Superionic phase transitions have attracted extensive interest for decades due to their promising applications and rich underlying physics. In particular, complicated many-body effects and nonadiabatic dynamics are believed to play essential roles, limiting the explanatory power of phenomenological approaches and obscuring the microscopic mechanisms at play. In this work, we develop a unified theoretical framework for describing solid-state ionic conduction. After reviewing the conventional approximations, we construct a general lattice model that applies to both normal ionic and superionic conductors. By incorporating the nonadiabatic concerted-hopping mechanism and the many-body Coulomb interaction within a self-consistent mean-field scheme, we identify these two effects as the fundamental driving forces behind type-I and type-II superionic phase transitions, respectively. Our model directly reproduces key experimental observations. Within this unified framework, we further provide a comprehensive comparison between the two types of transitions. Overall, our work offers microscopic insight into superionic phase transitions and provides guidance for the design and optimization of advanced solid-state ionic conductors.

The alternating current optimal power flow problem is a fundamental yet highly nonconvex optimization problem whose structure reflects both nonlinear power flow physics and the topology of the underlying network. Among convex relaxations, the second-order cone relaxation introduced by Jabr has proven particularly influential, serving as a computationally efficient alternative to semidefinite relaxations and a foundation for numerous strengthening techniques. In recent years, a variety of approaches have been proposed to tighten Jabr-type relaxations, including cycle-based constraints, convex envelopes of multilinear terms, and dual reformulations. However, these developments are often presented independently, concealing their common geometric and graph-theoretic foundations. This paper provides a structured review of strengthening techniques for the Jabr relaxation and develops a unifying perspective based on multilinear equalities. We reinterpret cycle constraints as multilinear consistency conditions, analyze their convexification through classical convex hull theory, and investigate the relationship between primal McCormick relaxations and dual extended formulations. In particular, we identify structural conditions under which these relaxations coincide and clarify the distinction between convexifying the interaction graph and convexifying the feasible set of the ACOPF. The resulting framework connects graph structure, multilinear convexification, and conic relaxations in a unified manner, offering both a conceptual synthesis of existing results and new insights for the design of stronger relaxations.

The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and establishes existence and uniqueness of invariant measures. In the previous paper, IFSs of $\ast$-measures were considered. In the present paper we deal with generalized invariant function systems (GIFSs) of $\ast$-measures, which are counterparts of GIFSs in the sense of Mihail and Miculescu. The notion of invariant $\ast$-measure is introduced for such GIFSs and we prove existence and uniqueness of such elements.

System outputs in Structural Health Monitoring (SHM), such as sensor measurements or extracted features like eigenfrequencies, are influenced not only by (potential) damage but also by environmental and operational variables (EOV). Identifying these factors and removing their effects from the data is essential before proceeding with further analysis. Most existing methods for this task focus on the expected values of system outputs, e.g., using different types of response surface modeling. However, it has been shown that confounding variables can also affect the (co-)variance of and between system outputs. This is particularly important because the covariance matrix is an essential building block in many damage detection methods in SHM. Beyond standard response surface modeling, a nonparametric kernel approach can be used to estimate a conditional covariance matrix that can change depending on the identified confounding factor. This improves our understanding of how, e.g., temperature affects the system outputs. In this work, we present a new confounder-adjusted version of feature reconstruction. It uses the conditional covariance matrix as the basis for (conditional) principal component analysis. The resulting (conditional) principal component scores are then used to reconstruct system outputs with the confounding influences removed. In particular, the new approach eliminates the confounders effect on both the mean and the covariance. As will be shown on load test data from the Vahrendorfer Stadtweg bridge in Hamburg, Germany, the reconstructed features can then be employed for monitoring, e.g., using an appropriate control chart, resulting in fewer false alarms and a higher probability of detecting damage.

The advent of large-scale surveys requires efficient ML techniques to exploit the information of massive datasets. We present OJALA, a transformer-based autoregressive foundation model designed to simultaneously classify astronomical objects and infer their physical parameters using 54 narrow bands from J-PAS, combined with broad bands from the DESI Legacy Imaging Surveys and WISE. The model is trained on $\sim20$ million synthetic SEDs generated from DESI DR1 spectra. We validate OJALA using a cross-matched sample of $\sim121,000$ objects between J-PAS and DESI. The model achieves a weighted F1-score of approximately 0.9 for spectral classification (stars, galaxies, and QSOs) at $i < 21$. For galaxies, we recover photo-z with a precision of $σ_{\rm NMAD} < 0.01$, while for QSOs, the precision improves significantly at $z > 1.5$, reaching $σ_{\rm NMAD} \approx 0.006$ at $z \approx 3.5$. We demonstrate robust estimation of physical properties for galaxies, recovering stellar masses and SFR with a scatter of approximately 0.11 dex and 0.22 dex, respectively. Furthermore, the model accurately predicts EWs for major optical emission lines, allowing for the derivation of extinction-corrected H$α$ luminosities with a scatter of 0.29 dex. OJALA successfully reproduces the BPT and WHAN diagnostic diagrams, classifying SF, AGN, and passive galaxies with F1-scores typically ranging from 70% to 90% depending on the diagnostic class. For stars, the model reliably infers effective temperature and metallicity, though surface gravity remains challenging. Finally, we show the modularity of the architecture by fine-tuning the pre-trained embeddings to predict BH masses, a property not included in the primary training, recovering spectroscopic virial estimates with a precision of approximately 0.5 dex. We release the code, model weights, and a comprehensive VAC for the J-PAS EDR.

As zero-emission zones emerge in European cities, fleet operators are shifting to electric vehicles. To maintain their current operations, a clear understanding of the charging infrastructure required and its relationship to existing power grid limitations is needed. This study presents an optimization frame-work for jointly designing charging infrastructure and schedules within a logistics distribution network, validated through agent-based simulations. We formulate the problem as a mixed-integer linear program and develop an agent-based model to evaluate various designs and operations under stochastic conditions. Our experiments compare rule-based and optimized strategies in a case study of the Netherlands. Results show that current commercial solutions suffice for middle-mile logistics, with central co-design yielding average cost reductions of 5.2% to 6.4% and an average 20.1% decrease in total installed power. While rule-based control effectively manages charging operations and mitigates delays, optimizing charge scheduling significantly reduces queuing times (99%), charging costs (13.5%), and time spent near capacity (10.9%). Our optimization-simulation framework paves the way for combining optimized infrastructure planning and realistic fleet operations in digital-twin environments.

Anisotropic photonic time crystals, enabled by periodic temporal modulation of a uniform anisotropic medium, exhibit asymmetric momentum-bandgap structures and offer unique control over light-matter interactions. Here, we introduce and construct temporal Weyl points in APTCs within a synthetic three-dimensional space defined by two phase parameters and the quasi-frequency. The temporal response reveals robust Fermi arcs linking TWPs of opposite topological charge. Unlike spatial counterparts, these Fermi arcs emerge only after the first temporal supercell comprising multiple periods of APTCs, reflecting causality. We further show that TWPs generate a directional near-zero radiation trajectory in momentum space with tunable radiation from stationary charges embedded in APTCs, while the associated Fermi arcs robustly suppress radiation at selected directions and frequencies. Our findings establish temporal Weyl physics in photonic time crystals and uncover new opportunities for topological control of light-matter interactions through the time dimension.

Smart contracts are self-executing programs that manage financial transactions on blockchain networks. Developers commonly rely on third-party code libraries to improve both efficiency and security. However, improper use of these libraries can introduce hidden vulnerabilities that are difficult to detect, leading to significant financial losses. Existing automated tools struggle to identify such misuse because it often requires understanding the developer's intent rather than simply scanning for known code patterns. This paper presents LibScan, an automated detection framework that combines large language model (LLM)-based semantic reasoning with rule-based code analysis, identifying eight distinct categories of library misuse in smart contracts. To improve detection reliability, the framework incorporates an iterative self-correction mechanism that refines its analysis across multiple rounds, alongside a structured knowledge base derived from large-scale empirical studies of real-world misuse cases. Experiments conducted on 662 real-world smart contracts demonstrate that LibScan achieves an overall detection accuracy of 85.15\%, outperforming existing tools by a margin of over 16 percentage points. Ablation experiments further confirm that combining both analysis approaches yields substantially better results than either method used independently.

We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the partition function estimation and has broader applications in various fields. We consider sampling and estimation for a wide class of non-log-concave distributions, particularly heavy-tailed ones, under relaxed assumptions beyond strong convexity, such as dissipativity. We develop an unbiased extension of quantum-accelerated multilevel Monte Carlo (QA-MLMC) to eliminate all biases from discretization and time truncation, together with introducing a change-of-measure approach and the Girsanov theorem via Radon-Nikodym derivatives. As a result, our approach achieves quantum complexity $\widetilde{\mathcal{O}}(ε^{-1})$ within error $ε$, whereas the classical MLMC requires $\widetilde{\mathcal{O}}(ε^{-2})$ and existing quantum algorithms yield biased estimators under stronger assumptions. Furthermore, our unified framework enables unbiased quantum sampling and estimation for certain heavy-tailed distributions after transformation. We provide several concrete applications of our approach in statistics, machine learning, and finance, towards more practical scenarios of the quantum acceleration of stochastic processes.

This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of interest lying in the range of the adjoint score operator. This result generalizes a key theorem Van Der Vaart (1991) and provides a unified framework linking differentiability and information, beyond Hilbert spaces. The paper develops a normed-space mean-square-differentiable models for two canonical problems: estimation of the average of a known transformation and estimation of a density at a point. In these applications, it shows that positive information holds if and only if the transformation has finite variance and if and only if the density has positive mass at the evaluation point, respectively. These findings offer a novel information-theoretic perspective on known minimax results and clarify the conditions under which root-n estimation is possible.

Large-amplitude prominence oscillations offer diagnostic information relevant to understanding the magnetic and plasma structure of solar prominences. Accurate prominence seismology requires the use of reliable models. The so-called pendulum model for large-amplitude longitudinal prominence oscillations has demonstrated robustness against observations and numerical simulations. Recent improvements have extended the model to situations with non-uniform gravity, thus leading to corrections that have implications for the inference of the magnetic field strength. In this study we quantify how the different model predictions given by the original and extended pendulum models impact the inference of the minimum magnetic field strength derived from the observed periods of large-amplitude longitudinal prominence oscillations. The analysis we conducted follows a Bayesian approach to solve the inference problem and assess the absolute and relative plausibilities of the two considered models in explaining the observed data, with their uncertainty. We find that the Bayesian solution to the inference problem provides well-constrained posteriors for the minimum magnetic field strength. However, the solutions from each adopted model differ, with differences increasing with the oscillation period. A model comparison analysis results in the extended model being more plausible in the full range of observed periods. However, the magnitude of the Bayes factor is not large enough to determine whether there is positive evidence supporting any of the models. We suggest computing model-averaged posteriors as the most reasonable solution to the inference problem.

Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail distributions in many empirical settings. A common intuition is that face-to-face interactions may be influenced by spatial constraints, and that the observed complex behaviors could arise from such physical limitations. Our models explore the impact of this constraint by simulating pedestrian dynamics, and studying the generated temporal network of contacts. Previous work showed that the inter-contact duration distribution is recovered with a pedestrian dynamic as simple as the two dimensional random walk, but this approach doesn't allow to recover the distribution of the number of times a pair of individuals has been in contact. One assumption is that the number of contact between individual arises from the social relationship between them, in other words a memory of past interactions. However, we here present models that are based on solely spatial rules, by adding simple targeting mechanisms to the two-dimensional random walk. We show that these models allow to recover a broad distribution of the number of contacts, revealing the importance of two ingredients: localized phases and controlled population mixing. This suggests that the observed heterogeneity in the contact numbers within the data does not necessarily emerge from underlying social relationships between individuals, since an equivalent distribution may be reproduced using a purely spatially based model, without the need for memory mechanisms.

With their emission-line dominated spectra, the appearance of Wolf-Rayet stars is shaped by their strong stellar winds. Yet, the physical mechanisms behind their high mass loss have long remained enigmatic. While we know nowadays that radiative driving is sufficient to explain WR-type outflows, a coherent description of them is still lacking, not least to the complex physical conditions invalidating some of the approximations sufficient for other hot-star winds. One promising instrument towards a better understanding of WR winds are comoving-frame, non-LTE stellar atmosphere models including a consistent solution of the hydrodynamics. While so far limited to 1D, their detailed treatment of the radiative transfer and the population numbers is key to overcome the traditional problem of connecting stellar structure models with observed spectra. By creating larger model sequences, we can identify previously unknown scalings and describe trends of WR wind quantities with fundamental stellar parameters and abundances. This article will present a summary of recent insights on WR-type winds, revealing a complex picture with various remaining challenges. Beside covering classical, hydrogen-free WR stars, we present new results to uncover dependencies of later-type WR stars and the presence of hydrogen-containing envelopes. We further discuss oncoming challenges and insights from 2D and 3D RHD simulations which need to be mapped into 1D dynamical atmosphere models.

We investigate baryogenesis in Standard Model (SM) extensions with new $SU(2)_L$ multiplet fields. We focus on sphalerogenesis, in which the baryon asymmetry of the Universe (BAU) is generated through the gradual decoupling of CP-violating electroweak (EW) sphaleron-like processes. We show that the observed BAU can be reproduced when the new fields possess CP-violating Yukawa interactions, which leave a CP-violating dimension-six operator involving the $SU(2)_L$ gauge fields at low energies. As representative examples, we study models with fermionic $SU(2)_L$ quintuplets and septuplets, and find that these field masses should be $\mathcal{O}(1)\,\mathrm{TeV}$ to explain the BAU. We also show that viable parameter regions for the BAU are consistent with current bounds on the electron electric dipole moment and thoroughly probed by future measurements such as ACME III and by mono-lepton searches at the HL-LHC. Our results provide a concrete and phenomenologically testable ultraviolet completion of sphalerogenesis.

It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum distance for error correction is not always the same as the minimum distance for error detection. Inspired by the idea that the channel will affect the distances between the codewords, we establish the scheme of a generalized network channel and a generalized network code. Then, we systematically define the distances for error correction and error detection under the scheme of the generalized network code. We consider the joint error correction and detection in the generalized network code and obtain a complete characterization by introducing a distance and its refined version for this purpose. We enhance our understanding of the relation between various distances for error correction and detection in generalized network codes by proving some bounds on these distances.

These notes give a brief introduction to differential Harnack inequalities and summarise the main results of the mini-course ``Li-Yau and Harnack estimates for nonlocal diffusion problems'', presented by the author at the Seasonal School on PDEs ``Oscillation Phenomena, PDEs, and Applications: A Comprehensive School in Mathematical Analysis'', held at Ghent University in October 2025.

In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of interval-valued data, let alone established estimation methods in high-dimensional settings. This paper presents a novel approach to estimating covariance matrices for high-dimensional interval-valued data while ensuring positive definiteness. We begin by assuming that the upper and lower bounds of interval-valued variables share the same dependency structure. Based on this assumption, we extend the classical soft-thresholding covariance matrix estimator to the interval-valued scenario, referred to as the Interval-valued Soft-Thresholding (IST) estimator. Subsequently, to ensure the positive definiteness of the estimator, we impose a positive definiteness constraint on the IST estimator. We derive an alternating direction method to solve the proposed problem and establish its convergence. Under some very mild conditions, we develop a non-asymptotic statistical theory for the proposed estimator. Simulation studies and applications to high-frequency financial data from the CSI 300 Index demonstrated the effectiveness of the proposed estimator.

Relationship-centered care relies on trust and meaningful connection. As AI enters clinical settings, we must ask not just what it can do, but how it should be positioned to support these values. We examine a "middle, not top" approach where AI mediates communication without usurping human judgment. Through studies of CLEAR, an asynchronous messaging system, we show how this configuration addresses real-world constraints like time pressure and uneven health literacy. We find that mediator affordances (e.g., availability, neutrality) redistribute interpretive work and reduce relational friction. Ultimately, we frame AI mediation as relational infrastructure, highlighting critical design tensions around framing power and privacy.

In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces of arbitrary regularity, might be of independent interest.

Nonlinear Thouless pumping has been established in periodic lattices; its counterpart in quasiperiodic lattices remains unexplored. Here, we show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction; as a result, an emergent topological structure induced by this local reconstruction governs the dynamics of the gap solitons. This enables solitons to adiabatically occupy a single topological band, realizing quasi-quantized Thouless pumping. In addition, the intrinsic lattice perturbations disrupt this band occupation, which drives solitons into a non-quantized drifting regime. However, even in this regime, we also find that the soliton transport is constrained by the topological properties of a critical rational approximant. Tuning nonlinearity or lattice scaling reveals a controllable switching among topological pumping, drifting, and localization. Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.

We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra homomorphism. Up to constant coefficients, determined by some specific linear systems with binomial entries, we describe their minimal generating polynomial sets. The advantage of our family with respect to some previous work is, on the one hand, the explicit description of the generating sets and, on the other hand, the simplicity of the exponents of the aforementioned quasi-monomial homomorphism. We also provide a code in Python which states and solves the linear systems that lead to a complete description of the minimal generating sets with a "Gröbner-free" approach.

In this contribution to the Halo-40 Proceedings, we discuss two topics regarding halo phenomena: The first is the pairing anti-halo effect on the neutron radius of halo nuclei and its restoration due to the coupling to the continuum; the second is the soft dipole excitation of deformed halo nuclei. We demonstrate the importance of Hartree-Fock-Bogoliubov and the relativistic Hartree-Bogoliubov theory in continuum for properly taking into account the halo nature of extended wave functions in calculations of neutron radii, as well as the soft dipole excitations of halo nuclei. It was shown that the anti-halo effect is very sensitive to the continuum coupling induced by Bogoliubov-type quasi-particles, which largely cancels the anti-halo effect on the neutron radius. The soft dipole excitations of deformed halo nuclei Ne-31 and Mg-37 are discussed within the deformed Woods-Saxon model. We point out that the sharp peak just above the threshold in the dipole response is created by the halo effect, and its strength can be used to identify the magnitude of deformation and the halo configuration in the Nilsson level scheme.

Two-dimensional (2D) materials have revolutionized all areas of development of high-performance electronic devices. In particular, the unique electronic and optical properties of II--VI semiconductor nanoplatelets have been found to be very promising for optoelectronics. However, not all properties of this intriguing class of materials are yet known. A new, previously unknown hexagonal 2D structure of ZnSe nanoplatelets whose energy is lower than the energies of all previously studied systems is found from first-principles calculations. This structure appears as a result of spontaneous reconstruction of the wurtzite structure and differs from it by the stacking order of the bulk and near-surface Zn atomic layers. The phonon spectrum, electronic structure, and band gap of the obtained nanoplatelets are calculated. The phonon spectra of the nanoplatelets are in complete agreement with the spectra observed in experiment and differ strongly from the vibrational spectra of ZnSe nanoclusters. The adsorption of ZnCl$_2$ and $L$-cysteine molecules on the surface of the nanoplatelets is studied and is shown to be accompanied by yet another spontaneous reconstruction of the hexagonal structure into a tetragonal one and a new rearrangement of Zn atoms in the near-surface layers. Calculations of the natural optical activity of nanoplatelets covered with $L$-cysteine reveal an increase in the specific (calculated per chiral molecule) optical activity, which is especially strong for the Janus structures, as compared to the free $L$-cysteine molecule.

The stability of subcritical perpendicular fast magnetosonic shocks, which are propagating at 1.7 times the fast magnetosonic speed, is investigated using two-dimensional PIC simulations. The plasma, composed of electrons and fully ionized nitrogen, is permeated by a uniform magnetic field oriented at 45 degrees to the simulation plane normal. This configuration results in a diamagnetic current that sustains the shocks magnetic ramp and is partially resolved within the simulation plane. The diamagnetic current drives an oblique lower-hybrid gradient drift instability within the ramp. This instability has been observed in magnetic reconnection experiments and studied in the framework of a Harris-type sheath in previous studies. It arises from a reactive coupling between the oblique Whistler wave, which is propagating backward in the electron rest frame, and the forward-propagating ion acoustic wave. Our simulations show that the magnetic component of this wave modulates the shocks magnetic field, while the electrostatic ion density modulation forces the shock to collapse into a magnetic piston and then reform. The reformation is not forced by an external perturbation as in previous simulations but by the oblique Whistler wave.

In this manuscript, we propose a novel optimal Global Navigation Satellite System (GNSS) time tracking algorithm to collectively steer an ensemble consisting of synchronising miniature atomic clocks towards standard GNSS time. The synchronising miniature atomic clocks generate a common synchronised time which has good short term performance but its accuracy and precision, which is measured by Allan variance, deteriorates in the long run. So, a supervisor designs and periodically broadcasts the proposed GNSS time tracking control to the ensemble miniature atomic clocks that steer the average of ensemble towards the average of GNSS receivers, which are receivers of GNSS time. The tracking control is constructed using a Kalman filter estimation process that estimates the difference in average of GNSS receivers and average of ensemble clocks by using relative clock readings between GNSS receivers and their adjacent ensemble clock. Under the influence of the periodically received tracking control, the stabilised ensemble clocks have better long term accuracy and precision over long averaging periods. Since the tracking control is designed to solely influence the average of the ensemble, the tracking process does not interfere with the synchronisation process and vice versa. The feedback matrix associated with the tracking control is obtained from an optimisation problem that minimises steady-state Allan variance. Numerical results are provided to show the efficacy of the proposed algorithm for enhancing long term performance.

We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two degree distributions, we determine the dominant survival strategies in all parameter regimes and provide asymptotics for the epidemic probability up to logarithmic factors.

Altermagnetism, the third class of collinear magnetic order, uniquely combines a zero net magnetization with spin polarized bands in reciprocal space, opening new avenues for two dimensional valleytronics and spintronics. Here, using first principles calculations, we predict that the Janus monolayer Cr2SSe, which possesses intrinsic inversion symmetry breaking, hosts a strain tunable multipiezo effect and exhibits distinctive valleytronic properties. The system displays pronounced spin splitting and band inversion at the X and Y high symmetry points in the Brillouin zone, giving rise to robust spin-valley locking. The degeneracy of these valleys is protected by diagonal mirror symmetry. Application of uniaxial strain breaks this symmetry, concurrently inducing piezovalley, piezoelectric, and piezomagnetic responses, a manifestation of the multipiezo effect. Critically, strain applied along orthogonal crystallographic directions yields opposite valley polarization, while under small compressive strain, we achieve selective reversal of valley polarization, enabling independent control of valence and conduction band valleys and promoting a single-spin-channel anomalous valley Hall effect. These findings establish a pathway for low-power, non volatile manipulation of valley degrees of freedom and enhanced spin transport efficiency, providing a theoretical foundation for the design of energy-efficient valleytronic devices.

Model merging has emerged as a powerful technique for combining specialized capabilities from multiple fine-tuned LLMs without additional training costs. However, the security implications of this widely-adopted practice remain critically underexplored. In this work, we reveal that model merging introduces a novel attack surface that can be systematically exploited to compromise safety alignment. We present TrojanMerge,, a framework that embeds latent malicious components into source models that remain individually benign but produce severely misaligned models when merged. Our key insight is formulating this attack as a constrained optimization problem: we construct perturbations that preserve source model safety through directional consistency constraints, maintain capabilities via Frobenius directional alignment constraints, yet combine during merging to form pre-computed attack vectors. Extensive experiments across 9 LLMs from 3 model families demonstrate that TrojanMerge, consistently achieves high harmful response rates in merged models while source models maintain safety scores comparable to unmodified versions. Our attack succeeds across diverse merging algorithms and remains effective under various hyperparameter configurations. These findings expose fundamental vulnerabilities in current model merging practices and highlight the urgent need for security-aware mechanisms.

We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on superconducting circuits. Using elementary concepts of random matrix theory, we obtain analytic expressions for the survival probability in mathematical models of platforms which, albeit stylized, have been previously shown to provide relevant benchmarks for experimental data. In particular, we show that the decay properties are sensitive to the property of the Hamilton operator to have extended states. The survival probability does not appear instead to depend on whether the interaction between qubits is described by a Gaussian orthogonal ensemble (often interpreted as a model of ''chaotic'' dynamics) or is modeled by an analytically solvable chain. We interpret this phenomenon as a manifestation of a general mechanism for the emergence of equilibration in purely unitary dynamics. Finally, under the same hypothesis of an initial preparation with projection on a large fraction of the extended eigenstates of the Hamilton operator, we show how to extend the classical Kac-Mazur-Montroll estimate of the return time to the quantum survival probability.

The problem of {\it critical patch size} -- a threshold condition for population persistence -- is investigated in the context of discrete habitats, modeled as graphs with a distinguished subset of vertices acting as sinks. These sinks impose boundary-like constraints analogous to Dirichlet conditions in continuous domains. The population proliferates locally at the vertices and diffuse across the network through the graph Laplacian. In the sinks the population cannot survive. The Dirichlet eigenvalue of the habitat is defined as the smallest eigenvalue of the principal submatrix of the Laplacian obtained by removing the rows and columns associated with sink vertices. This spectral parameter governs the habitat's viability: survival occurs when the Dirichlet eigenvalue of the habitat lies below a critical reaction-to-diffusion ratio. We study survival conditions for a sequence of random habitats built on binomial random graphs. We establish a law of large numbers for the corresponding sequence of Dirichlet eigenvalues and prove the emergence of a sharp threshold phenomenon: with high probability, a large random habitat is either viable or non-viable, depending on whether the reaction-to-diffusion ratio lies below or above this threshold. Our results provide the first general spectral theory for critical patch size on graphs, with implications for ecology, synthetic biology, and the modeling of processes on brain connectomes.