While magnetic confinement fusion (MCF) and inertial confinement fusion (ICF) remain the primary routes toward controlled fusion, progress is still constrained by energy loss, plasma instabilities, and the cost and complexity of large-scale facilities. The Dense Plasma Focus (DPF) device presents a compact, pulsed-power-driven alternative for producing fusion-relevant conditions and neutron emissions. However, the quantitative prediction of neutron yield in DPF devices poses a significant numerical challenge, primarily due to the imperative of self-consistently resolving kinetic ion behavior, electromagnetic energy coupling, and vacuum field evolution. This complexity often impedes a definitive understanding of the underlying neutron production mechanisms. To address this, we develop a fully electromagnetic hybrid simulation framework: ions are advanced kinetically with particle-in-cell, electrons are a quasi-neutral fluid, and Maxwell's equations are solved in both plasma and vacuum. The generalized Ohm law includes resistive, electron pressure-gradient, and Hall terms, with a predictor-corrector update for current density. We apply the model to a non-hollow 180 kA DPF geometry similar to the LLNL configuration. The simulated ion density, ion temperature, and axial electric field reproduce sheath formation, axial rundown, radial compression, and post-pinch expansion. The outer sheath front position agrees with fully kinetic benchmarks within 10\% over the available comparison interval. With a compact fit to the D-D fusion cross section, the predicted total neutron yield is 0.296e7, comparable in order of magnitude to reported fully kinetic results at similar currents and nearly two orders of magnitude higher than earlier hybrid results.

Scenario-based optimization problems can be solved via Benders decomposition, which separates first-stage (master problem) decisions from second-stage (subproblem) recourse actions and iteratively refines the master problem with Benders cuts. In conventional Benders decomposition, all subproblems are solved at each iteration. For problems with many scenarios, solving only a selected subset can reduce computation. We quantify the potential in selecting only those subproblems that yield cuts, and develop subproblem scoring and selection strategies. The proposed multi-criteria scoring methods combine historical subproblem performance metrics with problem-specific features, trained online via logistic regression to adapt to the changing likelihood of subproblem usefulness. Multiple stopping criteria balance exploration and exploitation: cut limits, proportional solve limits, and score thresholds. We evaluate our approach on a variant of the survivable network design problem, which serves as a testbed due to its natural decomposition into many subproblems of varying importance. Computational experiments on 135 test instances demonstrate the potential and practical performance of subproblem selection. Analysis reveals that 52.1% of all subproblems solved are unnecessary (they contribute no cuts and occur outside cut-free rounds). An oracle with perfect foresight reduces total solve times by 34.4%. Random selection performs significantly worse than full enumeration, showing that naive strategies can degrade performance. Our best-scoring and selection method achieves statistically significant improvements in both runtime and primal-dual integrals. These results provide empirical evidence that informed subproblem selection can improve Benders decomposition in this setting, while highlighting challenges in developing reliable prediction models.

We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for foliations on surfaces and to the existence of flips on threefolds.

Social agents both internalize collective norms and reshape them through creative action, yet computational models have not captured this bidirectional process within a unified framework. We propose a multi-agent simulation model grounded in active inference that formalizes the dialectical constitution of social reality on a structured social network. Each agent maintains an internal generative model, communicates with neighbors to form social priors, creates novel observations, and selectively incorporates others' creations into memory. Simulation experiments demonstrate three main findings. First, informationally cohesive social groups emerge endogenously, with representational alignment mirroring the cluster topology of the underlying network. Second, a circular mutual constitution arises between social representations and the observation distribution, maintained through agents' creative acts that project representational structure onto the external world. Third, the propagation of creations exhibits selective, heterogeneous patterns distinct from the stable diffusion of social representations, indicating that agents construct cultural niches through local interaction dynamics. These results suggest that the interplay between social conformity and creative deviation can give rise to the endogenous formation and differentiation of shared social reality.

High-precision high-fidelity spectrographs are the most powerful instruments for exoplanets detection and characterization. The sub-m/s radial-velocity precision, required to detect Earth-mass exoplanets, necessitates tackling all the sources of instrumental and stellar instabilities. We present the new high-precision high-fidelity spectrographs ESPRESSO, NIRPS, ANDES and RISTRETTO designed, developed, and operated with support of PlanetS.

Small changes in high altitude platform (HAP) attitude can cause significant deviations in HAP downlink beam directions, thereby severely degrading HAP downlink communication performance. In this paper, we develop a multimodal large language model (LLM) enabled beamforming framework to achieve robust HAP downlink communications.Specifically, we design a vision-language LLM (VL-LLM) that learns from multivariate flight telemetry to forecast short-term HAP attitudes under platform shaking and support delay-aware proactive beam steering.We design an offline forecast-error calibration procedure to obtain upper bounds on forecast errors and improve the reliability of proactive analog beam steering.Based on the attitude forecasts, we proactively update the analog beamformer and propose a QoS-driven beamforming and admission method with a lightweight feasibility-enforcement step to satisfy instantaneous transmit-power and QoS requirements.Simulation results indicate that the designed VL-LLM can accurately capture changes in the HAP attitude and the proposed beamforming method achieves a 22.1% higher user service ratio and a 12.5% higher sum-rate than representative baselines.The measured mean and p99 total latencies are 36.24 ms and 40.13 ms, respectively, supporting practical delay-aware deployment.

High altitude platforms (HAPs) are emerging as a key enabler for 6G coverage, yet limited energy must be split between propulsion and communications. Most prior HAP studies ignore propulsion power or rely on surrogates that miss hull-propeller interference, leading to misestimated communication power budgets and degraded beamforming. More importantly, HAP power allocation is intrinsically a multi-system, multidisciplinary problem in which aerodynamics, propulsion-system efficiency, and communication-system performance (quality of service (QoS) and energy efficiency (EE)) are tightly coupled.To address these challenges, this paper designs an interactive generative artificial intelligence (AI)-empowered HAP power allocation agent.By interacting with the AI agent, we develop an accurate propulsion power consumption model that takes into account the aerodynamic interference between the HAP's hull and the propeller. Assisted by the AI agent, we further formulate a HAP beamforming problem to improve user QoS and enhance the EE of the HAP communication system.This paper also proposes a QoS-enhanced energy-efficient (Q3E) beamforming algorithm to solve the formulated problem.Simulation results demonstrate the accuracy of the propulsion-power model and the effectiveness of the Q3E algorithm.

We introduce a \emph{spectral Dehn function} \[ Λ_{\mathcal{P}}(n):=\inf λ_1(Δ), \] where $λ_1(Δ)$ is the first Dirichlet eigenvalue of the random-walk Laplacian on a van Kampen diagram $Δ$, and the infimum runs over area-minimising diagrams with boundary length at most $n$. We prove a spectral-isoperimetric inequality relating $Λ_{\mathcal{P}}$ to the Dehn function, and show that its degree-free face-dual variant $Λ^\ast_{\mathcal P}$ characterises word-hyperbolicity: a finitely presented group is word-hyperbolic if and only if \[ \inf_n Λ^\ast_{\mathcal{P}}(n)>0. \] Every disk diagram satisfies a diagramwise filling-length bound \[ \mathrm{FL}_b(Δ)\cdot \operatorname{Area}(Δ) \ge c/λ_1(Δ); \] combined with a discrete Faber-Krahn inequality, this yields the sharp exponent $1/2$ in the quadratic case, attained by rectangular commutator grids over $\mathbb Z^2$. By passing to the free completion and introducing a hole-free-ancestor hereditary quasi-minimality condition, we obtain a spectral filling profile whose positivity criterion is a quasi-isometry invariant of finitely presented groups and again characterises word-hyperbolicity. The resulting profile carries finer information than the Dehn function: it separates presentations within the linear Dehn class.

This paper investigates the boundedness of bilinear pseudo-differential operators with symbols in the Hörmander class $BS_{\varrho,δ}^m(\mathbb{R}^n)$ in the previously unexplored regime $0 \leq \varrho < δ< 1$. We establish boundedness from $H^p(\mathbb{R}^n) \times H^q(\mathbb{R}^n)$ to $L^r(\mathbb{R}^n)$ (with $L^r$ replaced by $\mathrm{BMO}$ when $p=q=r=\infty$) under the probably optimal condition on the order $$m \leq m_\varrho(p,q) - \frac{n\max\{δ-\varrho,0\}}{\max\{r,2\}},$$ where $m_\varrho(p,q)$ is the critical order in the case $0\leqδ\leq\varrho<1.$ Furthermore, we develop refined pointwise estimates via sharp maximal functions, establishing that for $m \leq -n(1-\varrho)(\frac{1}{\min\{r_1,2\}}+ \frac{1}{\min\{r_2,2\}})$ with $1<r_{1},r_{2}<\infty$, the bilinear operators satisfy $$M^\sharp T_a(f_1,f_2)(x) \lesssim \mathcal{M}_{\vec{r}}(f_1,f_2)(x).$$ This extends the parameter range from the restrictive condition $0 \leq δ\leq \varrho < 1$ to the general setting $0 \leq \varrho \leq 1$, $0 \leq δ< 1$ with $δ> \varrho$ permitted, and generalizes previous results of Park and Tomita to distinct exponent pairs. Consequently, we obtain weighted norm inequalities for bilinear pseudo-differential operators under multilinear $A_{\vec{p},(\vec{r},\infty)}$ weights.

Although distributed lag non-linear models (DLNMs) are commonly used to quantify delayed and non-linear exposure-response relationships, most existing applications assume that these relationships are constant across space. However, in many geographical and environmental studies, local characteristics vary substantially across areas, making a spatially varying effect more realistic. Extending DLNMs to allow for spatial heterogeneity remains challenging, and only a limited number of modelling strategies have been proposed in literature. The most popular extension is a two-stage meta-analysis approach, which requires sufficiently large sample sizes at each location. Therefore, its usefulness is limited when working with sparse count data in small area data analyses. Although a number of alternative one-stage approaches have been introduced, their computational burden restricts their applicability in real-life data applications. In this paper, we introduce a computationally efficient Bayesian one-stage spatially-varying DLNM for count data. We define four model variants, differing in the assumed spatial dependence structure and the flexibility of the DLNM spline specification. To address the computational burden typically associated with these flexible models, we use Laplace approximations, offering an efficient alternative to classically used Markov Chain Monte Carlo (MCMC) approaches. Model comparison criteria are provided to facilitate the selection of a suitable model in a real-life data application. The proposed methods are evaluated through simulation studies, and their practical usefulness is illustrated through a real-life data application, investigating the temperature-mortality relationship in every municipality of Sicily, Italy.

We review the progresses made in global theoretical models of planetary system formation in the last decade using the example of the planetary system formation framework known as the Bern Model that has been continuously developed since before the beginning of the NCCR PlanetS. We highlight major developments and applications that have since been implemented, reflecting important recent advancements of planet formation theory overall, such as MHD wind-driven disk evolution, planetesimal evolution including fragmentation, dust evolution and pebble accretion, formation of planets in structured disks, interior structure models allowing for compositional gradients, as well as the analysis of the emerging planetary system architectures and the identification of different classes of architectures. We discuss how these new models impact the formation and evolution process and translate into different populations of planets and planetary systems. We also discuss the major strengths of the Bern Model, including successful predictions of the break in the planetary mass function at 30 MEarth, the prevalence of low-mass planets, the radius pile-up around 1 RJupiter, and the evaporation valley, with the recent New Generation Planetary Population Synthesis models with 100 seeds per disk providing quantitive matches to many RV-survey and Kepler diagnostics. This includes key characteristics of planetary system architectures. We also highlight the limitations of this model, some of them were addressed during the course of the NCCR PlanetS: the inclusion of the early phases of planet formation from dust to planetesimals, the hybrid pebble-planetesimals accretion of solids, simplified interior structure models, reliance on simplified parametrizations that may not encapsulate the full complexity of physical processes, and computational constraints.

This study investigates the structural evolution of even-even tungsten isotopes ($^{154\text{--}264}$W) using covariant density functional theory (CDFT) with four relativistic functionals: DD-ME1, DD-ME2, DD-PC1, and DD-PCX. Key nuclear properties, including binding energies, quadrupole deformation parameters, two-neutron separation energies, neutron pairing energies, nuclear radii, and potential energy curves, are analyzed to explore shape transitions and stability from neutron-deficient to neutron-rich isotopes up to the drip line. The results reveal a dynamic shape evolution, with spherical configurations at $N = 82$ and $N = 126$, prolate dominance in intermediate regions, and shape coexistence in isotopes such as $^{158}$W, $^{160}$W, $^{194}$W, $^{196}$W, $^{206}$W, and near $^{244\text{--}248}$W. A potential subshell closure at $N = 118$ is identified, supported by anomalies in separation energies and vanishing pairing energies. The neutron drip line is predicted at $N = 184$, marked by a return to spherical symmetry. Comparisons with experimental data and other theoretical models, including the deformed Hartree-Fock-Bogoliubov method with the Skyrme SLy4 interaction, the Finite Range Droplet Model, and the Relativistic Mean Field model with NL3, show strong agreement, validating the robustness of CDFT. These findings enhance our understanding of nuclear structure in the medium-to-heavy mass region and provide insights relevant to r-process nucleosynthesis, thereby guiding future experimental studies at radioactive ion beam facilities.

We propose a metadynamics-based (MetaD-based) approach for constructing the free energy surface (FES) of vacancy dynamics in crystals. In this approach, the vacancy FES can be constructed without explicitly defining a unique vacancy coordinate or introducing a set of parameters that strongly govern the FES topology, enabled by parallel bias MetaD with partitioned families (PB MetaDPF). In addition, the proposed approach is made more efficient and effective through a multi-hill strategy that exploits crystallographic symmetry. We demonstrate the validity of the proposed approach through applications to self-diffusion and impurity diffusion via monovacancies and divacancies in metallic and ionic crystals.

We study the effects of using the optical properties of irregular hexahedral grains in photoionization models of circumstellar nebulae around evolved stars. Dust opacities for the irregular grains were obtained from the scattering properties available in the TAMUdust2020 database and these were implemented in the spectral synthesis code cloudy. A sample of photoionization models that use opacities from both spherical and irregular hexahedral grains across a standard MRN size distribution (0.005 to 0.25 um) was produced. We consider the optical properties of graphite, amorphous carbon and silicate dust grains and find that differences between the model nebula continua calculated using spherical and irregular dust grains increase with the grain size, especially for graphite. In particular, we find that the luminosities at the infrared peak for the hexahedral grain models can be up to 60% higher than those from the equivalent spherical grain models for the largest grains. This result suggests that traditional spherical grain assumptions may lead to an overestimate of the dust mass in photoionized nebulae.

Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may exhibit myopic behavior and local trapping when the safeguarding action conflicts with the nominal optimal control. This paper develops a safety-aware infinite-horizon optimal control framework by embedding a barrier-Lyapunov function (BLF)-based safeguarding action into the system dynamics and introducing a barrier-regulating auxiliary variable, thereby reformulating the original constrained problem as an unconstrained one on an extended state space. To mitigate local trapping, we introduce an adaptive alignment-conditioned tangential excitation orthogonal to the safety direction, with activation adaptively modulated by the degree of directional alignment between the nominal and safeguarding controllers, and incorporate it as an admissible $\mathcal{L}2$ disturbance in an $H\infty$ formulation. For high-relative-degree systems under disturbances, we further augment the recursive high-order safe-set construction with barrier compensation terms to obtain a high-order BLF and formulate an adversarial disturbance attenuation problem, which is approximately solved via safe-exploration-enhanced online critic learning. Simulations demonstrate reduced local trapping, improved safety--performance trade-offs, and safe operation under disturbances.

Impacts play a fundamental role in shaping the physical and chemical properties of the objects in our Solar System. Given the challenges in replicating such collisions through laboratory experiments, computer simulations are an important tool to investigate their outcomes. Accurately modelling material properties such as shear strength, porosity, and the formation of cracks is crucial for understanding impacts on small bodies like asteroids and comets. Very large and massive objects are dominated by self-gravity and can be approximated as a fluid. In this regime the equation of state used to model the behaviour of the constituent materials plays a key role. However, for bodies of several hundred kilometres, which are already spheroidal due to self-gravity, shear strength must still be considered. This impact regime is most challenging to model and therefore often overlooked in publications. In this review we present different impact regimes and the relevant physics that must be included. We then discuss their application to a variety of Solar System objects and assess how recent observations and numerical simulations, focussing on the Smoothed Particle Hydrodynamics method, can be used to inform our understanding of impact processes and solar system formation.

Quantum repeaters constitute a promising platform for enabling long distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error-correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, initially we focus on the bosonic Gottesman Kitaev Preskill (GKP) code as a natural candidate for loss correction based quantum repeaters, which can be implemented at room temperature. We demonstrate that transmission loss can be suppressed across three related protocols at the expense of the introduction of logical errors. The third protocol, where a relay-like teleamplifier is applied is optimal. This approach enables medium-distance quantum communication without requiring higher level encoding. We compute the resulting secure key rates while leveraging analog syndrome information. Furthermore, we propose a concatenated Bell state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible transmission distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits.

Tomographic volumetric additive manufacturing (TVAM) requires projection patterns that achieve high in-part fidelity while suppressing unintended exposure outside the target. We present a scale-invariant projection optimization framework (SiPO) that decouples projection shape from absolute dose scaling. The method formulates projection design as a linear-fractional program based on normalized conformity and spillage metrics, which is converted into a linear program via the Charnes-Cooper transformation. Two practical deterministic cases are introduced for process control: minimizing dose spillage under strict material tolerances and maximizing target conformity under hard inhibition constraints. A matrix-free primal-dual hybrid gradient solver enables large-scale implementation. Numerical results demonstrate that the framework provides a clear trade-off between target fidelity and process separation and remains effective under 3D blur-aware forward models.

Phonon polaritons in van der Waals crystals enable exceptional light confinement and control over low-loss nanolight propagation. The polariton wavelength can be controlled by the crystal geometry, isotopic composition, or surrounding environment -- for which substrate engineering is particularly effective. However, existing approaches of substrate nanopatterning are binary and offer limited leverage. Here, we demonstrate local control over the wavelength of phonon polaritons in hexagonal boron nitride by employing a sinusoidally corrugated gold surface to smoothly vary the gap between the van der Waals crystal and metallic substrate. The nonuniform gap provides a continuous and nearly threefold local variation of the polariton wavelength across the structure, verified by near-field optical microscopy. Our platform further enables lateral nanofocusing by gradually compressing and decompressing the wavelength of propagating polaritons by a factor of around 2.5 achieved solely through substrate geometry, consistent with our local control experiments and theoretical calculations. Our results push the boundaries of substrate engineering and showcase a powerful method for precise and local tailoring of polaritonic modes.

We predict a giant cyclotron resonance in the nonlinear valley Hall response of inversion-asymmetric two-dimensional semiconductors subjected to crossed terahertz electric and static magnetic fields. By employing a two-band Hamiltonian that incorporates both linear and quadratic in momentum terms, thereby capturing the essential orbital texture and broken inversion symmetry, we develop a kinetic theory that accounts for antisymmetric skew scattering from impurities. Solving the Boltzmann transport equation we uncover resonant photocurrents that exhibit a sharp, polarity-switching cyclotron peak and a nontrivial polarization response dictated by the underlying D3h crystal symmetry. Our results establish a universal mechanism for frequency-selective, phase-sensitive valley current control, directly accessible in monolayer transition metal dichalcogenides. This work provides a pathway for harnessing resonant nonlinear transport in valleytronic and terahertz optoelectronic devices.

This work describes the context and approach for the detection of spectroscopic signatures from planets in the habitable zone of nearby stars. By understanding the limitations of current observatories, future telescopes can be understood, and their ability to characterize the atmospheres of exoplanets estimated. An example calculation is given for the signal-to-noise analysis for a planet like the current Earth of oxygen as a biosignature, and (an enhanced abundance) of hydrogen iodine as a technosignature. In the optimistic estimate, Earth is easily detected, O2 characterized in 20 hours, but signals from enhance HI are only visible after hundreds of hours, indicating the signals are too weak to realistically constrain.

A subgraph of the square lattice with all of its inner faces being 4-cycles is called a square-cell configuration. Prior work has provided explicit expressions for the total and average distances between vertex pairs in symmetric square-cell configurations, including well-structured families such as hexagonal square-cell configurations $H(n)$, trapezium square-cell configurations $T(n,k)$, and bitrapezium square-cell configurations $BT(n,k_1,k_2)$. In this article, we further extend the square-cell configuration from regular boundaries to irregular boundaries, which do not exhibit complete regularity or symmetry in their structure. We find the generalized expressions for the Wiener index and average distance of such irregular configurations, incorporating combinatorial and structural variations. Our results demonstrate how irregularity affects the growth and distribution of pairwise distances and provide a unifying framework that includes both symmetric and asymmetric square-cell graphs as exceptional cases. This generalization provides novel insights into the structural behaviour of square-cell frameworks characterized by complex or perturbed geometries.

Orbital angular momentum has recently emerged as an important carrier of angular momentum in solids, offering new pathways for spin orbitronic functionality beyond conventional spin transport. Here, we investigate the orbital Hall effect which generates orbital torques and their reciprocal process viz orbital pumping and the inverse orbital Hall effect (iOHE) in non-magnet/ferromagnet heterostructures. Using two port scattering parameter measurements on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 devices, we directly probe both orbital torque driven magnetization dynamics and orbital pumping within the same device platform. We observe that the transmission coefficients satisfy the symmetry relations required by Onsager reciprocity, demonstrating reciprocal conversion between charge, orbital and spin angular momenta. Our results establish orbital pumping as the reciprocal counterpart of orbital torque. Our experimental findings provide a unified framework for orbital transport phenomena.

Nuclear charge radii constitute a physical observable of growing significance across multiple subdisciplines of physics and related fields. Their determination relies on a combination of complementary experimental techniques and advanced theoretical frameworks. Current recommended values are informed by the outcomes of several independent working groups, each employing distinct methodological approaches and evaluation strategies. The present effort is directed toward a more precise and reliable extraction of charge radii, as well as the development of a modern, transparent, and methodologically robust compilation of recommended values.

In this paper, we study the weighted boundedness of the Dunkl fractional integral operator (i.e., Dunkl Stein-Weiss inequality) associated with the Dunkl operator on $\mathbb{R}$. Indeed, we obtain the Adams-type Dunkl Stein-Weiss inequality on Dunkl-Morrey spaces. Our result extends the classical Adams type Stein-Weiss inequality on Morrey space result to the Dunkl setting. Furthermore, we establish the weighted boundedness of the Dunkl fractional maximal function on Dunkl Morrey spaces.

Integrated sensing and communications (ISAC) has emerged as an intrinsic service of upcoming 6G wireless systems, enabling the reuse of communication signals for environmental sensing and supporting context-aware network functionalities. Meanwhile, the evolution of the wireless infrastructure toward distributed systems creates new opportunities for collaborative sensing from spatially separated nodes. Motivated by this trend, this work investigates a radio stripe aided ISAC system as a low-complexity implementation of a distributed system. We study the trade-off between achievable sum rate and sensing precision when downlink signals are used for target localization within the service area. By exploiting the architectural homogeneity of the radio stripes transceivers, each unit can be dynamically configured to operate in either communication or sensing mode. We formulate a targets localization problem considering the measurements of multiple sensing-communication configurations. Due to the large number of measurements and the continuity of the search space, we propose discretizing the service are and then solve the estimation problem in batches. The targets are finally estimated using a fusion strategy. Our results show that increasing the number devices and sensing APUs boosts sensing precision at the expense of degrading the sum rate. The latter remains constant for a given number of communication APUs regardless of their positions. Moreover, changing the number of antennas reveals a non-monotonic impact on sensing performance due to the trade-off between array gain and illumination uniformity.

We demonstrate that the equivariant unknotting number $\widetilde{u}(K)$ of a strongly invertible knot $K$ is bounded below by the $H$-torsion order $\widetilde{\mathrm{ord}}(K)$ of the involutive Bar-Natan homology $\widetilde{\mathrm{BN}}(K)$. This result serves as an equivariant analogue to the bound established by Alishahi. As an application, we identify five strongly invertible prime knots with crossing numbers at most $9$ for which the strict inequality $u(K) < \widetilde{u}(K)$ holds.

Direct effect analyses usually require deciding whether a focal variable is a pre-exposure confounder or a post-exposure mediator. In observational studies, that distinction may be unclear because timing is measured coarsely or the variable reflects an evolving process. Considering the average treatment effect (ATE) and the natural direct effect (NDE) as a common notion of the direct effect when the focal variable is a confounder and a mediator, respectively, we show that, in general, no single observed-data estimand recovers both the ATE when the focal variable is a confounder and the NDE when it is a mediator. Consequently, if a practitioner applies an NDE estimator when the variable is actually pre-exposure, the resulting estimate may have no clear causal interpretation. We identify a no-additive-interaction condition under which these quantities coincide, develop sensitivity bounds for departures from that condition, and propose an alternative model-robust estimand. This estimand equals the ATE when the variable is pre-exposure and an interventional direct effect when it is post-exposure. Moreover, within a natural class of outcome-free stochastic direct effects, it is the unique observed-data functional that remains causally interpretable under both structural roles of the focal variable. We derive an efficient influence function and a doubly robust estimator, yielding robustness at two levels: the estimand is model-robust across the two causal scenarios, and the estimator is doubly robust with respect to nuisance estimation. In simulations and in an NHANES application on elevated PFAS burden, kidney function, and uric acid, mediation-based analyses yielded materially different reported estimates.

In recent decades, the relevance of polarimetry in planetary sciences and astronomy has increased rapidly. Polarization is a fundamental property of light and can be modified by any scattering event. As such, polarization yields additional information that cannot be obtained by only assessing light's scalar properties. For instance, the polarization state of starlight scattered by planetary surfaces can provide useful insights on the composition, size, morphology, and porosity of regolith particles and might even indicate the presence of life. Beside being useful for characterization, polarimetry can also greatly enhance the detection of exoplanets. Here, polarization can be harnessed to enhance the contrast between the bright light of a star, which can be considered to be fully unpolarized, and the very dim but polarized light reflected by an exoplanet. In this paper, we discuss and review the current developments and advances in optical polarimetry and polarimetric instrumentation in Switzerland within the framework of the National Centre of Competence in Research PlanetS. We focus on their implications for the vast range of science cases that polarimetry can address within the research fields of planetary science and astronomy.

Uncertainties in renewable generation and demand dynamics challenge day-ahead scheduling. To enhance renewable penetration and maintain intra-day balance, we develop a multi-agent reinforcement learning framework for self-interested microgrids participating in peer-to-peer (P2P) electricity trading. Each microgrid independently bids both price and quantity while optimizing its own profit via storage arbitrage under time-varying main-grid prices. A market-clearing mechanism coordinating trades and promoting incentive compatibility is proposed. Simulation results show that the learned bidding policy improves renewable utilization and reduces reliance on high-carbon electricity, while increasing community-level economic welfare, delivering a win-win situation in emission reduction and local prosperity.