Direct Numerical Simulation (DNS) of a Mach 6 boundary layer over a flat plate is performed to assess the effect of spanwise non-uniform surface temperature on breakdown to turbulence under deterministic forcing. The streamwise location of laminar to turbulent transition in hypersonic boundary layers has a significant influence on viscous drag and aerodynamic heating of external surfaces of hypersonic vehicles. Previous work investigated the stabilization of hypersonic boundary layers by optimally growing streaks. More recently, DNS for a hypersonic boundary layer showed that it is possible to generate streaks through a spanwise non-uniform surface temperature distribution. The laminar computations showed the control method can stabilize the second Mack mode and it is robust across a range of Mach numbers and wall temperature ratios. In this work, two scenarios are investigated where two-dimensional (second Mack mode) and oblique (first Mack mode) disturbances dominate the initial linear stage of transition. It is found that weak control streaks with amplitude below 5% of the freestream velocity can reduce high-frequency shear-stress due to the second Mack mode by approximately 30% relative to the uncontrolled configuration, and delay transition. For first Mack mode dominated breakdown, the control streaks have no effect on transition location, but the peak amplitude of the spanwise-integrated wall heat flux is reduced. For the first and second Mack mode-dominated scenarios, the mean and high-frequency peak heat transfer are reduced approximately by 15% and 34%, respectively. The dominant mechanisms are identified and attributed to the pressure work contribution to turbulent kinetic energy and the second Mack mode dilatation work.

Elastic wave dispersion is studied in an octet truss lattice and compared with a designed rib lattice known to exhibit strong Cosserat elastic effects. Dispersion entails variation of wave speed with frequency. The phenomenon is experimentally investigated by exciting standing waves in specimens of different length at discrete frequencies. At lower frequencies corresponding to long wavelengths, wave propagation is classically non-dispersive. As wavelength approaches a small multiple of the rib length, dispersion is observed. The material exhibited cut-off frequencies above which no signals were propagated. The physical origin of the dispersion and cut-off is resonance of the ribs. Interpreted as micromorphic continua, cellular solid behavior reveals elastic constants associated with flexibility of the unit cell in comparison with that of the overall material.

We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike discontinuous Galerkin methods, our analysis of the proposed finite element method is based on a corresponding consistent variational formulation and a perturbed Galerkin method. In the variational formulation the divergence appears not only within subdomains, but also as an $L^2$-surface quantity on the interfaces. Furthermore, the traces of the finite element functions on the interfaces are replaced by $L^2$-distributions. The well-posedness of the perturbed Galerkin method is shown for an appropriate choice of subspaces, in a manner similar to that of the variational formulation. For the finite element method we use Raviart-Thomas elements for the dual variable and piecewise polynomials for the primal and hybrid variables, respectively. We perform an analysis of the discretization error which is explicit in the stabilization parameter $τ$. Numerical experiments for piecewise smooth solutions using finite element spaces of order~$q$ on curved quadrilateral meshes confirm the predicted convergence rate of $q+1$ for small values of $τ$. In the error analysis we observe the discretization error to be uniformly bounded in $τ$. Even for large $τ$ values the observed convergence rates for the primal and for the hybrid variables are $q+1$. For the dual variable the convergence rate depends on the stabilization parameter and the mesh-width, with an asymptotic rate of $q+\tfrac12$.

High Energy Physics (HEP) experiments like BESIII produce petabyte-scale data. Extracting physics results requires complex workflows (simulation, reconstruction, statistical analysis, etc.) that traditionally take experts months or years. Current manual methods are labor-intensive, prone to bias, and limit large-scale systematic scans. As data grows, this paradigm slows discovery. Large Language Models (LLMs) offer a solution. Their natural language understanding and code generation capabilities allow them to interpret scientific tasks and integrate with HEP tools (e.g., ROOT, BOSS) to act as an "AI partner" for autonomous analysis. We present Dr.Sai, an LLM-powered multi-agent system that translates natural language into rigorous physics workflows. As validation, Dr.Sai performed large-scale re-measurements of ten J/psi decay branching fractions - without manual coding. It successfully navigated the real BESIII computing environment and produced results matching established benchmarks. The article details Dr.Sai's architecture, the validation results, and performance evaluation. This work provides a blueprint for autonomous discovery, with relevance to other data-intensive fields like astronomy and genomics.

This work describes a few-body dynamics method based on the Faddeev integral equations in momentum space for determining the total cross sections of fusion and breakup reactions with two- and three-body final channels in the continuum, employing a cluster representation of the colliding nuclei. Total cross sections were obtained for the reactions $^3\text{He}(T,D)^4\text{He}$, $^3\text{He}(T,np)^4\text{He}$, $^3\text{He}(T,nD)^3\text{He}$, $^3\text{He}(^3\text{He},2p)^4\text{He}$, $^3\text{He}(^3\text{He},pD)^3\text{He}$, $^7\text{Li}(^3\text{He},\phantom{0}^4\text{He})^6\text{Li}$, $^7\text{Li}(^3\text{He},D^4\text{He})^4\text{He}$, and $^7\text{Li}(^3\text{He},T^3\text{He})^4\text{He}$, in which both the projectile and the target nucleus were treated in a cluster representation. The work also implements a two-potential method to determine the Coulomb $t-$matrix and to account for Coulomb effects in short-range dynamics in momentum space. Calculations of the initial-state Coulomb interaction were performed; furthermore, an estimate was obtained for the magnitude of the off-shell effect of the Coulomb $t-$matrix, as well as the magnitude of the atomic electron anti-screening effect on the Coulomb interaction of the colliding nuclei. The calculated contribution of the cluster mechanism to the total cross section of the considered fusion reactions in the kinetic energy range $T\in[1~\text{keV},20~\text{MeV}]$ is in good agreement with known experimental data.

We develop a mean-field description including spatial structure for a simplified version of the three-state active matter model studied by Venzel et al. (Phys. Rev. E 110, 014109 (2024)). The resulting triangular lattice of coupled nonlinear differential equations are integrated numerically using a fourth-order Runge-Kutta scheme. Starting from various ordered initial configurations, we probe the stability of the corresponding stationary states, revealing the presence of various high-density ordered structures in the density(\r{ho})-noise(η) plane. The results are compared with Monte Carlo simulations of the simplified model, yielding, in certain cases, unexpected transitions between ordered configuration types.

A novel Gamma-distributed geometric constellation design framework for integrated sensing and communication (ISAC) is proposed in this paper. In this framework, constellation points are modeled as samples drawn from a parameterized two-dimensional distribution, with a Gamma distribution for the amplitude and a uniform distribution for the phase. End-task performance metrics, namely, the probability of detection for sensing and mutual information for communication, are used as objective functions of the optimization problem, and the problem is solved via particle swarm optimization. We further derive analytical performance bounds for the proposed design, including the union bound on the symbol error rate for communication and the Cramer--Rao bound for sensing parameter estimation. The proposed method is compared with constellations obtained via end-to-end neural network design, demonstrating competitive performance while requiring significantly fewer parameters and no training data. Moreover, the proposed geometric constellation is more compatible with conventional system architectures than probabilistic or neural network-based designs.

Empirical researchers routinely invoke the no-interference or \textit{individualistic treatment response} (ITR) assumption to identify causal effects in observational studies, despite concerns that interference across units may arise in many economic settings. This paper studies the causal content of standard ITR-based identification formulas when arbitrary interference is present. We show that, under restrictions on dependence between treatment assignments across units, conventional ITR-based identification formulas -- including those underlying selection-on-observables, instrumental variables, regression discontinuity designs, and difference-in-differences -- identify well-defined causal objects: types of \textit{average direct effects} (ADEs). These results do not require knowledge of the interference structure or specification of exposure mappings. We also propose a sensitivity analysis framework that quantifies the robustness of statistical inference to violations of treatment-assignment independence under arbitrary interference.

The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple, research on theoretical properties and optimization for practical implementations has grown to a point where verifying correctness and reproducing proofs becomes challenging and intuition can sometimes be misleading. Lean is a purely functional programming language and interactive theorem prover whose community actively develops formal libraries for mathematics (Mathlib) and computer science (CSLib). In this work, we present our own endeavor of crafting a Lean framework around existential rules and the chase. We discuss design decisions concerning the nuances of chase definitions commonly found in the literature and show how these translate into Lean. To illustrate the framework's capabilities using known results, we show that the result of a chase is a universal model and outline the formalization for proving that without so-called "alternative matches" it is even a core. Beyond existing literature, we unify sufficient chase termination conditions in the likeness of Model-Faithful Acyclicity (MFA) into a common framework while also adding support for constants in rules.

DEKL 2.0 is a dependent type-theoretic framework for trace-indexed knowledge evolution. Its central claim is that the proof calculus remains monotone under standard structural rules, while non-monotonic behavior arises semantically from trace extension. Finite and infinite traces are first-class objects in the computational universe; knowledge is interpreted as a presheaf over the finite-trace category; and proposition-level reasoning is handled categorically with fixed-point support. We establish trace--reachability correspondence and completeness, characterize non-monotonicity by non-surjective restriction maps, and present a semantic interpretation based on the free category generated by a transition system. The framework unifies executable traces, typed witnesses, and knowledge revision in one dependent language.

Mueller matrix (MM) polarimetry is an effective, non-invasive tool for retrieving information from complex media. However, the finite dynamic range of optical detectors poses a significant challenge when measurements involve strong intensity contrasts, where bright regions risk saturation while dark regions suffer from poor signal-to-noise ratio. To address this challenge, this article presents a straightforward, high dynamic range methodology that does not require non-linear algorithms. The proposed technique relies on the direct addition of raw intensities captured at multiple exposure times prior to the calculation of the MM. By extending the effective well-depth of the detector, this technique allows the 16 MM elements to be calculated across different hardware configurations with a significantly improved signal-to-noise ratio in low-intensity regions while eliminating artifacts caused by saturation. This approach offers a simple yet efficient solution for the characterization of samples, eliminating the need for hardware modifications or software trade-offs.

This paper proposes a grouped pattern (GP) for sensing signals and a corresponding multi-periodogram algorithm for range estimation in integrated sensing and communications (ISAC) systems. GP partitions subcarriers into groups with an identical intra-group configuration replicated across groups, producing range profiles with periodic peaks and a structured multi-peak signature that improves low-SNR target detection. By identifying targets via cross-pattern peak validation, the proposed approach reduces missed detections and false alarms while requiring fewer dedicated sensing resources. Extensive simulations demonstrate a 16.5% extended detection range and a 61% reduced false alarm rate compared to conventional methods.

A hybrid approach to numerical weather prediction is investigated, in which the unperturbed physics-based ECMWF Integrated Forecasting System (IFS) is spectrally nudged toward forecasts from a machine-learned weather forecast model, trained to forecast on model levels. Nudging is applied only to the large scales of virtual temperature and vorticity, with the objective of improving large-scale forecast skill while preserving the dynamical and physical behaviour of the underlying physics-based model at smaller scales. Consistent with previous studies, spectral nudging substantially improves large-scale forecast skill relative to the free-running IFS, with gains of up to 1.5 days in the tropics and 12-18 hours in the extra-tropics, and a reduced frequency of forecast busts. These improvements are achieved while preserving forecast variability. The representation of extreme near-surface weather is maintained or improved. Tropical cyclone track forecasts benefit from improved large-scale steering flow, while storm intensity remains comparable to that of the physics-based model and more physically consistent than in pure machine-learned weather forecast models. These results confirm that scale-selective spectral nudging provides a practical pathway for combining machine-learning and physics-based forecasting systems.

We present the results from Meno, a simple autoformalizer that proves theorems in Lean by systematically exploring the space of both formal and informal proofs, and tactic ablation, a new method for exploring mathematical creativity under constraint. We show these tools in action on simple theorems found in Terrence Tao's Analysis I, selectively ablating solution paths associated with non-constructive proofs, and analyze the properties of the resulting population using Goedel Prover embeddings. Among other things, our analysis of this novel population reveals that they lie on low (one or two) dimensional submanifolds of the much higher-dimensional representation space, and far away from their corresponding human constructions.

Predicting three-dimensional thermal loads during tokamak disruptions is essential for ITER yet remains weakly developed. We present a physics-based workflow that couples MHD simulations of vertical displacement events with field line tracing on a realistic 3D first wall model and a transient wall thermal response. The approach is validated against JET discharges with beryllium main chamber armour, reproducing key global dynamics, non-axisymmetric current features, and the occurrence (or absence) of melting, thereby building confidence in the methodology. We then apply the same workflow to ITER-relevant conditions with tungsten (W) armour, consistent with the new 2024 ITER re-baseline, to assess disruption heat loads and their 3D localization. The resulting analysis demonstrates the resilience of the ITER W first wall against these events and provides predictions for the energy deposition and current flow profiles. Beyond these studies, the workflow enables scenario-by-scenario estimates of disruption-induced thermal loading, allowing to assess the disruption-budget consumption for these events in future devices.

We calculate second- and selected fourth-order conserved-charge fluctuations in $(2+1)$-flavor QCD using Möbius domain-wall fermions (MDWF) along a line of constant physics. Gauge ensembles were generated for two light-to-strange quark-mass ratios, $m_l/m_s=1/10$ and $1/27.4$, corresponding to heavier-than-physical and physical pion masses, respectively. For $m_l/m_s=1/10$, calculations were carried out on lattices with temporal extents $N_τ=12$ and $16$, enabling an assessment of lattice-spacing effects at heavier pion mass. For $m_l/m_s=1/27.4$, calculations were performed at $N_τ=12$, allowing us to study the light-quark-mass dependence down to the physical point. Below the pseudocritical temperature, second-order electric-charge, strangeness, and off-diagonal conserved-charge fluctuations are consistent with QMHRG2020 hadron resonance gas calculations. Across the crossover region, these observables rise rapidly and tend toward their Stefan--Boltzmann limits. Selected fourth-order cumulants were also computed at the physical pion mass. Although these observables are statistically more demanding, several channels with controlled uncertainties permit a first comparison with hadron resonance gas calculations.

There is a rapidly growing interest in using Large Language Models (LLMs) to automate complex network operations, but their reliable adoption requires rigorous assessment of their effectiveness and safety. Existing benchmarks do not address whether LLMs can successfully resolve errors in large-scale, interdependent network configurations without introducing new disruptions. Developing such a benchmark is challenging: scenarios must be diverse and increasingly complex, yet their evaluation must be straightforward and meaningful. In this paper, we present Cornetto, the first benchmark to evaluate LLM-driven network configuration repair functionally and at scale. Cornetto features a generation pipeline that synthesizes representative and plausible misconfiguration scenarios, coupled with an evaluation framework that uses formal verification to assess functional correctness of proposed fixes against ground-truth specifications. Using this pipeline, we synthesize a dataset of 231 problems for fixing configurations across varying network topologies (20--754 nodes) and diverse protocols. We evaluate 9 state-of-the-art LLMs and find that while they show promise, they often introduce regressions and their performance degrades at scale. Our results indicate that reliable LLM-powered network automation requires integrating LLMs into iterative workflows guided by formal verification.

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems naturally arise in many industrial flow processes with dominant advection or traveling fronts in the solution trajectories. To tackle this challenge, we extend the Deep Orthogonal Decomposition (DOD) method, recently introduced for related stationary problems, to the time-dependent setting. We introduce and rigorously analyze two DOD based approaches: Our approach is based on two novel adaptive deep learning-based surrogate models: The DOD-DL-ROM method which is a Reduced Order Model (ROM) that leverages the adaptive nature of DOD, and the DOD+DFNN method, which combines DOD with a generic Deep Feed-Forward Neural Network (DFNN). On the theory side, we generalize data-driven POD-based ROM arguments to the DOD setting, establishing a quantitative link between online performance and the regularity of an associated optimal map. Furthermore, we identify specific problem size and error tolerance requirements for DOD-based ROMs to outperform POD-based ROMs in hybrid-type problem classes, which is crucial for efficient computation. The significance of this work lies in its potential to accelerate the solution of complex PDEs, enabling faster design and optimization of industrial processes. The proposed approaches are demonstrated on a catalyst filter benchmark problem, showcasing their effectiveness and comparing favorably to traditional POD-based methods.

In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean--Vlasov diffusions with super-linear kernels. In this setting, the interaction depends on the laws of both the slow component and the fast oscillating process. Consequently, the frozen (parameterized) system exhibits McKean--Vlasov dynamics, forming a nonlinear Markov process and thereby rendering the analysis more complex compared to existing works. We develop a lifted semigroup argument and employ a generalized Khasminskii time discretization scheme to derive the small-noise limit of the slow variable, providing explicit convergence rates. Furthermore, we introduce the notion of a lifted viable pair and utilize a generalized functional occupation measure approach to establish the Laplace principle, which is equivalent to the large deviation principle. The main results of this work find broad applications in multi-scale models arising in fields such as machine learning and optimization theory. In particular, our results can be employed to analyze the dynamics of multi-scale consensus-based methods for multilevel optimization, where the coefficients typically satisfy local Lipschitz continuity on the interaction kernels.

Public clouds increasingly expose heterogeneous hardware, but their allocation interface remains built around rigid on-demand and spot service classes. This makes it hard to satisfy time-varying tenant objectives and operator constraints in oversubscribed, heterogeneous clusters without exposing internal application or infrastructure state. We present LaissezCloud, a cloud resource management platform for continuous re-negotiation of running allocations. Unlike spot instances, which use launch-time bids and unilateral preemption, LaissezCloud keeps allocations continuously contestable during execution: tenants and operators update bids online, and a running tenant keeps a resource only as long as its bid exceeds competing demand. Pricing serves both as a narrow waist and as an incentive-alignment mechanism between mutually untrusted participants: tenants express utility through bids, while operators price in power, cooling, or carbon constraints without exposing internal telemetry. Across a diverse set of accelerator workloads, LaissezCloud reduces performance degradation under contention by 8-23% versus on-demand and spot baselines, and scales to clusters of at least 10,000 nodes.

This lecture reviews the principles of particle-matter interactions, providing the essential physics background required to understand beam loss mechanisms in high-energy accelerators and their associated implications. The main interaction processes of photons and charged particles are introduced, together with an overview of nuclear reactions. The lecture then addresses electromagnetic and hadronic showers, which play a central role in particle-matter interaction physics. Following a brief overview of Monte Carlo simulation tools, with emphasis on FLUKA, the lecture concludes with a detailed examination of a representative LHC-type radiation shower.

Private Information Retrieval (PIR) allows clients to retrieve database entries without leaking retrieval indices, yet malicious servers seriously compromise retrieval correctness. Existing Authenticated PIR (APIR) schemes resist selective-failure attacks but rely on computational hardness assumptions. In contrast, information-theoretic PIR with Result Verification (itPIR-RV) achieves integrity without computational assumptions, yet only provides relaxed query privacy with no defense against selective-failure attacks. This paper focuses on unconditionally secure information-theoretic APIR (itAPIR) constructions. We propose the rigorous information-theoretic security definition for itAPIR with statistical privacy against selective-failure attacks and integrity as core properties, formalize the hierarchical relation between itAPIR and itPIR-RV as a relaxed variant with identical integrity but basic query privacy, and prove a conversion theorem that valid itPIR-RV schemes can be directly upgraded to secure itAPIR with no extra overhead. Our work bridges the theoretical gap, simplifies itAPIR design, and enables quantum-resistant PIR in malicious server environments.

Reinforcement learning (RL) effectively optimizes Large Language Model (LLM)-based recommenders by contrasting positive and negative items. Empirically, training with beam-search negatives consistently outperforms random negatives, yet the mechanism is not well understood. We address this gap by analyzing the induced optimization objective and show that: (i) Under binary reward feedback, optimizing LLM recommenders with Group Relative Policy Optimization (GRPO) is theoretically equivalent to maximizing the Area Under the ROC Curve (AUC), which is often misaligned with Top-$K$ recommendation; and (ii) Replacing random negatives with beam-search negatives reshapes the objective toward partial AUC, improving alignment with Top-$K$ metrics. Motivated by this perspective, we introduce Windowed Partial AUC (WPAUC), which constrains the false positive rate (FPR) to a window [$α,α+d$] to more directly align with Top-$K$ metrics. We further propose an efficient Threshold-Adjusted Windowed reweighting (TAWin) RL method for its optimization, enabling explicit control over the targeted Top-$K$ performance. Experiments on four real-world datasets validate the theory and deliver consistent state-of-the-art performance.

We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in homogeneous media with high wavenumber are particularly challenging due to the so-called pollution effect: the mesh size must be significantly smaller than the reciprocal of the wavenumber to achieve a desired accuracy. This challenge is amplified in heterogeneous media, which frequently occur in practical applications such as metamaterial simulations, since resolving the heterogeneity is necessary for obtaining reliable solutions. Our approach overcomes this difficulty by avoiding explicit resolution of the heterogeneity, while employing a mesh size that depends almost linearly on the reciprocal of the wavenumber. The approximation properties and stability of the method rely critically on the development and rigorous analysis of a novel, nonstandard variational formulation, which constitutes the main innovation of this work. Extensive numerical experiments are provided to validate our theoretical findings.

Snarks are $2$-connected cubic graphs that do not admit a proper $3$-edge-coloring. For a cubic graph $G$, its resistance $r(G)$ is the minimum number of edges whose removal results in a $3$-edge-colorable graph, while its flow resistance $r_f(G)$ is the minimum number of edges whose removal results in a graph admitting a nowhere-zero $\mathbb{Z}_2 \times \mathbb{Z}_2$-flow. In this paper, we provide an affirmative answer to a question recently posed by Allie, Máčajová, and Škoviera by constructing a family of cyclically $5$-edge-connected snarks for which the ratio $r_f(G)/r(G)$ is arbitrarily large.

In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bound on the total steady-state squeezing achievable in reservoir-engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances normalized to its corresponding input variance. The bound follows solely from canonical commutation relations and stability, and is saturated in the strong-coupling limit at 1. Furthermore, we show that adding independent parametric driving terms for each mode changes the quantum noise-gain balance and yields a distinct optimum bound, approaching 1/2. In addition, we show how these constraints allow us to reformulate the Duan inseparability criterion for a three-mode bosonic system in terms of a single parameter-dependent figure of merit. Our results apply directly to current electromechanical and nanomechanical experiments and indicate that the two-mode bounds can be experimentally approached even at room temperature.

By results of Dantzig (1951) and Adler (2013), computing the optimal solutions of a linear program is equivalent to finding optimal strategies in zero-sum bimatrix games. Dantzig's original result was incomplete, in the sense that the reduction of a linear program to a zero-sum game did not work for all possible linear programs. We show that, under a natural constraint qualification requiring either the existence of strongly optimal primal-dual solutions or of a strictly unbounded direction, computing the solution of a semidefinite program is equivalent to finding optimal strategies in an associated zero-sum semidefinite game. Our work builds upon Ickstadt, Theobald, and Tsigaridas (2024), where, similar to Dantzig's work, the proposed reduction cannot handle a certain subclass of semidefinite programs. Our main proof ingredients for the equivalence result include: (i) a semidefinite generalization of von Stengel's (2023) extension of Dantzig's construction; (ii) techniques for handling more general duality phenomena in the semidefinite setting; and (iii) an explicit bound for the (coordinates) of the solutions of a semidefinite program. As a by-product, the game value provides a certificate: it is zero if and only if strongly optimal solutions exist, and otherwise optimal strategies yield an infeasibility certificate for the primal or dual program.

The first-order (FO) model checking problem asks, given an FO sentence $ϕ$ and a graph $G$, whether $G$ is a model of $ϕ$. This problem is known to be $\mathsf{AW[*]}$-hard when parameterized by the quantifier rank of the formula. A classical algorithm decides this problem in XP-time parameterized by the number of variables in the formula. Due to $\mathsf{AW[*]}$-hardness, it is natural to ask about the complexity of the problem when restricted to some well-behaved class of graphs. There are many results describing graph classes $\mathcal{C}$ such that the FO model checking problem restricted to $\mathcal{C}$ admits an $\mathsf{FPT}$-time algorithm when parameterized by the quantifier rank of the formula. Parameterization by the quantifier rank is significantly more restrictive than parameterization by the number of variables. We investigate the graph classes $\mathcal{C}$ for which the FO model checking problem restricted to $\mathcal{C}$ admits an $\mathsf{FPT}$-time algorithm when parameterized by the number of variables in the formula. We characterize these classes in the monotone setting, and prove a slightly weaker result in the hereditary setting.

The operation of high-energy and high-intensity particle accelerators inevitably leads to the loss of a fraction of beam particles, either through controlled processes or accidental events. This article builds on a first lecture on particle-matter interactions to review the main beam loss mechanisms in high-energy and high-intensity accelerators and their implications for safe and efficient operation. It discusses the resulting risks of equipment and material damage, radiation effects on electronics, and radiation-protection hazards. The focus is on beam losses in hadron accelerators, with particular emphasis on the Large Hadron Collider at CERN, while also addressing proposed future facilities such as the Future Circular Collider and muon colliders.

The notions of infimum and maximal lower bounds of a set $\mathfrak M$ of bounded self-adjoint operators were mainly studied for a set $\mathfrak M$ of two elements. The present paper deals with more general sets $\mathfrak M$, where it is required that $\mathfrak M$ is nonempty and bounded from below. Kadison's theorem on the existence of the infimum of a two-element set is proved for a countable and weak-operator compact set $\mathfrak M$. Stott's recent results on the structure of the set of maximal lower bounds of a finite set of Hermitian matrices are discussed and partially generalized. We are also concerned with the greatest lower bound and maximal lower bounds under certain restrictions. It is shown that the set of all lower bounds of $\mathfrak M$ commuting with all elements of $\mathfrak M$ possesses the greatest element if $\mathfrak M$ is a set of pairwise commuting operators. The theorem of Moreland and Gudder on the existence of the greatest positive lower bound of a set of two positive matrices is extended to an arbitrary finite set of positive matrices.