The Allen-Cahn equation with Flory-Huggins potential is a fundamental and crucial model in phase field simulation for describing phase separation phenomena, which serves as a core tool in diverse branches of natural sciences. The numerical simulation of the Allen-Cahn equation is of great importance but poses significant challenges due to the strong nonlinearity and the presence of logarithmic singularities at $u=0,1$ in the Flory-Huggins potential. In this paper, we consider convex splitting schemes to %preserve this bound and guarantee unconditional unique solvability, which reduces the numerical simulation to solving a singular nonlinear system arising from spatial discretization at each time step. We propose an iterative solver that is specifically designed for such systems based on the alternating direction method of multipliers (ADMM) approach. The scheme possesses properties such as bound preserving and discrete energy stability. Building upon the recent unconditionally convergent ADMM framework for the Cahn-Hilliard equation (Li et al., 2026), our key theoretical contributions are twofold: (a) a proof of unconditional convergence when the multiplier update step size $α\in (0,\frac{\sqrt{5}+1}{2})$; (b) a rigorous establishment of the linear convergence for the embedded ADMM solver. This effectively liberates the solver from time-step constraints or strict separation conditions. Comprehensive numerical experiments validate our proposed ADMM framework, where its theoretical predictions are fully substantiated in practice, showcasing efficiency and robustness.

We determine the bipartite entanglement bounds of two interacting electrons in deeply interlocked Hopf-linked quantum rings via exact diagonalization of the unexpanded 3D Coulomb interaction. This identifies an exact continuous spatial symmetry that geometrically isolates the positive-parity Bell state, preventing classical interaction-driven localization. A non-coplanar geometric tilt ($α> 0$) is essential to lift the exchange degeneracy and maintain this maximally entangled manifold as a state of frozen entanglement. However, a higher-order Schrieffer-Wolff transformation demonstrates this geometric protection is fundamentally bounded; uncancelled inter-orbital momentum transitions inevitably induce dynamical parity mixing. This defines a critical interaction threshold ($λ_{crit}$) for irreversible entanglement collapse. Our analysis shows that the resulting bounding conditions reveal scaling limitations in mesoscopic semiconductor architectures, dictating the necessity of synthetic macroscopic platforms to achieve robust topological protection.

The Abbe diffraction limit, tied to the fundamental spatial bandwidth constraint imposed by any physical aperture, remains the primary barrier to achieving ultimate far-field optical resolution and precise light-matter interactions. However, current efforts to engineer structured light fields beyond this limit often come at the cost of massive sacrifices in energy efficiency. In this work, we mathematically complete the family of non-zero azimuthal-order Circular Prolate Spheroidal Wave Functions (CPSWFs), introducing them as a complete class of band-limited superoscillatory optical vortices carrying helical phase. Compared with classical Laguerre-Gaussian (LG) beams, we rigorously prove that these eigenmodes achieve the theoretical upper bound for extreme energy concentration under strict band-limited constraints. At the scale of light-matter interactions, this optimal concentration directly amplifies the intensity gradients and angular momentum densities that govern optical forces. This advantage translates directly into a 29.9% reduction in the trapping power threshold and a 2.3-fold increase in the subdiffraction orbital rotation speed of nanoparticles. Looking forward, this fundamental physical framework not only establishes strict mathematical boundaries for structured light fields but also serves as an absolute theoretical benchmark for deep-learning inverse design, and next-generation extreme optical micro-manipulation systems.

Ionization by radioactive decay products including $α$-particles, $β$-decay electrons, and fission fragments plays a central role in determining the nebular-phase ionization state and spectra of kilonovae. In this work, ionization cross sections, stopping powers, thermalization histories, and particle degradation spectra are calculated self-consistently for $α$-particles and fission fragments propagating through expanding kilonova ejecta. The treatment includes interactions with bound and free electrons, charge evolution of fission fragments, adiabatic energy losses, and particle spectra obtained from the continuous slowing-down approximation and Spencer--Fano formalism. The work per ion pair is evaluated for a range of ejecta compositions and ionization states. Despite the large differences in mass, charge, and injection energy between $β$-electrons, $α$-particles, and fission fragments, the resulting work per ion pair is found to be remarkably similar across all decay channels and target species considered. In particular, heavy-element ions exhibit nearly identical normalized ionization efficiencies for all decay products. This robustness arises because the ionization cross sections and stopping powers are governed by the same underlying collision physics, causing the ratio between ionization and energy loss to remain approximately constant over the relevant energy range. The results imply that the ionization state of late-time kilonova ejecta depends only weakly on the dominant radioactive decay channel, even in ejecta where $α$-decay and fission dominate the heating budget.

Cruz Chapital, Goto, Hayashi and the author showed that the game-theoretic variants $\mathfrak{s}_{\mathrm{game}^*}^\mathrm{I}$ and $\mathfrak{s}_{\mathrm{game}^{**}}^\mathrm{I}$ of the splitting number $\mathfrak{s}$ are consistently different, although the corresponding two games differ only in a minor case. This result suggests that even if two relational systems $\mathbf{R}=\langle X,Y,\sqsubset\rangle$, $\mathbf{R}^\prime=\langle X,Y,\sqsubset^\prime\rangle$ are the same modulo a countable set $C\subseteq X$, the associated cardinal invariants might be different. We study this phenomenon for the standard relational system of evasion and prediction and for a variation of it. We show that such a difference occurs for the standard one, but not for the variation.

Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes and Heston models. The framework takes classical contract and model data as input and returns classical estimates of selected option values. We solve the pricing PDEs after finite-difference discretization on spatial grids. For $N=2^n$ grid points per spatial direction and $d$ assets, the end-to-end gate complexity for single-point recovery, counted in elementary CNOT gates and one-qubit Pauli-axis rotations, has leading grid-size dependence $\widetilde{O}(d^2 N^{2+d/2})$ for local-volatility Black--Scholes and $\widetilde{O}(d^2 N^{d+2})$ for Heston. Relative to grid-based finite-difference baselines, these scalings correspond to polynomial improvement factors $N^{d/2}$ and $N^d$, respectively. These estimates translate to Clifford+T resources via standard compilation. We complement the complexity analysis with numerical benchmarks against standard classical methods. In the Heston setting, the framework recovers option prices across strikes together with the associated implied-volatility smile/skew. Overall, this work provides a complete end-to-end quantum pricing pipeline with explicit resource accounting and theoretical performance guarantees.

Software stack upgrades are a routine part of software maintenance and evolution, typically motivated by improved performance, stability, or functionality. Yet their impact on energy consumption - a growing concern for organizations pursuing sustainability - remains poorly understood. This paper presents a systematic method for measuring how different versions of core software stack components, such as Spring Boot and the Java Virtual Machine (JVM), influence the energy consumption of applications. Our approach evaluates combinations of framework versions, runtime versions, and execution platforms through automated benchmarking. Using a case study based on the Spring Petclinic REST application, we show that energy consumption varies substantially across Spring Boot and JVM versions, in some cases producing unexpected regressions. Notably, newer JVM releases and virtual threads (introduced in Java 21 and 23) yielded significant energy savings without requiring application changes. These results demonstrate that software upgrades can meaningfully affect energy usage and that measuring energy consumption provides valuable evidence for decision making in software maintenance and evolution.

We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term activated by the simultaneous co-firing of a cell group within a temporal window. We derive a closed-form Expectation-Maximisation algorithm whose key ingredient is a piecewise compensator that eliminates the systematic bias present in the naive integral formulation. A CP tensor decomposition reduces the hyperedge parameter count from O(N^K) to O(NR). Across eleven synthetic experiments the framework achieves pairwise recovery error below 5%, while revealing a systematic -22% bias on hyperedge weights that is non-monotonic in the kernel decay rate, ruling out a simple temporal-overlap explanation and motivating adaptive kernel methods. On multi-electrode recordings of mouse retinal ganglion cells, the model yields a +20.6 nat likelihood gain over the pairwise baseline, providing suggestive but not decisive evidence for higher-order interactions. Code and all experiments are publicly available at https://github.com/Hanii0210/hypergraph-hawkes.

The use of dual system estimation (DSE) is heavily used in Census Bureau operations. With DSE methods, it is important to implement methods to infer the population size among those with missing data from one or both data sources. The use of log-linear models, calculated through EM algorithms, promises a way for estimation of counts among all groups with incomplete recorded data, as displayed by Van der Heijden et al. 2022. Unfortunately, the numerical computations involved scale very poorly the more the population is divided, to the point where simultaneous analysis of several demographic and geographic factors, such as state of residence and ethnicity, becomes computationally infeasible. Here, an alternative method to calculate the log-linear estimates will be provided, which can calculate the maximum likelihood estimator in orders of computation lower than through the EM algorithm.

Stars on the asymptotic giant branch (AGB) play important roles in a number of astronomical contexts. To quantify these roles, it is necessary to establish the mass-loss characteristics of stars as they evolve up and beyond the AGB. We used an equidistant sample of 77 AGB stars in the inner Galactic bulge, selected on the existence and strength of OH1612\,MHz maser emission, to obtain information on the mass loss of O-rich AGB stars, and on its transformations in geometry and kinematics that occur at the tip of the AGB. Observations of circumstellar lines from several rotational transitions of $^{12}$CO, $^{13}$CO, and C$^{18}$O were performed with the Atacama Large Millimeter/submillimeter Array (ALMA), and, for a sub-sample, with the Atacama Pathfinder EXperiment telescope (APEX). The ALMA observations also provide continuum data. Existing infrared photometry was used to estimate colours and produce stellar light curves. Based on mid-infrared colour, CO line, and near-infrared variability characteristics, the objects were divided into four categories of distinct stellar and/or circumstellar properties. Various circumstellar CO line characteristics are presented and compared between the categories, such as morphologies and extents of brightness distributions (BDs), line profiles (LPs), line intensity ratios, and kinematics. A majority of the objects form a homogenous group with sharply, centrally peaked BDs and LPs of the soft-parabola type, while the rest show extended and complex BDs and/or LPs with high-velocity wings. The C$^{18}$O line and ALMA continuum detection rates vary significantly between the categories. CO line emission is also detected from interaction zones where the expanding circumstellar gas meets the interstellar medium.

Mechanism-mediated service markets with polymatroidal feasibility admit efficient, dominant-strategy incentive-compatible (DSIC) allocation, but these guarantees implicitly assume truthful execution by the marketplace operator. Modelling the operator as a strategic player, we establish a credibility trilemma: for single-parameter agents on a non-modular polymatroid, no static sealed-bid mechanism is simultaneously revenue-optimal, DSIC for agents, and credible for the operator. We introduce the Cost of Non-Credibility (CoNC) as a price-of-anarchy-style welfare-loss measure and obtain tight $Θ$-bounds across five topology classes (single-edge, series, parallel, tree, series-parallel), plus a matching upper bound $O(|\mathcal{S}|)$ on general DAGs realised by an $Ω(|\mathcal{S}|)$ witness on the SP-augmented sub-family, turning the trilemma into a structural quantity. Three structurally distinct resolutions follow: public broadcast or deferred-revelation commitment, administrative domain separation under settlement separation and four side conditions, and integrator competition orthogonal to mechanism execution under disjoint actors. An instance-level grounding over the edge-pricing market of Amin et al. confirms the trilemma's robustness on a refereed external setting. The result establishes marketplace neutrality as a first-order design constraint on polymatroidal service markets rather than an implementation detail: where the operator is a strategic player, credibility trades off against revenue optimality and agent incentive compatibility along structurally characterised lines.

The pyrochlore iridates R2Ir2O7 have emerged as a unique playground for exploring exotic quantum phenomena arising from the intricate interplay of strong spin-orbit coupling, electron correlations, and geometric frustration. While bulk crystals of these materials have revealed a rich landscape of correlated and topological states, recent breakthroughs in epitaxial thin-film synthesis and heterostructure engineering unlocked an entirely new dimension of discovery. This brief Perspective reviews recent advancements highlighting how new tuning knobs such as dimensional confinement, epitaxial strain, and interfacial coupling can be used to manipulate the delicate balance of competing interactions. We discuss several key discoveries enabled by this approach including the realization of the magnetic Weyl semimetal phase in (111) oriented films, strain-engineered magnetic multipolar orders, the emergence of a chiral spin liquid-like state in the quasi-2D limit, and the discovery of novel electronically anisotropic states at interfaces between pyrochlore iridates and other quantum materials, such as spin ice pyrochlores. These findings showcase that low-dimensional pyrochlore iridates provide ample opportunities for both theory and experiment to unravel, control and ultimately design novel quantum states of matter. We conclude by outlining key open questions and future directions ranging from the synthesis of new heterostructures to the application of advanced probes and the exploration of non-equilibrium phenomena.

The large-scale Electric Vehicle (EV) integration into the electricity grid has initiated significant challenges to grid stability issues due to dynamic loadability events. Although electric vehicle impacts on distribution systems are well studied, transmission-level investigations remain limited. In this research paper, case scenarios of EV load models as charging stations have been considered for stability analysis (Voltage and Frequency Stability) to address EV operation on the transmission grid. It is also noted that the operation of EV stations due to their high loadability causes more stability complexities to the grid compared to other loads in a power network. Simulations have been conducted on two different power networks of the IEEE-9 and IEEE-39 bus test systems, respectively.

Divide and Conquer (D&C) is a widely used algorithmic strategy for symmetric eigenvalue decomposition. Its natural parallelism makes D&C attractive on modern multicore CPUs and GPUs, but existing eigenvalue-only routines often default to QR-based methods because conventional D&C still materializes or replays large transformation matrices during the conquer phase. This paper proposes a boundary-row D&C algorithm for eigenvalue-only computation. The key observation is that the conquer phase only needs selected boundary rows/columns rather than the full accumulated eigenvector matrix. By propagating these boundary rows directly through the recursion, the proposed algorithm reduces the memory requirement from quadratic to linear space while also eliminating unnecessary matrix-vector work in the conventional lazy-replay formulation. We provide the algorithm, its time and space complexity analysis, correctness and stability arguments, optimized CPU and GPU implementations, and an evaluation against QR and D&C routines in standard numerical libraries.

The purposes of this article are threefold. First, to determine numerically when an arbitrary blowup of a smooth surface is smooth. We show the surface is smooth if and only if certain rational parameters involving log discrepancy and multiplicity of the exceptional divisors form a generalised Farey sequence within the dual graph of divisors. Second, in doing the above we provide an exposition of the Berkovich projective line $\mathbb P^1_{\text{an}}(\mathbb K)$ over the Puiseux series as a universal dual graph for divisors on a ruled surface. Third, to explain how non-Archimedean skew products interact with this multiplicity structure of the tree.

Security risk analysis typically treats control effectiveness as a static input, yet controls degrade through configuration drift, depend on monitoring systems that may themselves be degraded, and compete for finite remediation budgets. The FAIR Controls Analytics Model (FAIR-CAM) provides the theoretical framework for these dynamics but has so far remained theoretical. We present the first agent-based model to operationalize the core FAIR-CAM dynamics, making control physiology computationally observable, and release the implementation as open source. The simulation implements eight agent types, a multiplicative defense-in-depth susceptibility formula, a three-source variance model, budget-constrained remediation, and a narrative causation engine that produces a complete causal trace for every loss event. In a hospital ransomware scenario (N=1,000 iterations), three organizational dynamics emerge that static analysis cannot represent. First, emergent operational efficacy diverges from the analytical FAIR-CAM formula by approximately 17 percent, driven by correlated extrinsic variance; the divergence grows linearly with extrinsic frequency and vanishes under purely intrinsic drift. Second, a sharp queueing regime transition in the remediation pipeline approximately 2.8x expected loss when budget falls below a scenario-specific threshold (5-10 engineer-hours/month). Third, cascading monitoring failures propagate through the VMC topology: a single degraded VMC silently compounds undetected variance across the controls it manages. These dynamics are structural properties of the FAIR-CAM architecture and should generalize beyond the specific scenario studied.

We study the Fredholm solvability for a new class of nonlocal boundary value problems associated with group actions on smooth manifolds. Namely, we consider the case in which the group action is defined on an ambient manifold without boundary and does not preserve the manifold with boundary on which the problem is stated. In particular, the group action does not map the boundary to itself. The orbits of the boundary under the group action split the manifold into subdomains, and this decomposition, being combined with the $C^*$-algebra techniques, plays an important role in our approach to the analysis of the problem.

This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constructing a dissipative modified energy consisting of the original energy and a non-negative quadratic modification. We first test IMEX-LMMs with a simple multiplier, the first-order time difference of numerical solutions. Then, it is shown that the associated non-negative quadratic modification can be constructed if and only if two generating polynomials (corresponding to the LMM) are positive on $[-1,1]$. Based on this, the modified energy is proved to decay over time under a mild time-step restriction depending on the lower bounds of the associated generating polynomials. As a consequence, the energy dissipation of the well-known backward differentiation formula methods up to fifth order can be obtained straightforwardly. Furthermore, we construct for the first time (to the best of our knowledge) a sixth-order energy-dissipative IMEX-LMM and also prove the sixth-order barrier of energy-dissipative IMEX-LMMs when testing the simple multiplier. Some numerical experiments are conducted to verify our theoretical results.

This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general procedure for generating a logic whose Lindenbaum-Tarski algebra is isomorphic to a given abstract lattice. The approach identifies logical connectives preserved by the concretization map and derives corresponding proof rules and axioms. The paper establishes soundness and completeness results under suitable conditions, extends the framework to Cartesian products and multi-variable settings, and investigates the logical structure of non-Cartesian abstractions such as octagons. These observations suggest new connections between abstract interpretation, proof theory, and algebraic logic, providing a foundation for a systematic logical analysis of program abstractions.

Harmonic vibrational entropy is a key finite-temperature contribution to defect thermodynamics, but direct evaluation by dense Hessian diagonalization scales cubically with atom count and is too costly for supercell convergence, migration-path sampling, and high-throughput defect studies. We develop local surrogate models for harmonic entropy in multilattices, including semiconductors, ordered alloys, and multispecies crystals with multi-atom bases and internal degrees of freedom. Unlike Bravais lattices, multilattices contain internal-shift degrees of freedom and optical phonon modes coupled to acoustic strain; entropy models must therefore resolve sublattice and species labels. For finite-range or screened atomistic models, we prove sublattice-resolved locality and cutoff-error estimates that justify replacing the global entropy calculation by a local, symmetry-respecting regression problem with controlled truncation error. This turns vibrational entropy from a global spectral calculation into a reusable local site model with linear evaluation cost at fixed cutoff. Numerical tests confirm the predicted locality behavior and show that sublattice/species-resolved surrogates achieve accurate regression, transfer across supercell sizes, and linear-scaling evaluation on Stillinger--Weber Si and CdTe benchmarks. The resulting method enables repeated harmonic-entropy evaluations in multispecies defect calculations while retaining explicit stability, truncation, and surrogate-error controls.

Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=β\wmax/π$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches.

Scalable generation of nonclassical light sources on an integrated platform is a key requirement for photonic quantum information processing. In particular, realizing multiple indistinguishable squeezed light sources on a single chip is an essential step toward continuous-variable quantum computing. Here, we demonstrate the fabrication of two indistinguishable and independently controllable optical parametric oscillators on a thin-film lithium niobate (TFLN) platform. The device design focuses on reproducibility, independent tunability, and compatibility with larger telecom-wavelength continuous-variable photonic circuits. We observe up to 0.5 dB of directly measured squeezing below the shot-noise level from each source. By interfering the two modes on a beam splitter, we generate an EPR-type two-mode squeezed state and verify continuous-variable entanglement through violation of the Duan-Simon inseparability criterion. This is the first demonstration of two independently tunable squeezed-light sources on a single TFLN chip and their use for generating continuous-variable entanglement.

We present the DECam Mapping the Ancient Galaxy in CaHK (MAGIC) survey, a 54-night NOIRLab Survey Program to image $\gtrsim$5,000$\,$deg$^2$ of the southern hemisphere using a metallicity-sensitive narrow-band filter covering the Ca$\,$ii$\,$H&K lines centered at 3955$\,$A. This filter is installed on the Dark Energy Camera (DECam), mounted on the 4-m NSF Víctor M. Blanco Telescope. The survey reaches typical $10σ$ depths of $\text{mag}_{\text{CaHK}} \approx 22.5$, 3$-$4$\,$mag deeper than comparable surveys in the southern hemisphere. By combining photometry from this Ca$\,$ii$\,$H&K filter with existing DECam $g,r,i$ broadband photometry from the DECam Local Volume Exploration (DELVE) survey, MAGIC is deriving photometric metallicities for red giant branch stars down to the magnitude limit of usable proper motions from Gaia data release 3 (DR3). MAGIC has already imaged $\sim$3,000$\,$deg$^2$, supplemented by other affiliated observing programs that have used this filter to image star clusters, dwarf galaxies, and stellar streams. We overview MAGIC's survey strategy, describe data processing through the derivation of metallicities and photometric distances, and summarize early science results that have been published with this dataset. In addition, we present several new results, including the confirmation of a distant ($>5\,r_h$) member of the Reticulum II ultra-faint dwarf galaxy, on-sky density maps of low-metallicity stars into the distant Milky Way halo ($\sim150\,$kpc) recovering 13/14 ultra-faint dwarf galaxies in the current footprint, and a validation of our initial targeting of extremely metal-poor stars. Collectively, these results demonstrate that the MAGIC dataset enables cutting-edge studies of the faint, low-metallicity regime of the Milky Way and its substructures.

In joint multiuser decoding, a receiver recovers a set of messages from a single noisy aggregate of many simultaneous transmissions. Classical decoders rely on rule-based mechanisms such as successive interference cancellation, joint belief propagation, or list recovery, all of which become brittle or expensive as ambiguity increases. We propose CIDER, a learned multiuser decoder with masked-diffusion refinement steps. CIDER uses demixing to prevent duplicate-row collapse and uses parity-aware propagation to provide soft guidance from the code constraints. In higher-load regimes, we further improve reliability via a lightweight quality-guided remasking step that selectively re-decodes low-confidence sequences. On commonly used error-correcting codes, CIDER matches or improves on FFT-accelerated joint belief propagation-style decoding in symbol error rate while running more than $6\times$ to over $100\times$ faster, with the speedup widening as the blocklength grows. Code is available at https://github.com/jiyunyoung/CIDER.

Dense retrievers exhibit positional bias, favoring documents whose query-relevant information appears near the beginning and degrading retrieval performance when the information appears later. While prior work on positional bias in dense retrievers has largely focused on architectural explanations, we study how the positional distribution of evidence in training data affects retrieval-level bias direction. To test this, we construct synthetic position-targeted training sets in which query-relevant evidence appears at the beginning, middle, or end of documents, and fine-tune eight architecturally diverse pretrained models under position-skewed and balanced training distributions. At the ranking level, we observe a strong directional pattern across the examined models: skewed training distributions favor evidence at the corresponding positions. Position-balanced training reduces positional sensitivity by 57--87\% on position-aware benchmarks, with competitive mean retrieval performance in our controlled setting. Representation-level analyses further suggest that fine-tuning often reshapes learned positional preferences, although pre-existing architectural or pretraining-specific tendencies persist in some models. These results identify training-position distribution as a major controllable factor in retrieval-level position bias and suggest balanced data curation as a practical mitigation strategy.

Fine-tuning Large Language Models with untrusted data exposes models to backdoor attacks, where poisoned samples cause targeted misbehavior. Existing sample-filtering defenses rely on clustering, which requires sufficient data and can fail at extreme poison ratios. We propose GradSentry ({Grad}ient {Sentry}), a backdoor sample filtering method based on the spectral entropy of per-sample gradients. Our key finding is that poisoned samples produce gradients with higher spectral entropy compared to clean samples. GradSentry captures output-altering backdoor signatures using per-sample gradient spectra, avoiding pairwise sample comparisons and clustering during feature construction. Importantly, our method is training-agnostic: it works for both parameter-efficient fine-tuning methods like LoRA and full-parameter tuning, as the gradient analysis operates independently of which parameters are being updated during training. GradSentry requires no clustering, operates effectively across all poison ratios (1%--90%), and introduces minimal computational overhead (20-50ms per sample for 7B model). Evaluation on four QA datasets and four attack types demonstrates the effectiveness of spectral entropy for backdoor detection. Code is available at https://github.com/dongdongzhaoUP/GradSentry.

In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic traveling waves for this local model and provide a parameterization of these waves. Using Floquet-Bloch theory, perturbation theory, and spectral analysis, we then establish the modulational stability of these background periodic traveling wave solutions. Finally, we analyze the modulational instability of another extended Hunter-Saxton equation with cubic nonlinearities, following a similar approach.

Control charts for process monitoring are widely used in practice. Most control charts require the monitored (residuals) process to be serially independent (and to satisfy specified distributional assumptions), whereas undetected dependence (or violations of distributional assumptions) may severely affect the charts' performances. Therefore, (distribution-free) control charts for monitoring serial dependence are of utmost relevance for practice. Recently, various nonparametric control charts have been proposed for this purpose, which are based on ordinal patterns, and which showed an appealing performance in detecting different types of serial dependence. In this research, we further progress in this direction and develop novel nonparametric control charts being based on transcripts and algebraic distances (as derived from ordinal patterns). The performance of the newly proposed control charts is evaluated in a simulation study, and their application in practice is illustrated with a real-world data example from chemical industry.

We present a numerical study of the ultrametric properties of the set of RNA secondary structures with the maximum number of base pairs (energetically degenerate minima) within the maximum matching model (Nussinov algorithm). Using 18 natural small nuclear RNAs as examples, we show that the degree of nontrivial ultrametricity varies widely. We consider the optimization problem for the degree of nontrivial ultrametricity of RNA secondary structures with the maximum number of base pairs under a fixed nucleotide composition. It is found that permuting the nucleotide sequence can strongly change the degree of ultrametricity, indicating the key role of nucleotide order in shaping the hierarchical properties of RNA secondary structures.

Statistical procedures rarely retain all features of the observed data. A sufficient statistic removes information irrelevant to a parameter; a maximum likelihood estimate compresses an empirical objective into an optimizing point; and a hidden state in a sequential model compresses past observations into a learned representation. This article develops these practices under the unified notion of \emph{target-oriented statistical compression}: a useful summary preserves what matters for an inferential, predictive, or decision-relevant target, rather than every detail of the realized data path. The central object is the conditional target process \(M_n=\E(Z\given\G_n)\), where \(Z\) is the target and \(\G_n=σ(T_n)\) is the information retained by the compression map \(T_n\). When \((\G_n)\) is a decreasing filtration, \((M_n)\) is a reverse martingale with limit \(M_\infty=\E(Z\given\G_\infty)\). Exact sufficiency corresponds to lossless compression, while approximate summaries such as penalized estimators, principal components, and neural-network hidden states produce reverse quasi-martingale defects measuring coherence loss across compression levels. The diagnostic \(r_n=|M_n-M_{n-1}|\) is treated as an observable stability proxy, not as an unbiased estimator of the theoretical defect. Boundary degeneracy in sequential binary problems is developed as a central application. Practical boundary claims require joint assessment of boundary closeness, uncertainty control, and trajectory stability. The companion paper \citet{chang2025rm} develops the corresponding stopping procedures, finite-sample bounds, and numerical evidence; the present paper provides the broader theoretical infrastructure and extends the framework to Gaussian, Poisson, and quasi-martingale monitoring problems.