The demand for high-precision indoor localization has grown significantly with the rise of smart environments, industrial automation, and location-aware applications. While massive Multiple-Input and Multiple-Output (MIMO) systems enable millimeter-level accuracy by leveraging rich Channel State Information (CSI), most existing solutions are optimized for static environments, where users or devices remain fixed during data collection and inference. Real-world applications, however, often require real-time localization in changing environments, where rapid movement, unpredictable blockages, and dynamic channel conditions pose significant challenges. To address these challenges, we introduce two data augmentation techniques designed to resemble blocked antennas, enhancing the generalizability of localization models to dynamic scenarios. Additionally, we enhance an existing Deep Learning (DL) model by incorporating attention modules, improving its ability to focus on relevant channel features and antennas. We train our model on data from a static scenario, augmented with the proposed techniques, and evaluate it on a dataset collected in changing scenarios. We investigate the performance enhancements achieved by the data augmentation techniques and the Attention modules, and observe a localization accuracy improvement from a mean error of 286 mm, when trained without Attention and without data augmentations, to 66 mm, when trained with Attention and data augmentation. This shows that high localization accuracy can be maintained in changing environments, even without training data from those scenarios.

Human-AI collaboration faces growing challenges as AI systems increasingly outperform humans on complex tasks, while humans remain responsible for orchestration, validation, and decision oversight. To address this imbalance, we introduce Human Tool, an MCP-style interface abstraction, building on recent Model Context Protocol designs, that exposes humans as callable tools within AI-led, proactive workflows. Here, "tool" denotes a coordination abstraction, not a reduction of human authority or responsibility. Building on LLM-based agent architectures, we operationalize Human Tool by modeling human contributions through structured tool schemas of capabilities, information, and authority. These schemas enable agents to dynamically invoke human input based on relative strengths and reintegrate it through efficient, natural interaction protocols. We validate the framework through controlled studies in both decision-making and creative tasks, demonstrating improved task performance, reduced human workload, and more balanced collaboration dynamics compared to baseline systems. Finally, we discuss implications for human-centered AI design, highlighting how MCP-style human tools enable strong AI leadership while amplifying uniquely human strengths.

Rendering diffuse global illumination in real-time is often approximated by pre-computing and storing irradiance in a 3D grid of probes. As long as most of the scene remains static, probes approximate irradiance for all surfaces immersed in the irradiance volume, including novel dynamic objects. This approach, however, suffers from aliasing artifacts and high memory consumption. We propose Neural Irradiance Volume (NIV), a neural-based technique that allows accurate real-time rendering of diffuse global illumination via a compact pre-computed model, overcoming the limitations of traditional probe-based methods, such as the expensive memory footprint, aliasing artifacts, and scene-specific heuristics. The key insight is that neural compression creates an adaptive and amortized representation of irradiance, circumventing the cubic scaling of grid-based methods. Our superior memory-scaling improves quality by at least 10x at the same memory budget, and enables a straightforward representation of higher-dimensional irradiance fields, allowing rendering of time-varying or dynamic effects without requiring additional computation at runtime. Unlike other neural rendering techniques, our method works within strict real-time constraints, providing fast inference (around 1 ms per frame on consumer GPUs at full HD resolution), reduced memory usage (1-5 MB for medium-sized scenes), and only requires a G-buffer as input, without expensive ray tracing or denoising.

We investigate thermal and non-local electrical transport in four-terminal Josephson junctions formed by a normal region coupled to two transverse chiral superconducting leads, supporting phases characterized by Chern numbers ${\cal C}=0,\,1$\,and\,2. We identify the conditions under which a single chiral Majorana mode (${\cal C}=1$) produces a robust half-quantized thermal conductance, while non-local electrical conductance remains strongly suppressed by particle-hole symmetry. Thermal conductance quantization occurs near a superconducting phase difference $π$, but only in the low-doping regime of the central region and in the intermediate- to long-junction limits. At finite Zeeman fields, the thermal response broadly follows the topology of the isolated superconducting leads for the $C=1$ phase while, in the ${\cal C}=2$ phase, the thermal conductance generally deviates from quantization, depending on the momentum-space location of the Majorana modes. Our results establish clear criteria for probing chiral Majorana modes in Josephson junctions and highlight the essential role of momentum-space structure, finite-size geometry, and sample parameters in thermal transport.

Recent works have shown how the electrical properties of graphene nanoribbons (GNRs) show a size-dependence in terms of resistivity, charge neutrality point (CNP) and band structure once their widths drop below approximately 50 nm. It has been observed that the CNP switches sign below a certain GNR width, and in this article, we explore this via computational modelling of the electric field and the conductance of GNRs in the presence of an AFM tip. We show that CNP is expected to shift towards lower values as GNR width reduces as a result of the significantly enhanced electric field around edges, but that a change in sign is not expected. We also show experimentally via high-resolution Scanning Gate Microscopy (SGM) that there does not appear to be any significant difference between the edges and the bulk of a GNR, indicating that the switch in CNP is not due to differential doping, and may instead be due to variations in the band structure as a function of size.

In recent years, the widespread adoption of Machine Learning as a Service (MLaaS), particularly in sensitive environments, has raised considerable privacy concerns. Of particular importance are membership inference attacks (MIAs), which exploit behavioral discrepancies between training and non-training data to determine whether a specific record was included in the model's training set, thereby presenting significant privacy risks. Although existing defenses, such as adversarial regularization, DP-SGD, and MemGuard, assist in mitigating these threats, they often entail trade-offs such as compromising utility, increased computational requirements, or inconsistent protection against diverse attack vectors. In this paper, we introduce a novel inference-time defense mechanism called Neighborhood Blending, which mitigates MIAs without retraining the model or incurring significant computational overhead. Our approach operates post-training by smoothing the model's confidence outputs based on the neighborhood of a queried sample. By averaging predictions from similar training samples selected using differentially private sampling, our method establishes a consistent confidence pattern, rendering members and non-members indistinguishable to an adversary while maintaining high utility. Significantly, Neighborhood Blending maintains label integrity (zero label loss) and ensures high utility through an adaptive, "pay-as-you-go" distortion strategy. It is a model-agnostic approach that offers a practical, lightweight solution that enhances privacy without sacrificing model utility. Through extensive experiments across diverse datasets and models, we demonstrate that our defense significantly reduces MIA success rates while preserving model performance, outperforming existing post-hoc defenses like MemGuard and training-time techniques like DP-SGD in terms of utility retention.

Next-generation wireless networks at upper mid-band and millimeter-wave frequencies require accurate site-specific deterministic channel propagation prediction. Wireless ray tracing (RT) provides site-specific predictions but demands high-fidelity three-dimensional (3D) environment models with material properties. Manual 3D model reconstruction achieves high accuracy but requires weeks of expert effort, creating scalability bottlenecks for large environment reconstruction. Traditional vision-based 3D reconstruction methods lack RT compatibility due to geometrically defective meshes and missing material properties. This paper presents Holistic Reconstruction with Automated Material Assignment (HoRAMA) for wireless propagation prediction using NYURay. HoRAMA generates RT-compatible 3D models from RGB video readily captured using a smartphone or low-cost portable camera, by integrating MASt3R-SLAM dense point cloud generation with vision language model-assisted material assignment. The HoRAMA 3D reconstruction method is verified by comparing NYURay RT predictions, using both manually created and HoRAMA-generated 3D models, against field measurements at 6.75 GHz and 16.95 GHz across 12 TX-RX locations in a 700 square meter factory. HoRAMA ray tracing predictions achieve a 2.28 dB RMSE for matched multipath component (MPC) power predictions, comparable to the manually created 3D model baseline (2.18 dB), while reducing 3D reconstruction time from two months to 16 hours. HoRAMA enables scalable wireless digital twin creation for RT network planning, infrastructure deployment, and beam management in 5G/6G systems, as well as eventual real-time implementation at the edge.

This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given values of the parameters. Traditional continuation methods for one-dimensional parameterizations employ the previously computed solution as the initial guess for the next parameter value. These are usually very inefficient, since small step sizes increase computational cost, while larger steps could jeopardize the method convergence jumping to a different solution branch or missing the bifurcation point. To address these challenges, we propose a novel framework that combines: (i) arclength continuation, adaptively selecting new parameter values in higher dimension, and (ii) the deflation technique, discovering multiple branches to construct complete bifurcation diagrams. In particular, the arclength continuation method is designed to handle multiparametric scenarios, where the parameter vector $λ\in \mathbb{R}^p$ traces a curve $g(λ)$ within a $p$-dimensional parameter space. In addition, we introduce a zigzag path-following strategy to robustly track the bifurcation curves and surfaces, respectively, for two- and three-dimensional parametric spaces. Finally, we demonstrate its performance on two benchmark problems: the Bratu equation and the Allen-Cahn equation.

We revisit the problem of isospectral spherical space forms with non-cyclic fundamental groups after the works by Ikeda, Gilkey and Wolf. We find the first pair of spherical space forms with non-isomorphic fundamental groups and the same Laplace spectrum. This shows that the isomorphism class of the fundamental group is not audible among spherical space forms. We also found several instances where one can hear the fundamental group of a spherical space form (among spherical space forms).

Physical reservoir computing (RC) utilizes the intrinsic dynamical evolution of physical systems for efficient data processing. Emerging optoelectronic RC platforms,such as light-driven memristors, merge the benefits of electronic and photonic computation. However, conventional designs are often limited by the unipolar photoresponse of optoelectronic devices, which restricts reservoir state diversity and reduces computational accuracy. To overcome these limitations, we introduce an all-optically controlled RC system employing an oxide memristor array that demonstrates exceptional uniformity and stability. The memristive devices exhibit wavelength-dependent bipolar photoresponse, originating from light-induced dynamic evolution of oxygen vacancies. Tuning the power density and irradiation mode of dual-wavelength light pulses enables dynamic control of photocurrent relaxation and nonlinearity. By leveraging these unique device properties, we develop bipolar and parallel coding strategies to significantly enrich reservoir dynamics and enhance nonlinear mapping capability. In word recognition and time-series prediction tasks, the bipolar coding demonstrates markedly improved accuracy compared to unipolar coding. The parallel coding supports multi-source signal fusion within a single reservoir, maintaining high computational accuracy while significantly reducing hardware consumption. This work provides a high-performance approach to physical RC, paving the way for intelligent edge computing.

Modelling and simulating mine counter measure search missions performed by autonomous vehicles equipped with a sensor capable of detecting mines at sea is a challenging endeavour. To address this, we formulated and implemented the problem as a stochastic optimal control model. Our implementation computes an optimal path within a user chosen quadrilateral domain such that the mission duration is minimized for a given residual risk of undetected sea mines. First, we compare the stochastic optimal control implementation against the traditionally used boustrophedon implementation. We show that the mission duration in case of the stochastic optimal control implementation is shorter. Then, by building on our previous work, we introduce a novel mathematical approach that enables multiple autonomous survey vehicles to investigate the domain concurrently. We present results for up to six vehicles, including computed trajectories and an analysis of how mission duration varies with the number of vehicles. Our findings show that mission time decreases non-linearly, , i.e., we observe diminishing returns as more vehicles are added.

The dual-radiator Imaging Cherenkov detector (dRICH) is a key component of the forward particle identification system for the ePIC experiment at the Electron-Ion Collider (EIC). This study evaluates the dRICH performance using Geant4 simulations in the context of the global ePIC simulation stack, focusing on the optimization of the aerogel radiator and the impact of sensor noise. We compare two aerogel configurations: the initial design (n=1.019) and the current default (n=1.026). The latter, characterized by improved optical properties and a higher refractive index, demonstrates enhanced $π-K$ separation at high momenta, effectively extending the operational overlap with the $\mathrm{C_2F_6}$ gas radiator. Additionally, the study investigates the impact of Silicon Photomultiplier (SiPM) dark noise, showing that a 300 kHz noise rate per channel leads to a moderate reduction (approximately 1.5 GeV/c) in the $3σ$ separation threshold. These results validate the current dRICH design and quantify the purity levels achievable for both radiators under expected experimental conditions.

We present time-series medium-band (R~20-40) observations of the third interstellar object 3I/ATLAS (C/2025 N1) obtained with the 7-Dimensional Telescope (7DT), enabling spatially resolved monitoring of its gas and dust activity from 2025 July to September. The m400-band image (lambda_c = 400 nm, Delta lambda approx 25 nm) reveals the emergence of pronounced and spatially extended CN emission at heliocentric distances r_h < 3 au. This onset is consistently identified across multiple diagnostics, including a break in the light-curve evolution, excess reflectance, inward expansion of annular excess beyond 10,000-20,000 km, growth of the coma half-light radius from ~11,000 to ~19,000 km, and a rapid rise in the CN production rate Q_CN relative to Af rho. We further separate the CN-emitting and dust-scattered components through two-dimensional surface-brightness fitting into inner (dust) and outer (gas) components. The outer component preserves a nearly constant profile shape, varying only in normalization, implying relatively fast expansion of CN-bearing molecules. Together, these results reveal a transition in the optical from dust-dominated scattering at large heliocentric distances to volatile-driven, gas-dominated activity as 3I/ATLAS enters the inner Solar System. The timing and characteristics of the CN activation resemble the volatile enhancement observed in 2I/Borisov, suggesting that both known active interstellar objects exhibit comparable activation behavior at heliocentric distances of ~2-3 au.

Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic games. This motivates us to study the problem of characterizing the complexity and memory requirements for two-player stochastic games with Boolean combinations of qualitative reachability and safety objectives. Reachability objectives require that a given set of states is reached; safety requires that a given set is invariant. A qualitative winning condition asks that an objective is satisfied almost surely (AS) or (in negated form) with non-zero (NZ) probability. We study the determinacy and complexity landscape of the problem. We show that games with conjunctions of AS and NZ reachability and safety objectives are determined, and determining the winner is PSPACE-complete. The same holds for positive boolean combinations of AS reachability and safety, as well as for negations thereof. On the other hand, games with full Boolean combinations of qualitative objectives are not determined, and are NEXPTIME-hard. Our hardness results show a connection between stochastic games and logics with partially-ordered quantification. Our results shed light on the relationship between determinacy and complexity, and extend the complexity landscape for stochastic games in the multi-objective setting.

A flip of a graph is obtained by complementing the edge relation within a set of vertices. Flips are typically used to separate vertices in a graph, by increasing the distances between them. We show that in $K_{t,t}$-free graphs, every short sequence of flips can be simulated by a short sequence of vertex deletions that achieves a similar degree of separation: distances in the resulting graph are, up to a factor of three, at least as large as those obtained after the flips. This result provides a simple and uniform explanation of an emerging pattern in structural graph theory and finite model theory: the $K_{t,t}$-free fragment of a tameness notion for dense graphs often coincides with a tameness notion for sparse graphs. As immediate applications, we recover the following known equivalences. In the $K_{t,t}$-free setting, the dense notions (1) bounded shrub-depth, (2) bounded clique-width, (3) bounded flip-width, (4) monadic dependence, respectively, coincide with the sparse notions (1) bounded tree-depth, (2) bounded tree-width, (3) bounded expansion, and (4) no-where dense-ness. Furthermore, we reprove the result by Dreier and Toruńczyk (STOC 2025) stating that $K_{t,t}$-free classes of bounded merge-width have bounded expansion. Our proof provides explicit bounds and is direct, as it shows how to construct strong coloring orders (witnesses of bounded expansion) from merge sequences (witnesses of bounded merge-width). Along the way, we identify a new family of graph parameters, dubbed separation-width, that is sandwiched between the strong and weak coloring numbers, and is closely related to the merge-width parameters. We provide evidence that this family of graph parameters, apparently overlooked in the literature, may play a fundamental role in the study of sparse graphs.

We consider the problem of partitioning the edges of a graph into as few paths as possible. This is a~subject of the classic conjecture of Gallai and a recurring topic in combinatorics. Regarding the complexity of partitioning a graph optimally, Peroché [Discret. Appl. Math., 1984] proved that it is NP-hard already on graphs of maximum degree four, even when we only ask if two paths suffice. We show that the problem is solvable in polynomial time on subcubic graphs and then we present an efficient algorithm for ``almost-subcubic'' graphs. Precisely, we prove that the problem is fixed-parameter tractable when parameterized by the edge-deletion distance to a subcubic graph. To this end, we reduce the task to model checking in first-order logic extended by disjoint-paths predicates ($\mathsf{FO}\text{+}\mathsf{DP}$) and then we employ the recent tractability result by Schirrmacher, Siebertz, Stamoulis, Thilikos, and Vigny [LICS 2024].

Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We demonstrate that both of these constraints can be overcome in quantum chaotic sensors. Crucially, we establish that even in the presence of partial measurement accessibility, chaotic dynamics enables initial unentangled states to exhibit Heisenberg scaling of the quantum Fisher information, $I_α$ with time. In the weakly chaotic regime, we identify spin-coherent states placed at the edge of the regular islands in the mixed classical phase space as optimal initial states for enhanced sensitivity. On the other hand, in the strongly chaotic regime, $I_α$ is insensitive to the choice of the initial state. Notably, quantum-enhanced sensitivity is achieved even when a very low fraction ($\sim 5\%$) of the qubits are accessible. These results establish quantum chaos as a robust resource for quantum-enhanced sensing under realistic accessibility constraints on accessibility.

Cooperative air-ground delivery has emerged as a promising logistics paradigm by leveraging the complementary strengths of UAVs and ground carriers. However, effective dispatching in such heterogeneous systems faces two critical challenges: i) the heterogeneity between flight and road dynamics, ii) the scalability bottleneck raised by the exponential decision variables in large-scale fleets. To address these challenges, we propose HRL4AG, a Hierarchical Reinforcement Learning framework for cooperative Air-Ground delivery. Specifically, HRL4AG employs a high-level manager to tackle the scalability bottleneck by decomposing the joint action space, and mode-specific workers that encode distinct flight and road dynamics to address the heterogeneity. Furthermore, a novel internal reward mechanism is designed to guide the hierarchical policy learning, addressing the credit assignment problem in sparse-reward settings. Extensive experiments on two real-world datasets and an evaluation platform demonstrate that HRL4AG significantly outperforms state-of-the-art baselines, improving the delivery success rate by up to 26% while achieving an 80-fold increase in computational efficiency.

State delegations are often chosen through single-member district elections, creating a tension between respecting district majorities and reflecting the statewide electorate. First-past-the-post (FPTP) follows each district's majority but can yield a delegation seat share far from the party's statewide vote share. In contrast, proportional representation (PR), which makes a party's seat share correspond to its statewide vote share, requires departing from local majorities in some districts. We measure misrepresentation as a weighted sum of within-district misrepresentation, measured by the share of voters locally represented by their non-preferred party, and statewide misrepresentation, measured by the deviation of a party's seat share from its statewide vote share. The misrepresentation-minimizing rule is a cutoff rule determined by the relative weight of statewide misrepresentation. As this weight rises, the cutoff continuously shifts from FPTP's 50% to the PR cutoff that aligns the delegation's seat share with statewide vote shares. This shift makes gerrymandering harder, offering an alternative lever to limit gerrymandering. Using a majorization-based metric of geographic concentration, we show that concentrating support reduces misrepresentation only under the misrepresentation-minimizing rule. Within this class, FPTP and PR are uniquely characterized by the absence of cross-district spillovers and by gerrymandering-proofness, respectively. Using U.S. House elections, we infer the weights that rationalize outcomes, offering a novel metric for evaluating representativeness of district boundaries and electoral reform proposals.

Polar molecules, with their rich internal structure, offer immense potential for fundamental physics, quantum technology, and controlled chemistry. However, their utilization is currently limited because of slow and imperfect state detection and weak dipolar interaction, limiting fast and large-scale entanglement generation. We propose and analyze a scheme for quantum logic control and measurement-based state preparation in a hybrid platform of polar molecules and neutral atoms. The method leverages fast, high-fidelity atom-molecule gates and high-fidelity atomic ancilla measurements to overcome the common challenges in molecule-only platforms, while preserving their diverse structural advantages. The proposed atom-molecule controlled-phase gate is based on resonant dipole-dipole exchange between a molecular rotational transition and an atomic Rydberg transition, rendering it three orders of magnitude faster than any direct molecule-molecule entangling gate. We further study several applications of our scheme including the preparation of molecular GHZ states for quantum enhanced precision measurements, the preparation of exotic molecular qudit states with topological order, and measurement-altered criticality. Our scheme is applicable to any polar molecule. It expands the paradigm of quantum logic control and paves the way to large-scale molecular entangled states. More generally, it highlights a concrete hybrid quantum system in which each qubit is utilized in an optimal way and where the measurement-based approach can yield a significant advantage in near-term devices.

We present a feasibility study exploring the implementation of optical interferometry and speckle techniques with the 1.3-m Devasthal Fast Optical Telescope (DFOT) at ARIES, which is currently dedicated to photometric observations. Using the sCMOS camera as the DFOT backend, we perform interferometric speckle observations of several binary stars. Standard Speckle Interferometry (SI) algorithms are applied to analyze the recorded data. While this study does not aim to achieve the diffraction limit of DFOT or address a full science-driven resolution case, it serves as a crucial testbed for instrumentation, data acquisition, and analysis of Speckles with DFOT. Notably, we successfully identify and correct tracking-related positional errors in the observed binary systems, demonstrating the viability of the approach. These results provide strong motivation for more systematic observations and future implementation of optical interferometry techniques at meter-class telescopes.

Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new goodness-of-fit tests for log-symmetric distributions based on a recent characterization. These tests utilize the characteristic function as a novel tool and are constructed using an $L^2$-type weighted distance measure. The asymptotic properties of the resulting test statistic are studied. The finite-sample performance of the proposed method is assessed via Monte Carlo simulations and compared with existing procedures. The results under a range of alternative distributions indicate superior empirical power, while the proposed test also exhibits substantial computational efficiency compared to existing methods. The methodology is further illustrated using real data sets to demonstrate practical applicability.

We present a new technique for cooling arbitrary charged particles in a Penning trap by utilizing self-cooled electrons stored in a separate, macroscopically distant Penning trap as the cooling medium. The electrons decay predominantly to their motional ground state by emission of cyclotron radiation, which results in extremely low temperatures in the realm of single-digit quantum numbers in the motional degrees of freedom of the sympathetically cooled particle species. This opens up an exciting new frontier of tests of fundamental physics in Penning traps. This article provides a conceptual overview as well as a quantum-mechanical description of the involved cooling dynamics. The first implementation of this technique is currently being realized at the dedicated ELCOTRAP experiment at the Max Planck Institute for Nuclear Physics, which introduces special features for a quick iterative technical development cycle. Its current status, first results from commissioning, and future prospects will be presented.

Consider a network game with linear best responses and spillovers between players, and let agents endogenously choose their links. A planner considers interventions to subsidize actions and/or links between players, aiming to maximize a welfare function depending on equilibrium actions. The structure of the optimal intervention depends on whether links provide non-negative intrinsic value to agents. When they do, it is optimal to focus only on subsidizing actions. When the intrinsic value of links is negative, we give conditions for including link subsidies to be optimal. This reverses the basic structure of the optimal intervention in settings with exogenous links.

This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and quantitative symplectic geometry'' that took place at the University of Heidelberg on July 14--18, 2025.

We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic variational formulation based on the Lagrange--d'Alembert principle extends classical rigid-body dynamics to incorporate particle deformability by embedding translational, rotational, and deformation degrees of freedom within a unified energetic description. Second, particle deformation is realized within the Level Set DEM formalism through evolving level sets. The framework applies broadly to general particle geometries and topologies, and supports arbitrary deformation modes. The resulting deformable DEM retains the robustness, geometric and physical clarity, and scalability of classical DEM, while enabling physically grounded grain-scale deformability at a computational cost of the same order of magnitude as rigid DEM. Comparisons with full finite-element simulations demonstrate excellent agreement at both particle and system scales, establishing a general and extensible variational framework for modeling deformation in particulate systems.

In this paper, we present a 2-local proof labeling scheme with labels in $\{ 0,1,2\}$ for leader election in anonymous meshed graphs. Meshed graphs form a general class of graphs defined by a distance condition. They comprise several important classes of graphs, which have long been the subject of intensive studies in metric graph theory, geometric group theory, and discrete mathematics: median graphs, bridged graphs, chordal graphs, Helly graphs, dual polar graphs, modular, weakly modular graphs, and basis graphs of matroids. We also provide 3-local proof labeling schemes to recognize these subclasses of meshed graphs using labels of size $O(\log D)$ (where $D$ is the diameter of the graph). To establish these results, we show that in meshed graphs, we can verify locally that every vertex $v$ is labeled by its distance $d(s,v)$ to an arbitrary root $s$. To design proof labeling schemes to recognize the subclasses of meshed graphs mentioned above, we use this distance verification to ensure that the triangle-square complex of the graph is simply connected and we then rely on existing local-to-global characterizations for the different classes we consider. To get a proof-labeling scheme for leader election with labels of constant size, we then show that we can check locally if every $v$ is labeled by $d(s,v) \pmod{3}$ for some root $s$ that we designate as the leader.

Thermal correlators in holographic CFTs on a sphere exhibit bulk-cone singularities at points connected by null geodesics in the bulk. The operator product expansion analysis of the stress-tensor sector of the correlator shows that there are analogous singularities at spacelike separation for thermal CFTs on a plane. We show that these are associated with complex null geodesics. There is a phase transition between the real and complex spacelike geodesics underpinning this picture. We also provide a phase-shift calculation of the position of these generalised bulk-cone singularities.

Kink oscillation frequency is a key parameter for coronal seismology. It is still unclear how gravitational stratification affects the kink frequency in curved coronal loops. This work aims to investigate the effect of gravitational stratification on the frequency of kink oscillations in curved coronal loops and discuss their seismological potential. We conduct numerical computations within the ideal MHD framework to study different kink polarizations and harmonics in a curved, gravitationally stratified coronal loop. The oscillation frequencies derived from the Lagrangian displacement are compared with the WKB approximation. For the vertically polarized fundamental mode, the oscillation frequency deviates from the WKB approximation by about 18\% in the current numerical setup. Nevertheless, the oscillation frequency closely matches the local Alfvén frequency near the loop apex. On the other hand, the frequency of the horizontally polarized fundamental mode exhibits only a 7\% deviation in our current model from the WKB approximation and closely matches the local Alfvén frequency near one quarter of the loop. For the first overtones, the frequencies for both polarizations can be well described by the WKB approximation. The frequency of vertically polarized fundamental kink modes can be predicted by the local Alfvén frequency near the loop apex. In contrast, the WKB approximation remains highly reliable for estimating the frequency of horizontally polarized fundamental modes and first overtones, which is also well described by the local Alfvén frequency near one quarter of the loop. These results therefore pave the way for spatially dependent coronal seismology, enabling, e.g., the probing of magnetic field strength at different locations along a coronal loop.

There is a growing interest in researching game design processes, artifacts and culture through active game design. Tools and processes to support these attempts are limited, especially in terms of a) capturing smaller design decisions where rich tacit information is often situated, and b) visually tracking the project's growth and evolution. To address this gap, we present Reflection at Design Actualization (RDA), an open source tool and process for collecting granular reflections at playtesting moments and automatically recording the playtests, bringing reflection and data collection closer to the point where design decisions concretize. Three researchers engaged with and evaluated RDA in three varied game development projects, adhering to the principles of autobiographical design. We illustrate the designer experience with RDA through three themes, namely, designer-routine compromise, designer-researcher persona consolidation, and mirror effect of RDA. We further discuss the tool's challenges and share each designer's personal experience as case studies.