Monte Carlo particle transport problems play a vital role in scientific computing, but solving them on exiting von Neumann architectures suffers from random branching and irregular memory access, causing computing inefficiency due to a fundamental mismatch between stochastic algorithms and deterministic hardware. To bridge this gap, we propose MCPT-Solver, a spin-based hardware true random number generator (TRNG) with tunable output probability enabled by a Bayesian inference network architecture. It is dedicated for efficiently solving stochastic applications including Monte Carlo particle transport problems. First, we leverage the stochastic switching property of spin devices to provide a high-quality entropy source for the TRNG and achieve high generating throughput and process-voltage-temperature tolerance through optimized control logic and write mechanism designs. Next, we propose a hardware Bayesian inference network to enable probability-tunable random number outputs. Finally, we present a system-level simulation framework to evaluate MCPT-Solver. Experimental results show that MCPT-Solver achieves a mean squared error of 7.6e-6 for solving transport problems while demonstrating a dramatic acceleration effect over general-purpose processors. Additionally, the MCPT-Solver's throughput reaches 185 Mb/s with an area of 27.8 um2/bit and energy consumption of 8.6 pJ/bit, making it the first spin-based TRNG that offers both process-voltage-temperature tolerance and adjustable probability.

We compute the complete set of one-loop contributions to the muon anomalous magnetic moment, $a_μ=(g-2)_μ/2$, in the Doublet Left-Right Symmetric Model (DLRSM), based on the gauge group $SU(2)_{L}\otimes SU(2)_{R}\otimes U(1)_{B-L}$ with neutrino masses generated via the inverse seesaw (ISS) mechanism. We evaluate all four one-loop topologies VFF, SFF, FVV, and FSS arising from the extended gauge bosons ($W^{\prime}$, $Z^{\prime}$), the new scalar sector ($H_{3}^{0}$, $A_{1}^{0}$, $H_{R}^{\pm}$, $H_{L}^{\pm}$), and the heavy neutrino spectrum generated by the ISS mechanism, using the Casas--Ibarra parametrization to express the neutrino mixing in terms of physical observables. Imposing the experimental bound on $Δa_μ$, we establish that $v_{R}\lesssim1$ TeV is excluded, implying lower bounds $m_{W^{\prime}}\gtrsim325$ GeV, $m_{Z^{\prime}}\gtrsim385$ GeV, and $m_{N}\gtrsim700$ GeV under the manifest left-right symmetry condition $g_{R}=g_{L}$. Relaxing this condition to $g_{R}\neq g_{L}$ strengthens the gauge boson bounds to $m_{W^{\prime}}\gtrsim1625$ GeV and $m_{Z^{\prime}}\gtrsim1650$ GeV.

In the contact-geometric approach to general relativity, the sky of an event - namely, the set of all incoming light rays - forms a Legendrian submanifold of the spherical cotangent bundle of a Cauchy hypersurface. When the hypersurface is chosen to be the Minkowski hyperboloid, a hyperbolic version of the hodograph transform identifies this bundle with a thermodynamic phase space. We consider a uniformly accelerating observer starting on the hyperboloid and study the evolution of its skies. We show that the associated generating functions, after a suitable rescaling, admit a natural interpretation as reduced free energies of equilibrium thermodynamic systems governed by the relativistic Doppler effect. From this data, we extract an effective temperature that is proportional to the acceleration, in agreement with the scaling of the Unruh effect, although the numerical constant differs from the Unruh value.

Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and information hiding. This paper studies the uniform interpolation property in epistemic modal logics with distributed knowledge, which captures agents' collective reasoning abilities. Building on the bisimulation-quantifier perspective, we extend the canonical-formula and literal-elimination framework of Fang, Liu, and van Ditmarsch to distributed knowledge settings and introduce the concept of collective $p$-bisimulation. We show that, for distributed knowledge modal logics $\mathsf{K}_n\mathbf{D}$, $\mathsf{D}_n\mathbf{D}$, and $\mathsf{T}_n\mathbf{D}$, every satisfiable canonical formula's uniform interpolant omitting an atom $p$ is exactly its remainder of eliminating $p$. Then, we provide a finer analysis for the transitive and Euclidean systems $\mathsf{K45}_n\mathbf{D}$, $\mathsf{KD45}_n\mathbf{D}$, and $\mathsf{S5}_n\mathbf{D}$, and prove that every formula of modal depth $k + 1$ has a uniform interpolant of modal depth $2 k + 1$. Thus, we prove the uniform interpolation property in all the six distributed knowledge modal logics. Finally, we generalize the results to some variants with propositional common knowledge and discuss the method's limitations.

Derivative boundary conditions introduce challenges for mesh-free discretizations of PDEs on surfaces, especially when the domain is represented by randomly sampled point clouds. The recently developed two-step tangent-space RBF-generated finite difference (RBF-FD) method provides high accuracy on closed surfaces. However, it may lose stability when applied directly to surface PDEs with derivative boundary conditions. To enhance numerical stability, we develop a mesh-free method that couples the two-step tangent-space RBF-FD discretization with a quadratic programming (QP) procedure to stabilize the operator approximation for interior points near boundaries. For boundary points, we construct restricted nearest-neighbor stencils biased in the co-normal direction and employ a constrained quadratic program to approximate outward co-normal derivatives. The resulting method avoids using ghost points and does not require quasi-uniform node distributions. We validate the approach on elliptic problems, eigenvalue problems, time-dependent diffusion equations, and elliptic interface problems on surfaces with boundary. Numerical experiments demonstrate stable performance and high-order accuracy across a variety of surfaces.

In this work, we investigate a neutrinophilic low-mass dark matter model mediated by a pseudoscalar particle. Since dark matter lacks Standard Model gauge charges, new interactions are required to connect it to the visible sector. Traditional indirect detection searches for annihilation products, such as cosmic rays, become ineffective when the annihilation predominantly yields invisible neutrinos. In our model, the present-day annihilation cross section into neutrinos (manifesting as a neutrino line) falls below current indirect detection limits. We therefore constrain the model using complementary probes: the Lyman-$α$ forest, high-energy astrophysical neutrinos from active galactic nuclei and supernovae, direct detection via nucleon and electron scattering, and invisible Higgs decays. These observables provide stringent and multifaceted constraints on neutrinophilic dark matter interactions in the low-mass regime. Our results indicate that searches for the neutrino line from dark matter annihilations, neutrino self-interactions from supernovae and collider signatures, and invisible Higgs decays offer critical tests for the model's parameter space.

This paper investigates the thermoelastic fracture response of a transversely isotropic piezoelectric strip containing a vertical insulated crack under transient thermal shock loading and pre-existing stress fields. The analysis is conducted within the framework of generalized fractional heat conduction using the Ezzat model, which incorporates thermal relaxation and memory-dependent effects. The problem is formulated as a mixed boundary value problem governed by fractional thermoelastic equations. The Laplace transform technique is employed to obtain temperature and coupled fields in the transform domain. The resulting system of singular integral equations is solved using the Lobatto-Chebyshev collocation method to determine the displacement discontinuity and the associated thermal stress intensity factors at the crack tips. The transient response in the time domain is recovered through numerical inversion of the Laplace transform using the Stehfest algorithm. Numerical results for PZT-4 are presented to examine the influence of fractional order, thermal relaxation time, pre-existing stresses, and geometric parameters on temperature distribution, thermoelastic stress fields, and stress intensity factors. The results demonstrate significant deviations from classical Fourier predictions, revealing wave-like thermal behavior and inherent memory effects associated with fractional heat conduction. The present formulation establishes a unified framework for the analysis of thermoelastic fracture in piezoelectric ceramics and provides insights into the design and reliability of smart structures operating under severe thermal conditions.

In this paper, we study the nonlinear modulational instability of two-dimensional hydroelastic Stokes waves in infinite depth. We first justify a focusing cubic nonlinear Schrödinger (NLS) approximation result for 2D deep hydroelastic wave system in the spirit of Ifrim-Tataru [22]. Then we exploit the instability mechanism of the cubic NLS to prove that the Stokes waves are nonlinearly unstable under long-wave perturbations.

We study a transformation surface associated with a zero mean curvature surface in the three-dimensional Heisenberg group with respect to two left-invariant semi-Riemannian metrics. We investigate the duality and prove that the transformation surface also has zero mean curvature. Furthermore, we derive the Sym formula for the dual surface in both metric cases.

Edge deployment of large language models (LLMs) can reduce latency for interactive services, but mobility introduces service interruptions when an user equipment (UE) hands over between base stations (BSs). To promptly resume decoding, the target-side edge server must recover the UE context state, which can be provisioned either by token forwarding followed by prefill computation or by direct key-value (KV) cache transmission over backhaul. This paper proposes a unified handover (HO) design that jointly selects the prefill length and schedules backhaul KV cache delivery to minimize the worst-user LLM HO delay for multiple UEs. The resulting scheme admits a tractable step-wise solution with explicit feasibility conditions and a constructive rate-scheduling policy. Simulations show that the proposed method consistently outperforms baselines across a wide range of backhaul capacities, prefill speeds, and context sizes, providing practical guidelines for mobility-aware Edge LLM token streaming.

Anti-Stokes optical cooling in diamond nitrogen-vacancy (NV) centers is experimentally and numerically investigated. Photoluminescence-excitation spectroscopy reveals pronounced phonon-assisted anti-Stokes emission under excitation below the zero-phonon line (ZPL). However, the below-ZPL excitation drives photoinduced charge-state conversion between negatively-charged NV- and neutral NV0, thereby suppressing the NV- mediated cooling channel. Time-resolved photoluminescence (PL) measurements reveal an increase in the effective PL lifetime with excitation density, reflecting an increasing NV0 contribution. By fitting nanosecond and millisecond PL dynamics with a minimal rate-equation model, we extract effective optical pumping and charge-conversion rates, which enables us to quantitatively simulate the cooling performance. The simulations predict a self-limiting behavior of anti-Stokes cooling and clarify the excitation conditions under which net cooling can be sustained within this effective model. The estimated cooling power per NV center is comparable, on a microscopic basis, to values discussed for semiconductor quantum dots and rare-earth optical coolers. These results identify charge-state conversion as a key bottleneck for defect-based optical refrigeration.

We study feedback stabilization of continuous-time linear systems under finite data-rate constraints in the presence of unknown disturbances. A communication and control strategy based on sampled and quantized state measurements is proposed, where the quantization range is dynamically adjusted using reachable-set propagation and disturbance estimates derived from quantization parameters. The strategy alternates between stabilizing and searching stages to handle escapes from the quantization range and employs an additional quantization symbol to ensure robustness near the equilibrium. It guarantees input-to-state stability (ISS), improving upon existing results that yield only practical ISS or lack explicit data-rate conditions. Simulation results illustrate the effectiveness of the strategy.

In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}$-limit metric soliton [Bam23,CMZ23]. We first prove some estimates for noncollapsed $\mathbb{F}$-limit metric solitons with nonnegative Ricci curvature, and then obtain two dichotomy theorems for ancient Ricci flows. In particular, we show that: (1) for a noncollapsed ancient Ricci flow with nonnegative Ricci curvature, either its asymptotic volume ratio is always zero, or every tangent flow at infinity is a Ricci flat cone; (2) for a noncollapsed ancient Ricci flow with positively pinched Ricci curvature ($\operatorname{Ric}\ge \varepsilon R g$), either it is compact, or every tangent flow at infinity is a Ricci flat cone.

Accurate prediction of ionic conductivity is critical for the design of high-performance solid-state electrolytes in next-generation batteries. We benchmark molecular dynamics (MD) approaches for computing ionic conductivity in 21 lithium solid electrolytes for which experimental ionic conductivity has been previously reported in the literature. In particular, we compare simulations driven by density functional theory (DFT) and by universal machine-learning interatomic potentials (uMLIPs), namely a MACE foundation model. We find comparable performance between DFT and MACE, despite MACE on one GPU more than 350 times faster than DFT on a 64-CPU node. The framework developed here is designed to enable systematic comparisons with additional uMLIPs and fine-tuned models in future work.

We present a novel framework that jointly trains a neural network controller and a neural Riemannian metric with rigorous closed-loop contraction guarantees using formal bound propagation. Directly bounding the symmetric Riemannian contraction linear matrix inequality causes unnecessary overconservativeness due to poor dependency management. Instead, we analyze an asymmetric matrix function $G$, where $2^n$ GPU-parallelized corner checks of its interval hull verify that an entire interval subset $X$ is a contraction region in a single shot. This eliminates the sample complexity problems encountered with previous Lipschitz-based guarantees. Additionally, for control-affine systems under a Killing field assumption, our method produces an explicit tracking controller capable of exponentially stabilizing any dynamically feasible trajectory using just two forward inferences of the learned policy. Using JAX and $\texttt{immrax}$ for linear bound propagation, we apply this approach to a full 10-state quadrotor model. In under 10 minutes of post-JIT training, we simultaneously learn a control policy $π$, a neural contraction metric $Θ$, and a verified 10-dimensional contraction region $X$.

We provide an explicit construction and a closed dimension formula in terms of hook lengths for the irreducible representations for the symmetric groups $\mathfrak{S}_p$ and the Sergeev superalgebras $\mathcal{Y}_p$ over an algebraically closed field $\mathbb{F}$ of characteristic $p>0$.

Let $M$ be a closed manifold. We introduce a family of Legendrian isotopy invariants for Legendrians in $J^1M$, which we collectively call Legendrian higher torsion. Given a choice of a class $\mathcal{F}$ of fibre bundles over $M$, equipped with suitable unitary local systems, the Legendrian higher torsion of a Legendrian $Λ\subset J^1M$ is the subset of $H^*(M;\mathbf{R})$ consisting of higher Reidemeister torsion cohomology classes of fibre bundles $W$ over $M$ in the class $\mathcal{F}$ such that $Λ$ admits a generating function on a stabilization of $W$. For the class of tube bundles in the sense of Waldhausen we call the invariant tube torsion. In particular, we show that the tube torsion of a nearby Lagrangian $L \subset T^*M$ is well-defined when the stable Gauss map $L \to U/O$ is trivial and consists of a union of cosets of a normalized version of the Pontryagin character. We also identify a distinguished coset, invariant under Hamiltonian isotopy of $L$, which we call nearby Lagrangian torsion. We do not know whether nearby Lagrangians must have trivial tube torsion, as would follow from the nearby Lagrangian conjecture. However, we show that there exist Legendrians $Λ\subset J^1M$ with nontrivial tube torsion whose projection $Λ\to M$ is homotopic to a diffeomorphism.

The model of light-matter interaction in quantum electrodynamics typically relies on the Markovian approximation, which assumes that the system's future evolution depends solely on its current state, effectively treating it as a ``memoryless" process. However, this approximation is not valid in scenarios when retardation effects are significant. These memory and retardation effects have the potential to improve existing quantum technologies (e.g., large-scale quantum networks, quantum information processing) and unlock new phenomena for future applications. In this work, we show theory and experiments of a time-delayed coherent feedback system using a transmon artificial atom (treated as a qubit) embedded in a superconducting circuit waveguide, in both linear and nonlinear excitation regimes. By using a feedback loop with a delay time comparable to the qubit relaxation time, pronounced non-Markovian effects appear in the dynamics of the qubit evolution. We also show how the resonance fluorescence spectrum, including elastic and inelastic scattering (such as the well-known Mollow triplet), can be significantly modified through the interaction between the qubit and feedback loop to show genuine non-Markovian and quantum nonlinear phenomena that cannot be explained with instantaneous coupling parameters. This work presents the first experimental report of Mollow triplets in the non-Markovian regime.

Reverse engineering tools remain monolithic and imperative compared to the advancement of modern compiler architectures: analyses are tied to a single mutable representation, making them difficult to extend or refine, and forcing premature choices between soundness and precision. We observe that decompilation is the reverse of compilation and can be structured as a sequence of modular passes, each performing a granular and clearly defined interpretation of the binary at a progressively higher level of abstraction. We formalize this as provenance-guided superset decompilation (PGSD), a framework that monotonically derives facts about the binary into a relation store. Instead of committing early to a single interpretation, the pipeline retains ambiguous interpretations as parallel candidates with provenance, deferring resolution until the final selection phase. Manifold implements PGSD as a declarative reverse engineering framework that lifts Linux ELF binaries to C99 through a granular intermediate representation in ~35K lines of Rust and Datalog. On GNU coreutils, Manifold's output quality matches Ghidra, IDA Pro, angr, and RetDec on multiple metrics while producing fewer compiler errors, and generalizes across compilers and optimization levels.

RDMA link failures can render connections temporarily unavailable, causing both performance degradation and significant recovery overhead. To tolerate such failures, production datacenters assign each primary link with a standby link and, upon failure, uniformly retransmit all in-flight RDMA request over the backup path. However, we observe that such blanket retransmission is unnecessary. In-flight requests can be split into pre-failure and post-failure categories depending on whether the responder has already executed. Retransmitting post-failure requests is not only redundant (consuming bandwidth), but also incorrect for non-idempotent operations, where duplicate execution can violate application semantics. We present Varuna, a failure-type-aware RDMA recovery mechanism that enables correct retransmission and us-level failover. Varuna piggybacks a lightweight completion log on every RDMA operation; after a link failure, this log deterministically reveals which in-flight requests were executed (post-failure) and which were lost (pre-failure). Varuna then retransmits only the pre-failure subset and fetches/recovers the return values for post-failure requests. Evaluated using synthetic microbenchmarks and end-to-end RDMA TPC-C transactions, Varuna incurs only 0.6-10% steady-state latency overhead in realistic applications, eliminates 65% of recovery retransmission time, preserves transactional consistency, and introduces zero connectivity rebuild overhead and negligible memory overhead during RDMA failover.

For strongly quantum-degenerate systems at finite temperatures, the fermion sign problem remains the major obstacle to first-principles simulations. In this work, we apply the recently proposed pseudo-fermion method - designed to overcome the sign problem - to strongly quantum-degenerate uniform electron gases. We find that the pseudo-fermion method can efficiently and highly accurately infer the energy of the uniform electron gas while being free from the fermion sign problem. For example, in the strongly quantum-degenerate regime where RPIMC fails (33 spin-polarized electrons at the density parameter $r_s = 0.5$), the relative deviation between the pseudo-fermion method and the exact CPIMC result is only 0.6%. In particular, the pseudo-fermion method bridges the gap where neither CPIMC nor RPIMC can accurately simulate the regime $1 \le r_s \le 2$ at the reduced temperature $θ= 0.0625$. This work demonstrates that the pseudo-fermion method opens a new pathway for studying strongly quantum-degenerate systems in a sign-problem-free manner.

Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the \textit{renormalized entropy} $s_{2-q}$. Derived from the asymptotic scaling of the combinatorial $q$-factorial, this quantity yields a stable thermodynamic limit, remaining finite ($O(N^0)$) for systems with strong correlations. Furthermore, we clarify the physical origin of the nonlinearity parameter $q$ through the concept of \textit{Varentropy} (Variance of Entropy). By unifying the macroscopic variational principle with the microscopic Superstatistics framework, we derive the relation $|q-1| \simeq 1/C$, where $C$ is the heat capacity of the reservoir. This result suggests that power-law statistics provides a thermodynamic description of finite systems, where the finite heat capacity of the heat bath necessitates a generalization beyond the standard Boltzmann-Gibbs limit ($C \to \infty$).

This study examined how behavioral, emotional, and contextual factors influence Filipino students' willingness to use artificial intelligence (AI) for mental health support. Results showed that habit had the strongest effect on willingness, followed by comfort, emotional benefit, facilitating conditions, and perceived usefulness. Students who used AI tools regularly felt more confident and open to relying on them for emotional support. Empathy, privacy, and accessibility also increased comfort and trust in AI systems. The findings highlight that emotional safety and routine use are essential in promoting willingness. The study recommends AI literacy programs, empathic design, and ethical policies that support responsible and culturally sensitive use of AI for student mental health care.

We study the scaling properties of long-range loop-erased random walks (LR-LERW), where the underlying random walker performs Lévy-flight-like jumps with a power-law step-length distribution $P(\mathbf{r})\sim |\mathbf{r}|^{-(d+σ)}$. Using extensive Monte Carlo simulations, we measure the scaling relation $N \sim R^{d_N}$ between the loop-erased step number $N$ and the spatial extent $R$, and determine the geometric exponent $d_N$ for various values of $σ$ in spatial dimensions $d = 1, 2,$ and $3$, as well as at the marginal point $σ= 2$ in $d=4$ and $5$. We observe a continuous crossover from long-range (LR) to short-range (SR) behavior as $σ$ increases. Below the upper critical dimension $d<d_c=4$, for $σ< d/2$, loop erasure is asymptotically irrelevant and $d_N=σ$, consistent with Lévy-flight scaling. For $d/2 < σ< 2$, loop erasure becomes relevant and $d_N$ varies continuously toward the SR-LERW value. At the marginal points with $σ=d/2$ or $σ=2$, clear logarithmic corrections are observed. At and above the upper critical dimension, $d \geq 4$, the scaling at $σ=2$ is found to be $N \sim R^2/\ln R$, consistent with that of the corresponding Lévy flight. Our results provide a systematic numerical determination of $d_N(σ)$ for the LR-LERW across dimensions, and are consistent with $σ_* = 2$ as the boundary between LR and SR critical behaviors recently established in a broad variety of statistical models.

Achieving both broad solar-spectrum absorption and strong redox capability is critical for semiconductor photocatalysts in environmental remediation and energy conversion. Herein, an S-scheme heterojunction photocatalyst is constructed by coupling TiO2(B) nanorods with g-C3N4 nanosheets. Its well-matched band structure extends light absorption from the UV to the visible region and enables efficient charge separation. Under simulated sunlight irradiation, the 40 wt% g-C3N4/TiO2(B) heterojunction delivers a H2 evolution rate of 1.98 mmol g-1 h-1 for water reduction with methanol as the sacrificial agent, which is 1.5 and 2.0 times higher than those of pure g-C3N4 and TiO2(B), respectively. When exposed to amoxicillin wastewater instead of methanol solution, the heterojunction degrades 98.2% of amoxicillin and produces 20.70 umol g-1 of H2 within 90 min. Moreover, the heterojunction shows excellent photodegradation activity toward various organic antibiotics and dyes, owing to the S-scheme charge separation mechanism. This work highlights the promising potential of S-scheme heterojunctions for photocatalytic H2 production coupled with organic wastewater treatment.

This paper introduces a generalized matrix-valued Allen--Cahn model, where the unknown matrix-valued field belongs to $\mathbb{R}^{m_1\times m_2}$ with dimension $m_1\geq m_2$. By taking different values of $m_1$ and $m_2$, this model covers the classical scalar-valued, vector-valued, and square-matrix-valued Allen--Cahn equations. At the continuous level, the proposed model is proven to admit a unique solution satisfying the maximum bound principle (MBP) and the energy dissipation law. At the discrete level, a class of arbitrarily high-order exponential time differencing Runge-Kutta (ETDRK) schemes is investigated that preserve the MBP unconditionally. Moreover, we prove that the first- and second-order ETDRK schemes satisfy the discrete energy dissipation unconditionally, while third- and higher-order schemes preserve the discrete energy dissipation under suitable time-step constraints. The proof of sharp convergence order in time is provided. Numerical experiments are carried out to confirm our theoretical results.

We investigate the gravitational wave polarization modes and stability in Weyl geometry gravity within a Minkowski background. Our results indicate that the tensor sector consists of two standard modes propagating at the speed of light. Although the vector sector possesses a dynamical degree of freedom, it generates no polarization modes. The scalar sector, in contrast, features a mixture mode of breathing and longitudinal modes associated with a single scalar degree of freedom. This degree of freedom exhibits superluminal propagation and intrinsic amplitude decay, both driven by the background Weyl gauge field. We further discuss the observational detectability of this scalar mode. Our stability analysis reveals that, while the tensor and vector sectors are free from ghost and Laplacian instabilities, the scalar sector suffers from an Ostrogradsky ghost instability. These findings clarify the unique gravitational wave propagation characteristics in Weyl geometry gravity and provide theoretical foundations for testing the theory through future multi-messenger observations.

We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing on Kullback Leibler (KL) risk minimization, we develop a calibration framework to optimally tune predictive densities derived from on a broad class of flexible priors. Our proposed method addresses two key challenges in predictive inference: (a) severe data scarcity leading to highly imbalanced designs, in which replicates are available for only a small subset of units; and (b) distributional shifts in future covariates. To estimate predictive KL risk in LMMs, we use a data-fission approach that leverages exchangeability in the covariate distribution. We establish convergence rates for our proposed risk estimators and show how their efficiency deteriorates as data scarcity increases. Our results imply the decision-theoretic optimality of the proposed EB predictive density estimator. The theoretical development relies on a novel probabilistic analysis of the interaction between data fission, sample reuse, and the predictive heat-equation representation of George et al. (2006), which expresses predictive KL risk through expected log-marginals. Extensive simulation studies demonstrate strong predictive performance and robustness of the proposed approach across diverse regimes with varying degrees of data scarcity and covariate shift.

We study the ground-state phases of a two-dimensional dipolar supersolid subjected to external periodic confinement by numerically solving the extended Gross--Pitaevskii equation. Focusing on a regime in which the unconfined system forms an intrinsic triangular droplet crystal, we consider triangular, honeycomb, and square optical lattices and classify them into isostructural and heterostructural settings relative to the spontaneous supersolid order. We map out the stationary states as functions of the lattice depth $V_0$ and the commensurability ratio between the intrinsic droplet spacing and the external lattice period. For triangular and honeycomb confinements, the competition between the soft self-organized supersolid lattice and the rigid external potential can generate long-wavelength moiré superstructures in the weak- to intermediate-lattice regime, together with a sequence of reconstructed states including ring-like clusters and stripe-segment configurations. By contrast, the square lattice introduces strong symmetry mismatch between the intrinsic $C_6$ order and the imposed $C_4$ geometry, leading to frustration-induced anisotropic states and symmetry-reduced cluster arrangements. Our results establish dipolar supersolids under periodic confinement as an unconventional route to exploring moiré physics, where moiré superstructures arise from the competition between a self-organized soft lattice and an externally imposed rigid one.

We introduce a spin $z$-component ($S_{z}$) conserving symmetry-preserving ansatz and a shallow quantum phase estimation (QPE) routine of spin $x$ ($S_x$), and combine them into a spin-filtering variational quantum deflation (sfVQD) scheme for noisy intermediate-scale quantum (NISQ) computing era excited state calculations. The scheme encodes the spin information into a small ancilla register through controlled rotations under $\mathrm{exp} (iθ\hat{S}_{x})$ with only modest circuit overhead. The encoded information is then utilized to suppress spin contamination by screening, avoiding costly explicit evaluation on the total spin $\langle\hat{S}^{2}\rangle$. Because the screening module operates independently of the variational ansatz, it can also be employed with other excited-state calculation schemes based on variational quantum eigensolvers. As a demonstration, we apply sfVQD to LiH and BeH$_2$ with varying geometries to show markedly improved separation of singlet and triplet manifolds over conventional VQD without QPE-derived screening. These results suggest that ancilla-assisted symmetry screening provides a modular and NISQ-compatible route to securing excited state calculations of physically meaningful properties. We discuss how our scheme may naturally be extended to computing other conserved quantities.