Single-turn safety evaluation is a poor proxy for real fraud defense, where attackers escalate across multiple rounds. This paper evaluates fraud defenders under replay and adaptive multi-round attacks and measures when a defender refuses, not just whether it eventually refuses. On a frozen multi-round suite built from Fraud-R1, graph-context defenders improve early safe refusal relative to text-only baselines under both replay and adaptive fraud pressure, but they also produce substantially more benign over-refusal. Direct probing of the trained graph encoder, together with paired shuffle-risk ablations on both fraud and benign sides replicated across two seeds on the Qwen-1.5B backbone, localises this cost to how the defender LLM consumes structured context rather than to graph-encoder quality: the encoder cleanly separates fraud from benign, while the LLM responds primarily to the presence of structured graph fields and only secondarily, and asymmetrically, to risk-score magnitude. Temporal graph context is directionally stronger than static and significantly better grounded, but is not yet conclusively superior on the main refusal metrics. The contribution is evaluative and measurement-oriented: robust fraud assessment must be multi-round, must report refusal timing, must account for benign false positives alongside fraud-side safety gains, and must localize observed costs to the graph signal or to how the LLM consumes it.

We investigate controlling the lateral Goos-Hänchen (GH) shift for a TM-polarized field reflected from Otto structure containing four level N-type atomic medium. The N-type atomic configuration can be formed by coupling the standard three-level $Λ$ system to an additional upper energy level through a coherent driving field. The medium can then be switched from transparent to absorptive under the effect of the driving field. In the Otto structure, an air gap typically separates a dielectric prism from a metal film. We show that the sign and magnitude of the GH shift can be highly controlled when the air gap is replaced by the coherent atomic medium. This can be achieved by adjusting the strength of the applied fields to the atomic medium, while the geometrical characteristics of the proposed structure are unchanged.

This paper investigates an initial-boundary value problem for three-dimensional (3D) micropolar fluids in a strip domain, including both the compressible and the (homogeneous and inhomogeneous) incompressible cases in the absence of angular viscosity. The analysis is rendered difficult by two major obstacles: the degeneracy induced by vanishing angular viscosity, and the strong coupling between micro-rotation and velocity fields characterized by a non-dissipative anti-symmetric structure. Moreover, the presence of physical boundaries in the strip domain further compounds these obstacles. While the global well-posedness of the 2D incompressible Cauchy problem has been established in the literature, no results are available for the 3D system and the initial-boundary value problem in both two and three dimensions, particularly in the compressible case. By exploiting the intrinsic structure of the system and establishing delicate energy estimates, we overcome these difficulties and prove the global well-posedness of strong solutions near equilibrium in a strip domain.

In a recent work, Roelands and Tiersma proved that, for a compact convex set $K$, the space $A(K)$ of all real-valued continuous affine functions on $K$, is a JB-algebra if and only if there is a gauge-reversing bijection on $A_c(K)$, the set of positive real-valued continuous affine functions on $K$. In this paper, we show that every such gauge-reversing bijection on $A_c(K)$ is completely determined by the induced bijection on the set of extreme points of $K$.

We investigate the observational viability of a quadratic dark energy expansion (QDEE) model as a phenomenological extension of the standard $Λ\mathrm{CDM}$ cosmological framework. This approach introduces the additional degrees of freedom that permit mild late-time deviations from a constant dark-energy component while preserving the standard early-Universe behavior. We constrain the model using a comprehensive combination of cosmological datasets, including Planck 2018 cosmic microwave background (CMB) measurements, Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) and South Pole Telescope (SPT-3G) data, Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), and the Pantheon Plus type Ia supernova compilation. Our results show that the QDEE framework shifts the inferred Hubble constant toward higher values relative to $Λ\mathrm{CDM}$, partially alleviating the tension with local measurements while remaining consistent with early-Universe constraints. Bayesian model comparison indicates strong evidence in favor of this framework over standard $Λ\mathrm{CDM}$ across multiple dataset combinations. Posterior predictive checks further demonstrate that the model yields predictions consistent with the observed data within statistical uncertainties.

For an oriented graph $G$, the oriented discrepancy problem concerns the existence of a spanning subgraph of $G$ with a large imbalance between its forward and backward edge orientations. Freschi and Lo proved the Dirac-type Hamilton cycle result in oriented graphs, and asked for an analogue for powers of Hamilton cycles under a minimum-degree condition. We show that, for sufficiently large $n$, every oriented graph $G$ on $n$ vertices with minimum degree $δ(G)\geq 2n/3$ contains the square of a Hamilton cycle $H$ with $σ_{\max}(H)$ guaranteed to exceed a function depending on $δ(G)$ and $n$.

Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cramér-Rao bound (MCRB) is a widely recognized mean-squared-error (MSE) lower bound for this case, which has originally been used to describe the asymptotic behavior of the misspecified maximum likelihood (MML) estimator. Despite its widespread use, the MCRB lacks a rigorous characterization of the class of estimators for which it is valid. In this paper, we revisit the theory of parameter estimation under model misspecification and re-examine the foundations of the MCRB. We first demonstrate these limitations and examine a naive version of the MCRB, which relies only on local misspecified unbiasedness. We show that this bound is generally not tight and may be unattainable. To obtain a meaningful bound, we develop a new derivation based on the concept of pointwise equivalent models. By maximizing the naive bound for these models, we recover the classical MCRB, now supported by a constructive derivation, an explicit characterization of the associated estimator class, and an equality condition. This formulation establishes a formal link between local unbiasedness conditions and achievable bounds, offering new insights into the MCRB structure and its relevance to practical estimators. Finally, we define the notion of an efficient misspecified estimator and show that if it exists, it is achieved by the MML estimator.

This paper develops a multipole expansion method for the quasi-periodic elastic single layer potential $\mathcal{S}_D^{α,0}$ associated with the Kelvin tensor in one-dimensional periodic arrays. A key step in this approach is the derivation of translation addition theorems for the real vector spherical harmonics $V_{lm}$, $W_{lm}$, and $X_{lm}$. These addition theorems enable the exact calculation of all matrix entries of $\mathcal{S}_D^{α,0}$ in closed form. By working entirely within the spherical harmonic basis, the proposed analytical method overcomes the poor convergence and mesh-dependent issues commonly caused by the direct surface discretization of weakly singular kernels. Additionally, the involved infinite sums are evaluated exactly using polylogarithm functions, which eliminates the need for series truncation. As an application, the integral equation $\mathcal{S}_D^{α,0}[f]=φ$ is reduced to a linear system. This framework is further extended to dimer geometries consisting of two disjoint balls in each cell, where the off-diagonal matrices are explicitly formulated via the Lerch transcendent.

Large language models (LLMs) operate within fixed context windows that fundamentally limit conversational continuity. When context fills, compaction discards history irreversibly; when sessions end, all memory resets to zero. Existing solutions-larger context windows, retrieval-augmented generation for knowledge bases, and memory-augmented architectures such as MemGPT-either require model modification, impose provider lock-in, or do not address the compaction continuity problem. We present CALMem (Conversational Application-Layer Memory), an application-layer dual memory architecture that gives LLM-based conversational assistants virtually unbounded effective context without any modification to the underlying model. CALMem combines two complementary memory subsystems: an episodic memory layer built on sliding-window vector embeddings of conversation history, and a semantic memory layer of agent-writable structured facts. A token-budget-adaptive injection mechanism, called the MOIM (Message of Injected Memory), automatically retrieves and injects relevant past context each turn, scaling injection depth inversely with context pressure. A key contribution is intra-session retrieval: compacted away turns from the current session remain searchable, closing a gap unaddressed by prior work. The system is implemented as a pure application layer in a production Rust codebase, is provider-agnostic, and degrades to original LLM behaviour with zero overhead when disabled. We describe the architecture, design decisions, and performance characteristics, and analyse the trade-offs that guided each implementation choice.

Let $(\mathcal{B},\mathcal{A}, i, e, l)$ be a cleft extension of abelian categories. We prove that the functor $l$ preserves and reflects (Wakamatsu) tilting pairs of subcategories under certain conditions, unifying an abundance of known results. Then, we apply our results to the cleft extensions of module categories, and give characterizations of tilting pairs and Wakamatsu tilting pairs over $θ$-extension of rings and tensor rings, which not only recover the earlier results in this direction, but also obtain some new conclusions.

We continue our work on $\mathsf{GL}_2$ over $\mathbb{Q}$ in the ramified setting for \emph{Beyond Endoscopy}. We establish asymptotic formulas for each term of the trace formula when summing over $n<X$, using arbitrary smooth test functions at the places in $S=\{\infty,q_1,\dots, q_r\}$ where $2\in S$, for the standard representation, up to an error of $o(X)$. This yields an identity depending on a parameter $X$, leading to certain identities that can be regarded as a limit form of the trace formula for $\mathsf{GL}_2$ over $\mathbb{Q}$. On the spectral side, we employ the contour shift method and the Riemann-Lebesgue lemma. On the geometric side, both the identity part and the unipotent part contribute $o(X)$. The elliptic part was reduced to the hyperbolic part in a previous paper. Finally, using hyperbolic Poisson summation, we relate the hyperbolic part back to the spectral side and determine its contribution.

This paper develops a policy gradient method for entropy-regularized mean-field control in the discounted infinite-horizon setting. We consider randomized feedback policies and a coupled representative-particle/population system, in which the representative state evolves jointly with a population law governed by a McKean--Vlasov equation. The resulting value function is therefore defined on the product space $\mathbb R^d \times \mathcal P_2(\mathbb R^d)$. A key distinction from existing policy gradient methods for mean-field control is that, after computing the value function under a fixed policy, our approach does not require solving an additional equation to obtain the policy gradient. Instead, we derive an explicit policy gradient formula directly in terms of the value function. The formulation is based on an instantaneous advantage function, which quantifies the gain of taking a given action relative to the current randomized policy. We establish a Gâteaux policy-gradient formula, which gives the first-order variation of the objective along arbitrary policy perturbations, and then derive the corresponding ascent direction under finite-dimensional policy parametrization. The resulting formula leads to a model-based actor--critic scheme. The critic is obtained by solving the associated linear stationary Hamilton--Jacobi--Bellman equation for the value function, using cylindrical functions to represent dependence on the population law. The actor is then updated according to the derived policy-gradient formula. We further analyze the well-posedness of the PDE in a polynomial-growth function class. Finally, we illustrate the proposed method through numerical experiments on an LQR model and a crowd-motion problem.

We consider the 4$d$ mass-energy double critical NLS \[ (i\partial_t+Δ)u = -|u|^2 u + |u| u. \] In Luo (2024) and Cheng--Miao--Zhao (2016), the authors established a scattering/blowup dichotomy for solutions satisfying the energy constraint $E(u_0)< E^c(W)$, where $W$ is the energy-critical NLS ground state and $E^c$ is the energy for the underlying cubic NLS. We prove that the scattering/blowup dichotomy persists even at the energy threshold $E(u_0)=E^c(W)$.

ADASS used to hold a regular FITS BoF (Birds of a Feather meeting). As other data formats started to be used along with FITS, this became a Data Formats BoF, and there was some element of competition between formats, together with an occasional attempt to create a unified Format that could replace FITS as the only astronomical format needed. The impetus for this year's BoF came from an acceptance that astronomy would have to work with multiple formats in the foreseeable future, and a question: Did the use of multiple formats make it difficult to write general-purpose utilities, for example visualisation programs such as SAOImage/DS9, and if so was this a problem? The resulting discussion was interesting, and although it came to no ultimate conclusion, it at least made it clearer why such a conclusion was hard to reach.

We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy higher-priority constraints as much as possible even when no feasible solution exists. To address this issue, we introduce a new solution framework based on the notion of a hierarchically optimal shift, which captures the hierarchy among constraints by sequentially minimizing constraint violations according to their priorities. Based on this concept, we define a hierarchically optimal solution as an optimal solution of a suitably shifted problem, thereby providing a well-defined notion of optimality even in the absence of feasibility. Furthermore, we propose a novel augmented Lagrangian method equipped with a framework for infeasibility control. The core component is an infeasibility control problem, which generates a sequence of approximate shifts converging to the hierarchically optimal shift. This approach enables explicit and systematic handling of prioritized constraint violations, in contrast to existing methods that treat all constraints uniformly. Under suitable assumptions, we show that the generated sequence of shifts converges to the hierarchically optimal shift, and that any accumulation point of the primal iterates is a hierarchically optimal solution. Numerical experiments show that the proposed method achieves solutions consistent with the prescribed constraint hierarchy for both feasible and infeasible cases.

Conditional average treatment effects (CATEs) are increasingly estimated from observational data and used to guide policy and individualized treatment decisions. Before such estimates can be trusted in practice, their predictive fitness needs to be assessed, yet observational data alone offer limited opportunities for doing so. We propose CATE Assessment via Fitness Evaluation (CAFE), a formal framework for directly assessing the goodness-of-fit of a CATE estimate learned from observational data, rather than the full underlying outcome model, using evidence from a randomized trial. CAFE partitions the trial covariate space according to estimated propensity scores (or the like) and compares observationally derived conditional treatment effects with group-level experimental averages. The framework accommodates a broad class of CATE learners, including parametric models and flexible machine learning methods such as causal forest and boosting. We establish theoretical guarantees under both the null and alternative hypotheses, and introduce a maximum-type extension to improve sensitivity to localized lack of fit. When both randomized trial and observational data are available, we further develop a two-stage procedure to detect the existence of unobserved confounders. Extensive numerical studies show the utility of the CAFE approach when assessing observational-derived CATE estimates.

In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find a predominance of non-periodic structures (over 96%) that extend across the entire range of possible diversities. These non-periodic structures are resolved by establishing whether a structure will accommodate or reject additional local structures. This property, structural selectivity, is treated as a signature of an underlying ordering principle. The major result of the paper is the determination that roughly 35% of the non-periodic structures are selective and, hence, ordered in some way. This selectivity extends up to a diversity of ~ 9, well beyond the upper threshold for diversity in periodically ordered states.

In a work of Heath-Brown, it is proved that in the Pilz divisor problem, the normalized error term $Δ_3(x)$ has a distribution function. In this paper, we prove an analogue of this result in the setting of GL(3). For a given self-dual GL(3) Hecke--Maass cusp form $f$ with normalized Fourier coefficients $A_f(n,m)$, let $Δ_f(x)=\sum_{n\leqslant x}A_f(n,1)$. We show that the function $x^{-1/3}Δ_f(x)$ has a distribution function and we obtain a quantitative rate of convergence for the limiting distribution.

Let $P$ be a set of $n$ points in the plane, and let $\mathcal C$ be a collection of $n$ simple $k$-intersecting curves, meaning that every two distinct curves of $\mathcal C$ meet in at most $k$ points. A classical theorem of Pach and Sharir from 1998 gives the upper bound $I(P,\mathcal C)=O_k(n^{(3k+1)/(2k+1)})$. We prove that this bound can be improved when one excludes a complete local incidence pattern. More precisely, for any fixed integers $s>k+1\ge 2$, if there do not exist $s$ points of $P$ such that every $(k+1)$-tuple among them is contained in a distinct curve of $\mathcal C$, then $I(P,\mathcal C)=o(n^{(3k+1)/(2k+1)})$. In the special case of pseudo-segments, this extends Solymosi's theorem on dense point-line arrangements to dense arrangements of pseudo-segments.

We consider the problem of modeling a single qubit in contact with a one-dimensional waveguide beyond the standard perturbative and Markovian approximations. Using the recently developed input-output hierarchical equations of motion (io-HEOM), we investigate multiple examples of such waveguides, characterized by different spectral densities. Our examples highlight that the io-HEOM method can accurately capture non-Markovianity in waveguide QED from two distinct origins. The first source of non-Markovianity is spatially non-local coupling between the qubit and the waveguide. By examining two examples with non-local coupling, we show how the coupling function affects the steady-state bound photons, and demonstrate the release of these photons when the qubit energy is quenched. The second source of non-Markovianity is non-linear dispersion. We illustrate this scenario using the example of a cavity array with point-like coupling, where the non-linear dispersion leads to persistent oscillations due to Van Hove singularities in the spectral density.

We investigate the mixing properties of a randomized Chirikov standard map on $\mathbb{T}^2$. While the deterministic dynamics exhibit obstructions to global ergodicity, we establish explicit almost-sure quantitative exponential mixing when kicking strengths are sufficiently large. To achieve this, we formulate a criterion for incompressible random dynamical systems, reducing quantitative exponential mixing to serval verifiable conditions. Additionally, we provide a milder parameter condition to derive qualitative exponential mixing and enhanced dissipation.

Clinicians are expected to disclose harmful medical errors to patients and families in line with ethical, regulatory, and patient care standards, yet these conversations remain challenging because of their emotional complexity and limited training opportunities. Most physicians still learn primarily through lectures and observation, while static video tools-though available-are underused, lack adaptability across specialties, and deliver delayed, generic feedback. These gaps restrict skill development, reduce self-efficacy, and contribute to avoidance of disclosure conversations, ultimately compromising patient care and eroding trust. To address these needs, we designed CandorMD -- an AI-assisted simulation system that provides real-time practice, actionable feedback, and diverse practice environments tailored to individual learning needs. We conducted semi-structured interviews with physicians, risk managers, patient advocates, and communication experts to understand current practices, identify gaps, and collect feedback on CandorMD. Based on these insights, we present findings and design recommendations for the future of AI-supported medical communication training.

We revisit a result of Mittal--Ylvisaker that states that the rescaled maximum of a stationary sequence of Gaussian random variables has a Gaussian limit if correlations decay sufficiently slowly. Taking a new approach we relax the conditions for the Gaussian limit and give an extension to smooth non-stationary random fields.

High-redshift ($z\gtrsim6$) quasars trace the earliest supermassive black holes and intense star formation, offering key laboratories for black hole-galaxy evolution at cosmic dawn. While far-infrared studies have revealed large dust reservoirs and strong [C II] emission, the physical conditions and molecular gas content of their ISM remain uncertain. We present ALMA Band 3 observations of the redshifted CO(7-6) and [C I](2-1) emission lines and dust continuum in a sample of 18 quasars at $z \sim 6$. We detected CO(7-6) in 15/18, [C I](2-1) in 6/18, and continuum in 13/18 sources. Line luminosities and continuum fluxes were used to estimate molecular gas masses from CO, [C I], and dust, and a hierarchical Bayesian cross-calibration of all four tracers yielded consistent per-source $M_{\rm H_2}$ estimates and conversion factors. Comparison with PDR and XDR model grids using the $L_{\rm [CII]}/L_{\rm [CI]}$ and $L_{\rm CO(7--6)}/L_{\rm TIR}$ ratios suggests gas densities of $n > 10^4$ cm$^{-3}$ and radiation fields of $G_0 \sim 10^3$--$10^4$ for sources consistent with PDR solutions, while many quasars fall outside the model parameter space. The $L'_{\rm CO(7-6)}/L'_{\rm [CI](2-1)}$ ratio indicates that a large fraction of the molecular gas resides in a warm and highly excited phase. Together these results suggest that classical PDR heating alone cannot explain the observed line ratios and that additional volumetric processes such as X-ray irradiation, turbulence and shocks, or enhanced cosmic-ray heating likely influence the excitation of the cold ISM. They demonstrate the power of multi-line diagnostics in revealing the excitation and structure of the cold ISM in early quasar host galaxies and highlight the need for joint analysis of CO, [C I], [C II], and dust emission to characterize star formation and AGN-driven heating at cosmic dawn.

We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it. The argument relies crucially on ideas that may, at least in retrospect, be attributed to Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna.

In this paper, we introduce the notion of Ricci Killing spinors on Riemannian spin manifolds, which form a class between generalized Killing spinors and standard Killing spinors. We prove an existence theorem for Ricci Killing spinors that are not Killing spinors on a certain class of Sasakian manifolds. This yields new examples of manifolds admitting generalized Killing spinors.

During an infectious disease outbreak, providing accurate answers to policy questions about transmission requires a detailed model of the natural history of infectiousness. Unfortunately, direct measures of infectiousness are generally unavailable. Instead, we often rely on indirect proxies, such as viral load measured by PCR or antigen tests, viral culture to detect replication-competent virus, or symptom onset, each of which reflects different aspects of viral dynamics or host response. However, these proxies vary in terms of the ease of collection, scalability, and their relationship to viral shedding and therefore underlying infectiousness. Here, we use data from five prospective, densely sampled cohorts with longitudinal data on multiple proxies of viral shedding for approximately 2,000 infections to develop a Bayesian joint model for the within-host viral kinetics of SARS-CoV-2 infection. Modeling the joint distribution allows us to infer the trajectory of infectious virus shedding -- the most direct correlate of infectiousness -- for individuals who contribute only PCR data, and to compute derived quantities that are inaccessible from any single proxy alone. These include the population-level probability and expected duration of ongoing infectiousness as a function of time since diagnosis, stratified by variant, vaccination status, and infection history; the residual risk of releasing an individual from isolation; and personalized, real-time estimates of infectiousness that are sequentially updated as new test results become available.

String C-groups are precisely the automorphism groups of abstract regular polytopes. A certain regular d-polytope C_d with an automorphism group of order 2^{2d-1}, discovered by Conder and shown to have the smallest number of flags among all regular d-polytopes of high ranks, also has the important extremal property to be the unique minimal d-polytope, with respect to combinatorial covering, among all finite regular d-polytopes with 2-power automorphism groups. In other words, the automorphism group of C_d is a quotient group of every finite string C-group of rank d and 2-power order; and every finite regular d-polytope with an automorphism groups of 2-power order covers C_d. The existence of a unique minimal element among string C-groups of 2-power order and given rank is remarkable in itself.

We study exact defect $g$-functions for integrable line defects in two-dimensional integrable quantum field theory and use them to probe defect fusion. We consider three settings: fusion of purely transmitting topological defects, fusion of non-topological defects with reflection and transmission, and fusion of a defect with an integrable boundary. For topological defects, the separated logarithmic $g$-function is additive, and the fusion limit is controlled by the multiplicative composition of transmission factors. For non-topological defects, separation-dependent phases in the Bethe-Yang equations produce oscillatory finite-size effects, while the fused defect is described by effective reflection and transmission amplitudes. In the Ising examples studied here, fusion involving non-topological defects lowers the finite localized contribution to the entropy, whereas topological defect-boundary fusion leaves it unchanged.

The origin of dust in early-type galaxies (ETGs) remains a long-standing question, with proposed sources being mass loss from evolved stars, galaxy mergers, or grain growth in the interstellar medium. To investigate the dominant source of dust in ETGs, we analyzed near-infrared spectra of 30 ETGs obtained with AKARI, focusing on the SiO and CO absorption features tracing the photospheres of old stellar populations. We also derived the dust mass using near- to far-infrared photometric data obtained by 2MASS, WISE, and AKARI. We find that the dust mass correlates with the summed equivalent widths of the SiO and CO absorption features. This trend suggests that a significant fraction of dust in ETGs may originate from mass loss from evolved stars, consistent with an internal production scenario. The dust mass shows no anti-correlation with diffuse X-ray luminosities, suggesting that dust in ETGs is not strongly interacting with X-ray plasma. Moreover, polycyclic aromatic hydrocarbons (PAHs) are detected in the near-infrared spectra. We find that the PAH intensity shows no correlation with the equivalent widths of SiO and CO, but correlates with the luminosity of hot and warm dust components. This suggests that PAHs may be of external origin associated with galaxy merger remnants, heated by the activities of galactic nuclei.