We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low regularity spaces and the high frequency limit, such solutions can be approximated by a sum of incoming and reflected pulses constructed using incoming and reflected phases and profiles that satisfy transport equations. New low-regularity estimates comparing the size of pulses to the size of their profiles are required. Earlier geometric optics results for pulses assumed much higher regularity, and considered only propagation in free space or transversal reflection at boundaries.

Due to regulatory compliance and governance management, modern (permissioned) blockchains require flexible endorsement, which allows the endorsement policy for each contract or state object to be individually defined. To enable flexible endorsement, Hyperledger Fabric employs an execute-order-validate (EOV) paradigm, in which transactions first undergo speculative execution and endorsement, and are only then ordered and validated. Meanwhile, most blockchain systems, including the platform targeted in this work (i.e., ChainMaker), still follow a conflict-free order-execute framework. We argue that the EOV paradigm still faces several limitations, notably high abort rates in high-contention workloads such as those in Decentralized Finance (DeFi). To avoid refactoring our system and better suit DeFi applications, we try to integrate flexible endorsement into the classical order-execute architecture and accordingly propose a new framework. The key challenge is to deterministically remove problematic transactions from an ordered list, while preserving censorship resistance and decentralization for the remaining ones. We instantiate this framework on top of Tendermint, a seminal Byzantine fault-tolerant (BFT) protocol adopted in our system, and thereby propose FlexTender. By elegantly embedding endorsements into consensus, FlexTender incurs no additional messaging overhead in the normal case. Empirical evaluation using an Ethereum USDT workload demonstrates that FlexTender achieves up to $10.6\times$ speedup in throughput over an EOV simulation on the same platform.

In conventional radiotherapy, the probability of controlling tumor growth is quantified using Tumor Control Probability (TCP) models. Instead, the probability of experiencing a side effect after the irradiation of healthy tissues and organs is typically assessed using the concept of Normal Tissue Complication Probability (NTCP), an additional crucial metric for evaluating and comparing treatment plans. This work is dedicated to the development, implementation, and application of a general mechanistic model to describe the effects of particle therapy (PT) on different tissue organizations beyond Poissonian assumptions, extending the Generalized Stochastic Microdosimetric Model (GSM2), i.e., a stochastic radiobiological model that describes the time evolution of DNA lesions in a cell nucleus according to microdosimetric principles, to the study of macroscopic biological systems. Specifically, we extend the biological stage of radiation damage of the GSM2 model to larger spatial and temporal scales, involving cell populations with a specific geometric and functional architecture. The model's single-cell resolution allows it to account for energy deposition and tissue heterogeneity, considering different organ volume effects, cell type distributions, and oxygen gradients for different radiation qualities of the beam, that is, type, energy, and LET of radiation, and various fractionation schemes. We show the interplay between physical and environmental parameters on the induction of side effects on healthy tissues, for different radiation qualities and fractionation schemes, and we highlight the impact of biochemical heterogeneities in the target environment, for tumor response.

The evolution of protoplanetary disks, especially in the early stages of planetary formation, as dust grows, is the cornerstone of the birth of planets. The mechanisms involved in the growth of sub-micrometric dust grains into planetesimals within a very short time frame are a challenging field of study, while the initial conditions remain relatively undefined. One of the main challenges is to unambiguously identify the dust properties within the disk, and our goal is to break this barrier by investigating the light scattered by dust particles lying on the protoplanetary disk surface from many recent promising observations. In this study, we used a set of 30 polarized light images composed of new VLT/SPHERE observations to examine the light scattered by dust grains. For each ring-shaped system, we used the new DRAGyS tool to estimate the disk geometry using the substructures visible on the surface and to extract the limb-brightening-corrected scattering phase function, which encodes the dust grains' physical properties. Finally, we compared our results with the AggScatVIR database of numerical scattering phase functions of nonspherical dust. We combined our measurements of disk geometry to estimate an average disk flaring of about 1.357. First, we recovered the two categories of scattering phase functions based on their shape, as determined in previous studies. Category I is monotonically decreasing and can be explained by fractal organic aggregates with small monomers of 100nm, or compact aggregates with medium porosity and big monomers of 400nm. Category II is defined by a bell-shaped scattering phase function and can be explained by sub-micrometric irregular grains or compact aggregates with low porosity. This statistical study offers general trends about dust populations, but the degeneracy is too strong to apply this method to a unique disk analysis.

We study systems of σ-algebras ordered by refinement and introduce the notion of an endogenous probability measure, invariant under admissible refinement transformations. We prove existence and structural properties of such measures on finite systems and show how refinement operators induce a natural dynamical structure on the lattice of σ-algebras.

The possible bound state of the $c\bar{c}+n+^{10}$Be system, representing a hypothetical charmonium-nucleus configuration, is investigated. The analysis is conducted within a three-cluster framework, in which the binary subsystems are treated as $n+^{10}\textrm{Be}$, $^{10}\textrm{Be}+c\bar{c}$, and $c\bar{c}+n$. The hyperspherical harmonics method is employed to provide a convenient description of this three-cluster configuration. The calculations are performed using effective $^{10}\textrm{Be}\textrm{-}c\bar{c}$ potentials constructed via the single-folding procedure. These potentials have been derived recently on the basis of state-of-the-art lattice QCD results from the HAL QCD Collaboration, which provided interactions for the spin-$3/2$ $J/ψN$, spin-$1/2$ $J/ψN$, spin-$1/2$ $η_{c}N$, and spin-averaged $J/ψN$ channels, all obtained at nearly physical pion masses. The numerical results indicate that the central binding energies of the spin-$3/2$ $J/ψ+n+^{10}$Be, spin-$1/2$ $J/ψ+n+^{10}$Be, and spin-$1/2$ $η_{c}+n+^{10}$Be systems are 3.47, 3.55, and 1.91 MeV, respectively. The corresponding root-mean-square nuclear matter radii are predicted to be approximately 2.49, 2.48, and 2.60 fm.

For a connected weighted hypergraph, we give a randomized almost-linear-time solver for the Poisson problem for the cut-based hypergraph Laplacian in the natural input size $P=\sum_{e\in E}|e|$, the sum of hyperedge sizes. For every fixed constant $C>0$, our randomized algorithm runs in $P^{1+o(1)}$ time and, with high probability over its internal randomness, returns a primal point and a dual certificate, with additive optimality gap at most $\exp(-\log^C P)$. A key step is to rewrite the Fenchel dual as a convex-flow problem on an auxiliary $O(P)$-arc graph, yielding a near-optimal dual flow. The main difficulty is primal recovery, because this flow does not by itself determine a primal potential. Our main new ingredient is a recovery theorem showing that, for primal recovery, the detailed routing of the dual flow inside each hyperedge gadget can be discarded: one nonnegative scalar per hyperedge is enough. After the necessary finite-precision rounding, these scalars define a linear-cost min-cost-flow instance on the auxiliary graph, and solving it exactly recovers a primal potential. Finally, a ground-vertex reduction from regularized objectives to the Poisson solver gives randomized almost-linear-time resolvent/proximal primitives for the same cut-based hypergraph Laplacian.

Biological neurons perform arithmetic computations - including additive integration and divisive gain modulation - through synaptic conductance changes and shunting inhibition, enabling context-dependent information processing that far exceeds simple threshold-and-fire models. Replicating these capabilities in compact hardware remains a fundamental challenge for neuromorphic engineering. Here, we demonstrate artificial neuron circuits based on Ovonic threshold switches (OTS) that physically implement three arithmetic operations: SUM, PARALLEL, and DIVISION. The SUM and PARALLEL neurons exploit MOSFET-controlled dendritic conductances, producing output firing rates that collapse onto invariant curves as a function of combined inputs - satisfying the canonical criteria for neuronal addition. The DIVISION neuron leverages a JFET-based shunting pathway, inspired by GABA_A-mediated inhibition in the cortex, to achieve divisive gain modulation well described by a Hill-type function (R2 ~ 0.95, Hill exponent n ~ 1.3), consistent with nonlinear normalization observed in visual and olfactory circuits. Applying the DIVISION neuron to pixel-wise image normalization under non-uniform illumination recovers obscured visual content, mirroring contrast normalization in the visual cortex. Compared to CMOS-based division implementations, the proposed approach offers improvements in energy efficiency and scalability exceeding an order of magnitude, establishing a viable path toward compact, brain-inspired analog computing.

We propose a noise-mitigation quantum simulation strategy for near-term quantum devices based on Quantum Circuit Learning (QCL), which is in particular effective for integrable quantum spin chains. The method trains a shallow variational circuit to approximate a deeper time-evolution circuit by learning the conserved charges and only a small amount of dynamical information in the system. Under realistic noise models, the learned circuit maintains both conserved quantities and dynamical observables significantly closer to their true values than the noisy simulation of the original circuit. This demonstrates QCL as an effective, physics-informed error mitigation strategy, producing shorter, more robust circuits without exponential sampling overhead.

Machine learning (ML)-based API recommendation helps developers efficiently identify suitable APIs to complement the application code. However, code datasets used to train ML models often exhibit a long-tail distribution, leading to unreliable API recommendations, especially for infrequently used API methods at the tail of the distribution. To address this issue, we propose N-version API Recommendation (NvRec), which leverages N different versions of ML models to enhance the reliability of API sequence recommendations by suppressing unreliable outputs entailing tail APIs. NvRec leverages a set of available ML models and profiles their performance on individual API methods with their tail properties. The generated model profile is used at inference time to filter out unreliable API recommendations and determine the final output. We implement NvRec using five API recommendation models, including CodeBERT, CodeT5, MulaRec, UniXcoder, and CodeT5+, and evaluate it on a public benchmark dataset constructed from compilable Java projects. For the three-version NvRec, we find that the combination of CodeT5, MulaRec, and UniXcoder achieves the highest true accept rate of 83.8%, with a rejection rate of 80.7%, when majority voting is restricted to highly reliable candidates. In contrast, the five-version configuration achieves its highest true accept rate of 83.1% with simple majority voting, while reducing the rejection rate to 69.0%. Overall, the five-version configuration offers a better balance between true accept rate and rejection rate.

Virtual cell (VC) models aim to predict cellular responses to any perturbations in silico and have emerged as a promising approach for drug discovery and precision medicine. Yet, a clear gap still remains: while models routinely reported impressive results on standard benchmarks, it is unclear whether their predictions are truly meaningful in practice. This is mainly due to limitations in current evaluation setups, which are often overly simplified or inconsistent, and do not reflect the complexity and variability of real biological systems. Here, we introduce a standardized and modular benchmarking framework for virtual cell prediction. Our framework evaluates diverse models under in-the-wild challenging scenarios, including unseen cell contexts, unseen perturbations, and cross-dataset generalization, which better reflect practical applications. Our analysis shows that model performance is highly context-dependent and shaped by task design and evaluation criteria. In commonly used setups, performance is often overestimated, and naive dataset aggregation can even reduce performance. When evaluated under more strict conditions, model performance drops markedly, indicating limited robustness to shifts across cellular contexts. In unseen perturbation settings, models including simple linear approaches capture global transcriptional trends but fail to recover fine-grained perturbation-specific effects. In addition, different evaluation metrics focus on different biological properties, leading to substantially different model rankings. Together, our framework provides a more reliable and biologically grounded evaluation, offering clearer guidance for applying virtual cell models in real scenarios.

We present a rank-$23$ algorithm for general $3\times3$ matrix multiplication that uses $56$ additions/subtractions and $23$ multiplications, for a total of $79$ scalar operations in the standard bilinear straight-line model. This improves the recent sequence of $60$-, $59$-, and $58$-addition rank-$23$ schemes. The algorithm works over arbitrary associative, possibly noncommutative, coefficient rings. Its tensor coefficients are ternary, meaning that every coefficient lies in $\{-1,0,1\}$. Correctness is certified by the $729$ Brent equations over $\mathbb{Z}$, and the verifier also expands the straight-line program and performs additional finite-field and noncommutative implementation tests.

Context: Many organizations are keen to incorporate generative~AI (GenAI) into their software development processes. Technology acceptance models, such as the Unified Theory of Acceptance and Use of Technology (UTAUT), are traditionally used to identify individual-level barriers to the acceptance of new technologies and can facilitate the transition to GenAI. However, UTAUT has seen limited use within software engineering (SE) research. Objective: Using UTAUT as an example, to identify key areas for future research on GenAI acceptance, including the role of Bayesian approaches for data analysis. Method: We review foundational and SE-specific literature on UTAUT and analyze its emerging applications for GenAI in SE. Results: We identify three priorities for future research: (1) identifying and refining constructs to account for GenAI's nature and transformational impact; (2) improving operationalization practices to strengthen construct validity and cross-study comparability; and (3) incorporating Bayesian analysis to support small-sample inference by integrating prior knowledge, iterative model updating, and simulation of scenarios. Conclusion: UTAUT is a suitable candidate to combine with Bayesian analysis for practical insights on individual-level barriers to GenAI use in SE, but additional theories should be considered.

Despite the rise of token communication (TokCom) as a new paradigm beyond traditional bit communication, existing approaches have primarily adopted artificial intelligence (AI)-centric designs that rely on semantic recovery via large models. Meanwhile, their physical-layer designs, such as token-bit mapping and power allocation, remain conventional and do not reflect token-level semantics. These semantics-agnostic designs can lead to significant semantic loss, particularly at low signal-to-noise ratio (SNR) levels. To address this issue, we propose hierarchical TokCom (H-TokCom), a framework that embeds semantic structure directly into physical-layer design. The key idea is to group semantically similar tokens into clusters and hierarchically assign their bit representations, where each token is represented by a cluster-level prefix and a token-specific suffix. As long as the cluster bits are correctly delivered, errors in the suffix bits typically map the received token to another within the same semantic cluster, resulting in only limited semantic distortion. This robustness is further strengthened by allocating more transmit power to the prefix bits than to the suffix bits. Simulation results show that H-TokCom achieves substantial semantic-similarity gains over conventional TokCom across the considered SNR range, increasing the semantic similarity from $0.206$ to $0.279$ at $γ=3$ dB on COCO, corresponding to a gain of $0.073$ $(35.4\%)$.

Future uncrewed aerial vehicle (UAV) systems increasingly combine heterogeneous communication technologies, such as low-latency aerial mesh, terrestrial cellular, and satellite links, to improve robustness and coverage. Multipath transport is a natural mechanism for aggregating these links, yet its ability to support real-time UAV services in highly heterogeneous environments remains insufficiently characterized. We present a measurement-driven study based on UAV flight experiments in an integrated network comprising UAV-to-UAV aerial mesh, private cellular, and low Earth orbit (LEO) satellite connectivity. Using Multipath TCP (MPTCP) as a representative lossless, in-order multipath transport framework, we find that aggregation can preserve end-to-end connectivity under severe link outages. However, large round-trip time (RTT) heterogeneity amplifies packet reordering, leading to substantial receiver-side buffering and bursty delivery. In addition, when the available links do not provide sufficient capacity for the offered load, pronounced sender-side buffering emerges. These effects cause real-time streaming to violate delay constraints, including cases where aggregate capacity is sufficient. To interpret these results, we formalize the distinction between connectivity continuity and service continuity and show empirically that maintaining connectivity is necessary but not sufficient for timely real-time delivery in multi-technology UAV networks. The findings motivate multipath designs that explicitly account for delay constraints, rather than optimizing for connectivity alone.

Let $k\ge 2$ be fixed integer, $0<c<1$ a constant. Consider a graph $G$ with $n$ vertices and average degree $cn$. We answer a question of Simon Griffiths by showing that $G$ has $k$ vertices such that their neighborhoods together cover at least $\min(1-(1-c)^{k},\sqrt{c})n$ vertices. This result is essentially tight.

It is not known whether the realisation part of the $s$-cobordism theorem holds for smooth 4-manifolds, nor whether every pair of smoothly $h$-cobordant 4-manifolds is also smoothly $s$-cobordant. We provide some new conditions under which these questions admit a positive answer. We also give conditions under which the `standard' method to construct an $h$-cobordism with specified torsion cannot work.

We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete $\mathbb{G}_m$-variety with finite fixed locus. Our results include novel characterizations of when the Bialynicki-Birula decomposition is filterable or forms a stratification, showing that these properties are invariant under reversing the $\mathbb{G}_m$-action. We additionally classify the smooth projective toric varieties for which the Bialynicki-Birula decomposition either may or must be a stratification. Our study of $\mathbb{G}_m$-convexity and $\mathbb{G}_m$-rigidity -- properties recently introduced by Buch--Chaput--Perrin -- answers several questions posed in their $\textit{Equivariant rigidity of Richardson varieties}$. In particular, assuming only filterability of the decomposition, we show that the Bialynicki-Birula cell closures are determined by their $\mathbb{G}_m$-equivariant Chow classes.

We theoretically demonstrate that quantum fluctuations inherent to antiferromagnets can generate scalar spin chirality at zero temperature even in coplanar ordered magnets. In a kagome antiferromagnet with coplanar ground-state spin configurations, the quantum-fluctuation-induced scalar spin chirality is shown to arise at zero temperature when an effective time-reversal-like antiunitary symmetry is broken in the Hamiltonian describing fluctuations, and a magnetic point group of the classical ground state allows for its presence. The scalar spin chirality fluctuations are shown to grow further with increasing temperature by thermally excited magnons. These scalar spin chirality fluctuations can reach a magnitude comparable to the static one predicted for noncoplanar spin structures, highlighting their physical implications in coplanar spin systems.

We formulate and prove Parseval-Rayleigh identities for graded Artinian Gorenstein algebras over fields of positive characteristic. Specializing the general result, we provide an alternative proof of the Parseval-Rayleigh identities of generic Artinian reductions of Stanley-Reisner rings of oriented simplicial spheres.

Accurately linking microscopic energy deposition from ionizing radiation to emergent biological outcomes remains a central challenge in radiobiological modelling, particularly when stochastic damage induction, cell-cycle dynamics, and spatial organisation within irradiated tissues must be treated explicitly and consistently across scales. To address this, we introduce a stochastic agent-based radiobiological modelling framework for simulating biological response to particle irradiation, developed as an explicit single-cell extension of the Generalized Stochastic Microdosimetric Model (GSM2). Each cell is represented as an autonomous agent whose internal state, including DNA lesion counts, cell-cycle phase, and oxygenation level, evolves according to a continuous-time Markov chain driven by GSM2 transition rates. Radiation-induced damage induction, repair, misrepair, cell-cycle progression, proliferation, and migration are treated as competing stochastic events resolved through a next-event, event-driven algorithm, which provides computationally efficient scaling with system size while preserving full single-cell resolution. The framework is applied to three-dimensional tumour spheroids irradiated with 1H and 12C ions across a range of energies and dose rates. We characterise the spatiotemporal evolution of cell-cycle phase composition and spheroid volume following irradiation, and examine the dependence of cell survival on dose rate over four orders of magnitude. Several empirically established trends in biological response, including the dose-rate dependence of cell survival, its attenuation at high LET, and the inverse dose rate effect in split-dose irradiation, emerge from the model through the explicit coupling of particle arrivals, damage accumulation, and repair kinetics, without recourse to empirical correction factors as typically done.

We establish a half-space theorem à la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.

We establish an Itô-type formula for finite $p$-variation paths with jumps for arbitrary $p\geq 1$. The formula is stated in a fully pathwise form and separates the reduced rough integral from explicit left- and right-jump correction terms. In the càdlàg case, only the left-jump correction remains, while in the continuous case, both jump correction terms vanish and the formula recovers the corresponding continuous arbitrary-regularity change-of-variable formula. The proof is based on the reduced rough path framework and a refinement Riemann-Stieltjes convergence criterion adapted to discontinuous paths. This approach allows us to handle the higher-order Taylor expansions required for large values of $p$ and to control the interaction between rough increments and discrete jumps. As applications, we derive Itô-type formulas for stochastic processes whose sample paths have finite $p$-variation, including pure-jump models and mixed fractional Brownian-jump signals. The latter class includes cases with Hurst parameter $H\leq 1/3$, which fall outside the regime $2\leq p<3$. We also obtain chain-rule identities for nonlinear observables of càdlàg finite-$p$-variation solutions of random differential equations with jumps, together with a pathwise log-wealth decomposition.

Flexible-antenna systems, which use a small number of radio frequency (RF) chains to dynamically access a large set of candidate antenna locations, have emerged as a hardware-efficient architecture for 6G networks. Acquiring accurate channel state information (CSI) is critical for these systems, but it typically incurs a prohibitive pilot overhead that scales with the massive number of candidate locations. To address this bottleneck, we propose a unified sensing-assisted channel estimation framework tailored for flexible-antenna systems. It reduces the full CSI reconstruction problem to a consistent two-stage process: it first resolves the dominant DOAs from the uplink data symbols by exploiting the spatial geometry, requiring no dedicated sensing pilot, and then calibrates the associated path gains using a minimal number of calibration pilots. Building on this pipeline, we develop two Newton-MUSIC algorithms tailored to different propagation environments. For line-of-sight (LOS)-dominant environments with uncorrelated sources, we propose SOC-Newton-MUSIC, which leverages second-order covariance (SOC) for low-complexity DOA sensing. For non-line-of-sight (NLOS) environments with coherent multipath, where the number of sources may exceed the number of activated RF chains, we propose FOC-Newton-MUSIC, which exploits fourth-order cumulants (FOC) to restore source identifiability and structurally expand the available spatial degrees of freedom (DOFs) through a continuous difference co-array. In both cases, by reformulating the spatial spectrum search as a continuous optimization problem, we replace exhaustive dense grid searches with parallelized Newton refinements.

The long-standing assumption of symmetric radio emission beams from the two magnetic poles of pulsars is challenged by observational evidence of asymmetry and underfill. Direct testing of this symmetry remains difficult for most pulsars. As an indirect test, we collected polarization profiles of 11 interpulse pulsars observed with the Five-hundred-meter Aperture Spherical radio Telescope, MeerKAT, and Parkes. We developed a rotating vector model incorporating aberration and retardation effects to fit the position angle swings of selected pulsars, thereby determining the intrinsic emission region corresponding to the observed pulse windows. Based on both the conal and fan beam models, we compared three key parameters-beam radius, magnetic azimuth width, and emission intensity-between the intrinsic emission regions of the main pulse and interpulse. Among the eight pulsars with a confirmed double-pole geometry, none exhibits similarity in the azimuth width. Only two show potentially similar beam radii, while six demonstrate comparable emission intensities within specific parameter spaces. These results indicate that the emission beams from the two magnetic poles of a pulsar may be generally dissimilar in size, suggesting that the physical conditions governing pair production and particle acceleration differ between the two poles. The random distribution of active emission regions further implies inhomogeneity within the polar cap, which may originate from the differences in local magnetic field structure or surface properties.

We use coupled-channel calculations to explore the nature of near-threshold bound states in a simplified model of Rb+KRb. This is a prototype for systems with very strong coupling at short range and chaotic behavior for the short-range states. We find that there are states with strong long-range character that exist close to threshold and probably persist to depths at least 100 GHz below each threshold. These states are only weakly coupled to the short-range states and do not form part of the chaotic manifold. Since they spend little time at short range, they are relatively insensitive to destruction by laser light. They can thus have long lifetimes that are unrelated to the density of states and can cause narrow Feshbach resonances when the states are shifted across thresholds by external fields.

Order picking travel dominates much of warehouse effort, and exact routing is especially valuable when storage is scattered so pick locations are not fixed in advance. We address the single picker routing problem (SPRP) and its scattered-storage variant (SPRP-SS) in single-block and two-block rectangular warehouses. We propose two mixed-integer linear programming formulations that exploit structural properties of optimal tours to simplify connectivity modelling and remove redundant edge configurations: a Configuration Connectivity model tailored to single-block layouts and an Edge Connectivity model that extends to two-block layouts. In extensive computational experiments on large randomly generated benchmark sets for single-block and two-block rectangular layouts, we compare these formulations against established MILP and network-flow baselines for SPRP and SPRP-SS and report computational gains tied to the structural restrictions. The results support using compact, solver-based exact routing models in industrial settings where dynamic programming is cumbersome to integrate, particularly for SPRP-SS and for routing subproblems embedded in larger planning or warehouse-design optimizations.

We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly as $\text{polylog}(m)$) to the extended semi-discrete sine kernel. As an application, we show fixed-energy universality of bulk local statistics of complex Hermitian Wigner matrices matching the covariance structure of GUE and with a finite $4+\varepsilon$ moment for $\varepsilon>0$. This application demonstrates that it is possible to obtain universality of bulk local statistics under near-optimal moment assumptions without using a Dyson Brownian motion relaxation step, which was a key ingredient in many results on this topic.

Mirror symmetry predicts an action by the fundamental group of a conjectural stringy Kähler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the action is still an open problem in general. We propose that this action can be studied on the $A$-side via a moduli space of Legendrians isotopic to the FLTZ Legendrian. For the $A_{n-1}$ singularity, we construct an annular braid-group action on the corresponding partially wrapped Fukaya category by exact autoequivalences. The standard braid subgroup recovers the Seidel--Thomas action on the derived category, while the additional annular generator corresponds to tensor product with $\mathcal O(-1)$. We additionally extend the Floer theoretic approach to homological mirror symmetry for toric varities to the setting of semiprojective toric Deligne-Mumford stacks over an arbitrary field.

We present a comprehensive theoretical investigation of hyperfine-resolved excitation and detection of the low-energy isomeric state of $^{229}$Th in trapped $^{229}\mathrm{Th}^{3+}$ ions. Using a quantum master equation approach, we analyze the dependence of the isomeric population on laser linewidth, detuning, and irradiation time, showing that their proper matching is essential for efficient excitation. We further propose two nuclear-state detection schemes based on three hyperfine-resolved electronic fluorescence channels at 690, 984, and 1088 nm. Our analysis shows that the 690-nm and 984-nm scheme yields detectable photon rates on the order of $10^4~\mathrm{s}^{-1}$ per ion for each wavelength, whereas the 1088-nm scheme achieves a higher rate on the order of $10^5~\mathrm{s}^{-1}$ per ion. By quantifying the trade-off between irradiation time and scan-step size, we show that the nuclear transition can be located within one month for a 100-MHz uncertainty using currently available vacuum-ultraviolet laser technology. These results provide practical guidance for trapped-ion $^{229}\mathrm{Th}$ spectroscopy and the development of nuclear clocks.