A single CPU core sustains 32 million order messages per second at sub-microsecond median end-to-end host-path response latency, 4.7-11 times faster than the best available open-source matching engines on identical hardware. Scaled out, a single 96-core commodity server (~$1,630/month) sustains ~640 million messages per second across 10,000 symbols, over 20 times the provisioned capacity of the U.S. consolidated quote feed. We reach these numbers by attacking the storage layer that sets matching latency. The dominant order-book implementation, linked lists chained through a balanced tree, imposes two costs on every operation: pointer-chased traversal to the insertion point, and root-to-leaf search to locate the target price level. Under micro-bursts these costs produce tail-latency spikes that degrade market quality precisely when liquidity is most needed. We present two data-structure contributions that eliminate them. The first is the Priority-Indicated Node (PIN), a priority queue in which entries occupy fixed-capacity, contiguously addressable slots, with indicators encoding the entry's global priority status. Unlike heaps, which require O(log n) comparisons per operation, the PIN resolves insertion position directly from the indicators without comparing entries; indicator updates are O(1), independent of queue size. A depth-aware capacity model sizes each PIN so hot entries fit within L1 residency. The second targets a broader inefficiency: balanced search trees search from root to leaf on every insertion and deletion, even when the caller already knows the key's in-order neighbors, which in electronic trading are available at zero cost. Neighbor-aware insertion and deletion use known neighbor references to attach or remove a node with O(1) reference writes, followed by single-path rebalancing, across red-black, AVL, and B+-tree variants.

In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing certain double Lambert series to single Lambert series. As applications, we derive identities related to recent conjectures of Andrews, Dixit, Schultz, and Yee, and of Amdeberhan, Andrews, and Ballantine. We also propose a new proof of a result of Amdeberhan, Andrews, and Ballantine.

Effective field theory (EFT) provides a systematic framework for parametrizing possible higher-energy corrections to general relativity through higher-curvature interactions. In this work, we investigate gravitational lensing in both weak- and strong-field regimes for EFT-corrected Reissner-Nordström black hole spacetimes, focusing on both weakly charged and near-extremal configurations. Using the strong deflection limit formalism, we derive the corresponding corrections to the deflection angle, photon sphere radius, critical impact parameter, and strong lensing coefficients induced by higher-derivative curvature-electromagnetic interactions. Our analysis is restricted to purely geometrical corrections associated with modifications of the background spacetime geometry, without including polarization-dependent corrections to the photon propagation law. We show that strong gravitational lensing observables in charged black hole backgrounds can provide complementary probes of effective interactions between gravity and electromagnetic fields. These results suggest that future high-precision observations of strong lensing phenomena may place constraints on higher-curvature EFT couplings beyond general relativity.

We bootstrap the four-point next-to-maximally helicity-violating (NMHV) form factor of the chiral stress-tensor supermultiplet in planar maximally supersymmetric Yang-Mills theory through three loops at the symbol level. At two loops, an ansatz built from NMHV leading singularities and the relevant five-point one-mass integral function space is fixed uniquely by physical constraints; the resulting ratio function symbol contains 78 letters, all drawn from the 88-letter alphabet previously identified in the four-point MHV sector. At three loops, using this 88-letter alphabet as input and imposing extended Steinmann relations satisfied by the minimally-subtracted hard function, together with other physical constraints, we determine the three-loop symbol uniquely. Both results pass soft, double-soft and directional dual conformal invariance (DDCI) checks, provide the first multi-loop non-MHV form-factor data, and support the universality of the 88-letter alphabet for four-point form factors beyond the MHV sector.

Inertial particles in turbulence form clusters, which strongly affect particle collisions and transport properties. Clustering models based on statistically stationary turbulence implicitly assume the instantaneous-equilibrium approximation when applied to time-varying non-equilibrium turbulence. However, the validity of this approximation remains unclear. In this study, the temporal response of inertial particle clustering in non-equilibrium turbulence was investigated using direct numerical simulation of homogeneous isotropic turbulence with unsteady forcing. Periodic responses of the flow and clustering intensity were evaluated by varying the forcing period. The flow showed non-equilibrium scaling for all forcing periods. The relationship between instantaneous energy dissipation rate and clustering intensity showed hysteresis exceeding statistically stationary fluctuations when the forcing period exceeded several large-eddy turnover times. For the particles with the largest inertia, clustering intensity took values of 0.80 and 1.56 times the reference value at the same instantaneous energy dissipation rate. This shows that the instantaneous-equilibrium approximation is not appropriate under such conditions. A linear relaxation model was constructed from transient responses, in which clustering intensity approaches the instantaneous-equilibrium value with a finite relaxation time. The relaxation time scaling was identified as $τ_g = 1.0 T_\mathrm{e}(t)\,\mathrm{St}(t)^{0.40}$, where $T_\mathrm{e}(t)$ and $\mathrm{St}(t)$ are the instantaneous large-eddy turnover time and Stokes number. The model reduced the maximum relative error from 49% to 10% for the particles with the largest inertia and from 76% to 22% in an independent validation case. These results demonstrate that finite-time relaxation improves prediction accuracy for clustering intensity in non-equilibrium turbulence.

We introduce a Szilard-type thermodynamic valuation of side-information channels induced by Bell-type correlations. In each round, a two-level working system is thermalized with a degenerate Hamiltonian, so that its physical microstate is a uniform classical bit. A trusted referee embeds this bit into a finite two-player XOR game, and a correlation resource produces a compressed controller bit. The controller uses only this compressed bit as side information for feedback. The construction is formulated first for arbitrary finite XOR games. The referee encoding makes the game-winning event equivalent to correct prediction of the physical microstate. Consequently, the induced side-information channel is binary symmetric, with success probability equal to the XOR-game winning probability of the supplied behaviour. The reversible Szilard feedback value is therefore fixed by the mutual information between the microstate and the controller record. Optimizing over local, quantum, and nonsignalling behaviour sets turns the corresponding game values into local, quantum, and nonsignalling thermodynamic ceilings. The construction is an effective-channel valuation, not a claim that Bell nonlocality is thermodynamic fuel. The controller receives only the compressed prediction bit, not the auxiliary variables that define the game. The thermodynamic costs of the referee, the correlation resource, and the preprocessing are not included. When controller-memory reset is included in a full cycle, the net work is non-positive, consistently with the second law.

We study orbifold compactifications of heterotic strings on Enriques surfaces. We classify the inequivalent shift vectors for both the E8\times E8 and Spin(32)/Z2 lattices, and analyse the light spectrum of the resulting models. We show that these models can be interpreted as compactifications of ten-dimensional non-supersymmetric heterotic strings on Enriques surfaces. For certain classes of shifts, the moduli-independent tachyons inherited from the parent theories are projected out.

We study Rota--Baxter operators on vertex algebras using the integrated $λ$-bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the difference between the deformed and original brackets yields a two-cocycle in vertex algebra cohomology. This generalizes the classical relation between Rota--Baxter operators and Hochschild two-cocycles. We also characterize when this two-cocycle is trivial, showing that non-scalar operators give rise to non-trivial cohomology classes.

We establish the existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory. We establish a sharp upper bound for the largest eigenvalue of the associated Ricci matrix in terms of the maximum degree. Turning to structural properties, notably, the existence of a positive-curvature Einstein metric implies the tree must be a caterpillar. Furthermore, these metrics exhibit radial monotonicity, with edge weights decreasing strictly away from the maximal edge.

Let $G$ be a simple connected graph on $n$ vertices, and let $λ_1(G),λ_2(G),\ldots,λ_n(G)$ be the eigenvalues of its adjacency matrix $A(G)$. For $p>0$, define the $p$-energy of $G$ by $\mathcal E_p(G)=\sum_{i=1}^n |λ_i(G)|^p$. We prove that, for every real number $p\ge 2$ and every simple connected graph $G$ on $n$ vertices, $$ \mathcal E_p(G)\ge \mathcal E_p(P_n), $$ where $P_n$ denotes the path on $n$ vertices. Moreover, for each fixed $p>2$, equality holds if and only if $G\cong P_n$. Together with the previously known star-minimality results, this completes the solution of two questions of Nikiforov. The proof combines two different comparison principles. For $2<p<4$, we use a bipartite reduction, a Mellin representation of fractional powers, and a determinant comparison involving matching generating polynomials and tree shifts. For $p\ge4$, we prove a second-order stop-loss comparison for the squared singular values of bipartite graphs. This comparison is established by rank-one spectral-shift estimates, deletion-minimal counterexamples, and a finite certified analysis of the terminal sparse-sun configurations.

Answering a question of Goode, we show that $k$-triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a relational language of bounded arity is trivial. We use our collapse result, along with other facts about $k$-triviality and $k$-total triviality, to generate examples of (strongly) $k$-distal theories. The collapse result immediately implies that no stable theory can be strictly $k$-distal for some $k\geq 3$, partially answering a question of Walker. Moreover, all known examples of non-distal (strongly) $k$-distal theories are $k$-ary, rendering (strong) $k$-distality moot as a $(k+1)$-ary dividing line; we give four classes of examples that are not $k$-ary. We also show that just as distality is not preserved under taking reducts, neither is (strong) $k$-distality.

We introduce a battery-explicit thermodynamic witness of post-quantum Bell correlations. In each round, a single supplied excitation is routed into an explicit two-level battery if and only if a Bell-game condition is satisfied. The routing operation is implemented by an energy-preserving controlled SWAP, with all logical control registers taken to be degenerate. Thus the correlation resource does not create energy; it only determines the probability that the supplied excitation reaches the battery. The construction is first formulated for finite two-player XOR games. For any such game, the mean battery charge is exactly the game success probability multiplied by the battery gap. Optimizing over local, quantum, or nonsignalling behaviours therefore turns the corresponding game values into local, quantum, or nonsignalling thermodynamic ceilings. For the CHSH game, Tsirelson's bound becomes a strict quantum ceiling on the mean battery charge, while a PR-box behaviour reaches the single-excitation cap. The witness is trusted-module rather than device-independent: it assumes calibrated Hamiltonians, correct classical wiring, and a trusted energy-preserving battery module. We also discuss a reversible-controller implementation, finite-statistics certification from work data, robustness to imperfect battery readout, and cyclic bookkeeping showing that no positive net work is obtained once fuel restoration and memory erasure are included.

This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI) systems. Starting from the definition of geometric frequency, which provides a geometrical interpretation of frequency in electric circuits that admits a natural decomposition into symmetric and antisymmetric components associated with amplitude variation and rotational motion, respectively, we show that complex frequency arises as its restriction to the two-dimensional Euclidean plane. For LTI systems, it is shown that the complex frequencies computed from the system's states subject to a non-isometric transformation, coincide with the original system's eigenvalues. This equivalence is demonstrated for diagonalizable systems of any order. The paper provides a unified geometric interpretation of eigenvalues, bridging classical linear system theory with differential geometry of curves. The paper also highlights that this equivalence does not generally hold for nonlinear systems. On the other hand, the geometric frequency of the system can always be defined, providing a geometrical interpretation of the system flow. A variety of examples based on linear and nonlinear circuits illustrate the proposed framework.

We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

The expected signature uniquely determines the law of a random rough path under a moment-growth condition, yet finite-sample bounds for estimating its truncations from a single long dependent trajectory remain unavailable. We study a strictly stationary stochastic process equipped with a geometric rough-path lift, observed in non-overlapping blocks of equally-spaced samples, and prove a non-asymptotic mean-squared error (MSE) bound for the block-averaging estimator of its truncated expected signature. Under moment and stationarity assumptions together with a direct covariance-decay condition on block signatures -- strictly weaker than $α$-mixing and applicable to long-range-dependent processes -- the error separates into a discretization term and a fluctuation term, with rates determined respectively by path regularity and dependence strength. A levelwise rough-factorial variance analysis keeps finite-truncation constants explicit and yields an optimal allocation rule under a fixed observation budget. We verify the assumptions for independent-coordinate fractional Ornstein--Uhlenbeck processes in three regimes: short-range (Hurst $1/4<H<1/2$), semimartingale ($H=1/2$), and long-range ($H>1/2$); in all three, the block-signature covariance is summable, so the fluctuation term decays at the same rate as in the independent-block case, even under long memory at $H>1/2$. Monte Carlo experiments show empirical slopes steeper than the guaranteed upper-bound rates.

We investigate the synergy between large-scale structure (LSS) observations and gravitational wave (GW) events for testing modified gravity. In particular, we forecast the LSS $\times$ GW cross-correlation signal using Stage-IV LSS surveys, such as Euclid, in combination with future detections from the Einstein Telescope. This cross-correlation provides a novel probe of fundamental physics, potentially revealing deviations from the $Λ$CDM paradigm that may not be accessible through electromagnetic observations alone. We describe the considered modified gravity scenarios, the relevant LSS and GW observables, and the synthetic forecast methodology. Our results demonstrate that combining LSS and GWs can significantly enhance constraints on departures from General Relativity, opening a new window for multi-messenger cosmology. We further assess the observational requirements GW experiments must meet to improve upon constraints obtainable from LSS alone.

We demonstrate how the transport properties of molecular polaritons in optical cavities can be extracted from a microscopic modeling of pump-probe spectroscopy. Our approach combines a mean-field treatment of the light-matter Hamiltonian with a perturbative expansion of both light and matter components, along with spatial coarse-graining. This approach extends semiclassical cavity spectroscopy to multimode light-matter interactions, providing full access to spatially resolved transient spectra. By simulating a microscopy experiment with counter-propagating pump and probe pulses, we compute the differential transmission and show how molecular dephasing and persistent dark exciton populations drive sub-group-velocity transport of the root-mean-square displacement. We analyze transport across the polariton dispersion, showing how velocity renormalization correlates with excitonic weight, consistent with experimental observations, and further its dependence on the rate of molecular dephasing. Our results highlight the need to consider measured spectroscopic observables when characterizing transport in polaritonic systems.

Inclusive, differential and production-mode cross-section measurements of the Higgs boson are performed in the $H \to ZZ^{*} \to 4\ell$ decay channel. The analysis uses proton-proton collision data produced at the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s}=13.6$ TeV and recorded with the ATLAS detector, corresponding to an integrated luminosity of 164 fb$^{-1}$. The inclusive fiducial cross-section for the $H \to ZZ^{*} \to 4\ell$ process is measured to be $σ_{\textrm{fid}} = 3.65^{+0.35}_{-0.33}~\textrm{fb}$, in agreement with the Standard Model prediction of $σ_{\textrm{fid}}^{\textrm{SM}} = 3.68 \pm 0.17~\textrm{fb}$. Differential cross-sections are measured as a function of key kinematic observables of the Higgs boson and the four-lepton final state. Cross-sections are measured for the main production-modes in several exclusive regions of the Higgs boson production phase space and combined to measure an overall Higgs boson signal strength, defined as the measured cross-section normalised to the SM prediction, of $μ= 0.99 \pm 0.13$. The results are interpreted in terms of modifications of Higgs boson couplings using the $κ$ framework, within the Standard Model Effective Field Theory, and in scenarios probing the Higgs boson self-coupling. All the results are consistent with Standard Model expectations.

We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with the principal eigenvectors of the covariance matrix, thereby establishing a direct and explicit connection with PCA. Our analysis covers both finite and infinite prompt regimes. In the infinite-prompt limit, we prove convergence to globally optimal solutions aligned with the leading spectral direction, while in the finiteprompt setting we show that the same behavior emerges up to sampling effects. We further extend the analysis to an in-context setting with spiked Wishart covariances, where attention successfully recovers the underlying signal direction. These results demonstrate that attention inherently performs PCA-like computations under unsupervised objectives, providing a theoretical foundation for its representation-learning capabilities.

We propose a new approach to measuring the CP-violating phase in neutrino mixing using atmospheric neutrinos, differing significantly from prior work. We develop an up-down flux ratio for sub-GeV atmospheric neutrinos that incorporates realistic detection effects and reduces systematic uncertainties. For the example of Hyper-Kamiokande -- the first experiment with sufficient atmospheric-neutrino statistics in this energy range -- our approach can surpass the sensitivity of the Tokai to Hyper-Kamiokande (T2HK) long-baseline experiment near $\mathit{δ_\mathrm{CP} = 90^\circ}$ and $\mathit{270^\circ}$. Realizing this potential will require additional, but realistic, work to reduce theoretical uncertainties. Success will provide an important, complementary probe to multi-\$1B accelerator-based experiments.

The correct inferential object in claims reserving is the conditional predictive distribution $p(R \mid \mathcal{D}, \hatθ)$, where $\mathcal{D}$ is the observed triangle held fixed. We refer to this as the conditioning principle. All existing bootstraps violate it by resampling functions of $\mathcal{D}$ inside the predictive loop, producing an $O(1)$ coverage error that does not vanish as the triangle grows. The Dirichlet-Gamma hierarchy admits a bootstrap that satisfies the principle exactly: $S^{IBNP}_i = X^{obs}_i (1-W_i)/W_i$ with $W_i \sim \mathrm{Beta}(c\hat{F}_{I-i}, c(1-\hat{F}_{I-i}))$ sampled directly from its predictive distribution. Only the allocation proportion $W_i$ is simulated; the observed triangle is held fixed. It thus inherits calibration from any development-proportion method (Chain-Ladder, Bornhuetter-Ferguson, Cape Cod, or other), making it model-agnostic. The coverage deficit is $O(I^{-1/2})$, independent of the number of development periods. Under compound Poisson data-generating processes the bootstrap is conservative for every $F_{I-i} \in (0,1)$: the predictive standard deviation analytically exceeds the true value by the factor $1/\sqrt{F_{I-i}}$. The ODP bootstrap violates the principle through two mechanisms in opposite directions: re-estimation inflates bootstrap variance under the ODP DGP, while missing accident-year frailty deflates it under frailty DGPs. The resulting coverage discrepancy is $Ω(1)$ regardless of $I$, providing a structural explanation for the cross-portfolio miscalibration heterogeneity documented by Meyers (2015). Chain-Ladder, Bornhuetter-Ferguson and Cape Cod emerge as credibility estimators under diffuse, informative and pooling priors respectively, with identical structure for counts and amounts. The concentration $c$ serves as a diagnostic: $\hat{c} < 30$ signals non-stationary development.

The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack model and the Over-Dispersed Poisson (ODP) framework-provide measures of uncertainty but rely on second-moment assumptions or quasi-likelihood variance structures without clear generative interpretations. This paper develops a Negative Binomial Chain-Ladder (NB-CL) model that embeds the CL method within a full likelihood-based framework. The key contribution is a micro-level derivation showing that the negative binomial distribution arises naturally from a Poisson-Gamma construction: claims arrive according to a Poisson process with Gamma-distributed accident-year heterogeneity, and aggregation yields negative binomial incremental counts. This derivation gives the dispersion parameter $κ$ a structural interpretation as accident-year heterogeneity, rather than an ad-hoc overdispersion adjustment. The NB-CL model generalises the Poisson Chain-Ladder model in the limit $κ\to \infty$, shares the point estimates of the ODP model while differing in its variance function (quadratic vs. linear), and unifies the Chain-Ladder family within a single probabilistic hierarchy. A parametric bootstrap procedure is developed to incorporate both process and parameter uncertainty. Simulation studies confirm near-nominal coverage under correct specification once the dispersion parameter is bias-corrected, and a controlled degradation under model misspecification. Empirical illustrations on claim count data (Australian motor bodily injury) and paid amounts (Taylor-Ashe) document both the structural reading of $κ$ and the working-approximation status of the model in the amounts case.

We study the topological properties of bordisms interpolating between different 9d gauged supergravities obtained from compactification of type IIB string theory on $\mathbb{S}^1$ with a non-trivial $\mathsf{SL}(2,\mathbb{Z})$ bundle. We describe how such bordisms implement the needed monodromies through stacks of $[p,q]$ 7-branes or gravitational solitons of non-trivial topology. For the later mechanism, we see that the topology of the bordism becomes increasingly complicated for large monodromies, which results in the associated bordisms being arbitrarily suppressed, against expectations on the breaking of global symmetries in Quantum Gravity. Motivated by this, we propose a refinement of the Swampland Cobordism Conjecture for the first bordism group $Ω_1({\rm B}G)$ with a $G$ duality bundle. We argue that even if gravitational solitons can realize the monodromies associated with elements of the commutator subgroup of $G$, if the number of needed commutators is unbounded (in other words, the commutator width of $G$ diverges) then an infinite number of duality defects realizing elements in $G$ need to be included. We test this proposal for different duality groups $G$, and see that our expectations are realized, often in non-trivial ways.

We undertake a systematic study of the mapping properties of forms based on distance graphs in $\mathbb{Z}^{d}$ to see how the structure of a graph, $G$, affects the $\ell^{p}$ improving estimates of the form, $Λ_{G}$, based on $G$. This extends previous work on $\ell^{p}$ improving properties for the spherical averaging operator, which corresponds to a distance graph of a single distance. We obtain $\ell^{p}$ improving estimates for the collection of forms based on all graphs with 2, 3, and 4 vertices, as well as chains and simplexes of any size in $\mathbb{Z}^{d}$. Surprisingly, certain mapping properties only seem to depend on the number of vertices in the graph, not its structure, and forms based on subgraphs of a graph, $G$, do not necessarily inherit all mapping properties from $G$.

In this work, we investigate the linear stability of a magnetized Einstein-Maxwell solution describing a static, axially symmetric black hole (BH) immersed in a uniform magnetic field $B$. We probe the dynamics of an external charged scalar field through its quasinormal modes (QNMs), combining frequency- and time-domain analyses. We find a critical value of the field charge at which the QNM spectrum exhibits universal power-law scaling with an exponent of approximately $1/2$. This critical behavior admits a simple interpretation in terms of a transition between a confined regime, where waves remain effectively trapped within a region of characteristic size $\sim 1/B$, and a deconfined regime, where the field reaches distances $\gg 1/B$ and the damping rate becomes parametrically small. These results provide qualitative and quantitative insights that may inform more realistic scenarios involving highly magnetized compact objects.

As generative AI tools increasingly influence creative practice, they raise longstanding HCI questions about how creatives learn complex software and how they can be better supported. We conducted an interview study with artists and hobbyists (n=8) and a follow-up survey (n=159) to understand how this population approaches and seeks guidance for GenAI image tools. We found that creatives commonly use either self-experimentation or tutorials to explore GenAI tools, yet many struggle with confusing AI terminology. To gain further insight into creatives' learning experiences, we developed a research probe to elicit creatives' perceptions of structured guidance. Our user study with 17 creatives revealed that, even when creatives described the guidance as helpful for understanding AI, many still preferred self-experimentation, feeling that guidance could limit their creativity. Our findings highlight a central tension in supporting AI literacy for creatives: balancing guidance and promoting literacy while preserving creative freedom.

We study a class of bilevel interdiction problems in which the follower's optimization problem is computationally intractable. Motivated by network defense applications, we introduce the Randomized Max-Vertex-Coverage Interdiction (RMVCI) problem under matroid constraints. In this zero-sum Stackelberg game, the leader commits to a randomized interdiction strategy over feasible vertex subsets, while the follower, after observing the induced protection probabilities, chooses a matroid-constrained attack to maximize the expected coverage of network edges. The main challenge stems from the fact that the follower's problem is a matroid-constrained maximum vertex coverage problem and is therefore NP-hard. To address this difficulty, we first develop a general approximation framework for bilevel optimization problems with hard follower responses. The framework is based on replacing the follower's value function by a surrogate objective that approximates the follower's optimal payoff while preserving tractability of the leader's optimization problem. For the RMVCI problem, we formulate the follower's problem as an integer linear program, establish a tight integrality gap of $4/3$ for its linear relaxation, and derive a polynomial-time $4/3$-approximation algorithm via pipage rounding. We then show that a carefully designed surrogate objective admits a marginal-probability reformulation that transforms the randomized interdiction problem into a tractable optimization problem over the leader's matroid polytope. This yields a polynomial-time $2$-approximation algorithm for RMVCI under general matroid constraints. Beyond the specific application studied here, our results provide a new perspective on approximation methods for {general} bilevel optimization problems.

Aims. We constrain the dynamical perturbations of the spiral arms in the Milky Way disk, based on the non-axisymmetric streaming motions of RGB stars revealed by APOGEE and \textit{Gaia}. Methods. We develop a revised steady-state radial-velocity response model that incorporates both the \(V_{R,\sin}\) and the dynamically important \(V_{R,\cos}\) components for a two-armed logarithmic spiral potential. The model is validated using orbit integrations with \texttt{AGAMA} and Bayesian parameter recovery with \texttt{dynesty}, and is applied to the smoothed two-dimensional radial-velocity field of RGB stars while accounting for Lindblad and corotation resonances. Results. The revised model reproduces the phase and amplitude of the mock radial-velocity field to the \(\sim2\%\) level, substantially improving upon earlier \(V_{R,\sin}\)-only formulations. Applied to the observational data, it yields a robust pitch angle of \(p \simeq 10^\circ\) and a local surface density contrast of \(ξ\simeq 5\)--\(18\%\) at the solar radius. The radial scale length is less well-constrained (\(h_{R,1} \simeq 40\)--\(50\,\mathrm{kpc}\)) due to intrinsic parameter covariance. Resonance effects strongly shape the velocity field, thus affecting the fitting: the radial velocity becomes extremely large near the Lindblad resonances, whereas it vanishes close to the corotation resonance. Conclusions. Our results demonstrate that including both the \(V_{R,\sin}\) and \(V_{R,\cos}\) terms is essential for a physically consistent interpretation of stellar streaming motions induced by a spiral potential. The observed kinematics constrain the spiral pattern speed to \(Ω_{p} \approx 10\)--\(20\,\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}\).

Artificial intelligence is increasingly entering digital games through diverse functions. While prior work has shown that player attitudes toward game AI are strongly context-dependent, less is known about how these attitudes are structurally combined within different groups of players. This study addresses this gap by modeling players' cross-context AI acceptance as interpretable attitude profiles. Based on questionnaire data from 771 digital game players, we apply Archetypal Analysis (AA) to centered acceptance ratings across eight representative AI application contexts in games. The analysis identifies seven distinctive profiles: AI-Skeptics, Broad AI-Supporters, Creative-Play Explorers, Experience-Oriented Supporters, Systemic Order Advocates, Emotion-Centered Supporters, and Governance-Skeptics. Exploratory one-vs-rest (OvR) logistic regressions further suggest that profile membership is associated with players' perceived AI literacy, gaming habits, disciplinary background, personality traits, and application-specific priorities. By shifting attention from isolated acceptance judgments to patterned preference structures, this study provides an exploratory empirical vocabulary for segmenting game AI audiences and offers preliminary design implications for more context-sensitive and player-sensitive AI integration in digital games.

The nitrogen-vacancy (NV) center in diamond exists in different charge states with distinct photoluminescence properties, which are sensitive to the nanoscale electrochemical environment. Hence, the NV charge state is emerging as a powerful all-optical platform for nanoscale sensing and imaging. Although significant progress has been made in engineering near-surface NV centers in bulk diamond, controlling the NV charge state in fluorescent nanodiamonds (FNDs) has proven challenging, limiting the sensitivity and reliability of FND-based charge state sensing. Here, we demonstrate reliable, reversible switching between the fluorescent NV$^0$ and non-fluorescent NV$^+$ charge states in sub-30 nm FNDs via surface oxidation and hydrogenation, respectively, for single particles and particle powder. In aqueous electrochemical cells, we demonstrate voltage and ion concentration imaging based on the NV charge state in self-assembled FND layers on transparent substrates. Applied voltages reliably modulate the FND PL with a sensitivity of up to 16 mV Hz$^{-1/2}$. Importantly, FND PL is also modulated by local changes in salt concentration with a sensitivity of up to 1.8% per millimolar NaCl, enabling all-optical imaging of ion concentration gradients at the microscale. Our results represent a significant step toward realizing fast, stable, and scalable nanoscale charge- and voltage-imaging technologies with sub-micrometer spatial resolution.