We investigate a question posed by Huaipeng Chen: if $X$ and $Y$ are paracompact submetrizable spaces and $f:X\to Y$ is a perfect map, can $X$ and $Y$ be submetrized by metrics $ρ$ and $d$ respectively such that $f$ remains perfect with respect to the induced topologies?

The chain length of a set family $\mathcal{S} \subseteq 2^{[m]}$ is the largest ascending sequence of sets in containment order in the union-closure of $\mathcal S$. In this work, we provide a significantly simpler and more optimal characterization of the sparsifiability of set systems in terms of their chain length, improving on the work of Brakensiek and Guruswami [STOC 2025]. Our proof relies on a generalization of Karger's [SODA 1993] famous contraction algorithm and its recent linear algebraic extensions [Khanna-Putterman-Sudan SODA 2024], and our resulting bounds show that, just as VC dimension characterizes the \emph{additive sparsifiability} of a set system, chain length governs the \emph{multiplicative sparsifiability}. As a corollary, we obtain improved bounds for weighted CSP sparsification.

We investigate the impact of nonequilibrium ionisation (NEI) and the metagalactic radiation-field on the thermal evolution, virial shock stability, and absorption signatures of gas surrounding galaxies. Using 1D, spherically symmetric hydrodynamical simulations with an extended version of the hydra code, we follow dark-matter growth, gas dynamics, time-dependent ionisation and cooling in the presence of the UV background. We explicitly track all ions of H, He, C, N, O, Ne, Mg, Si, S, and Fe in haloes of mass 1e11-1e13Msun from z=100 to z=0. Without a UV background, NEI enhances post-shock cooling due to underionised gas, reducing pressure support and raising the minimum mass for stable shock formation. Including the UV background pre-ionises the IGM, suppressing NEI, and restoring the CIE threshold. The IGM temperatures deviate from thermal equilibrium due to adiabatic expansion and collapse, while ionisation remains close to equilibrium in the presence of a UV background, except in transient rapidly cooling regions where NEI occurs. We compute absorption columns of OVI, CIV, and HI, showing that a photoionised IGM may produce substantial warm-ion columns extending beyond Rvir, including OVI column densities comparable to observed values. Our models indicate weak halo-mass dependence and extended distributions. We also find that z>~3 haloes can produce CIV (NCIV~1e13-15cm^-2) and HI (NHI~1e15-17cm^-2) columns out to ~10Rvir. Our results highlight the role of the UV background in regulating the thermal state and observable signatures of the gas surrounding galaxies, and emphasize the importance of accounting for IGM contributions when interpreting CGM absorption-line observations.

Toric prevarieties are non-separated analogues of toric varieties. Perling \cite{Perling_equivariant_sheaves_tor_var} provided a combinatorial description of equivariant quasicoherent sheaves on toric varieties, extending earlier ideas of Klyachko, who outlined a general framework for equivariant torsion free sheaves in an unpublished work \cite{kly_sheaf}. In this article, we present a combinatorial description of equivariant quasicoherent sheaves on toric prevarieties.

We propose a control-theoretic interpretation of recommender systems and use this perspective to analyze how fairness interventions shape long-term system behavior. Fairness concerns arise for both users and creators, ranging from opinion polarization and representation bias on the user side to popularity bias on the creator side. A central insight of our analysis is that fairness should not be viewed as a simple trade-off against utility. When optimized over time, it can in fact be beneficial for overall system performance. Realizing these gains, however, requires a clear understanding of the underlying dynamics.

In this work, we study the effect of the magnetic field on the production of neutral pions in photon-photon interactions in ultraperipheral Pb-Pb collisions at the LHC. The calculation is performed within the equivalent photon approximation, including a magnetic-field dependence in the decay width $Γ(π^0\toγγ)$, from which the corresponding production cross section is computed. We find that the reduction of the two-photon decay width in the presence of a strong magnetic field leads to a substantial reduction (by a factor of about 2-3) of the $π^0$ production cross section at LHC energies.

Novel sensors that leverage the quantum properties of atoms for measuring propagating electromagnetic fields are becoming increasingly practical for a variety of applications. These sensors rely on the phenomenon of electromagnetically induced transparency (EIT), which is induced in a confined vapor of alkali atoms when the atoms are excited to a high-energy quantum state, known as a Rydberg state, with multiple resonant optical fields. In this state, the atoms are highly sensitive to electromagnetic radiation and yield a measurement output proportional to the magnitude of an impinging electric field when resonant with a Rydberg-Rydberg transition. In this paper, we consider the use of Rydberg sensors for a tomographic imaging application through a set of modeled system dynamics. Our contribution includes a novel method for placing nulls in the image by modulating the radiated local oscillator (LO) that is used to recover phase information from the received signal. We also present an algorithm for deblurring the image.

We study the design of computationally efficient randomized algorithms for the $k$-server problem. Existing randomized algorithms with the best known competitive ratios are, on the one hand, inherently implicit and, on the other hand, employ a rounding scheme that maintains a distribution over exponentially many configurations. In this work, we introduce a derandomization framework that transforms any randomized $k$-server algorithm on a hierarchically separated tree into one that uses only $O(\log k)$ random bits for request sequences of arbitrary length; hence maintaining a distribution over only polynomially many server configurations. Leveraging this black-box derandomization, we obtain the first polynomial-time randomized $k$-server algorithm on arbitrary $n$-point metrics with a polylogarithmic competitive ratio. Our results also have implications for the advice complexity of the $k$-server problem.

We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into the product of tall-skinny matrices, and the columns of these matrices are further represented using the tensor train (TT) format, also know as matrix product states (MPS). This two-level low-rank format fits naturally into our existing Kraus is King scheme (arXiv:2409.08898v2 [math.NA]) for the Lindblad equation, whose underlying operations are arithmetic on the columns of the tall-skinny matrices. We show how these operations can be performed efficiently in the TT/MPS format, with particular emphasis on density matrix rank-truncation. We conclude with extensive numerical experiments demonstrating the convergence of this scheme and its efficiency in simulating systems with up to $10^{19}$ degrees of freedom using only modest compute resources.

Motivated by previous efforts toward mathematically analyzing the treatment of monomials in spatial branch-and-bound, we study the convex hull of the graph of a simple monomial on a nonnegative box domain in arbitrary dimension, where at most one of the variable lower bounds is positive. We give: (i) a description via linear inequalities, and (ii) a formula for the volume.

The Lamb-Chaplygin dipole is a traveling wave solution to the 2D incompressible Euler equation, whose orbital stability was established in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 2025] assuming the odd symmetry in $x_2$ (O) and non-negativity in upper half-plane (N). This paper is devoted to further study of its stability in the following two aspects. Firstly, we prove the spectral stability of the linearized operator around the Lamb-Chaplygin dipole without conditions (O) or (N), based on the index theory established in [Lin-Zeng, 2022]. This excludes an instability mechanism by unstable eigenmodes, and provides rigorous evidence towards nonlinear stability in this general setting. Secondly, assuming (O) and (N), we refine the orbital stability results in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 2025] quantitatively by proving a linear bound of the fluctuation and a uniform control of the moving velocity. Instead of using a variational approach, our proof relies on the construction of a new coercive Lyapunov functional with a delicate mixed structure: it is quadratic in the interior region, but linear in the exterior region.

Excesses in di-photon, $Zγ$, and $WW$ spectra indicate the existence of a new Higgs boson with mass $152 \pm 1$ GeV. However, no excess is observed in the $ZZ$ channel. This pattern aligns with a Real Higgs Triplet model with hypercharge $Y = 0$ ($Δ$SM). A prediction of this model is the Drell--Yan production of scalars at the LHC, which dominantly decay to electroweak bosons, thus enhancing the cross sections of triboson channels such as $WWZ$, $WZZ$, and $WWW$. Interestingly, both ATLAS and CMS have reported higher-than-expected significances for such processes: $6.4σ$ (observed) vs $4.7σ$ (expected) in the $VVZ$ (where $V = W$ or $Z$) channel and $4.4σ$ vs $3.6σ$ in $WWZ$, suggesting the possibility that these signals may be manifestations of an extended Higgs sector. We investigate whether the $Δ$SM can account for these triboson excesses through electroweak production and decay of triplet scalars. We find that while current data prefers a non-zero new physics signal ($2.6σ$), the $Δ$SM predicts more events than observed, such that it is consistent with data but not preferred over the SM. However, this tension could be clarified with Run~3 and HL-LHC data.

Results of speckle interferometry observations at the 4.1 m SOuthern Astrophysical Research (SOAR) telescope obtained during 2024-2025 are presented. We present 5316 measurements of relative positions and magnitude differences in 3532 pairs (including 524 unpublished measures made before 2024) with median and minimum separations of 0.19" and 12 mas, respectively; non-resolutions of 1723 stars are documented as well. More than 400 pairs have been resolved here for the first time and not resolved by Gaia; among those are 222 TESS objects of interest, 46 inner subsystems in known wider binaries within 100 pc, and 43 subdwarfs. Positional measurements are used to compute or improve binary orbits; elements of 202 orbits with meaningful errors are given here, while preliminary and tentative orbits are published elsewhere. Of special note are orbits with large and accurately measured eccentricties (e.g. e=0.9866+/-0.0014 for J13038-2035) and orbits of pre-main sequence binaries. Appendix contains parameters of 86 binaries used for calibration of pixel scale and orientation.

In this study, we identify a class of redundant transitivity constraints in a 0-1 integer linear programming formulation of the clique partitioning problem. The transitivity constraints in this class can be removed from the formulation without changing the optimal solution set, although each transitivity constraint defines a facet of the associated polytope. This leads to a smaller formulation that is particularly effective for instances arising from correlation clustering, where edge weights are drawn from $\{-1,1\}$. Our computational experiments show that the resulting formulation outperforms existing formulations on such instances.

Although the Sierpiński triangle has planar area $0$, it is uniformly non-flat: at every point and every scale, its nearby points span a two-dimensional region of comparable size. We prove a sharp version of this statement, showing that the Feng--Wu thickness of $E$ is exactly $\sqrt{3}/6$, the inradius of a unit equilateral triangle. More precisely, if $E$ is the standard Sierpiński triangle of side length $1$ and $B(x,r)$ denotes the closed disk of radius $r$ centered at $x$, then for every $x\in E$ and every $0<r\le 1$, the convex hull of $E\cap B(x,r)$ contains an equilateral triangle of side length $r$. Consequently, $\operatorname{conv}(E\cap B(x,r))$ contains a closed disk of radius $(\sqrt{3}/6)r$; this constant is best possible. The proof is elementary -- boundary edges of all construction triangles survive in the limit set, and self-similarity reduces the problem to the normalized range $1/2\le r\le 1$.

In Beyond 5G (B5G) networks, intelligent, flexible traffic management is essential to meet the stringent speed and reliability requirements of new applications. This paper presents an improved User Plane Function (eUPF) design that uses a Deep Q-Network (DQN) agent for real-time path selection between Multi-access Edge Computing (MEC) and cloud endpoints. The path selection problem is formulated as a Partially Observable Markov Decision Process (POMDP). We propose a novel passive delay measurement method that uses eBPF programs to link TEID-based timestamps in GTP-U traffic, allowing for low-cost delay estimation without active testing. Experiments show that the DQN agent substantially outperforms a random baseline, with lower average latency, more stable rewards, and more reliable low-delay path choices. These results demonstrate the effectiveness of AI-driven control in B5G core networks and the promise of reinforcement learning for modern network management.

Symmetric submodular function minimization admits purely combinatorial algorithms using special orderings of the ground set. Extending the minimum-cut algorithm of Nagamochi and Ibaraki (1992), Queyranne (1998) showed that the maximum adjacency ordering yields a pendent pair, which can be used to find a nontrivial minimizer. Nagamochi (2010) later introduced the minimum degree ordering, which yields a flat pair and leads to the identification of extreme sets. Despite the apparent similarity between these two algorithms, their connection remained unclear. In this paper, we introduce yet another ordering called minimum capacity ordering, and extend it to a one-parameter family of orderings, called $α$-orderings, that unifies these two previously known orderings. We prove a general inequality for $α$-orderings, and our framework recovers the known pendent-pair and flat-pair results as special cases, corresponding to $α= -1$ and $α= 1$, respectively. For each $α\in [-1, 1]$, the last two elements of an $α$-ordering form a contractible pair, i.e., a pair whose contraction preserves the existence of a nontrivial minimizer, which leads to a contraction algorithm that finds a nontrivial minimizer of a symmetric submodular function in $O(n^3)$ oracle calls, where $n$ is the cardinality of the ground set. In addition, we discuss the ranges of $α$ that ensure $α$-ordering to obtain these special pairs.

Molecular dipoles near interfaces emit highly directional radiation due to near-field interactions, making surface-bound fluorophores sensitive probes of local physicochemical changes. We introduce smart coverslips, stably coated with uniform, brightly fluorescent nanobead films, that exploit refractive-index-dependent emission shifts for sensitive micro-refractometry in small volumes. Supercritical-angle fluorescence refractometry uses single back-focal-plane images to allow us real-time RI sensing and nanometric thin-film height measurements without the need for multi-angle or multi-wavelength acquisition. Our fast, label-free, and non-invasive approach allows measurements of thin-film properties and monitoring of interfacial dynamics on a standard inverted microscope and is broadly applicable to nanobiophotonics, chemical sensing, and in-situ materials analysis.

We design a system with a binary suspension of colloids and a surface that triggers the self-assembly of crystallites with a finite thickness. The proposed design allows controlling the number of layers forming the aggregate and constrains the two types of particles to lie on different planes. These functionalities are achieved by decorating the colloids and the surface with multiple DNA oligomers featuring specific interactions. The surface triggers a chain of reactions between DNA oligomers, leading to localized self-assembly. Equilibrium principles control the thickness of the aggregates. Instead, compositional order is achieved by engineering the reaction kinetics between DNA oligomers in a way that limits interactions between colloids of the same type. We validate our design using theory and reaction-diffusion simulation algorithms, which capture the multibody nature of the interactions. This work demonstrates how engineering the kinetics provides a new avenue for controlling the morphology of aggregates assembled by DNA.

Emerging classical and quantum device concepts demand precise spatial control over the optoelectronic properties of two-dimensional (2D) materials, but deterministic engineering via local multiaxial strain distributions remains challenging. Using Ga$_2$Se$_2$, we demonstrate a material-agnostic platform in which nanostructure geometry deterministically prescribes in-plane strain profiles in suspended van der Waals membranes. We first use hyperspectral photoluminescence mapping and experimentally-constrained finite element analysis to quantify the experimental biaxial and uniaxial strain gauge factors that relate strain to the change in bandgap. We next show that a two-component analytical model can predict, with less than 12% error, spatially-resolved bandgap shifts arising from multiaxial strain distributions in complex geometries, including the interactions between adjacent nanostructures. Finally, we demonstrate that this approach can be extended to other materials. The results demonstrate that nanostructure design provides a quantitative, deterministic framework for the realization of designed strain and bandgap distributions in 2D materials.

The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper presents three efficient quaternion iterative algorithms for computing the Moore-Penrose pseudoinverse: (i) the quaternion rapid iterative method (QRAPID), (ii) the quaternion strong approximate inverse (QSAI), and (iii) the quaternion hyperpower iterative method of order nineteen (QHPI19). Convergence theorems and perturbation bounds are established to ensure numerical stability and robustness. The QSAI method is further employed as a preconditioner for quaternion Krylov subspace solvers, resulting in substantial reductions in the iteration count and runtime for large-scale linear systems. Comprehensive numerical experiments demonstrate that the proposed algorithms achieve an accuracy comparable to or better than existing approaches, including quaternion SVD, quaternion Newton-Schulz, and classical hyperpower schemes, while offering significant computational savings. The practical utility of the framework is illustrated through two representative applications: image completion via CUR decomposition and signal filtering, which confirm its scalability and effectiveness in real-world multidimensional data applications.

Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness and the prohibitive computational complexity of PDE-constrained optimization. In this work, we introduce a data-driven framework leveraging Latent Dynamics Networks (LDNets) to construct efficient surrogate models of the forward operator. By mapping low-dimensional parameters, representing ectopic activation sites or ischemic region descriptors, to the ECG signals via latent dynamics governed by neural ordinary differential equations, our approach circumvents the computational burden of evaluating high-fidelity cardiac models during iterative parameter estimation. The surrogate is trained offline on high-fidelity data, enabling rapid and robust inversion. We validate the proposed framework through rigorous numerical experiments with synthetic data across both 2d and 3d geometries. Results show that the LDNet-based surrogate achieves precise reconstruction of cardiac parameters while drastically reducing computational overhead, thereby enabling near real-time clinical applications.

Large language models are increasingly embedded into systems that interact with user data, retrieved web content, and external tools, creating a new attack surface: prompt injection, where malicious commands embedded in untrusted data override the trusted command and induce unintended behavior. Existing defenses mainly rely on fine-tuning the model to preserve an explicit boundary between trusted commands and the untrusted data portion, so that the model learns to prioritize the trusted field and ignore malicious commands in data. However, we observe that while these defenses can block obviously malicious responses caused by injected commands, they generalize poorly to real-world scenarios where the model's response to the injected command is much nearer to the correct response. This is because existing methods typically train against only a fixed set of hand-crafted attack targets, which yields a loose boundary around the correct response and leaves it easier to bypass. To address this challenge, we propose LocalAlign, a more generalizable prompt injection defense inspired by adversarial training. LocalAlign automatically and efficiently generates adversarial examples in which the command embedded in the data portion induces a response that stays near to the correct response while still being wrong. We generate such near-but-wrong adversarial examples using prompting and a single inference step. This design enforces a tighter robustness boundary around the correct response: even small response shifts induced by commands in untrusted data are explicitly penalized. Moreover, the resulting adversarial examples can vary substantially in quality across samples. To address this issue, we further introduce a margin-aware alignment algorithm that quantifies each sample's distance to the correct response and assigns larger training weight to nearer ones.

We demonstrate a paraffin-coated planar reflective multipass vapor cell for compact optical atomic magnetometry. The cell has an internal volume of $12 \times 12 \times 8~\mathrm{mm}^3$ and supports 20 optical passes with a total transmittance exceeding $65\%$, while maintaining a longitudinal spin-relaxation time of $^{87}\mathrm{Rb}$ longer than $1~\mathrm{s}$. The planar geometry provides spatially separated input and output beams, enabling compact optical integration. A single-cell free-induction-decay (FID) magnetometer reaches $10~\mathrm{pT}/\sqrt{\mathrm{Hz}}$ in the geomagnetic-field range, presently limited by current-source noise in the field coils. A two-cell differential configuration achieves a sensitivity of $\sim 28~\mathrm{fT}/\sqrt{\mathrm{Hz}}$ over the $1$--$15~\mathrm{Hz}$ band for bias fields of $0.3$--$0.7~\mathrm{G}$. These results establish that paraffin-coated planar multipass cells offer high optical depth, long coherence times, and an integration-friendly platform for ultrasensitive magnetometry.

Surfactant self-assembly at solid-liquid interfaces governs interfacial stability, transport, and reactivity across many technologies, yet resolving interfacial surfactant phases and their transition kinetics in situ remains challenging. Here, we establish an atomistically grounded plasmonic framework that quantitatively maps interfacial surfactant phases and phase transitions onto optical signatures. Distinct morphologies differ in packing and hydration, modifying the effective permittivity within the optical near field and producing surfactant phase-specific plasmonic extinction peak shifts. Using cetyltrimethylammonium bromide on silica as a prototypical surfactant-surface system, we combine atomistic simulations, electronic-structure calculations, and continuum electrodynamics to translate molecular morphologies into predicted spectral shifts for literature-reported surface phases. We experimentally confirm the predicted ordering and magnitude of steady-state peak shifts during stepwise concentration changes, and extract transition kinetics from exponential relaxations of the time-resolved peak shift. A key mechanistic signature is reversal of the spectral shift direction upon transition from an impermeable bilayer to a water-accessible, channel-containing phase, consistent with hydration-driven reduction of the local effective permittivity. Because the approach relies on dielectric contrast in the plasmonic near field and works through a dielectric overlayer, it provides a broadly applicable route for real-time identification of interfacial surfactant phases and their kinetics in aqueous conditions.

Visualization in historical research is shifting from isolated attempts to systematic practices. However, data-driven evidence about how historians actually use visualization remains scarce. We present a corpus-driven, mixed-methods study that combines analysis of images from 4,142 research articles across history and digital humanities journals with a collaboratively developed visualization taxonomy and a semi-automatic labeling pipeline. We construct a corpus of 14,021 images, classify 4,831 visualization instances using a hierarchical, domain-informed taxonomy, and analyze patterns of visualization adoption across venues, history subfields, and time. To interpret these patterns, we conduct interviews with 11 historians and use HiFigAtlas system as a boundary object to support joint inspection of the corpus. We identify distinct roles for visualizations in historical research: primary-source, evidence-synthesis, communicative, confirmative, and exploratory. We further find that while historians pursue diverse goals with figures, persistent epistemological and practical barriers, such as uncertainty, provenance, justification burden, and publication constraints, impede the adoption of visualization. This work contributes a grounded account of visualization use in historical scholarship and points to opportunities to better support domain-specific needs.

We prove a projection-triangle statement for projective Calabi--Yau threefold conifold degenerations and use it to organize an intersection-space Hodge atom shadow package. For a nodal central fiber $X_0$, assume the relevant Banagl--Budur--Maxim, multi-node gluing, mixed-Hodge-module, and specialization-splitting hypotheses, so that $ψ_π(F)\simeq \mathcal{IS}^{H}_{X_0}\oplus\mathcal C^H_Σ$. Projection of the variation morphism to the intersection-space summand defines $\operatorname{var}_I:ϕ_π(F)\to\mathcal{IS}^{H}_{X_0}$, and the octahedral axiom gives $P^H\to P^H_I\to\mathcal C^H_Σ\xrightarrow{+1}$, where $P^H=\operatorname{Cone}(\operatorname{var})[-1]$ and $P^H_I=\operatorname{Cone}(\operatorname{var}_I)[-1]$. This realizes the intersection-space atom shadow package $\mathsf{HA}^{I}(X_0)$ and compares it with the intersection-homology package $\mathsf{HA}^{IH}(X_0)$. Under the self-dual specialization-splitting hypothesis, the projected variation object satisfies $\mathbb D P^H_I\simeq Q^H_I(3)$, where $Q^H_I=\operatorname{Cone}(\operatorname{can}_I)[-1]$. Under the mixed-Hodge realization of Banagl's middle exact sequence, we isolate a rigid--vanishing filtration and identify the IIB vanishing atom with the realized kernel. For the classical $125$-node quintic, the middle-degree IC--intersection-space defect has rank $202$. The construction remains at Hodge-realization level and identifies $\mathcal C^H_Σ$ and $Δ_{I/IC}(X_0)$ as geometry-side handoff objects for future DT/BPS comparisons.

5G Core networks are entering a decisive phase of post-quantum (PQ) migration: operators and vendors are beginning to advertise PQ-TLS 1.3, PQ-IPsec, and hybrid KEM support across the Service-Based Interface (SBI) and N2, N3, N4 reference points, in line with 3GPP TS 33.501, emerging IETF drafts, and NIST FIPS 203, 204, 205. Yet deploying PQ primitives does not guarantee PQ security. A Network Function may advertise ML-KEM-768 and silently fall back to X25519; negotiate a hybrid KEM but authenticate with ECDSA-P256; present an ML-DSA leaf on a classical chain; or skip mutual TLS altogether. These failures are silent on the wire, and today scanners (testssl.sh, sslyze, Qualys) together with 5G-specific fuzzers are PQ-unaware and telecom-blind. We present PQC Validator, a layered PQC assurance framework purpose-built for the cloud-native 5G Core, comprising a PQ Crypto Engine (L1), a PQ Conformance Prober (L2), a PQ Robustness Tester (L3), a PQ Overhead Meter (L4), and an eBPF Attestation Plane for wire-level ground truth. Its scope spans the full control-plane cryptographic surface: an independent PQ-TLS 1.3 client and server, a strongSwan-driven PQ-IPsec harness for N2/N3/N4, an eBPF/XDP/TC monitoring plane that extracts wire-level ground truth on negotiated groups and signatures, and a Kubernetes-native UI that auto-discovers NFs and emits structured PQ evidence classifying every endpoint as classical, hybrid-pq, or full-pq. A compliance suite spans TLS, PQC, 3GPP SBI, NRF OpenAPI, and security hardening, while a protocol fuzzer exercises CVE-class regressions and downgrade paths.

We demonstrate that in highly magnetized pair plasmas, nonlinear Alfven waves with wave-number $k \leq k_0 = ω_p^2 /(δω_B)$ ($δ=( δB)/B_0$ are relative fluctuations of the magnetic field) experience powerful modulational instability. In the two-fluid approximation, we develop an analytic set-up for circularly polarized (CP) Alfven mode in its frame (where the initial configuration is stationary; it is moving with relativistic, amplitude-dependent Alfven velocity $v_A (σ, δ) $, while both charges experience different, amplitude-dependent, synchrotron gyration). PIC simulations using EPOCH code demonstrate that for Alfven waves with $k$ near $k_0$, large, parametrically-driven density fluctuations develop, and lead to fast modulational instability. Charge separation effects, for a CP wave in magnetized pair plasma, might be temporarily important; on longer time-scales the density fluctuations are charge neutral and in symmetric pair plasma quickly grow to large amplitudes. In highly magnetized plasma, $σ\gg 1$, high frequency modes $k / k_0 \sim (2-3 ) \times σ\gg 1 $ are quickly generated; for smaller plasma magnetization, the dominant mode is at the Bragg's condition $k = 2 k_0$. Long term behavior of CP and LP modes is similar. We discuss application of the results to the physics of Fast Radio Bursts generated/propagating in the magnetospheres of magnetars.

We uncover a close connection between the second moment of the degree of a typical vertex in a random subgraph and the pairwise negative correlation (p-NC) property. On one hand, we exploit this connection to prove the p-NC property for non-adjacent edges in minimal spanning trees on complete graphs. On the other hand, we apply the classical p-NC property of uniform spanning trees to derive a universal upper bound on the second moment of the degree of a uniformly chosen vertex in uniform spanning trees on finite, connected, regular graphs, thereby resolving an open question posed by Nachmias and Peres. Furthermore, we determine that the optimal upper bound is exactly 6, and the method for achieving this optimal bound is interesting in itself -- the proof uses Edmonds' matroid polytope theorem.