We report our optical observations of the Crab pulsar using the Imager of MPPC-based Optical photoN counter from Yamagata (IMONY), a high-time-resolution photon-counting imager with 100 ns timing resolution, mounted on the 3.8 m Seimei telescope in Japan (f/D~6). The detector format was upgraded from a $4\times4$ to an $8\times8$ GAPD array with larger pixels ($100$ to $200~{μm}$), resulting in a 14".5 field of view on the Seimei telescope. We conducted nightly optical observations for one week, including two nights of simultaneous optical and radio observations with the 64 m Usuda radio telescope. Thanks to the large diameter of the Seimei telescope and the high time resolution of IMONY, we successfully detected optical Single Pulses (SPs) emitted in each rotation. Moreover, we found an optical peak timing drift of $30\pm7.9~\mathrm{μs}$ over three days, with a significance of $3.9σ$. The corresponding emission region size is 9.1 km, which is equivalent to 0.006 times the light cylinder radius of the Crab pulsar. We ruled out the possibility of a pulsar glitch and suggested that the optical pulsed emission region of the Crab pulsar may fluctuate due to the spatial drift and variations in the magnetospheric caustics.

We present high spatial resolution ($\lesssim$1.0''), multi-wavelength observations of UGC 2369S, a nearby luminous infrared galaxy showing three distinct cores separated on kpc scales in near-infrared (NIR) imaging with significant X-ray emission. Utilizing optical/NIR adaptive optics (AO), radio, \chandra X-ray, as well as archival HST imaging, we perform a comprehensive study of AGN activity, obscuration, and host properties. As one of the clearest cases of a triple-nucleus merger at $\simeq$3 kpc separations, UGC 2369S is the first to be studied with high-resolution observations at multiple wavelength. We find that the northern core, having possibly the most massive black hole in the system ($\rm M_{BH}\simeq10^{8}\,M_{\odot}$) is consistent with a heavily obscured AGN. However, its high dust extinction ($\rm A_v>5$), hydrogen column density ($N_\mathrm{H}\gtrsim 10^{25}\,\rm cm^{-2}$) and non-detection of optical coronal lines and coronal X-ray emission leave the identification inconclusive. The other two cores show no evidence for black-hole activity and instead exhibit signatures of tidal disruption. From stellar mass surface density and stellar velocity dispersion maps, we infer that the strongly varying gravitational potential in this three-body system may have cannibalized the stellar bulge of the southwestern core, leaving a metal enriched remnant. An ongoing survey focusing on similar triple systems could help us understand how they evolve and help benchmark numerical simulations, providing insight into gravitational wave predictions and the formation of the most massive black holes.

We analyze a clean sample of 1,118 late-type, face-on galaxies without AGN contamination from the MaNGA survey. Their photometric structures are quantified via two-component (bulge+disk) decompositions on deep $g$-band images from the DESI Legacy Survey. Using a disk central surface brightness of $μ_{\rm 0,d,cor}$(g) = 22 $\pm$ 0.3 mag arcsec$^{-2}$ (corrected for inclination and cosmic dimming) as the classification threshold, we identify 159 low surface brightness (LSB) galaxies, 388 LSB candidates, and 571 high surface brightness (HSB) galaxies. LSB galaxies are predominantly low-mass ($M_\ast < 3 \times 10^{10}$ M$_\odot$), exhibiting 29\% larger effective radii, 15\% lower star formation rates (SFRs), and 12\% reduced gas-phase metallicities than HSB counterparts at comparable masses. These differences cause systematic offsets from standard scaling relations. Despite comparable gas content, LSB galaxies host older stellar populations, longer gas depletion times, and less efficient star formation. Spatially resolved analyses further reveal that LSB galaxies display centrally suppressed $Σ_{\rm SFR}$, flatter SFR gradients, and rising specific SFR profiles toward their outskirts. Together with steeper negative metallicity gradients, these trends suggest ongoing gas accretion fueling outer-disk star formation. Consistently, the outer regions of LSB galaxies exhibit stronger H$δ_A$ absorption and lower D$_n$4000 indices, indicating fading A-star populations. Moreover, LSB galaxies show lower $Σ_{\ast}$ across all $R/R_e$ and more centrally depleted stellar mass profiles on an absolute radial scale, compared with HSB and large-size star-forming galaxies. Collectively, LSB galaxies represent a distinct population with slow evolution, inefficient star formation, and continued susceptibility to late-time gas accretion and peripheral star formation.

Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial measurements across multiple recording sessions. By accumulating pairwise covariance estimates across sessions where different subsets of neurons are observed, we reconstruct the full connectivity matrix without requiring simultaneous recording of all neurons. A Granger-causality refinement step enforces biological constraints via projected gradient descent. Through systematic experiments on synthetic networks modeling small brain circuits, we characterize a fundamental control-estimation tradeoff: stimulation aids identifiability but disrupts intrinsic dynamics, with the optimal level depending on measurement density. We discover that the ``incorrect'' linear approximation acts as implicit regularization -- outperforming the oracle estimator with known nonlinearity at all operating regimes -- and provide an exact characterization via the Stein--Price identity.

Tear film rupture on the corneal surface plays a critical role in ocular health and visual comfort. Conventional theoretical approaches often idealize the cornea as a perfectly smooth surface, ignoring the surface roughness that are characteristic of healthy as well as diseased eyes. In this study, we develop a comprehensive mathematical model to investigate tear film dynamics over the corneal surface incorporating the effects of surface roughness, slip, van der Waals forces, and lipid transport at the film-air interface. The corneal surface is represented by a small-amplitude periodic modulation. Steady-state solutions obtained using asymptotics reveal nonlinear corrections to the base profile at $O(η^2)$, which are confirmed numerically. Linear stability analysis performed using the Floquet theory demonstrates that an increase in the amplitude of roughness destabilizes the film. Specifically, both the dominant growth rate and the most unstable wavenumber increase with the roughness amplitude. Nonlinear simulations show that surface roughness significantly accelerates tear-film rupture. The slip coefficient, amplitude of roughness of the corneal surface and the initial film profile are found to significantly influence the rupture time. Moreover, the location of the rupture is sensitive to the initial disturbance. These results highlight the crucial role of surface topography and slip in determining tear film stability. The predicted rupture times are consistent with the experimental observations. The proposed model provides a realistic and accurate prediction of tear film dynamics and rupture over the corneal surface. This study offers a new perspective on tear film instability and will help address challenges such as contact lens failure which is related to tear film behavior.

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded domains without a strictly positive lower bound. For densities bounded away from zero, we give sufficient conditions under which the framework of \cite{shen2001} applies directly. For densities lacking a positive lower bound, the equivalence between Hellinger and weighted $L_2$-norm distance fails, invalidating the original theory. We propose a novel shifting method that lifts the true density $g_0$ to a sequence of proxy densities $g_{0,n}$. We prove a modified convergence theorem applicable to these shifted densities, preserving the optimal rate. We also construct a Gaussian sieve prior that achieves the minimax rate $\varepsilon_n=n^{-p/(2p+1)}$ for any integer $p\geq1$. Numerical results confirm that our estimator approximates the true density well and validates the theoretical convergence rate.

The physical origin of fast radio bursts (FRBs) remains an unsolved mystery in astrophysics, with the magnetar central engine model as the leading framework. Systematically searching for physical associations between FRBs and the energetic astrophysical transients (ATs) that form magnetars provides a critical test of this scenario, and key clues to FRB progenitors. We perform a systematic search for FRB-AT associations using a sample of 3765 unique FRBs, combining the second CHIME/FRB catalog with 124 additional localized FRBs with measured redshifts. We develop a 3D Bayesian inference framework that jointly incorporates angular separation, positional uncertainty, and redshift constraints to quantify the association probability of candidate pairs. Through spatial cross-matching, we identify 14 FRB-optical transient and 15 FRB-gamma-ray burst (GRB) candidate pairs. Our framework recovers the previously reported high-significance association between FRB 20180916B and AT 2020hur, with an association probability of 0.9998. For the proposed candidate FRB 20190309A and short GRB 060502B, our analysis yields an association probability of 0.83, which is insufficient to claim statistically significant association. No new statistically significant FRB-AT associations are found for all remaining candidates. Our work demonstrates that small angular separation alone is insufficient to confirm FRB-AT associations, and high-precision FRB localization is essential for definitive identification.

Phase transitions in a modified Nishimori model, including the model considered by Kitatani, on a two-dimensional square lattice are investigated using a tensor-network-based sampling scheme. In this model, generating bond configurations is computationally demanding because of the correlated random interactions. The employed sampling method enables hierarchical and independent sampling of both bonds and spins. This approach allows high-precision calculations for system sizes up to $L=256$. The results provide clear numerical evidence that the spin-glass and ferromagnetic transitions are separated on the Nishimori line, supporting the existence of an intermediate Mattis-like spin-glass phase. This finding is consistent with the reentrant transition numerically observed in the two-dimensional Edwards-Anderson (EA) model. Furthermore, critical exponents estimated via finite-size-scaling analysis indicate that the universality class of the transitions differs from that of the standard independent and identically distributed EA model.

Due to the absence of clean reference signals and spatial cues, monaural unsupervised speech dereverberation is a challenging ill-posed inverse problem. To realize it, we propose augmented reverberant-target training (ARTT), which consists of two stages. In the first stage, reverberant-target training (RTT) is proposed to first further reverberate the observed reverberant mixture signal, and then train a deep neural network (DNN) to recover the observed reverberant mixture via discriminative training. Although the target signal to fit is reverberant, we find that the resulting DNN can effectively reduce reverberation. In the second stage, an online self-distillation mechanism based on the mean-teacher algorithm is proposed to further improve dereverberation. Evaluation results demonstrate that ARTT achieves strong unsupervised dereverberation performance, significantly outperforming previous baselines.

Given a set P of points on the plane, a polygon with vertices in P is said to be empty if it contains no element of P in its interior. We show that every set of n points in general position on the plane determines at least $Ω(n^{20/11})$ empty convex pentagons (also known as 5-holes). This result improves upon the previous bound of $Ω(n\cdot(\log n)^{4/5})$ obtained by Aicholzer et al. [JCT A, 2020], and significantly narrows the gap with respect to the conjectured $Ω(n^2)$ lower bound (which, if true, would be tight). Unlike some of the other works in this line of research, our proof does not require computer assistance.

Parameterized quantum circuits (PQCs) are central to quantum machine learning and near-term quantum simulation, but their scalability is often hindered by barren plateaus (BPs), where gradients decay exponentially with system size. Prior explanations, including expressivity, entanglement, locality, and noise, are often presented in ways that conflate two distinct issues: concentration of the measured observable and loss of parameter sensitivity caused by circuit dynamics. We develop a unified statistical framework that separates these mechanisms. We show that several standard BP explanations, including locality- and entanglement-related effects, can be understood through a single phenomenon that we term observable concentration (OC). Importantly, we prove that avoiding OC is necessary but not sufficient for trainability. Beyond OC, we identify two distinct mid-circuit sources of gradient suppression. First, mid-circuit information loss occurs when parameter perturbations propagate into degrees of freedom that are inaccessible to the final measurement, yielding little or no response. Second, mid-circuit information scrambling occurs when local perturbations rapidly spread across the system and become effectively undetectable on the measured subsystem. We support our theory with explicit constructions and numerical evidence, including quantum convolutional neural network architectures that exhibit information-loss-induced barren plateaus despite the absence of observable concentration.

The criticality hypothesis posits that biological neural networks operate near a phase transition, yet within standard Gaussian mean-field theories this regime appears fragile and requires fine tuning. Here we show that heavy-tailed synaptic connectivity provides a robust alternative mechanism. By developing a dynamical mean-field theory for Cauchy-distributed couplings, we reduce the macroscopic dynamics to a one-dimensional gradient flow with a global Lyapunov potential. The resulting theory exhibits a continuous phase transition in which collective activity grows with the square root of the distance to criticality, and static susceptibility diverges only as the square root rather than linearly as in Gaussian mean-field theories. This structure gives rise to an emergent automatic gain control: activity-dependent noise fluctuations suppress the effective gain at high activity levels while preserving high susceptibility near the critical point. Extending this mechanism to general symmetric $α$-stable inputs, we identify heavy-tailed synapses as a key microscopic origin of robust near-critical dynamics in disordered neural circuits.

Peephole optimizations are a core component of modern optimizing compilers. It rewrites specific instruction into semantically equivalent but more efficient forms. In practice, creating a new peephole optimization often starts from a concrete optimization instance and requires lifting it into a more general rewrite rule that matches a wider range of instruction patterns. This generalization step is critical to optimization effectiveness, but it is also difficult: producing rules that are both correct and sufficiently general typically demands substantial manual effort and domain expertise. Existing approaches such as Hydra attempt to automate this task with program synthesis, but their generalization capability is often limited by search-space explosion, under-generalization, and restricted support for diverse instruction domains. We present LPG, large language model aided peephole optimization generalization, a framework that uses large language models (LLMs) to generalize peephole optimizations. The design of LPG is motivated by the observation that LLMs are effective at semantic abstraction and exploratory reasoning, while formal analyses are necessary to ensure that generated rules are sound and profitable. Based on this observation, LPG adopts a closed-loop workflow that integrates LLM-driven symbolic constant generalization, structural generalization, constraint relaxation, and bitwidth/precision generalization with feedback from syntactic validation, semantic verification, and profitability checking. We evaluate LPG on real-world peephole optimization issues drawn from the LLVM ecosystem. Overall, LPG successfully generalizes 90 out of 102 optimizations. On the integer-focused subset that is directly comparable to Hydra, LPG generalizes 74 out of 81 optimizations, whereas Hydra generalizes 35.

Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an adversarial wildfire that targets infrastructure while respecting realistic fire spread dynamics. We design a wind-assisted fire spread set based on the Rothermel fire spread model and propose principled convex relaxations of this set, including a new relaxation of the inner product over Euclidean balls. We present test cases derived from the recent Park, Eaton, and Palisades fires in California and solve models to identify the minimum time-to-outage of multiple-element contingencies and the maximum load shed associated with a sequence of element outages caused by a realistic wildfire. We use the minimum time-to-outage values to screen contingencies and construct security-constrained optimal power flow models that promote operational resilience against wildfire.

The integration of Large Language Models (LLMs) into cybersecurity education for criminal justice professionals is currently hindered by the "statelessness" of reactive chatbots and the risk of hallucinations in high-stakes legal contexts. To address these limitations, we propose the CyberJustice Tutor, an educational dialogue system powered by an Agentic AI framework. Unlike reactive chatbots, our system employs a "Think-Plan-Act" cognitive cycle, enabling autonomous goal decomposition, longitudinal planning, and dynamic context maintenance. We integrate a Pedagogical Scaffolding Layer grounded in Vygotsky's Zone of Proximal Development (ZPD), which dynamically adapts instructional support based on the learner's real-time progress. Furthermore, an Adaptive Retrieval Augmented Generation (RAG) core anchors the agent's reasoning in verified curriculum materials to ensure legal and technical accuracy. A comprehensive user study with 123 participants, including students, educators, and active law enforcement officers, validated the system's efficacy. Quantitative results demonstrate high user acceptance for Response Speed (4.7/5), Ease of Use (4.4/5), and Accuracy (4.3/5). Qualitative feedback indicates that the agentic architecture is perceived as highly effective in guiding learners through personalized paths, demonstrating the feasibility and usability of agentic AI for specialized professional education.

In the present work, we propose to investigate the production of $d_{N Ω}$ in the $Ω^{-} d \rightarrow p d_{N Ω}^-$ process by utilizing an effective Lagrangian approach, where $d_{N Ω}$ is identified as $NΩ$ bound state with the binding energy $E_{b}=2.46$ MeV. Experimentally, the J-PARC hadron facility proposed to investigate the $K^{-}p \rightarrow Ω^{-} \bar{K}^{(*)0} K^{+}$ process, which is expected to yield an $Ω$ beam with the momentum of approximately 3 GeV. Additionally, theoretical studies of the $ψ(2S) \rightarrow Ω^{-} \barΩ^{+}$ process at BESIII provided an $Ω$ beam with the momentum of 774 MeV. Considering these two potential $Ω$ beam sources, our estimations show that for the $Ω^{-} d \rightarrow p d_{N Ω}^-$ process, the cross sections are $\Big(329.7^{+26.9}_{-49.6}\Big)$ $μ$b, $\Big(174.0^{+26.5}_{-38.2}\Big)$ $μ$b, $\Big(16.9^{+7.4}_{-7.7}\Big)$ $μ$b, and $\Big(2.0^{+1.8}_{-1.4}\Big)$ $μ$b at $P_Ω =$ 0.7, 0.9, 2.0, and 4.0 GeV, respectively, where the central values are estimated with $Λ_{r}=1.0$ GeV, and the errors come from the variation of $Λ_{r}$ from 0.8 to 1.2 GeV. We also estimate the differential cross sections, which reach the maximum at the forward angle limit. In addition, since the $d_{N Ω}$ dibaryon predominantly decays into $ΞΛ$. Therefore, we further investigate the $Ω^{-} d \rightarrow p Ξ^- Λ$ process and estimate the relevant cross sections. It is expected that the present estimations can be tested by further experimental measurements at J-PARC and STCF in the future.

In this paper, we employ the Wilf-Zeilberger (WZ) method to prove a supercongruence conjecture posed by Z.-W. Sun: for any prime $p$, \begin{align*} \sum_{k=0}^{\frac{p-3}{2}}\frac{92k^2+61k+9}{(2k+1)64^k}{2k \choose k}{3k \choose k}{4k \choose 2k}\equiv 6p+16p^2\left(\frac{-1}{p}\right) \pmod{p^3}, \end{align*} where $\left(\frac{\cdot}{p}\right)$ denotes the Legendre symbol. Our proof relies on combinatorial identities and symbolic summation techniques.

We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points, iteratively refining the approximation to converge toward the simultaneous convex hull of factorable function graphs. The framework is underpinned by three key contributions: (i) a new class of explicit inequalities for products of functions that strictly improve upon standard factorable and composite relaxation schemes; (ii) a proof establishing that the simultaneous convex hull of multilinear functions over axis-aligned regions is fully determined by their values at corner points, thereby generalizing existing results from hypercubes to arbitrary axis-aligned domains; and (iii) the integration of computational geometry tools, specifically voxelization and QuickHull, to efficiently approximate feasible regions and function graphs. We implement this framework and evaluate it on randomly generated polynomial optimization problems and a suite of 619 instances from \texttt{MINLPLib}. Numerical results demonstrate significant improvements over state-of-the-art benchmarks: on polynomial instances, our relaxation closes an additional 20--25\% of the optimality gap relative to standard methods on half the instances. Furthermore, compared against an enhanced factorable programming baseline and Gurobi's root-node bounds, our approach yields superior dual bounds on approximately 30\% of \texttt{MINLPLib} instances, with roughly 10\% of cases exhibiting a gap reduction exceeding 50\%.

Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.

SIMON and SPECK were among the first efficient encryption algorithms introduced for resource-constrained applications. SIMON is suitable for Internet of Things (IoT) devices and has rapidly attracted the attention of the research community to understand its structure and analyse its security. To analyse the security of an encryption algorithm, researchers often employ cryptanalysis techniques. However, cryptanalysis is a resource and time-intensive task. To improve cryptanalysis efficiency, state-of-the-art research has proposed implementing heuristic search and sampling methods. Despite recent advances, the cryptanalysis of the SIMON cypher remains inefficient. Contributing factors are the large size of the difference distribution tables utilised in cryptanalysis and the scarcity of differentials with a high transition probability. To address these limitations, we introduce an analysis of differential properties of the SIMON32 cypher, revealing differential characteristics that pave the way for future efficiency enhancements. Our analysis has further increased the number of targeted rounds by identifying high probability differentials within a partial difference distribution table of the SIMON cypher, exceeding existing state-of-the-art benchmarks. The code designed for this work is available at https://github.com/johncook1979/simon32-analysis.

We introduce the Pólya threshold graph model and derive its stochastic and algebraic properties. This random threshold graph is generated sequentially via a two-color Pólya urn process. Starting from an empty graph, each time step involves a draw from the urn that produces an indicator variable, determining whether a newly added node is universal (connected to all existing nodes and itself) or isolated (connected to no existing nodes). This construction yields a random threshold graph with an adjacency matrix that admits an explicit representation in terms of the draw sequence. Using the structure of the Pólya draw process, we derive the exact degree distribution for any arbitrary node, including its mean and variance. Furthermore, we evaluate a distance-based decay centrality score and provide an explicit expression for its expectation. On the algebraic side, we explicitly characterize the Laplacian matrix of the random threshold graph, obtaining a closed-form description of its spectrum and corresponding eigenbasis. Finally, as an application of these structural results, we analyze discrete-time consensus dynamics on Pólya threshold graphs.

The generation of a trapping potential for dark-state polaritons in a two-dimensional electromagnetically induced transparency system is theoretically studied. We show that such a trap can arise from a spatially inhomogeneous effective mass of the dark-state polariton. Because this mass inhomogeneity can be engineered by tuning the parameters of the control fields, the motion, spatial profile, and coherent behavior of bound dark-state polaritons can be tailored accordingly. Our results enable spatial controls of optical information and provide a possible route toward realizing Bose-Einstein condensation of dark-state polaritons in a trapping potential.

Guaranteeing the safety of nonlinear systems with bounded inputs remains a key challenge in safe autonomy. Backup control barrier functions (bCBFs) provide a powerful mechanism for constructing controlled invariant sets by propagating trajectories under a pre-verified backup controller to a forward invariant backup set. While effective, the standard bCBF method utilizes the same backup controller for both set expansion and safety certification, which can restrict the expanded safe set and lead to conservative dynamic behavior. In this study, we generalize the bCBF framework by separating the set-expanding controller from the verified backup controller, thereby enabling a broader class of expansion strategies while preserving formal safety guarantees. We establish sufficient conditions for forward invariance of the resulting implicit safe set and show how the generalized construction recovers existing bCBF methods as special cases. Moreover, we extend the proposed framework to parameterized controller families, enabling online adaptation of the expansion controller while maintaining safety guarantees in the presence of input bounds.

The widespread deployment of large language models (LLMs) calls for post-hoc methods that can flexibly adapt models to evolving safety requirements. Meanwhile, the rapidly expanding open-source LLM ecosystem has produced a diverse collection of models that already exhibit various safety-related functionalities. This motivates a shift from constructing safety functionality from scratch to reusing existing functionality from external models, thereby avoiding costly data collection and training procedures. In this paper, we present Cross-Model Neuron Transfer (CNT), a post-hoc method that reuses safety-oriented functionality by transferring a minimal subset of neurons from an open-source donor LLM to a target LLM. By operating at the neuron level, CNT enables modular function-level adaptation, supporting both function addition andfunction deletion. We evaluate CNT on seven popular LLMs across three representative applications: safety disalignment, alignment enhancement, and bias removal. Experimental results show that CNT achieves targeted safety-oriented functionality transfer with minimal performance degradation (less than 1% for most models), consistently outperforming five baselines, demonstrating its generality and practical effectiveness.

The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing mathematical algorithms are of little help. Here I will summarize the state-of-the-art of worldline integration focusing on examples from QED in vacuum and in constant external fields.

We use localized topologies to prove existence and optimal regularity results for the divergence equation $\mathrm{div} (v) = F$ in critical cases $v \in L_1(Ω;\mathbb{R}^m)$ or $v \in C_0(Ω;\mathbb{R}^m)$, i.e. we characterize those $F$ for which a solution $v$ exists whose norm is bounded by an appropriate norm of $F$. We assume $Ω$ satisfies a Poincaré inequality or an extension property. We apply the general theory to give examples of admissible $F$ in each case.

This paper provides a behavioral analysis of the post-pandemic transformation of work, using a dataset of approximately 41 billion mobile geolocation records from 73.5 million individuals in the five largest U.S. metropolitan areas from the pre- to post- pandemic periods. By tracking movements between corporate headquarters, residences, and other points of interest, we document a structural shift in work patterns. Office based workdays declined from 42% in 2019 to 20.7% in 2022, before settling at 29.1% in 2023, a new equilibrium significantly below pre-pandemic levels. A "midweek mountain" peak of office attendance on Tuesdays through Thursdays, emerged as a robust new phenomenon post-pandemic. The nature of remote work has also changed: both in and after the pandemic, employees working from home allocated significantly more time to non-work locations like parks and malls during the workday. These findings indicate that the pandemic catalyzed a lasting transformation not just in work arrangements but also in the integration of personal and professional life, with implications for corporate policy, urban economics, and the future of work.

We investigate multipartite quantum correlations by analyzing the mutual information of N-partite states for both free bosonic and fermionic fields in the background of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Focusing on multipartite GHZ and W states, we examine how the Hawking effect influences the N-partite mutual information when one observer hovers near the event horizon while the remaining observers stay in the asymptotically flat region. By tracing over the inaccessible modes inside the event horizon, we derive analytical expressions for the N-partite mutual information in dilaton spacetime for both bosonic and fermionic fields. Our results show that fermionic mutual information is larger than its bosonic counterpart under the influence of the dilaton black hole, whereas the fermionic relative entropy of coherence (REC) is smaller than the bosonic REC. Moreover, the mutual information of GHZ states is consistently larger than that of W states, while the REC of GHZ states is smaller than that of W states in curved spacetime. These findings indicate that the choice of quantum resources should be tailored to the particle species and state structure in relativistic quantum information tasks to optimize their operational efficiency.

More than 200 moons exist in our Solar System, yet no exomoon has been confirmed to date. While the innermost two planets of the Solar System lack natural satellites and most studies favour the existence of exomoons around long-period planets, some theoretical studies that take tidal dissipation, orbital decay, and migration processes into account suggest that exomoons may survive around short-period exoplanets. We investigated the impact of exomoons on planetary thermal phase curves and assessed their detectability within a theoretical framework. We simulated the thermal phase curves of exomoon-exoplanet systems, including mutual transits and occultations, and explored their dependence on planetary orbital periods across a wide range of systems. Close-in airless exomoons maintain large day-night temperature contrasts, amplifying the thermal phase-curve signal of the system. When the exomoon transits or is occulted by the exoplanet, the transit depth varies with the planetary phase, and the occultation depth varies with the exomoon's phase. The maximum occultation depth can reach $\sim$ 20 ppm for long-period systems. For short-period planets, the signal can reach up to $\sim$100 ppm, although such configurations may not be dynamically stable over long timescales. If exomoons are not accounted for, the planetary temperature distribution retrieved from observed thermal phase curves may overestimate the planetary day-night temperature contrast and underestimate the planetary horizontal heat transport. In principle, the periodic exomoon-exoplanet mutual occultation signal could be extracted using methods such as box-fitting least squares, providing a framework for future observational studies and instrument planning.

Efficient text entry remains a primary bottleneck preventing Virtual Reality (VR) from evolving into a viable productivity platform. To address this, we conducted an empirical comparison of six physical input systems across three interaction styles Controller Driven, Free Hand, and Virtual Touch evaluating both discrete tap typing and continuous gesture typing (swiping), alongside a speech to text (Voice) condition as a non physical reference modality. Results from 21 participants show that the Controller Driven Tap Gesture Combo (CD TGC) delivers the best productivity performance, achieving speeds 2.25 times higher than the slowest system and 30% faster than the current industry standard, while reducing error rates by up to 68%. A clear trade off emerged between performance and perceived usability: although controller based gesture input led on speed and accuracy, participants rated Virtual Touch Tap Typing highest in subjective experience, scoring 80% higher on the System Usability Scale (SUS) than the lowest rated alternative. We further observe that Free Hand interaction remains limited by tracking stability and physical fatigue, whereas Voice input introduces practical constraints related to privacy, editing control, and immersive engagement. Together, these findings characterize the tension between throughput and natural interaction in immersive text entry and provide data driven guidance for future VR interface design.