Preference learning refers to the learning of latent patterns from ranking and preference data of different kinds. Typical aims of preference learning are to infer a shared consensus ranking, to learn individual-level preferences, and to perform unsupervised clustering. The Mallows model is among the few approaches that can achieve all these objectives jointly. Previous work has developed computationally tractable methods for Bayesian inference based on a MCMC Metropolis-Hastings scheme, where clustering is performed via a finite mixture of Mallows models. Inference on the number of clusters is then conducted a posteriori. Here we propose a Bayesian nonparametric Mallows model, based on a Dirichlet process mixture model. This allows joint inference on the number of non-empty clusters and on the clustering allocation, as well as posterior inference on cluster-specific parameters. The implementation of the proposed sampling algorithm is integrated into the existing R package BayesMallows, which also supports data in the form of incomplete rankings and pairwise comparisons. Simulated data show good performance of the nonparametric model compared to a finite mixture model in terms of recovery of the correct number of clusters, while empirical data on movie ratings show the model's effectiveness in providing personalized movie recommendations on discarded ratings.

The realization of on-chip photonic circuits requires scalable and deterministic single-photon emitters (SPEs) at room temperature, which remain a challenge in van der Waals materials. In this work, we report a novel three-step fabrication process for the generation of spatially controlled SPE arrays in hexagonal boron nitride (hBN). The process comprises site-selective gallium (Ga) focused ion beam milling, nanoscale conformal carbon deposition over the patterned regions, and subsequent thermal annealing. The synergistic combination of these steps resulted in a site-correlated emitter yield of ($\sim 89\%$) across 100 fabrication sites. Second-order autocorrelation measurements revealed pronounced three-level emitter dynamics where the best emitters exhibited high purity ($g^{(2)}(0)=0.15 \pm 0.09$).To the best of our knowledge, this is the first lithography-free, direct-write approach combining Ga-ion milling, selective carbon engineering, and thermal annealing to deterministically generate \hBN{} \SPE{}s. The reproducibility of the method is validated across multiple independently fabricated samples. These results establish a scalable, lithography-free pathway toward on-demand SPE arrays relevant to integrated quantum photonics.

This study investigated how additively manufactured nozzles with body-centered cubic lattice structures reduce the flame flashback propensity in a hydrogen jet flame burner. Five different configurations of a jet flame combustor were investigated, with a focus on mixing duct walls incorporating porous media. The nozzles were manufactured by the powder bed fusion of metals using a laser beam process. The lattice parameters were varied by the volume fraction and the strut diameter. For the experiments, pure hydrogen was used as fuel under atmospheric conditions at various equivalence ratios and Reynolds numbers of 9,000 - 12,000. Flow field measurements, flame imaging, and spectral proper orthogonal decomposition of the flame dynamics were employed to identify possible transition mechanisms from a stable operation to flashback. The flow fields and the flame shapes showed only minor effects from wall modifications, preserving general flow characteristics across configurations. The flow dynamics in the combustion chamber were dominated by large-scale coherent structures in the shear layer, specifically Kelvin-Helmholtz instabilities. The results demonstrated that the nozzle with the coarsest porous wall structure significantly improved the flashback resistance compared to a nozzle with a solid wall. It is concluded that the primary mitigation mechanism was a cooling effect by unburnt mixture flowing through the porous media. The findings confirmed that the integration of lattice structures through additive manufacturing provides a viable strategy for hydrogen flashback mitigation by manipulating the coupled interaction between the flame and the thermal conditions of the wall.

The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which $X$-$Z$ error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the $6.6.6$ color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hardware. In this work, we propose the iterative low-order decoding (ILOD) algorithm, which alternates between $X$- and $Z$-type sub-Hamiltonians, approximating cross-type correlations through Bayesian priors that reweight each type's couplings using the other type's inferred error configuration. This halves the maximum body count of interaction terms in the Hamiltonian, accelerating the solver, restoring convergence at larger code distances, and reducing the total spin count for 2-body embedding by a factor of $2.5$. For the toric code, ILOD attains a threshold of $4.73%$ versus $4.83%$ for the joint formulation, with the empirical runtime ratio scaling as $(0.81)^d$. For the $6.6.6$ color code, their thresholds agree within statistical uncertainty for small code distances, and ILOD remains convergent for larger distances where the joint formulation fails to converge despite a larger annealing budget.

We develop a general framework for matching KSVZ-like ultraviolet completions featuring vector-like fermions and a spontaneously broken $\mathrm{U}(1)_{\mathrm{PQ}}$ symmetry onto the Standard Model Effective Field Theory and the low-energy axion-like particle effective theory. The framework applies to arbitrary vector-like fermion representations and PQ-charge assignments, and systematically captures the effective interactions generated in both sectors. We then perform a comprehensive phenomenological analysis of the resulting SMEFT operators, based on global fits to electroweak precision, Higgs, and flavor observables, obtaining robust bounds on the corresponding Wilson coefficients that are largely independent of the details of the ultraviolet realization. These constraints can subsequently be translated into the QCD axion and ALP parameter space, providing indirect probes of ALP couplings. We further investigate several representative examples of the interplay between the SMEFT and ALP sectors, illustrating how direct ALP searches and indirect precision and flavor observables provide complementary information on the same underlying dynamics. We find that, over large regions of parameter space, indirect constraints derived from the SMEFT analysis dominate over direct ALP probes, except in scenarios where the PQ-charge assignment permits mass mixing with Standard Model fermions. Overall, our results establish a unified framework for connecting ultraviolet completions, SMEFT analyses, and ALP searches, enabling both the interpretation of existing constraints and the exploration of future signals within a common theoretical setting.

The origin of cosmic acceleration remains a central problem in cosmology, commonly attributed to a cosmological constant within the $Λ$CDM model or to dynamical dark energy. Here, we develop an alternative approach in which acceleration emerges from quantum post-selection, a standard feature of quantum theory that is not usually incorporated into cosmological modelling. While quantum theory admits both pre-selected and post-selected ensembles, quantum cosmological models are almost exclusively formulated in terms of initial conditions. Building on previous work on post-selected quasiclassical dynamics, we construct a minimal predictive cosmological model in which post-selection and coarse-graining generate effective late-time acceleration without introducing a cosmological constant, dark energy, or modifications of general relativity. The resulting expansion history is highly constrained theoretically and depends on at most two parameters beyond standard Friedmann evolution. Confrontation with type Ia supernova and cosmic chronometer data yields statistically competitive fits while naturally avoiding the coincidence problem. The model also reproduces the standard radiation- and matter-dominated behaviour at early times and predicts a present-day jerk parameter significantly different from the $Λ$CDM value. These results suggest that cosmic acceleration may arise as a macroscopic quantum cosmological effect rather than from additional cosmological fluids or modified gravitational dynamics.

Conventional nonparametric regression methods for two-dimensional non-rectangular domains often overlook domain geometry and allow smoothing across boundaries. In spatial and geostatistical applications, this assumption is frequently invalid because domain boundaries typically constrain interactions among observations. Accommodating spatially varying smoothness is also substantially more challenging than in the univariate setting, and most existing methods do not adequately capture this local structure of the target function. To address these challenges, we propose Bayesian triangulation splines, which constructs locally adaptive splines over a polygonal domain. The method employs constrained Delaunay triangulations to respect boundary geometry and adapt to heterogeneous smoothness. A carefully designed prior further improves empirical performance. Under a global Sobolev smoothness assumption, we show that the proposed method achieves the optimal posterior contraction rate and adapts to unknown smoothness. We also show that the method exhibits ideal spatial adaptation in the sense that it achieves the oracle rate for inhomogeneous or locally varying structural features. Crucially, this oracle guarantee is not specific to constrained Delaunay triangulations, but holds over any triangulation satisfying weak shape-regularity conditions. Simulation studies confirm that the proposed method outperforms existing approaches by achieving higher estimation accuracy while maintaining low model complexity.

Future 6G heterogeneous wireless networks (HWNs) are expected to support multiple radio access technologies (RATs), dynamic wireless environments, and applications with diverse quality-of-service (QoS) requirements. In such environments, network selection (NS) cannot rely only on instantaneous radio measurements or static ranking rules. Instead, access decisions must account for the evolving wireless state, service intent, packet-level QoS behavior, and candidate-RAT dynamics. This paper proposes a large language model (LLM)-based digital twin (DT) framework for stable, application-aware RAT selection under candidate-set evolution. The main idea is to shift NS from an instantaneous decision-matrix operation to a decision process over an evolving wireless DT state. The constructed DT combines site-specific geometry, Sionna RT-based propagation descriptors, ns-3 packet-level QoS emulation, service context, candidate-RAT information, and decision memory. Rather than acting as a general-purpose controller for 6G networks, the LLM is used for DT-grounded decision intelligence in this specific NS task. On top of this DT, a unified intent agent translates user and service requirements into structured decision priorities for two complementary NS branches: an LLM-assisted multi-attribute decision-making branch (MADM--LLM--NS) and a direct LLM-based ranking branch (LLM--NS). To improve decision stability, the framework further introduces history-aware adaptive normalization (HAAN) and DT-memory-driven retrieval-augmented in-context learning (RA--ICL). Numerical results show that the proposed framework reduces rank-reversal problem and unnecessary handover events, while improving service-aware QoS satisfaction compared with representative MADM-based NS baselines.

We investigate a problem, that describes coupling between diffusion and reaction inside a thin circular cylindrical tube. The asymptotic solution of the posed problem is derived by means of the boundary functions method. We perform comparison of this asymptotic solution against corresponding exact solution, which revealed serious methodological drawbacks of known Fick-Jacobs reduction approach. The results obtained may be used to study a wide range of reaction-diffusion problems, when the Fick-Jacobs method cannot be applied.

Agent memory is moving to graphs, and the provenance defenses now being built for it all check one thing: the provenance of the records an agent retrieves. We show that this entire class of defense is blind by construction. A long-term graph memory runs a global selection step over writable graph structure, so structure that an untrusted principal writes changes \emph{which} authenticated facts are selected while the cited evidence stays fully authenticated; faithful information-flow control (IFC), checking the provenance of what the reader uses (all of it authenticated), makes the byte-identical decision to no defense at all, across document-QA substrates and real multi-session agent memory. In the most consequential instance, a no-source structural write silently misdirects $28$ irreversible ledger transfers over $499$ live actions: faithful IFC permits every one, and \authselect\ prevents every one. We then characterize exactly which memories are exposed: a selector admits the channel when its structural term can reallocate an $Ω(1)$ share of top-$k$ membership past a selected fact's margin. Personalized PageRank can, since a sourceless write reroutes conserved random-walk mass; a content-fixed reranker cannot, and Graphiti's node-distance, which leans on structure \emph{more} than PageRank does, stays immune. Reallocatability, not reliance, is the predictor. We prove the immune case in general and the open case under a chokepoint condition we verify. Closing the channel forces any provenance defense to recompute selection on the authenticated subgraph, which is what \authselect\ does, at zero over-block and $2$--$3\%$ latency.

We establish a canonical Bernstein--Zelevinsky filtration for Casselman--Wallach representations that is analogous to the $p$-adic case. In addition, we outline an approach to Casselman's comparison conjecture and prove it for general linear groups, as well as for quasi-split even orthogonal groups in some special cases. We also give some applications of the Bernstein--Zelevinsky filtration, such as to the study of highest derivatives and the indecomposability of mirabolic restrictions.

This is a response to the paper ''Why Slop Matters''. By offering both immanent and external critique, we argue that the authors' reasoning neglects the socio-technical context of AI slop. Our paper presents an ethical and social science informed response that centers the debate on the social function and aesthetic value of AI slop. We conclude that AI slop is an important research subject but call for a contextual and culturally-grounded debate on the issue. To that end, we discuss some key elements of an agenda for future research on the phenomenon of AI slop.

Reference frame mismatch among communication parties introduces errors in quantum cryptographic protocols. As the number of participants increases, aligning reference frames becomes increasingly difficult, complicating multipartite quantum cryptographic implementations. Here, we theoretically and experimentally investigate multipartite reference-frame-independent (RFI) quantum cryptographic communication using Greenberger-Horne-Zeilinger (GHZ) states. We generalize the bipartite RFI security parameter $C$ to an $N$-party parameter $C_N$ and derive the asymptotic secret key rate expressed solely in terms of experimentally accessible quantities. We analyze the key rate under global and local depolarizing noise models and find that increasing the number of parties $N$ enhances robustness against global depolarizing noise while increasing vulnerability to local channel noise. We also present a proof-of-principle experimental demonstration of four-party RFI quantum cryptographic communication using four-photon GHZ states, confirming the reference-frame invariance of both the $C_4$ parameter and the secret key rate under various reference frame rotations.

For any closed surface of genus at least $3$, equipped with any bounding spin structure, we show that the index difference, viewed as a map from the fundamental group of the space of Dirac-invertible Riemannian metrics to $\KO^{-4}(*)$, is non-trivial. For products of two such surfaces, equipped with any spin structure, we prove that the corresponding space of Dirac-invertible Riemannian metrics is not contractible. We discuss the relationship of this result to the existence of metrics with harmonic spinors in dimension $4$.

The quark-gluon plasma (QGP) is a deconfined state of strongly interacting matter formed at extreme temperature and energy density in ultra-relativistic nucleus-nucleus collisions at RHIC and the LHC. High transverse momentum jets, produced in initial hard scatterings, traverse the QGP and lose energy via elastic and radiative processes, an effect known as jet quenching. The nuclear modification factor, $R_{\mathrm{AA}}$, defined as the ratio of the Pb+Pb jet yield to the $pp$ cross section scaled by the nuclear thickness function, is widely used to quantify jet quenching. However, its value depends strongly on both the $pp$ jet spectral shape and the strength of the quenching, complicating comparisons across jet selections. The fractional energy loss, $S_{\text{loss}}$, quantifying the average medium-induced momentum shift of jets, is designed to mitigate this dependence. In central Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$, we compile and compare published ATLAS and ALICE measurements of jet suppression for inclusive single-jet and dijet selections across multiple jet radii, considering (i) the ratio of the nuclear modification factor at a given radius to that at a reference radius of 0.2, and (ii) the fractional energy loss. The radius dependence of this ratio differs between single-jet and dijet measurements, and between ATLAS calorimeter jets and ALICE charged-particle jets, reflecting differences in kinematic event selections and jet constituents. Expressing the results in terms of $S_{\text{loss}}$ allows direct, radius-differential comparisons across experiments with reduced sensitivity to the $pp$ spectral slope. Combining these approaches enables constraints on the radius dependence of jet modification that account for selection biases, and facilitates cross-experiment benchmarking of jet quenching models.

In the infinite dilution limit, we show that the solvent-mediated potential of mean force (PMF) between solutes, extracted from the hypernetted-chain (HNC) closure of the Ornstein-Zernike equations, can expressed as a convolution between solute-specific generalised excluded volume functions. In the limit of a structureless solvent of point particles and hard core solutes, this recovers the exact Asakura-Oosawa depletion potential as the overlap between excluded volume spheres. The methodology can be deployed for ultrasoft particle systems such as those encountered in dissipative particle dynamics (DPD), where the solvent-mediated PMF can be recovered with considerable accuracy. These results confirm that in coarse-grained molecular DPD simulations the parametrisation of the non-bonded repulsions is sensitive to the assumed intramolecular bond lengths if they are smaller than the range of the DPD potential, due to the overlap of the soft excluded volume functions.

Multipole-Padé approximants provide a compact representation of dynamical response functions in terms of a small number of collective modes. Here, we generalize this framework to incorporate momentum dependence across the full Brillouin zone of 2D metals by constructing a symmetry-conserving, anisotropic representation of the inverse dielectric function. This analytic form enables efficient and accurate evaluation of quantities involving dynamical screening, including spectral features and correlation energies. We construct such compact representations for a set of seven two dimensional metals spanning distinct electronic regimes, and show that a small number of dispersive plasmonic modes suffices to accurately describe the dielectric response across the full Brillouin zone, while also yielding accurate correlation energies. The proposed representation therefore establishes a direct bridge between {\it ab initio} calculations and analytical models of screening, opening new avenues for applications in condensed matter systems.

Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations provide a better description of Rydberg states than time-dependent density functional theory. However, benchmarks have so far focused on the excitation energy, while assessments of dipole moments remain limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane waves basis set are used to compute the dipole moments of several Rydberg states of a set of molecules. Plane waves provide a flexible representation of the diffuse Rydberg orbitals, revealing limitations of atomic orbitals basis sets. A commonly used single-augmented atomic basis set yields inaccurate dipole moments even when the excitation energy is insensitive to the basis representation, and discrepancies with plane waves calculations persist for the most diffuse states even when extra augmented diffuse functions are added. The generalized gradient approximation functional PBE gives good agreement with higher-level calculations where available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ behavior of the effective Kohn--Sham potential.

Let $G$ be a loopless multigraph with maximum degree $Δ(G)$, average degree $\overline{d}(G)$, density $Γ(G)$, and chromatic index $χ'(G)$. A multigraph $G$ is called edge-$Δ$-critical if $Δ(G)=Δ$, $χ'(G)=Δ(G)+1$ and $χ'(H) \le Δ(G)$ for every proper subgraph $H\subset G$. Vizing conjectured that if $G$ is an edge-$Δ$-critical simple graph on $n$ vertices, then $\overline{d}(G) \ge Δ-1+\tfrac{3}{n}$. Motivated by this, we conjecture that every edge-$Δ$-critical multigraph $G$ satisfies $\overline{d}(G) \ge \tfrac{2Δ+2}{3}$, which is best possible. We first give a general lower bound in this direction. For any such graph $G$, \[ \overline{d}(G) \ge \begin{cases} \frac{\sqrt{17}-3}{2}(Δ+1) & \text{if } Δ\le 112;\\[4pt] \frac{Δ+\sqrt{2Δ-1}}{2} & \text{if } Δ\ge 113. \end{cases} \] This bound can be further improved under an additional condition on the multiplicity $μ$. In this case, \[ \overline{d}(G)\ge \min\left\{ \frac{2μΔ+2μ(2μ-1)}{4μ-1},\; \frac{\sqrt{17}-3}{2}(Δ+1) \right\}. \] We also confirm the conjecture for $Δ\in \{2,3,4,5,6,7,8\}$. As a consequence, Goldberg's conjecture~\cite{Goldberg1984} holds for $Δ(G)\in\{2,3,4,5\}$, that is, every multigraph $G$ with $χ'(G)\ge Δ(G)+1$ satisfies $Γ(G)\ge Δ(G)$.

In this short note, we improve the upper bound on the condition number of the univariate B-spline basis of order $k$ from $k 2^k$ to $O(\sqrt{k}\log k\,2^k)$ for all $k\ge 2$.

We study the finite-scale one-component degeneration problem for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations under a scale-invariant bound and smallness of the vertical component. Qualitative compactness gives convergence, in the harmonic-pressure quotient, toward the strict two-and-a-half-dimensional boundary, but it does not provide a quantitative rate. This paper proves, in an explicitly abstract trace-obstruction skeleton associated with the old observable closure, that the standard old observable package is insufficient to force a logarithmic or power selected-trace rate. The negative result is an envelope/skeleton theorem, not a Navier--Stokes counterexample. After excluding elementary high-frequency escape by parabolic trace drop and fixed-window analytic obstruction by finite-dimensional Lojasiewicz control, the remaining obstruction is an all-order finite-mode flat branch. We identify the Navier--Stokes-specific mechanism needed to control this branch: strict Schur trace-projectability may fail, but the resulting defect can be visible through the relaxed vertical-pressure channel. In active finite-window models, strict Schur phantoms are relaxed-visible. The final theorem is a conditional dichotomy: either relaxed anti-phantom closure holds and yields conditional logarithmic strict-shadow selection, or there exists an NS-realizable, cleaned, relaxed-invisible, unaligned left-singular cascade.

In this paper, we investigate a stochastic averaging principle for a large class of mechanical systems in the presence of random vibrations. We show that a known deterministic averaging principle for affine connection control systems with large-amplitude high-frequency inputs also holds for non-periodic stochastic inputs. The randomly vibrating mechanical system is described by a stochastic differential equation whose solutions do not depend on its interpretation in the sense of Ito, Stratonovich, or Sussmann. We also show that solutions of this stochastic differential equation can be directly computed from a single ordinary differential equation. We illustrate our theoretical results by the example of stochastic source seeking with a nonholonomic vehicle.

Quasars can serve as standard candles through an empirical scaling relation between their ultraviolet (UV) and X-ray luminosities. As high-redshift probes, it is critical to test whether this relation evolves with redshift. In this work, we reconstruct the Hubble diagram of the Pantheon+ sample using the deep learning--based LADDER algorithm and use it as a reference to investigate the quasar scaling relation. Our results, which are consistent with those from Gaussian process regression and narrow-bin analyses, show that the potentially contaminated sample at $z<0.7$ differs significantly from the $z>0.7$ sample; thus, it should be further screened or excluded when quasars are used as cosmological probes. We find that the scaling relation exhibits a non-linear redshift dependence that cannot be accounted for by a simple linear correction, and that this behavior is a feature of the current data sample rather than a consequence of cosmological model misspecification. To use quasars as standardizable candles, further modeling of the scaling relation and intrinsic dispersion, or more advanced data processing techniques, is required.

Contemporary theoretical descriptions of nuclear structure rely mainly on microscopic, single-particle frameworks often in competition with collective degrees of freedom, especially when deformation plays a dominant role. Such phenomena are prominent in the rare-earth region, where rotational band structures and enhanced electric quadrupole transitions are systematically examined. The Confined beta-Soft (CBS) rotor model, introduced by N. Pietralla and O.M. Gorbachenko, bridges the gap between the X(5) critical point and the rigid-rotor limit in the region where the R_4/2 = E(4+)/E(2+) ratio lies between 2.904 and 3.333. In the present work, the CBS framework is employed to calculate ground-state band energies, associated B(E2) transition rates, and beta-band excitations of even-even nuclei in the rare-earth region. The theoretical results are systematically compared with available experimental data, and predictions are provided for nuclear observables that have not yet been measured, offering guidance for future experimental investigations.

We have developed a fabrication technique for Josephson junctions that employs a three-dimensional patterned, low-loss substrate instead of commonly used organic resists. The technique enables the fabrication of high-quality trilayer junctions from a wide range of geometries and materials, including high-melting-point superconductors such as tantalum or niobium. The junction electrodes are free from intentionally introduced oxides and organic materials, which are known sources of decoherence. We fabricate and characterize underdamped Nb/AlOx/Nb junctions of different sizes in several geometries. Such junctions enable manufacturing of quantum circuits operating at higher speeds and elevated temperatures.

The package \texttt{rbreak} implements methods for detecting structural breaks and estimating break locations for linear multiple regression models under general linear restrictions on the coefficient vector. Restrictions can be within regimes, across regimes, or both, and are supported in two forms: an affine parameterization (Form A: \texttt{delta = S*theta + s}) and explicit linear constraints (Form B: \texttt{R*delta = r}). It provides break date estimation with confidence interval, a restricted sup-F test for the null of no structural change, simulation of critical values by Monte Carlo, and a bootstrap restart procedure to reduce the risk of convergence to spurious local optima. It also implements a generalized regression tree (linear model tree) procedure where each leaf contains a linear regression rather than a local average. This note explains the methods and illustrates them with applications.

Cache partitioning is among the strongest structural defenses against eviction-based cache side channels, yet a decade-old design issue has blocked its widespread deployment in secure shared-OS settings. The issue is that write-shared coherence collapses under strict partitioning. We present SCP (Secure and Coherent Partitioning), which combines strict eviction isolation with write-shared coherence by partitioning only the tags, sharing a single data pool, and sizing the data pool so capacity-driven cross-partition eviction cannot occur. Timing obfuscation extends protections to the inter-partition lookup path. Coherence-based leakage on shared-writeable lines is mitigated by routing those writes through to the LLC once a leakage threshold is crossed, which makes attacker write probe latency independent of victim activity. Using gem5 for implementation, SCP mitigates Prime+Probe and Flush+Reload, which are the basis for more sophisticated cache attacks. We also demonstrate that a shared-writeable-line attack is mitigated. All these attacks yield results no better than random guessing. SCP's hardware cost is a modest +2.8% LLC SRAM. Performance matches DAWG within 0.3% IPC on the SPEC CPU2017 benchmarks that we evaluated. Sharing-intensive microbenchmarks demonstrate a tunable security-performance tradeoff based on a system-specified leakage threshold.

Given a finite collection of Lagrangian submanifolds $\mathscr L$ in a compact symplectic manifold $X$, we construct a cyclic, filtered, strictly unital curved $A_{\infty}$ category $\mathcal L$ and develop Floer theory of closed-open maps and open-closed maps. Using them, we prove that, whenever the map from the quantum cohomology of $X$ to the Hochschild cohomology of the Fukaya category $\mathcal L$ with objects $\mathscr L$ is injective, the following consequences follow: (1) any other Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by $\mathscr L$, and (2) the Hochschild homology and cohomology of the Fukaya category are isomorphic to quantum cohomology. In the exact case a similar result was obtained in [Ab]. We also provide some applications.

Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary effects are encoded by a free-energy functional. For incompressible mixtures with more than two phases, however, robust computation is substantially more difficult because the numerical method should preserve the balance structure of the continuum model, maintain the saturation constraint, dissipate energy, and treat all phases symmetrically even when density ratios are arbitrary. Existing structure-preserving methods are largely developed for binary flows or for formulations that distinguish a reference phase, so a genuinely symmetric N-phase discretization remains lacking. The practical problem is therefore to construct a fully-discrete method for N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture models that retains the key thermodynamic and conservation properties of the continuum equations for arbitrary density ratios. Here we propose a symmetric fully-discrete method for the N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture model with arbitrary density ratios. The method yields a fully-discrete problem in which every solution satisfies exact phase volume conservation, phase mass conservation, total volume conservation, total mass conservation, and a discrete energy-dissipation law. In addition, if the volume-saturation constraint holds for the initial data, then it is preserved at every time step. We numerically verify these structure-preserving properties and demonstrate the robustness of the method in representative multiphase flow problems. The resulting scheme provides a computational framework for incompressible N-phase mixture flows with complex interfacial dynamics and arbitrary density contrasts.

Nonlinear structure growth generates higher-order correlations and morphological features in the cosmic density field that cannot be fully characterized by two-point statistics. Upcoming surveys will measure these features with greater precision, making it essential to develop methods capable of extracting as much cosmological information as possible from them. Field-level inference (FLI) is one such approach, in which cosmological parameters are constrained by comparing observed maps to forward-modeled maps, either directly or through learned summaries that retain map-level information. In this work, we compare FLI with power-spectrum-based inference using the same forward-modeling pipeline for generating weak lensing maps, with the goal of quantifying the gain from map-level analysis relative to two-point statistics. We perform this comparison with both implicit and explicit inference methods, using 8-million-parameter forward models based on Lagrangian perturbation theory and particle-mesh (PM) N-body evolution. The two FLI approaches yield closely consistent posteriors; this agreement, together with coverage tests confirming the calibration of the implicit analyses, gives us confidence in the recovered field-level constraints. Relative to the power-spectrum-based analyses, these results show significant gains in cosmological information, especially when small scales are included in the PM-based forward model. We then discuss the remaining challenges that must be addressed before PM-based explicit FLI can be applied to observational datasets.