical $J_3$ for both ferromagnetic ($K<0$) and antiferromagnetic ($K>0$) Kitaev models, with the resulting ordered states forming exact dual pairs under a four-sublattice duality transformation that maps $(K,J_3) \rightarrow (-K,J_3)$. An external magnetic field further softens the preexisting paramagnon modes, thereby enhancing magnetic order. Perturbative Raman calculations show that while the Kitaev-like Raman vertex probes only itinerant matter Majorana fermions, the response from the $J_3$-like vertex features both matter Majoranas and visons. Four-vison excitations produce a sharp peak accompanied by a two-fermion continuum, whereas two-vison excitations yield a continuum closely resembling the single-matter-fermion density of states. These results provide a unified perspective on the dynamical signatures of $J_3$-perturbed KSL and are helpful for interpreting experimental spectra in candidate Kitaev materials with sizable $J_3$ interactions.

We prove that the algebra of invariants of a complete path algebra under the action of a homogeneous group of continuous algebra automorphisms is a complete path algebra and preserves finite or tame representation type.

This paper introduces a neural network model that learns multiple attributes as images and performs associated, sequential recall of the learned memories. Briefly, the model presented here is an associative memory model that extends previous models [1] by increasing the number of attributes. In the real world, memory recall generates a chain of associations consisting of complex and diverse data with meaningful relations. However, because this experimental system is designed to implement and verify the processing operations behind such operations, we believe it is not a problem if the associative memory (i.e., the chain of data) is composed of attributes that do not necessarily have clear relation with each other. Accordingly, the attribute-processing systems prepared in this study consist of five types: the C.CB-RN system for processing color attributes, the S.CB-RN system for shape attributes, and the V.CB-RN system for size attributes, as adopted in our previous paper [1], as well as the SV.CB-RN system for processing the names of the world's most beautiful scenery (spectacular view names) and the CN.CB-RN system for processing constellation names. As before, the data presented to each CB-RN system are represented as image patterns using QR codes [2]. These five types of CB-RN systems will be combined and trained with QR code pattern images of the attribute elements of each system. After that, when a pattern image of an attribute element is presented to any of the CB-RN systems, a mechanism will be constructed in which a chain (associative) recall of pattern images of related attribute elements in the other trained systems will be generated.

Collapse-locality is an untested loophole in the violation of Bell's inequalities. The core of the argument is that the time value of photon detection is delayed by the time Tc required by the collapse of its quantum state. The value of Tc is given by the underlying theory of quantum collapse, and is mostly unknown. Depending on the value of Tc, detections in the performed Bell's experiments may have not been truly space-like separated events. This implies that the inequalities may have been violated as a consequence of (conspiratorial) information propagating at subluminal speed. We report an optical Bell experiment which closes the weaker ('essential') form of this loophole regardless the theory of quantum collapse. This is possible thanks to unique features of the setup. These features are: classical signals sent to the stations to define a time reference, and variable distance between the stations leaving all other parameters constant.

Precision measurements of time-reversal (T) symmetry violating moments probe physics beyond the Standard Model. We show that precision spectroscopy of paramagnetic lanthanide and actinide ions doped into noncentrosymmetric crystals offers a promising platform for extending the sensitivity of searches for T-violation in nuclear physics. The unpaired valence electron in these ions allows the engineering of highly-coherent hyperfine transitions that are insensitive to magnetic fields, yet highly sensitive to new physics. These systems also provide other advantages for new physics searches, including large numbers of ions that can be measured in doped crystals, strong electric polarization of the ions by the crystal fields, enhancement of T-violating nuclear moments in nonspherical nuclei, and accurate comagnetometers generated by crystal symmetry. We estimate the new physics sensitivity of these proposed systems to be two orders of magnitude better than existing constraints.

In this paper, we prove polynomial growth bounds for the Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on the torus \T^d (d \ge 2), following and extending a result of Joseph Thirouin on \T [Thi17]. The key ingredient is the establishment of Strichartz estimates for the fractional Schrödinger equation on \T^d. To this end, we employ uniform estimates for oscillatory integrals to overcome the lack of uniformity that arises in higher dimensions.

Two data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to analyze the unsteady flow obtained by solving the Reynolds-averaged Navier-Stokes (RANS) equations in a 1.5-stage axial turbine. The reduced-order reconstructed pressure, dominant mode shapes, and dynamic features of these dominant modes in the downstream stator of the turbine are compared between POD and four DMD variants. It is found that the DMD methods based on the amplitude criterion, the Tissot criterion, and the sparsity-promoting DMD (SP-DMD) achieve reconstruction accuracy comparable to that of POD, while the frequency criterion proves unsuitable for the present problem. The second and third POD and DMD modes capture the dominant pressure fluctuation structures within the stator, and there is similarity between the corresponding POD and DMD spatial modes. The unsteady flow is primarily governed by neutral DMD modes characterized by high amplitudes and low frequencies corresponding to the basic and harmonic frequencies driven by the rotor passing frequency. While the POD analysis provides accurate reconstruction for the original snapshots, the time evolution of each POD mode does not reflect the true dynamic feature of the system. In particular, they misrepresent the fundamental frequencies of the problem. In addition, the correlations between the dominant modes in the downstream stator and the turbine adiabatic efficiency are explored across different stator clocking configurations. It is found that a clocking configuration with higher adiabatic efficiency at 50% span corresponds to a larger spatial and time component of the second and third DMD mode pair, and similarly a larger second POD mode.

Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $Δ$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(Δ)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(Δ)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.

The two-dimensional ferroelectric (FE) material CuInP$_2$S$_6$ (CIPS) has garnered considerable interest due to its out-of-plane ferroelectricity at room temperature. However, a notable discrepancy exists between experiments and density functional theory (DFT) calculations regarding the ground state of CIPS thin films: experiments suggest a state with net polarization, while DFT predicts an antiferroelectric (AFE) state as the lowest-energy state. Here, we investigate the stability of polarization states in CIPS thin films by combining first-principles calculations with the deep potential (DP) method. Our results reveal that for films thicker than the bilayer, an AFE state that has intralayer AFE ordering in the inner layers and intralayer FE ordering in the two surface layers has the lowest electronic energy. This state is significantly lower than the uniform FE state. In addition, we find that a ferrielectric (FiE) state with pure intralayer FE ordering is very close to the AFE state in energy. By using the DP model, we calculated the phonon free energy of CIPS thin films. For the monolayer, the intralayer FE ordering possesses a lower phonon free energy than the intralayer AFE ordering. This energetic preference for the intralayer FE ordering maintains as the thickness grows. Consequently, when the phonon-free energy is incorporated, the FiE state becomes energetically favorable over the AFE state for multilayers CIPS. Our findings demonstrate that the inclusion of vibrational entropy stabilizes the FiE state as the ground state in multilayers CIPS at finite temperatures, reconciling the previous discrepancy between experimental observations and DFT predictions. This insight is vital for understanding the FE properties of CIPS and its potential applications in devices.

Community associations rely heavily on resident surveys to guide decisions about amenities, infrastructure, and services. However, survey responses reflect perceptions that may not directly correspond to underlying operational conditions. This study bridges that gap by calibrating survey-based satisfaction measures against objective utilization data. Using parking and facility data from Tellico Village, we map perceived problem rates to utilization exceedance probabilities to estimate behavioral congestion thresholds. Results show that dissatisfaction emerges near effective capacity - once spatial, temporal, and informational constraints are considered - rather than at nominal capacity limits. Perceived difficulty is concentrated among active users and is shaped by operational frictions and incomplete system knowledge. These findings demonstrate that perceived congestion reflects constraints on access and reliability, not simply physical shortages. By distinguishing between effective and nominal capacity, the proposed framework enables more accurate diagnosis of system conditions. We propose incorporating behavioral metrics into community performance frameworks to support better decision-making, reduce unnecessary capital expansion, and target operational improvements more effectively.

Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing reasonable probabilistic guarantees may require many samples, which can be costly. To remedy this, we propose that calibration of reachable sets be performed using active learning strategies. In order to produce a probabilistic guarantee on the active learning, we adapt the Pick-to-Learn algorithm, which produces generalization bounds for standard supervised learning, to the active learning setting. Our method, Approximate Pick-to-Learn, treats the process of choosing data samples as maximizing an approximate error function. We can then use conformal prediction to ensure that the approximate error is close to the true model error. We demonstrate our technique for a simulated drone racing example in which learning is used to provide an initial guess of the reachable tube. Our method requires fewer samples to calibrate the model and provides more accurate sets than the baselines. We simultaneously provide tight generalization bounds.

We reassess the direct collapse black hole (DCBH) interpretation of UHZ1 (UNCOVER-26185), a gravitationally lensed galaxy at $z_\mathrm{spec}=10.054$. That interpretation rests on a hard ($2-7$ keV) X-ray excess detected with Chandra, attributed to a Compton-thick AGN with an inferred $2-10$ keV luminosity of $L_\mathrm{X,int}\sim10^{46}~\mathrm{erg~s^{-1}}$ (Bogdan et al. 2024). The resulting extreme X-ray to rest-frame optical-IR ratio was taken as the hallmark signature of an "outsize black hole galaxy" at cosmic dawn. We analyse the full 2.2 Ms Chandra imaging dataset -- including 0.95 Ms of unpublished observations -- and present new JWST/MIRI photometry at $λ_\mathrm{obs}>5~μ\mathrm{m}$. Across the full range of plausible Chandra data reductions, the $2-7$ keV excess at the position of UHZ1 reaches a significance of only $2.3-2.9σ$; the originally reported $4.2-4.4σ$ detection is sensitive to the specific astrometric alignment adopted and is not robustly reproducible. Moreover, the hard X-ray signal does not grow with the additional exposure, contrary to expectations for a steady source, indicating that any excess is not persistent. UHZ1 is also undetected in all nine MIRI imaging bands. Fitting red/obscured AGN SED templates to the tightest MIRI upper limit, we constrain the bolometric luminosity of any buried AGN to $L_\mathrm{bol}<1.3\times10^{45}~\mathrm{erg~s^{-1}}$. These conclusions are further supported by independent JWST spectroscopy (Alvarez-Marquez et al. 2026), which reveals no AGN signatures in the rest-frame UV or optical. Taken together, the multiwavelength data paint a consistent picture of UHZ1 as a low-mass, metal-poor, star-forming galaxy in the early Universe, with no compelling evidence for a luminous obscured AGN, regardless of its proposed formation channel.

Coronal plumes and chromospheric jet-like structures are believed to be highly dynamic. We report the first direct observations of a propagating kink wave in a chromospheric jet-like structure and its associated plumelet structure in the upper corona of the solar polar region, using data from the High Resolution Imager (HRI) of the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter (SO). The dark jet-like structure exhibits transverse oscillation during upward propagation, with a period of approximately 95s and a displacement of about 193km. The corresponding plumelet also displays transverse motion, with an oscillation period of around 99s and a displacement of about 315km. Given that both the dark jet-like structure and the plumelet share the same magnetic skeleton and have similar oscillation period, we suggest that these oscillations are the same transverse propagating wave originating in the chromosphere. This scenario is further supported by a 3D magnetohydrodynamic (MHD) simulation, in which both vertical and transverse perturbations were introduced in a stratified magnetic flux tube. The simulation successfully reproduces the upward propagation of a kink wave through both the chromospheric jet-like structure and the coronal plumelet. These results highlight the potential role of transverse waves in transferring energy from the lower solar atmosphere to the corona.

Let n denote the number of variables and m the number of equations in a sparse polynomial system over the binary field. We study the inconsistency probability of randomly generated sparse polynomial systems over the binary field, where each equation depends on at most k variables and the number of variables grows. Associating the system with a hypergraph, we show that the inconsistency probability depends strongly on structural properties of this hypergraph, not only on n,m, and k. Using inclusion--exclusion, we derive general bounds and obtain tight asymptotics for complete k-uniform hypergraphs. In the 2-sparse case, we provide explicit formulas for paths and stars, characterize extremal trees and forests, and conjecture a formula for cycles. These results have implications for SAT solving and cryptanalysis.

Purpose: To develop a motion-robust and geometrically-accurate quantitative CEST approach using radial k-space sampling, locally low-rank reconstruction and neural network quantification. Methods: The acquisition schedule was generated via deep learning optimization. The optimized sequence accuracy was validated in numerical simulations in digital phantoms. The spokes per measurement count was optimized using simulations and in vivo ablation studies in a healthy subject. Five healthy subjects were repeatedly scanned, and regions of interest were defined. Tissue maps from the proposed sequence were compared to an EPI-based quantitative CEST sequence. Motion sensitivity and test-retest reproducibility was assessed using the coefficient of variation (CV) and intraclass-correlation coefficient (ICC). Results: 3D quantitative CEST maps were acquired in 11 minutes using 34 spokes per measurement. Numerical simulations showed a mean error of <14% for all tissue parameters. In vivo tissue-parameter values agreed well with prior CEST-MRF studies in brain. The mean ICC over all tissue maps was 0.92 in white matter (WM) and 0.87 in grey matter (GM). The mean inter-subject CV was 5.4%/3.4% (WM/GM) and the motion vs. no-motion error was 265% for EPI but 8.6% for the radial acquisition. Conclusion: A motion-robust and geometrically accurate quantitative radial CEST pulse sequence and reconstruction framework is demonstrated. This approach enables accurate, reproducible 3D brain quantitative CEST imaging in clinically relevant scan times.

Design of soft matter capable of controllable microscale dynamics is a frontier of modern science. Jiahao Chen et al. demonstrate that an electric field can drive particle-like solitons-skyrmions in a chiral nematic along a preprogrammed trajectory with a variable speed within a two-dimensional plane. The effect is rooted in flexoelectric polarization of a deformed director field.

The Pak-Stanley labeling is a bijection between the regions of the $m$-Shi arrangement and the $m$-parking functions. Mazin generalized this labeling to every deformation of the braid arrangement and proved that this labeling is always surjective onto a set of directed multigraph parking functions. We provide a right inverse to the generalized Pak-Stanley labeling, and identify a class $\mathcal{C}$ of arrangements for which this labeling is bijective. The class $\mathcal{C}$ includes the multi-Shi arrangements and the multi-Catalan arrangements. We also show that the arrangements in $\mathcal{C}$ are the only transitive arrangements for which the generalized Pak-Stanley labeling is bijective.

We consider real hyperplane arrangements whose hyperplanes are of the form $\{x_i - x_j = s\}$ for some integer $s$, which we call deformations of the braid arrangement. In 2018, Bernardi gave a counting formula for the number of regions of any deformation of the braid arrangement $\mathcal{A}$ as a signed sum over some decorated trees. He further showed that each of these decorated trees can be associated to a region $R$ of the arrangement $\mathcal{A}$, and hence we can consider the contribution of each region to the signed sum. Bernardi also implicitly showed that for transitive arrangements, the contribution of any region of the arrangement is $1$. We remove the transitivity condition, showing that for any deformation of the braid arrangement the contribution of a region to the signed sum is $1$. This provides an alternative proof of the original counting formula, and sheds light on the geometry underlying the formula. We further use this new geometric understanding to better understand the contribution of a tree.

We provide simple presentations in terms of generators and relations for the invariant subring of both the Orlik--Solomon algebra and Varchenko--Gel'fand ring of the type $A_n$ reflection arrangement acted upon by the type $A_{n-1}$ reflection group. This may be interpreted as a presentation for the cohomology of the ``mixed configuration space" of $n$ red points and one blue point. We provide increasingly refined descriptions of the invariant ring starting with the total dimension and ending with the simple presentation in terms of generators and relations.

We study the problem of building space-efficient, in-memory indexes for massive key-value datasets with highly skewed value distributions. This challenge arises in many data-intensive domains and is particularly acute in computational genomics, where $k$-mer count tables can contain billions of entries dominated by a single frequent value. While recent work has proposed to address this problem by augmenting compressed static functions (CSFs) with pre-filters, existing approaches rely on complex heuristics and lack formal guarantees. In this paper, we introduce a principled algorithm, called AutoCSF, for combining CSFs with pre-filtering to provably handle skewed distributions with near-optimal space usage. We improve upon prior CSF pre-filtering constructions by (1) deriving a mathematically rigorous decision criterion for when filter augmentation is beneficial; (2) presenting a general algorithmic framework for integrating CSFs with modern set membership data structures beyond the classic Bloom filter; and (3) establishing theoretical guarantees on the overall space usage of the resulting indexes. Our open-source implementation of AutoCSF demonstrates space savings over baseline methods while maintaining low query latency.

We introduce a GPU-accelerated multigrid Gaussian-Plane-Wave density fitting (FFTDF) approach for efficient Fock builds and nuclear gradient evaluations within Kohn-Sham density functional theory, as implemented in the GPU4PySCF module of PySCF. Our CUDA kernels employ a grid-based parallelization strategy for contracting Gaussian basis function pairs and achieve up to 80% of the FP64 peak performance on NVIDIA GPUs, with no loss of efficiency for high angular momentum (up to f-shell) functions. Benchmark calculations on molecules and solids with up to 1536 atoms and 20480 basis functions show up to 25x speedup on an H100 GPU relative to the CPU implementation on a 28-core shared memory node. For a 256-water cluster, the ground-state energy and nuclear gradients can be computed in ~30 seconds on a single H100 GPU. This implementation serves as an open-source foundation for many applications, such as ab initio molecular dynamics and high-throughput calculations.

Open source software (OSS) sustainability depends not only on code contributions but also on governance structures that define who decides, who acts, and how responsibility is distributed. We lack systematic empirical evidence of how projects formally codify roles and authority in written artifacts. This paper investigates how OSS projects define and structure governance through their GOVERNANCE.md files and related documents. We analyze governance as an institutional infrastructure, a set of explicit rules that shape participation, decision rights, and community memory. We used Institutional Grammar to extract and formalize role definitions from repositories hosted on GitHub. We decompose each role into scope, privileges, obligations, and life-cycle rules to compare role structures across communities. Our results show that although OSS projects use a stable set of titles, identical titles carry different responsibilities, and different labels describe similar functions, which we call role drift. Still, we observed that a few actors sometimes accumulate technical, managerial, and community duties. %This creates the Maintainer Paradox: those who enable broad participation simultaneously become governance bottlenecks. By understanding authority and responsibilities in OSS, our findings inform researchers and practitioners on the importance of designing clearer roles, distributing work, and reducing leadership overload to support healthier and more sustainable communities.

The growing replication crisis across disciplines such as economics, finance, and other social sciences as well as computer science undermines the credibility of academic research. Current institutional solutions -- such as artifact evaluations and replication packages -- suffer from critical limitations, including shortages of qualified data editors, difficulties in handling proprietary datasets, inefficient processes, and reliance on voluntary labor. This paper proposes a novel framework leveraging new technological advances in trusted-execution environments (TEEs) -- exemplified by Intel Trust Domain Extensions (TDX) -- to address the replication crisis in a cost-effective and scalable manner. Under our approach, authors execute replication packages within a cloud-based TEE and submit cryptographic proofs of correct execution, for which journals or conferences can efficiently verify without re-running the code. This reallocates the operational burden to authors while preserving data confidentiality and eliminating reliance on scarce editorial resources. As a proof of concept, we validate the feasibility of this system through field experiments, reporting a pilot study replicating published papers on TDX-backed cloud VMs, finding average costs of \$1.35--\$1.80 per package with minimal computational overhead relative to standard VMs and high success rates even for novice users with no prior TEE experience. We also provide a conduct formal analysis showing that TEE adoption is incentive-compatible for authors, cost-dominant for journals, and constitutes an equilibrium in the certification market. The findings highlight the potential of TEE technology to provide a sustainable, privacy-preserving, and efficient mechanism to address the replication crisis in academia.

We propose a unified framework to draw inferences for regression coefficients in a generalized linear model (GLM) following Lasso-based variable selection. We adapt to non-Gaussian GLMs a recently developed parametric programming strategy for post-selection inference in the linear model with a Gaussian response by drawing parallels between maximum likelihood estimation in GLMs and least squares estimation in linear models. We then conduct post-selection inference based on a linearized model for pseudo response and covariate data strategically created based on the raw data. Using synthetic data generated from regression models for three different types of non-Gaussian responses in simulation experiments, we demonstrate that the proposed method effectively corrects the naive inference that ignores variable selection while achieving greater efficiency than a polyhedral-based post-selection adjustment.

We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing memory decoherence, while entanglement requests arrive according to Poisson and bursty ON--OFF processes. Using a queueing-theoretic framework, we couple physical-layer memory dynamics with congestion-dependent service behavior to analyze stability, delay, and fidelity trade-offs. Operating regimes are characterized in terms of the load parameter, showing that fixed cutoff policies impose a fundamental fidelity--latency trade-off together with strict stability limits. Queue-aware adaptive control strategies are then introduced that dynamically adjust memory cutoff times and the number of parallel entanglement-generation channels. Cutoff adaptation restores stability near critical load by trading fidelity for service capacity, whereas resource scaling increases capacity without degrading entanglement quality. Under bursty traffic, joint adaptation suppresses delay spikes while activating additional channels only during congestion periods. The framework is further extended to a two-user shared-resource scenario in which independent traffic flows compete for a common resource pool. Stability is determined by aggregate load, while adaptive resource redistribution stabilizes queues that diverge under fixed partitioning. These results provide a queue-aware congestion-control perspective for adaptive resource management in quantum networks.

Let $S$ be a set of $n$ points in a polygon $P$ with $m$ vertices. The geodesic unit-disk graph $G(S)$ induced by $S$ has vertex set $S$ and contains an edge between two vertices whenever their geodesic distance in $P$ is at most one. In the weighted version, each edge is assigned weight equal to the geodesic distance between its endpoints; in the unweighted version, every edge has weight $1$. Given a source point $s \in S$, we study the problem of computing shortest paths from $s$ to all vertices of $G(S)$. To the best of our knowledge, this problem has not been investigated previously. A naive approach constructs $G(S)$ explicitly and then applies a standard shortest path algorithm for general graphs, but this requires quadratic time in the worst case, since $G(S)$ may contain $Ω(n^2)$ edges. In this paper, we give the first subquadratic-time algorithms for this problem. For the weighted case, when $P$ is a simple polygon, we obtain an $O(m + n \log^{2} n \log^{2} m)$-time algorithm. For the unweighted case, we provide an $O(m + n \log n \log^{2} m)$-time algorithm for simple polygons, and an $O(\sqrt{n} (n+m)\log(n+m))$-time algorithm for polygons with holes. To achieve these results, we develop a data structure for deletion-only geodesic unit-disk range emptiness queries, as well as a data structure for constructing implicit additively weighted geodesic Voronoi diagrams in simple polygons. In addition, we propose a dynamic data structure that extends Bentley's logarithmic method from insertions to priority-queue updates, namely insertion and delete-min operations. These results may be of independent interest.

We examine the Lyness mapping (an integrable $N$th-order discrete system which can be generated from a one-dimensional reduction of the Hirota-Miwa equation) from the point of view of deautonomisation. We show that only the $N=2$ case can be deautonomised when one works with the standard form of the mapping. However it turns out that deautonomisation is possible for arbitrary $N$ when one considers the derivative form of the Lyness mapping. The deautonomisation of the derivative of the $N=2$ case leads to a result we have never met before: the secular dependence in the coefficients of the mapping enters through two different exponential terms instead of just a single one. As a consequence, it turns out that a limit of this multiplicative dependence towards an additive one is possible without modifying the dependent variable. Finally, the analysis of the `late' singularity confinement of the $N=2$ case leads to a novel realisation of the full-deautonomisation principle: the dynamical degree is not given (as is customary) simply by the solution of some linear or multiplicative equation, but is present in the growth of the non-linear (and non-integrable) late-confinement conditions.